Classical Answer Set Programming is a widely known knowledge representation framework based on the logic programming paradigm that has been extensively studied in the past decades. Semantic theories for classical answer sets are implicitly three-valued in nature, yet with few exceptions, computing classical answer sets is based on translations into classical logic and the use of SAT solving techniques. In this paper, we introduce a variation of Kleene three-valued logic with strong connectives, R3\" role=\"presentation\">R3, and then provide a sound and complete proof procedure for R3\" role=\"presentation\">R3 based on the use of signed tableaux. We then define a restriction on the syntax of R3\" role=\"presentation\">R3 to characterize Kleene ASPs. Strongly-supported models, which are a subset of R3\" role=\"presentation\">R3 models are then defined to characterize the semantics of Kleene ASPs. A filtering technique on tableaux for R3\" role=\"presentation\">R3 is then introduced which provides a sound and complete tableau-based proof technique for Kleene ASPs. We then show a translation and semantic correspondence between Classical ASPs and Kleene ASPs, where answer sets for normal classical ASPs are equivalent to strongly-supported models. This implies that the proof technique introduced can be used for classical normal ASPs as well as Kleene ASPs. The relation between non-normal classical and Kleene ASPs is also considered.

In this extended abstract, we discuss the use of iteratively-supported formulas (ISFs) as a basis for computing strongly-supported models for Kleene Answer Set Programs (ASPK). ASPK programs have a syntax identical to classical ASP programs. The semantics of ASPK programs is based on the use of Kleene three-valued logic and strongly-supported models. For normal ASPK programs, their strongly supported models are identical to classical answer sets using stable model semantics. For disjunctive ASPK programs, the semantics weakens the minimality assumption resulting in a classical interpretation for disjunction. We use ISFs to characterize strongly-supported models and show that they are polynomially bounded.

The use of UAVs, in particular, micro VTOL UAVs, is becoming prevalent in emergency rescue and security applications, among others. In these applications, the platforms are tightly coupled to the human users and these applications require great flexibility in the interaction between the platforms and such users. During operation, one continually switches between manual, semi-autonomous and autonomous operation, often re-parameterising, breaking in, pausing, and resuming missions. One is in continual need of modifying existing elementary actions and behaviours such as FlyTo and TrackObject, and seamlessly switching between such operations. This paper proposes a flight command and setpoint abstraction layer that serves as an interface between continuous control and higher level elementary flight actions and behaviours. Introduction of such a layer into an architecture offers a versatile and flexible means of defining flight behaviours and dynamically parameterising them in the field, in particular where human users are involved. The system proposed is implemented in prototype and the paper provides experimental validation of the use and need for such abstractions in system architectures.

Integrating logical and probabilistic reasoning and integrating reasoning over observations and predictions are two important challenges in AI. In this paper we propose P-MTL as an extension to Metric Temporal Logic supporting temporal logical reasoning over probabilistic and predicted states. The contributions are (1) reasoning over uncertain states at single time points, (2) reasoning over uncertain states between time points, (3) reasoning over uncertain predictions of future and past states and (4) a computational environment formalism that ground the uncertainty in observations of the physical world. Concrete robot soccer examples are given.

In this paper we consider a problem of scanningan outdoor area with a team of heterogeneous Unmanned AirVehicles (UAVs) equipped with different sensors (e.g. LIDARs).Depending on the availability of the UAV platforms and themission requirements there is a need to either minimise thetotal mission time or to maximise certain properties of thescan output, such as the point cloud density. The key challengeis to divide the scanning task among UAVs while taking intoaccount the differences in capabilities between platforms andsensors. Additionally, the system should be able to ensure thatconstraints such as limit on the flight time are not violated.We present an approach that uses an optimisation techniqueto find a solution by dividing the area between platforms,generating efficient scan trajectories and selecting flight andscanning parameters, such as velocity and flight altitude. Thismethod has been extensively tested on a large set of randomlygenerated scanning missions covering a wide range of realisticscenarios as well as in real flights.

Integrating logical and probabilistic reasoning and integrating reasoning over observations and predictions are two important challenges in AI. In this paper we propose P-MTL as an extension to Metric Temporal Logic supporting temporal logical reasoning over probabilistic and predicted states. The contributions are (1) reasoning over uncertain states at single time points, (2) reasoning over uncertain states between time points, (3) reasoning over uncertain predictions of future and past states and (4) a computational environment formalism that ground the uncertainty in observations of the physical world. Concrete robot soccer examples are given.

This paper proposes an image matching system using aerial images, captured in flight time, and aerial geo-referenced images to estimate the Unmanned Aerial Vehicle (UAV) position in a situation of Global Navigation Satellite System (GNSS) failure. The image matching system is based on edge detection in the aerial and geo-referenced image and posterior automatic image registration of these edge-images (position estimation of UAV). The edge detection process is performed by an Artificial Neural Network (ANN), with an optimal architecture. A comparison with Sobel and Canny edge extraction filters is also provided. The automatic image registration is obtained by a cross-correlation process. The ANN optimal architecture is set by the Multiple Particle Collision Algorithm (MPCA). The image matching system was implemented in a low cost/consumption portable computer. The image matching system has been tested on real flight-test data and encouraging results have been obtained. Results using real flight-test data will be presented.

DyKnow is a framework for stream reasoning aimed at robot applications that need to reason over a wide and varying array of sensor data for e.g. situation awareness. The framework extends the Robot Operating System (ROS). This paper presents the architecture and services behind DyKnow's run-time reconfiguration capabilities and offers an analysis of the quantitative and qualitative overhead. Run-time reconfiguration offers interesting advantages, such as fault recovery and the handling of changes to the set of computational and information resources that are available to a robot system. Reconfiguration capabilities are becoming increasingly important with the advances in areas such as the Internet of Things (IoT). We show the effectiveness of the suggested reconfiguration support by considering practical case studies alongside an empirical evaluation of the minimal overhead introduced when compared to standard ROS.

Robots are increasingly expected to move out of the controlled environment of research labs and into populated streets and workplaces. Collision avoidance in such cluttered and dynamic environments is of increasing importance as robots gain more autonomy. However, efficient avoidance is fundamentally difficult since computing safe trajectories may require considering both dynamics and uncertainty. While heuristics are often used in practice, we take a holistic stochastic trajectory optimization perspective that merges both collision avoidance and control. We examine dynamic obstacles moving without prior coordination, like pedestrians or vehicles. We find that common stochastic simplifications lead to poor approximations when obstacle behavior is difficult to predict. We instead compute efficient approximations by drawing upon techniques from machine learning. We propose to combine policy search with model-predictive control. This allows us to use recent fast constrained model-predictive control solvers, while gaining the stochastic properties of policy-based methods. We exploit recent advances in Bayesian optimization to efficiently solve the resulting probabilistically-constrained policy optimization problems. Finally, we present a real-time implementation of an obstacle avoiding controller for a quadcopter. We demonstrate the results in simulation as well as with real flight experiments.

