Dissertations / Theses on the topic 'Probability Hypothesis Density filter'

Multiple target tracking concerns the estimation of an unknown and time-varying number of objects (targets) as they dynamically evolve over time from a sequence of measurements obtained from sensors at discrete time intervals. In the Bayesian filtering framework the estimation problem incorporates natural phenomena such as false measurements and target birth/death. Though theoretically optimal, the generally intractable Bayesian filter requires suitable approximations. This thesis is particularly motivated by a first-order moment approximation known as the Probability Hypothesis Density (PHD) filter. The emphasis in this thesis is on the further development of the PHD filter for handling more advanced target tracking problems, principally involving multiple group and extended targets. A group target is regarded as a collection of targets that share a common motion or characteristic, while an extended target is regarded as a target that potentially generates multiple measurements. The main contributions are the derivations of the PHD filter for multiple group and extended target tracking problems and their subsequent closed-form solutions. The proposed algorithms are applied in simulated scenarios and their estimate results demonstrate that accurate tracking performance is attainable for certain group/extended target tracking problems. The performance is further analysed with the use of suitable metrics.

The majority of research in feature-based SLAM builds on the legacy of foundational work using the EKF, a single-object estimation technique. Because feature-based SLAM is an inherently multi-object problem, this has led to a number of suboptimalities in popular solutions. We develop an algorithm using the SC-PHD filter, a multi-object estimator modeled on cluster processes. This algorithm hosts capabilities not typically seen with feature-base SLAM solutions such as principled handling of clutter measurements and missed detections, and navigation with a mixture of stationary and moving landmarks. We present experiments with the SC-PHD SLAM algorithm on both synthetic and real datasets using an autonomous underwater vehicle. We compare our method to the RB-PHD SLAM, showing that it requires fewer approximations in its derivation and thus achieves superior performance.
En aquesta tesis es desenvolupa aquest algoritme a partir d’un filtre PHD amb un únic grup (SC-PHD), una tècnica d’estimació multi-objecte basat en processos d’agrupació. Aquest algoritme té unes capacitats que normalment no es veuen en els algoritmes de SLAM basats en característiques, ja que és capaç de tractar falses característiques, així com característiques no detectades pels sensors del vehicle, a més de navegar en un entorn amb la presència de característiques estàtiques i característiques en moviment de forma simultània. Es presenten els resultats experimentals de l’algoritme SC-PHD en entorns reals i simulats utilitzant un vehicle autònom submarí. Els resultats són comparats amb l’algoritme de SLAM Rao-Blackwellized PHD (RB-PHD), demostrant que es requereixen menys aproximacions en la seva derivació i en conseqüència s’obté un rendiment superior.

La poursuite multi-cibles a pour objet le suivi d'un ensemble de cibles mobiles à partir de données obtenues séquentiellement. Ce problème est particulièrement complexe du fait du nombre inconnu et variable de cibles, de la présence de bruit de mesure, de fausses alarmes, d'incertitude de détection et d'incertitude dans l'association de données. Les filtres PHD (Probability Hypothesis Density) constituent une nouvelle gamme de filtres adaptés à cette problématique. Ces techniques se distinguent des méthodes classiques (MHT, JPDAF, particulaire) par la modélisation de l'ensemble des cibles comme un ensemble fini aléatoire et par l'utilisation des moments de sa densité de probabilité. Dans la première partie, on s'intéresse principalement à la problématique de l'application des filtres PHD pour le filtrage multi-cibles maritime et aérien dans des scénarios réalistes et à l'étude des propriétés numériques de ces algorithmes. Dans la seconde partie, nous nous intéressons à l'étude théorique des processus de branchement liés aux équations du filtrage multi-cibles avec l'analyse des propriétés de stabilité et le comportement en temps long des semi-groupes d'intensités de branchements spatiaux. Ensuite, nous analysons les propriétés de stabilité exponentielle d'une classe d'équations à valeurs mesures que l'on rencontre dans le filtrage non-linéaire multi-cibles. Cette analyse s'applique notamment aux méthodes de type Monte Carlo séquentielles et aux algorithmes particulaires dans le cadre des filtres de Bernoulli et des filtres PHD.