Qualitative spatio-temporal reasoning is an active research area in Artificial Intelligence. In many situations there is a need to reason about intertemporal qualitative spatial relations, i.e. qualitative relations between spatial regions at different time-points. However, these relations can never be explicitly observed since they are between regions at different time-points. In applications where the qualitative spatial relations are partly acquired by for example a robotic system it is therefore necessary to infer these relations. This problem has, to the best of our knowledge, not been explicitly studied before. The contribution presented in this paper is two-fold. First, we present a spatio-temporal logic MSTL, which allows for spatio-temporal stream reasoning. Second, we define the concept of a landmark as a region that does not change between time-points and use these landmarks to infer qualitative spatio-temporal relations between non-landmark regions at different time-points. The qualitative spatial reasoning is done in RCC-8, but the approach is general and can be applied to any similar qualitative spatial formalism.

Describing persons and their actions is a challenging problem due to variations in pose, scale and viewpoint in real-world images. Recently, semantic pyramids approach [1] for pose normalization has shown to provide excellent results for gender and action recognition. The performance of semantic pyramids approach relies on robust image description and is therefore limited due to the use of shallow local features. In the context of object recognition [2] and object detection [3], convolutional neural networks (CNNs) or deep features have shown to improve the performance over the conventional shallow features.We propose deep semantic pyramids for human attributes and action recognition. The method works by constructing spatial pyramids based on CNNs of different part locations. These pyramids are then combined to obtain a single semantic representation. We validate our approach on the Berkeley and 27 Human Attributes datasets for attributes classification. For action recognition, we perform experiments on two challenging datasets: Willow and PASCAL VOC 2010. The proposed deep semantic pyramids provide a significant gain of 17.2%, 13.9%, 24.3% and 22.6% compared to the standard shallow semantic pyramids on Berkeley, 27 Human Attributes, Willow and PASCAL VOC 2010 datasets respectively. Our results also show that deep semantic pyramids outperform conventional CNNs based on the full bounding box of the person. Finally, we compare our approach with state-of-the-art methods and show a gain in performance compared to best methods in literature.

Learning to recognize common activities such as traffic activities and robot behavior is an important and challenging problem related both to AI and robotics. We propose an unsupervised approach that takes streams of observations of objects as input and learns a probabilistic representation of the observed spatio-temporal activities and their causal relations. The dynamics of the activities are modeled using sparse Gaussian processes and their causal relations using a probabilistic graph. The learned model supports in limited form both estimating the most likely current activity and predicting the most likely future activities. The framework is evaluated by learning activities in a simulated traffic monitoring application and by learning the flight patterns of an autonomous quadcopter.

Building complex systems such as autonomous robots usually require the integration of a wide variety of components including high-level reasoning functionalities. One important challenge is integrating the information in a system by setting up the data flow between the components. This paper extends our earlier work on semantic matching with support for adaptive on-demand semantic information integration based on ontology-based introspection. We take two important standpoints. First, we consider streams of information, to handle the fact that information often becomes continually and incrementally available. Second, we explicitly represent the semantics of the components and the information that can be provided by them in an ontology. Based on the ontology our custom-made stream configuration planner automatically sets up the stream processing needed to generate the streams of information requested. Furthermore, subscribers are notified when properties of a stream changes, which allows them to adapt accordingly. Since the ontology represents both the systems information about the world and its internal stream processing many other powerful forms of introspection are also made possible. The proposed semantic matching functionality is part of the DyKnow stream reasoning framework and has been integrated in the Robot Operating System (ROS).

Visual feature descriptors are essential elements in most computer and robot vision systems. They typically lead to an abstraction of the input data, images, or video, for further processing, such as clustering and machine learning. In clustering applications, the cluster center represents the prototypical descriptor of the cluster and estimates the corresponding signal value, such as color value or dominating flow orientation, by decoding the prototypical descriptor. Machine learning applications determine the relevance of respective descriptors and a visualization of the corresponding decoded information is very useful for the analysis of the learning algorithm. Thus decoding of feature descriptors is a relevant problem, frequently addressed in recent work. Also, the human brain represents sensorimotor information at a suitable abstraction level through varying activation of neuron populations. In previous work, computational models have been derived that agree with findings of neurophysiological experiments on the represen-tation of visual information by decoding the underlying signals. However, the represented variables have a bias toward centers or boundaries of the tuning curves. Despite the fact that feature descriptors in computer vision are motivated from neuroscience, the respec-tive decoding methods have been derived largely independent. From first principles, we derive unbiased decoding schemes for biologically motivated feature descriptors with a minimum amount of redundancy and suitable invariance properties. These descriptors establish a non-parametric density estimation of the underlying stochastic process with a particular algebraic structure. Based on the resulting algebraic constraints, we show formally how the decoding problem is formulated as an unbiased maximum likelihood estimator and we derive a recurrent inverse diffusion scheme to infer the dominating mode of the distribution. These methods are evaluated in experiments, where stationary points and bias from noisy image data are compared to existing methods.

Building complex systems such as autonomous robots usually require the integration of a wide variety of components including high-level reasoning functionalities. One important challenge is integrating the information in a system by setting up the data flow between the components. This paper extends our earlier work on semantic matching with support for adaptive on-demand semantic information integration based on ontology-based introspection. We take two important stand-points. First, we consider streams of information, to handle the fact that information often becomes continually and incrementally available. Second, we explicitly represent the semantics of the components and the information that can be provided by them in an ontology. Based on the ontology our custom-made stream configuration planner automatically sets up the stream processing needed to generate the streams of information requested. Furthermore, subscribers are notified when properties of a stream changes, which allows them to adapt accordingly. Since the ontology represents both the system's information about the world and its internal stream processing many other powerful forms of introspection are also made possible. The proposed semantic matching functionality is part of the DyKnow stream reasoning framework and has been integrated in the Robot Operating System (ROS).

Trajectories are used in many target tracking and other fusion-related applications. In this paper we consider the problem of modeling trajectories as Gaussian processes and learning such models from sets of observed trajectories. We demonstrate that the traditional approach to Gaussian process regression is not suitable when modeling a set of trajectories. Instead we introduce an approach to Gaussian process trajectory regression based on an alternative way of combing two Gaussian process (GP) trajectory models and inverse GP regression. The benefit of our approach is that it works well online and efficiently supports sophisticated trajectory model manipulations such as merging and splitting of trajectory models. Splitting and merging is very useful in spatio-temporal activity modeling and learning where trajectory models are considered discrete objects. The presented method and accompanying approximation algorithm have time and memory complexities comparable to state of the art of regular full and approximative GP regression, while havinga more flexible model suitable for modeling trajectories. The novelty of our approach is in the very flexible and accurate model, especially for trajectories, and the proposed approximative method based on solving the inverse problem of Gaussian process regression.

We present a novel approach for segmenting different motions from 3D trajectories. Our approach uses the theory of transformation groups to derive a set of invariants of 3D points located on the same rigid object. These invariants are inexpensive to calculate, involving primarily QR factorizations of small matrices. The invariants are easily converted into a set of robust motion affinities and with the use of a local sampling scheme and spectral clustering, they can be incorporated into a highly efficient motion segmentation algorithm. We have also captured a new multi-object 3D motion dataset, on which we have evaluated our approach, and compared against state-of-the-art competing methods from literature. Our results show that our approach outperforms all methods while being robust to perspective distortions and degenerate configurations.

Answer Set Programming is a widely known knowledge representation framework based on the logic programming paradigm that has been extensively studied in the past decades. The semantic framework for Answer Set Programs is based on the use of stable model semantics. There are two characteristics intrinsically associated with the construction of stable models for answer set programs. Any member of an answer set is supported through facts and chains of rules and those members are in the answer set only if generated minimally in such a manner. These two characteristics, supportedness and minimality, provide the essence of stable models. Additionally, answer sets are implicitly partial and that partiality provides epistemic overtones to the interpretation of disjunctiver ules and default negation. This paper is intended to shed light on these characteristics by defining a semantic framework for answer set programming based on an extended first-order Kleene logic with weak and strong negation. Additionally, a definition of strongly supported models is introduced, separate from the minimality assumption explicit in stable models. This is used to both clarify and generate alternative semantic interpretations for answer set programs with disjunctive rules in addition to answer set programs with constraint rules. An algorithm is provided for computing supported models and comparative complexity results between strongly supported and stable model generation are provided.

Skeletonisation is a key process in character recognition in natural images. Under the assumption that a character is made of a stroke of uniform colour, with small variation in thickness, the process of recognising characters can be decomposed in the three steps. First the image is segmented, then each segment is transformed into a set of connected strokes (skeletonisation), which are then abstracted in a descriptor that can be used to recognise the character. The main issue with skeletonisation is the sensitivity with noise, and especially, the presence of holes in the masks. In this article, a new method for the extraction of strokes is presented, which address the problem of holes in the mask and does not use any parameters.

Characters recognition in natural images is a challenging problem, asit involves segmenting characters of various colours on various background. Inthis article, we present a method for segmenting images that use a colour percep-tion graph. Our algorithm is inspired by graph cut segmentation techniques andit use an edge detection technique for filtering the graph before the graph-cut aswell as merging segments as a final step. We also present both qualitative andquantitative results, which show that our algorithm perform at slightly better andfaster to a state of the art algorithm.

We propose an unsupervised stream processing framework that learns a Bayesian representation of observed spatio-temporal activities and their causal relations. The dynamics of the activities are modeled using sparse Gaussian processes and their causal relations using a causal Bayesian graph. This allows the model to be efficient through compactness and sparsity in the causal graph, and to provide probabilities at any level of abstraction for activities or chains of activities. Methods and ideas from a wide range of previous work are combined and interact to provide a uniform way to tackle a variety of common problems related to learning, classifying and predicting activities. We discuss how to use this framework to perform prediction of future activities and to generate events.

We consider the directed Steiner tree problem (DSTP) with a constraint on the total number of arcs (hops) in the tree. This problem is known to be NP-hard, and therefore, only heuristics can be applied in the case of its large-scale instances.For the hop-constrained DSTP, we propose local search strategies aimed at improving any heuristically produced initial Steiner tree. They are based on solving a sequence of hop-constrained shortest path problems for which we have recently developed efficient label correcting algorithms.The presented approach is applied to finding suitable 3D locations where unmanned aerial vehicles (UAVs) can be placed to relay information gathered in multi-target monitoring and surveillance. The efficiency of our algorithms is illustrated by results of numerical experiments involving problem instances with up to 40 000 nodes and up to 20 million arcs.

Guarding the perimeter of an area in order to detect potential intruders is an important task in a variety of security-related applications. This task can in many circumstances be performed by a set of camera-equipped unmanned aerial vehicles (UAVs). Such UAVs will occasionally require refueling or recharging, in which case they must temporarily be replaced by other UAVs in order to maintain complete surveillance of the perimeter. In this paper we consider the problem of scheduling such replacements. We present optimal replacement strategies and justify their optimality.

We consider the directed Steiner tree problem (DSTP) with a constraint on the total number of arcs (hops) in the tree. This problem is known to be NP-hard, and therefore, only heuristics can be applied in the case of its large-scale instances. For the hop-constrained DSTP, we propose local search strategies aimed at improving any heuristically produced initial Steiner tree. They are based on solving a sequence of hop-constrained shortest path problems for which we have recently developed ecient label correcting algorithms. The presented approach is applied to nding suitable 3D locations where unmanned aerial vehicles (UAVs) can be placed to relay information gathered in multi-target monitoring and surveillance. The eciency of our algorithms is illustrated by results of numerical experiments involving problem instances with up to 40 000 nodes and up to 20 million arcs.

This paper presents a comparison of two light-weight and low-cost airborne mapping systems. One is based on a lidar technology and the other on a video camera. The airborne lidar system consists of a high-precision global navigation satellite system (GNSS) receiver, a microelectromechanical system (MEMS) inertial measurement unit, a magnetic compass and a low-cost lidar scanner. The vision system is based on a consumer grade video camera. A commercial photogrammetric software package is used to process the acquired images and generate a digital surface model. The two systems are described and compared in terms of hardware requirements and data processing. The systems are also tested and compared with respect to their application on board of an unmanned aerial vehicle (UAV). An evaluation of the accuracy of the two systems is presented. Additionally, the multi echo capability of the lidar sensor is evaluated in a test site covered with dense vegetation. The lidar and the camera systems were mounted and tested on-board an industrial unmanned helicopter with maximum take-off weight of around 100 kilograms. The presented results are based on real flight-test data.

Reasoning about time and space is essential for many applications, especially for robots and other autonomous systems that act in the real world and need to reason about it. In this paper we present a pragmatic approach to spatio-temporal stream reasoning integrated in the Robot Operating System through the DyKnow framework. The temporal reasoning is done in the Metric Temporal Logic and the spatial reasoning in the Region Connection Calculus RCC-8. Progression is used to evaluate spatio-temporal formulas over incrementally available streams of states. To handle incomplete information the underlying first-order logic is extended to a three-valued logic. When incomplete spatial information is received, the algebraic closure of the known information is computed. Since the algebraic closure might have to be re-computed every time step, we separate the spatial variables into static and dynamic variables and reuse the algebraic closure of the static variables, which reduces the time to compute the full algebraic closure. The end result is an efficient and useful approach to spatio-temporal reasoning over streaming information with incomplete information.

The ability to automatically, on-demand, apply pattern matching over streams of information to infer the occurrence of events is an important fusion functionality. Existing event detection approaches require explicit configuration of what events to detect and what streams to use as input. This paper discusses on-demand semantic event processing, and extends the semantic information integration approach used in the stream processing middleware framework DyKnow to incorporate this new feature. By supporting on-demand semantic event processing, systems can automatically configure what events to detect and what streams to use as input for the event detection. This can also include the detection of lower-level events as well as processing of streams. The semantic stream query language C-SPARQL is used to specify events, which can be seen as transformations over streams. Since semantic streams consist of RDF triples, we suggest a method to convert between RDF streams and DyKnow streams. DyKnow is integrated in the Robot Operating System (ROS) and used for example in collaborative unmanned aircraft systems missions.

Random set based methods have provided a rigorous Bayesian framework and have been used extensively in the last decade for point object estimation. In this paper, we emphasize that the same methodology offers an equally powerful approach to estimation of so called extended objects, i.e., objects that result in multiple detections on the sensor side. Building upon the analogy between Bayesian state estimation of a single object and random finite set estimation for multiple objects, we give a tutorial on random set methods with an emphasis on multiple extended object estimation. The capabilities are illustrated on a simple yet insightful real life example with laser range data containing several occlusions.

Simple Temporal Networks with Uncertainty (STNUs) allow the representation of temporal problems where some durations are uncontrollable (determined by nature), as is often the case for actions in planning. It is essential to verify that such networks are dynamically controllable (DC) – executable regardless of the outcomes of uncontrollable durations – and to convert them to an executable form. We use insights from incremental DC verification algorithms to re-analyze the original verification algorithm. This algorithm, thought to be pseudo-polynomial and subsumed by an O(n5) algorithm and later an O(n4) algorithm, is in fact O(n4) given a small modification. This makes the algorithm attractive once again, given its basis in a less complex and more intuitive theory. Finally, we discuss a change reducing the amount of work performed by the algorithm.

Simple Temporal Networks with Uncertainty (STNUs) allow the representation of temporal problems wheresome durations are uncontrollable (determined by nature), as is often the case for actions in planning. It is essentialto verify that such networks are dynamically controllable (DC) – executable regardless of the outcomesof uncontrollable durations – and to convert them to an executable form. We use insights from incrementalDC verification algorithms to re-analyze the original verification algorithm. This algorithm, thought to bepseudo-polynomial and subsumed by an O(n⁵) algorithm and later an O(n⁴) algorithm, is in fact O(n⁴) givena small modification. This makes the algorithm attractive once again, given its basis in a less complex andmore intuitive theory. Finally, we discuss a change reducing the amount of work performed by the algorithm.

After natural disasters such as earthquakes, floods, hurricanes, tornados and fires, providing emergency management schemes which mainly rely on communications systems is essential for rescue operations. To establish an emergency communications system during unforeseen events such as natural disasters, we propose the use of a team of unmanned aerial vehicles (UAVs). The proposed system is a post-disaster solution and can be used whenever and wherever required. Each UAV in the team has an onboard computer which runs three main subsystems responsible for end-to-end communication, formation control and autonomous navigation. The onboard computer and the low-level controller of the UAV cooperate to accomplish the objective of providing local communications infrastructure. In this study, the subsystems running on each UAV are explained and evaluated by simulation studies and field tests using an autonomous helicopter. While the simulation studies address the efficiency of the end-to-end communication subsystem, the field tests evaluate the accuracy of the navigation subsystem. The results of the field tests and the simulation studies show that the proposed system can be successfully used in case of disasters to establish an emergency communications system.

Color description is a challenging task because of large variations in RGB values which occur due to scene accidental events, such as shadows, shading, specularities, illuminant color changes, and changes in viewing geometry. Traditionally, this challenge has been addressed by capturing the variations in physics-based models, and deriving invariants for the undesired variations. The drawback of this approach is that sets of distinguishable colors in the original color space are mapped to the same value in the photometric invariant space. This results in a drop of discriminative power of the color description. In this paper we take an information theoretic approach to color description. We cluster color values together based on their discriminative power in a classification problem. The clustering has the explicit objective to minimize the drop of mutual information of the final representation. We show that such a color description automatically learns a certain degree of photometric invariance. We also show that a universal color representation, which is based on other data sets than the one at hand, can obtain competing performance. Experiments show that the proposed descriptor outperforms existing photometric invariants. Furthermore, we show that combined with shape description these color descriptors obtain excellent results on four challenging datasets, namely, PASCAL VOC 2007, Flowers-102, Stanford dogs-120 and Birds-200.

State-of-the-art texture descriptors typically operate on grey scale images while ignoring color information. A common way to obtain a joint color-texture representation is to combine the two visual cues at the pixel level. However, such an approach provides sub-optimal results for texture categorisation task.In this paper we investigate how to optimally exploit color information for texture recognition. We evaluate a variety of color descriptors, popular in image classification, for texture categorisation. In addition we analyze different fusion approaches to combine color and texture cues. Experiments are conducted on the challenging scenes and 10 class texture datasets. Our experiments clearly suggest that in all cases color names provide the best performance. Late fusion is the best strategy to combine color and texture. By selecting the best color descriptor with optimal fusion strategy provides a gain of 5% to 8% compared to texture alone on scenes and texture datasets.

A GM-PHD filter is used for pedestrian tracking in a crowdsurveillance application. The purpose is to keep track of thedifferent groups over time as well as to represent the shape ofthe groups and the number of people within the groups. In-put data to the GM-PHD filter are detections using a state ofthe art algorithm applied to video frames from the PETS 2012benchmark data. In a first step, the detections in the framesare converted from image coordinates to world coordinates.This implies that groups can be defined in physical units interms of distance in meters and speed differences in metersper second. The GM-PHD filter is a Bayesian framework thatdoes not form tracks of individuals. Its output is well suitedfor clustering of individuals into groups. The results demon-strate that the GM-PHD filter has the capability of estimatingthe correct number of groups with an accurate representationof their sizes and shapes.

This paper focuses on approximate reasoning based on the use of approximation spaces. Approximation spaces and the approximated relations induced by them are a generalization of the rough set-based approximations of Pawlak. Approximation spaces are used to define neighborhoods around individuals and rough inclusion functions. These in turn are used to define approximate sets and relations. In any of the approaches, one would like to embed such relations in an appropriate logical theory which can be used as a reasoning engine for specific applications with specific constraints. We propose a framework which permits a formal study of the relationship between properties of approximations and properties of approximation spaces. Using ideas from correspondence theory, we develop an analogous framework for approximation spaces. We also show that this framework can be strongly supported by automated techniques for quantifier elimination.

Visual tracking of objects under varying lighting conditions and changes of the object appearance, such as articulation and change of aspect, is a challenging problem. Due to its robustness and speed, distribution field tracking is among the state-of-the-art approaches for tracking objects with constant size in grayscale sequences. According to the theory of averaged shifted histograms, distribution fields are an approximation of kernel density estimates. Another, more efficient approximation are channel representations, which are used in the present paper to derive an enhanced computational scheme for tracking. This enhanced distribution field tracking method outperforms several state-ofthe-art methods on the VOT2013 challenge, which evaluates accuracy, robustness, and speed.

In this article we investigate the problem of human action recognition in static images. By action recognition we intend a class of problems which includes both action classification and action detection (i.e. simultaneous localization and classification). Bag-of-words image representations yield promising results for action classification, and deformable part models perform very well object detection. The representations for action recognition typically use only shape cues and ignore color information. Inspired by the recent success of color in image classification and object detection, we investigate the potential of color for action classification and detection in static images. We perform a comprehensive evaluation of color descriptors and fusion approaches for action recognition. Experiments were conducted on the three datasets most used for benchmarking action recognition in still images: Willow, PASCAL VOC 2010 and Stanford-40. Our experiments demonstrate that incorporating color information considerably improves recognition performance, and that a descriptor based on color names outperforms pure color descriptors. Our experiments demonstrate that late fusion of color and shape information outperforms other approaches on action recognition. Finally, we show that the different color–shape fusion approaches result in complementary information and combining them yields state-of-the-art performance for action classification.

Searching with a sensor for objects and to observe parts of a known environment efficiently is a fundamental prob- lem in many real-world robotic applications such as household robots searching for objects, inspection robots searching for leaking pipelines, and rescue robots searching for survivors after a disaster. We consider the problem of identifying and planning efficient view point sequences for covering complex 3d environments. We compare empirically several variants of our algorithm that allow to trade-off schedule computation against execution time. Our results demonstrate that, despite the intractability of the overall problem, computing effective solutions for coverage search in real 3d environments is feasible.

This paper considers extended targets that have constant extension shapes, but generate measurements whose appearance can change abruptly. The problem is approached using multiple measurement models, where each model corresponds to a measurement appearance mode. Mode transitions are modeled as dependent on the extended target kinematic state, and a multiple model extended target PHD filter is used to handle multiple targets with multiple appearance modes. The extended target tracking is evaluated using real world data where a laser range sensor is used to track multiple bicycles.

High level reasoning is becoming essential to autonomous systems such as robots. Both the information available to and the reasoning required for such autonomous systems is fundamentally incremental in nature. A stream is a flow of incrementally available information and reasoning over streams is called stream reasoning. Incremental reasoning over streaming information is necessary to support a number of important robotics functionalities such as situation awareness, execution monitoring, and decision making.This paper presents a practical framework for semantically grounded temporal stream reasoning called DyKnow. Incremental reasoning over streams is achieved through efficient progression of temporal logical formulas. The reasoning is semantically grounded through a common ontology and a specification of the semantic content of streams relative to the ontology. This allows the finding of relevant streams through semantic matching. By using semantic mappings between ontologies it is also possible to do semantic matching over multiple ontologies. The complete stream reasoning framework is integrated in the Robot Operating System (ROS) thereby extending it with a stream reasoning capability.

In this paper we consider the problem of searching for an arbitrarily smart and fast evader in a large environment with a team of unmanned aerial vehicles (UAVs) while providing guarantees of detection. Our emphasis is on the fast execution of efficient search strategies that minimize the number of UAVs and the search time. We present the first approach for computing fast search strategies utilizing additional searchers to speed up the execution time and thereby enabling large scale UAV search. In order to scale to very large environments when using UAVs one would either have to overcome the energy limitations of UAVs or pay the cost of utilizing additional UAVs to speed up the search. Our approach is based on coordinating UAVs on sweep lines, covered by the UAV sensors, that move simultaneously through an environment. We present some simulation results that show a significant reduction in execution time when using multiple UAVs and a demonstration of a real system with three ARDrones.

Efficient task allocation with timing constraints to a team of possibly heterogeneous robots is a challenging problem with application, e.g., in search and rescue. In this paper a mixed-integer linear programming (MILP) approach is proposed for assigning heterogeneous robot teams to the simultaneous completion of sequences of tasks with specific requirements such as completion deadlines. For this purpose our approach efficiently combines the strength of state of the art Mixed Integer Linear Programming (MILP) solvers with human expertise in mission scheduling. We experimentally show that simple and intuitive inputs by a human user have substantial impact on both computation time and quality of the solution. The presented approach can in principle be applied to quite general missions for robot teams with human supervision.

This paper presents a cardinalized probability hypothesis density (CPHD) filter for extended targets that can result in multiple measurements at each scan. The probability hypothesis density (PHD) filter for such targets has been derived by Mahler, and different implementations have been proposed recently. To achieve better estimation performance this work relaxes the Poisson assumptions of the extended target PHD filter in target and measurement numbers. A gamma Gaussian inverse Wishart mixture implementation, which is capable of estimating the target extents and measurement rates as well as the kinematic state of the target, is proposed, and it is compared to its PHD counterpart in a simulation study. The results clearly show that the CPHD filter has a more robust cardinality estimate leading to smaller OSPA errors, which confirms that the extended target CPHD filter inherits the properties of its point target counterpart.

The automatic, on-demand, integration of information from multiple diverse sources outside the control of the application itself is central to many fusion applications. An important problem is to handle situations when the requested information is not directly available but has to be generated or adapted through transformations. This paper extends the semantic information integration approach used in the stream-based knowledge processing middleware DyKnow with support for finding and automatically applying transformations. Two types of transformations are considered. Automatic transformation between different units of measurements and between streams of different types. DyKnow achieves semantic integration by creating a common ontology, specifying the semantic content of streams relative to the ontology and using semantic matching to find relevant streams. By using semantic mappings between ontologies it is also possible to do semantic matching over multiple ontologies. The complete stream reasoning approach is integrated in the Robot Operating System (ROS) and used in collaborative unmanned aircraft systems missions.

Automated specification, generation and execution of high level missions involving one or more heterogeneous unmanned aircraft systems is in its infancy. Much previous effort has been focused on the development of air vehicle platforms themselves together with the avionics and sensor subsystems that implement basic navigational skills. In order to increase the degree of autonomy in such systems so they can successfully participate in more complex mission scenarios such as those considered in emergency rescue that also include ongoing interactions with human operators, new architectural components and functionalities will be required to aid not only human operators in mission planning, but also the unmanned aircraft systems themselves in the automatic generation, execution and partial verification of mission plans to achieve mission goals. This article proposes a formal framework and architecture based on the unifying concept of delegation that can be used for the automated specification, generation and execution of high-level collaborative missions involving one or more air vehicles platforms and human operators. We describe an agent-based software architecture, a temporal logic based mission specification language, a distributed temporal planner and a task specification language that when integrated provide a basis for the generation, instantiation and execution of complex collaborative missions on heterogeneous air vehicle systems. A prototype of the framework is operational in a number of autonomous unmanned aircraft systems developed in our research lab.

Autonomous systems situated in the real world often need to recognize, track, and reason about various types of physical objects. In order to allow reasoning at a symbolic level, one must create and continuously maintain a correlation between symbols denoting physical objects and sensor data being collected about them, a process called anchoring.In this paper we present a stream-based hierarchical anchoring framework. A classification hierarchy is associated with expressive conditions for hypothesizing the type and identity of an object given streams of temporally tagged sensor data. The anchoring process constructs and maintains a set of object linkage structures representing the best possible hypotheses at any time. Each hypothesis can be incrementally generalized or narrowed down as new sensor data arrives. Symbols can be associated with an object at any level of classification, permitting symbolic reasoning on different levels of abstraction. The approach is integrated in the DyKnow knowledge processing middleware and has been applied to an unmanned aerial vehicle traffic monitoring application.

When parts of the states in a goal POMDP are fully observable and some actions are deterministic it is possibleto take advantage of these properties to efficiently generate approximate solutions. Actions that deterministically affect the fully observable component of the world state can be abstracted away and combined into macro actions, permitting a planner to converge more quickly. This processing can be separated from the main search procedure, allowing us to leverage existing POMDP solvers. Theoretical results show how a POMDP can be analyzed to identify the exploitable properties and formal guarantees are provided showing that the use of macro actions preserves solvability. The efficiency of the method is demonstrated with examples when used in combination with existing POMDP solvers.

Simple Temporal Networks with Uncertainty (STNUs) allow the representation of temporal problems where some durations are determined by nature, as is often the case for actions in planning. As such networks are generated it is essential to verify that they are dynamically controllable – executable regardless of the outcomes of uncontrollable durations – and to convert them to a dispatchable form. The previously published FastIDC algorithm achieves this incrementally and can therefore be used efficiently during plan construction. In this paper we show that FastIDC is not sound when new constraints are added, sometimes labeling networks as dynamically controllable when they are not. We analyze the algorithm, pinpoint the cause, and show how the algorithm can be modified to correctly detect uncontrollable networks.

We consider the problem of detecting all moving and evading targets in 2.5D environments with teams of UAVs. Targets are assumed to be fast and omniscient while UAVs are only equipped with limited range detection sensors and have no prior knowledge about the location of targets. We present an algorithm that, given an elevation map of the environment, computes synchronized trajectories for the UAVs to guarantee the detection of all targets. The approach is based on coordinating the motion of multiple UAVs on sweep lines to clear the environment from contamination, which represents the possibility of an undetected target being located in an area. The goal is to compute trajectories that minimize the number of UAVs needed to execute the guaranteed search. This is achieved by converting 2D strategies, computed for a polygonal representation of the environment, to 2.5D strategies. We present methods for this conversion and consider cost of motion and visibility constraints. Experimental results demonstrate feasibility and scalability of the approach. Experiments are carried out on real and artificial elevation maps and provide the basis for future deployments of large teams of real UAVs for guaranteed search.

We consider the problem of detecting moving and evading targets by a team of coordinated unmanned aerial vehicles (UAVs) in large and complex 2D and 2.5D environments. Our approach is based on the coordination of 2D sweep lines that move through the environment to clear it from all contamination, representing the possibility of a target being located in an area, and thereby detecting all targets. The trajectories of the UAVs are implicitly given by the motion of these sweep lines and their costs are determined by the number of UAVs needed. A novel algorithm that computes low cost coordination strategies of the UAV sweep lines in simply connected polygonal environments is presented. The resulting strategies are then converted to strategies clearing multiply connected and 2.5D environments. Experiments on real and artificial elevation maps with complex visibility constraints are presented and demonstrate the feasibility and scalability of the approach. The algorithms used for the experiments are made available on a public repository.

This paper presents an autonomous robotic system that incorporates novel Computer Vision, Machine Learning and Data Mining algorithms in order to learn to navigate and discover important visual entities. This is achieved within a Learning from Demonstration (LfD) framework, where policies are derived from example state-to-action mappings. For autonomous navigation, a mapping is learnt from holistic image features (GIST) onto control parameters using Random Forest regression. Additionally, visual entities (road signs e.g. STOP sign) that are strongly associated to autonomously discovered modes of action (e.g. stopping behaviour) are discovered through a novel Percept-Action Mining methodology. The resulting sign detector is learnt without any supervision (no image labeling or bounding box annotations are used). The complete system is demonstrated on a fully autonomous robotic platform, featuring a single camera mounted on a standard remote control car. The robot carries a PC laptop, that performs all the processing on board and in real-time.

Perception-action (P-A) learning is an approach to cognitive system building that seeks to reduce the complexity associated with conventional environment-representation/action-planning approaches. Instead, actions are directly mapped onto the perceptual transitions that they bring about, eliminating the need for intermediate representation and significantly reducing training requirements. We here set out a very general learning framework for cognitive systems in which online learning of the P-A mapping may be conducted within a symbolic processing context, so that complex contextual reasoning can influence the P-A mapping. In utilizing a variational calculus approach to define a suitable objective function, the P-A mapping can be treated as an online learning problem via gradient descent using partial derivatives. Our central theoretical result is to demonstrate top-down modulation of low-level perceptual confidences via the Jacobian of the higher levels of a subsumptive P-A hierarchy. Thus, the separation of the Jacobian as a multiplying factor between levels within the objective function naturally enables the integration of abstract symbolic manipulation in the form of fuzzy deductive logic into the P-A mapping learning. We experimentally demonstrate that the resulting framework achieves significantly better accuracy than using P-A learning without top-down modulation. We also demonstrate that it permits novel forms of context-dependent multilevel P-A mapping, applying the mechanism in the context of an intelligent driver assistance system.

In extended/group target tracking, where the extensions of the targets are estimated, target spawning and combination events might have significant implications on the extensions. This paper investigates target spawning and combination events for the case that the target extensions are modeled in a random matrix framework. The paper proposes functions that should be provided by the tracking filter in such a scenario. The results, which are obtained by a gamma Gaussian inverse Wishart implementation of an extended target probability hypothesis density filter, confirms that the proposed functions improve the performance of the tracking filter for spawning and combination events.

We propose a novel method for iterative learning of point correspondences between image sequences. Points moving on surfaces in 3D space are projected into two images. Given a point in either view, the considered problem is to determine the corresponding location in the other view. The geometry and distortions of the projections are unknown as is the shape of the surface. Given several pairs of point-sets but no access to the 3D scene, correspondence mappings can be found by excessive global optimization or by the fundamental matrix if a perspective projective model is assumed. However, an iterative solution on sequences of point-set pairs with general imaging geometry is preferable. We derive such a method that optimizes the mapping based on Neyman's chi-square divergence between the densities representing the uncertainties of the estimated and the actual locations. The densities are represented as channel vectors computed with a basis function approach. The mapping between these vectors is updated with each new pair of images such that fast convergence and high accuracy are achieved. The resulting algorithm runs in real-time and is superior to state-of-the-art methods in terms of convergence and accuracy in a number of experiments.

This paper presents an overview of the extended target tracking research undertaken at the division of Automatic Control at Linköping University. The PHD and CPHD filters for multiple extended target tracking under clutter and unknown association are summarized, with focus on the Gaussian mixture and Gaussian inverse Wishart implementations. The paper elaborates on measurement set partitioning, the measurement generating Poisson rates, the probability of detection, and practical examples of measurement models.

This report contains pseudo-code for, and a computational complexity analysis of, the Gaussian inverse Wishart Probability Hypothesis Density filter.

Research with collaborative robotic systems has much to gain by leveraging concepts and ideas from the areas of multi-agent systems and the social sciences. In this paper we propose an approach to formalizing and grounding important aspects of collaboration in a collaborative system shell for robotic systems. This is done primarily in terms of the concept of delegation, where delegation will be instantiated as a speech act. The formal characterization of the delegation speech act is based on a preformal theory of delegation proposed by Falcone and Castelfranchi. We show how the delegation speech act can in fact be used to formally ground an abstract characterization of delegation into a FIPA-compliant implementation in an agent-oriented language such as JADE, as part of a collaborative system shell for robotic systems. The collaborative system shell has been developed as a prototype and used in collaborative missions with multiple unmanned aerial vehicle systems.

State-of-the-art object detectors typically use shape information as a low level feature representation to capture the local structure of an object. This paper shows that early fusion of shape and color, as is popular in image classification, leads to a significant drop in performance for object detection. Moreover, such approaches also yields suboptimal results for object categories with varying importance of color and shape. In this paper we propose the use of color attributes as an explicit color representation for object detection. Color attributes are compact, computationally efficient, and when combined with traditional shape features provide state-of-the-art results for object detection. Our method is tested on the PASCAL VOC 2007 and 2009 datasets and results clearly show that our method improves over state-of-the-art techniques despite its simplicity. We also introduce a new dataset consisting of cartoon character images in which color plays a pivotal role. On this dataset, our approach yields a significant gain of 14% in mean AP over conventional state-of-the-art methods.

This work addresses the problem of fast, online segmentationof moving objects in video. We pose this as a discriminative onlinesemi-supervised appearance learning task, where supervising labelsare autonomously generated by a motion segmentation algorithm. Thecomputational complexity of the approach is signicantly reduced byperforming learning and classication on oversegmented image regions(superpixels), rather than per pixel. In addition, we further exploit thesparse trajectories from the motion segmentation to obtain a simplemodel that encodes the spatial properties and location of objects at eachframe. Fusing these complementary cues produces good object segmentationsat very low computational cost. In contrast to previous work,the proposed approach (1) performs segmentation on-the-y (allowingfor applications where data arrives sequentially), (2) has no prior modelof object types or `objectness', and (3) operates at signicantly reducedcomputational cost. The approach and its ability to learn, disambiguateand segment the moving objects in the scene is evaluated on a numberof benchmark video sequences.

The world in which we live is becoming more and more automated, exemplified by the numerous robots, or autonomous vehicles, that operate in air, on land, or in water. These robots perform a wide array of different tasks, ranging from the dangerous, such as underground mining, to the boring, such as vacuum cleaning. In common for all different robots is that they must possess a certain degree of awareness, both of themselves and of the world in which they operate. This thesis considers aspects of two research problems associated with this, more specifically the Simultaneous Localization and Mapping (SLAM) problem and the Multiple Target Tracking (MTT) problem.The SLAM problem consists of having the robot create a map of an environment and simultaneously localize itself in the same map. One way to reduce the effect of small errors that inevitably accumulate over time, and could significantly distort the SLAM result, is to detect loop closure. In this thesis loop closure detection is considered for robots equipped with laser range sensors. Machine learning is used to construct a loop closure detection classifier, and experiments show that the classifier compares well to related work.The resulting SLAM map should only contain stationary objects, however the world also contains moving objects, and to function well a robot should be able to handle both types of objects. The MTT problem consists of having the robot keep track of where the moving objects, called targets, are located, and how these targets are moving. This function has a wide range of applications, including tracking of pedestrians, bicycles and cars in urban environments. Solving the MTT problem can be decomposed into two parts: one part is finding out the number of targets, the other part is finding out what the states of the individual targets are.In this thesis the emphasis is on tracking of so called extended targets. An extended target is a target that can generate any number of measurements, as opposed to a point target that generates at most one measurement. More than one measurement per target raise interesting possibilities to estimate the size and the shape of the target. One way to model the number of targets and the target states is to use random finite sets, which leads to the Probability Hypothesis Density (PHD) filters. Two implementations of an extended target PHD filter are given, one using Gaussian mixtures and one using Gaussian inverse Wishart (GIW) mixtures. Two models for the size and shape of an extended target measured with laser range sensors are suggested. A framework for estimation of the number of measurements generated by the targets is presented, and reduction of GIW mixtures is addressed. Prediction, spawning and combination of extended targets modeled using GIW distributions is also presented. The extended target tracking functions are evaluated in simulations and in experiments with laser range data.

This paper presents a new prediction update for extended targets whose extensions are modeled as random matrices. The prediction is based on several minimizations of the Kullback-Leibler divergence and allows for a kinematic state dependent transformation of the target extension. The results show that the extension prediction is a significant improvement over the previous work carried out on the topic.

This paper presents an algorithm for reduction of Gaussian inverse Wishart mixtures. Sums of an arbitrary number of mixture components are approximated with single components by analytically minimizing the Kullback-Leibler divergence. The Kullback-Leibler difference is used as a criterion for deciding whether or not two components should be merged, and a simple reduction algorithm is given. The reduction algorithm is tested in simulation examples in both one and two dimensions. The results presented in the paper are useful in extended target tracking using the random matrix framework.

In Gilholm et al.'s extended target model, the number of measurements generated by a target is Poisson distributed with measurement rate γ. Practical use of this extended target model in multiple extended target tracking algorithms requires a good estimate of γ. In this paper, we first give a Bayesian recursion for estimating γ using the well-known conjugate prior Gamma-distribution. In multiple extended target tracking, consideration of different measurement set associations to a single target makes Gamma-mixtures arise naturally. This causes a need for mixture reduction, and we consider the reduction of Gamma-mixtures by means of merging. Analytical minimization of the Kullback-Leibler divergence is used to compute the single Gamma distribution that best approximates a weighted sum of Gamma distributions. Results from simulations show the merits of the presented multiple target measurement-rate estimator. The Bayesian recursion and presented reduction algorithm have important implications for multiple extended target tracking, e.g. using the implementations of the extended target PHD filter.

This paper presents a random set based approach to tracking of an unknown number of extended targets, in the presence of clutter measurements and missed detections, where the targets extensions are modeled as random matrices. For this purpose, the random matrix framework developed recently by Koch et al. is adapted into the extended target PHD framework, resulting in the Gaussian inverse Wishart PHD (GIW-PHD) filter. A suitable multiple target likelihood is derived, and the main filter recursion is presented along with the necessary assumptions and approximations. The particularly challenging case of close extended targets is addressed with practical measurement clustering algorithms. The capabilities and limitations of the resulting extended target tracking framework are illustrated both in simulations and in experiments based on laser scans.

The main contribution of this paper is a practicalsemantic information integration approach for stream reasoningbased on semantic matching. This is an important functionality for situation awareness applications where temporal reasoning over streams from distributed sources is needed. The integration is achieved by creating a common ontology, specifying the semantic content of streams relative to the ontology and then use semantic matching to find relevant streams. By using semantic mappings between ontologies it is also possible to do semantic matching over multiple ontologies. The complete stream reasoning approach is integrated in the Robot Operating System(ROS) and used in collaborative unmanned aircraft systems missions.

Autonomous systems require a lot of information about the environment in which they operate in order to perform different high-level tasks. The information is made available through various sources, such as remote and on-board sensors, databases, GIS, the Internet, etc. The sensory input especially is incrementally available to the systems and can be represented as streams. High-level tasks often require some sort of reasoning over the input data, however raw streaming input is often not suitable for the higher level representations needed for reasoning. DyKnow is a stream processing framework that provides functionalities to represent knowledge needed for reasoning from streaming inputs. DyKnow has been used within a platform for task planning and execution monitoring for UAVs. The execution monitoring is performed using formula progression with monitor rules specified as temporal logic formulas. In this thesis we present an analysis for providing spatio-temporal functionalities to the formula progressor and we extend the formula progression with spatial reasoning in RCC-8. The result implementation is capable of evaluating spatio-temporal logic formulas using progression over streaming data. In addition, a ROS implementation of the formula progressor is presented as a part of a spatio-temporal stream reasoning architecture in ROS.

Complex mission or task specification languages play a fundamentally important role in human/robotic interaction. In realistic scenarios such as emergency response, specifying temporal, resource and other constraints on a mission is an essential component due to the dynamic and contingent nature of the operational environments. It is also desirable that in addition to having a formal semantics, the language should be sufficiently expressive, pragmatic and abstract. The main goal of this paper is to propose a mission specification language that meets these requirements. It is based on extending both the syntax and semantics of a well-established formalism for reasoning about action and change, Temporal Action Logic (TAL), in order to represent temporal composite actions with constraints. Fixpoints are required to specify loops and recursion in the extended language. The results include a sound and complete proof theory for this extension. To ensure that the composite language constructs are adequately grounded in the pragmatic operation of robotic systems, Task Specification Trees (TSTs) and their mapping to these constructs are proposed. The expressive and pragmatic adequacy of this approach is demonstrated using an emergency response scenario.

This paper presents a Gaussian-mixture implementation of the phd filter for tracking extended targets. The exact filter requires processing of all possible measurement set partitions, which is generally infeasible to implement. A method is proposed for limiting the number of considered partitions and possible alternatives are discussed. The implementation is used on simulated data and in experiments with real laser data, and the advantage of the filter is illustrated. Suitable remedies are given to handle spatially close targets and target occlusion.

This paper presents a Gaussian-mixture implementation of the phd filter for tracking extended targets. The exact filter requires processing of all possible measurement set partitions, which is generally infeasible to implement. A method is proposed for limiting the number of considered partitions and possible alternatives are discussed. The implementation is used on simulated data and in experiments with real laser data, and the advantage of the filter is illustrated. Suitable remedies are given to handle spatially close targets and target occlusion.

This paper presents a cardinalized probability hypothesis density (CPHD) filter for extended targets that can result in multiple measurements at each scan. The probability hypothesis density (PHD) filter for such targets has already been derived by Mahler and a Gaussian mixture implementation has been proposed recently. This work relaxes the Poisson assumptions of the extended target PHD filter in target and measurement numbers to achieve better estimation performance. A Gaussian mixture implementation is described. The early results using real data from a laser sensor confirm that the sensitivity of the number of targets in the extended target PHD filter can be avoided with the added flexibility of the extended target CPHD filter.

This report contains properties and approximations of some matrix valued probability density functions. Expected values of functions of generalised Beta type II distributed random variables are derived. In two Theorems, approximations of matrix variate distributions are derived. A third theorem contain a marginalisation result.

This paper presents a cardinalized probability hypothesis density (CPHD) filter for extended targets that can result in multiple measurements at each scan. The probability hypothesis density (PHD) filter for such targets has already been derived by Mahler and a Gaussian mixture implementation has been proposed recently. This work relaxes the Poisson assumptions of the extended target PHD filter in target and measurement numbers to achieve better estimation performance. A Gaussian mixture implementation is described. The early results using real data from a laser sensor confirm that the sensitivity of the number of targets in the extended target PHD filter can be avoided with the added flexibility of the extended target CPHD filter.