Using a set of samples that are associated with weights (namely the particle method) to represent the distribution of interest for filtering under very general hypotheses (often referred to as the sequential Monte Carlo, SMC approaches or particle filters) has gained high attention in the last two decades. However, the particle method suffers from problems such as sample depletion, huge computational time and challenges raised in multi-target tracking (MTT). Aiming to address these problems and challenges, this thesis investigates efficient particle filtering from two perspectives that deal with different number of objects of interest: single-object and multi-object. On one side, novel resampling schemes, fast implementations of particle filters are developed under the Bayesian framework. On the other side, improved particle implementations of the probability hypothesis density (PHD) filter, namely the particle PHD filters are presented to deal with MTT. Resampling is a critical step in the implementation of particle filters that is of practical and theoretical significance. Firstly, various resampling methods and new developments are compared and classified into different categories, providing a comprehensive overview of resampling methods. General discussions about statistical effects of resampling are given with emphasis on robustness and identical distribution testing. New deterministic, adaptive and fast resampling schemes are put forward separately. Further, to increase the computing speed of the particle filter, a fast likelihood computing method based on numerical fitting is proposed, where the likelihood of particles is numerically fitted by the likelihood probability density function (Li-PDF) instead of directly computing it based on measurements. This is the first attempt that applies numerical fitting to enable real-time particle filtering.

Cette thèse est consacrée au problème d'estimation bayésienne pour le filtrage statistique, dont l'objectif est d'estimer récursivement des états inconnus à partir d'un historique d'observations, dans un modèle stochastique donné. Les modèles stochastiques considérés incluent principalement deux grandes classes de modèles : les modèles de Markov cachés et les modèles de Markov à sauts conditionnellement markoviens. Ici, le problème est abordé sous sa forme générale dans la mesure où nous considérons le problème du filtrage mono- et multi objet(s), ce dernier étant abordé sous l'angle de la théorie des ensembles statistiques finis et du filtre " Probability Hypothesis Density ". Tout d'abord, nous nous intéressons à l'importante classe d'approximations que constituent les algorithmes de Monte Carlo séquentiel, qui incluent les algorithmes d'échantillonnage d'importance séquentiel et de filtrage particulaire auxiliaire. Les boucles de propagation mises en jeux dans ces algorithmes sont étudiées et des algorithmes alternatifs sont proposés. Les algorithmes de filtrage particulaire dits " localement optimaux ", c'est à dire les algorithmes d'échantillonnage d'importance avec densité d'importance conditionnelle optimale et de filtrage particulaire auxiliaire pleinement adapté sont comparés statistiquement, en fonction des paramètres du modèle donné. Ensuite, les méthodes de réduction de variance basées sur le théorème de Rao-Blackwell sont exploitées dans le contexte du filtrage mono- et multi-objet(s) Ces méthodes, utilisées principalement en filtrage mono-objet lorsque la dimension du vecteur d'état à estimer est grande, sont dans un premier temps étendues pour les approximations Monte Carlo du filtre Probability Hypothesis Density. D'autre part, des méthodes de réduction de variance alternatives sont proposées : bien que toujours basées sur le théorème de Rao-Blackwell, elles ne se focalisent plus sur le caractère spatial du problème mais plutôt sur son caractère temporel. Enfin, nous abordons l'extension des modèles probabilistes classiquement utilisés. Nous rappelons tout d'abord les modèles de Markov couple et triplet dont l'intérêt est illustré à travers plusieurs exemples pratiques. Ensuite, nous traitons le problème de filtrage multi-objets, dans le contexte des ensembles statistiques finis, pour ces modèles. De plus, les propriétés statistiques plus générales des modèles triplet sont exploitées afin d'obtenir de nouvelles approximations de l'estimateur bayésien optimal (au sens de l'erreur quadratique moyenne) dans les modèles à sauts classiquement utilisés; ces approximations peuvent produire des estimateurs de performances comparables à celles des approximations particulaires, mais ont l'avantage d'être moins coûteuses sur le plan calculatoire

This dissertation presents solutions to two open problems in estimation theory. The first is a tractable analytical solution for problems in multi-target filtering which are too complex to solve using traditional techniques. The second explores a new approach to the nonlinear filtering problem for a general class of models. The approach to the multi-target filtering problem which involves jointly estimating a random process of the number of targets and their state, developed using the probability hypothesis density (PHD) filter alleviates the intractability of the problem by avoiding explicit data association. Moreover, the notion of linear jump Markov systems is generalized to the multiple target case to accommodate births, deaths and switching dynamics to derive a closed form solution to the PHD recursion for this so-called linear Gaussian jump Markov multi-target model. The proposed solution is general enough to accommodate a broad class of practical problems which are deemed intractable using traditional techniques. Based on this closed form solution, an efficient method is developed for tracking multiple maneuvering targets that switch between multiple models without the need for gating, track initiation and termination, or clustering for extracting state estimates. The approach to the nonlinear filtering problem explores the framework of the virtual linear fractional transformation (LFT) model which localizes the nonlinearity to the feedback with a simple and sparse structure. The LFT is an exact representation for any differentiable nonlinear mapping and therefore amenable to a general class of problems. An alternative analytical approximation method is presented which avoids linearization of the state space model. The uncorrelated structure of the feedback connection gives of the state space model. The uncorrelated structure of the feedback connection gives better second-order moment approximation of the nonlinearly mapped variables. By arranging the unscented transform in the feedback, the prediction and estimation steps are derived in closed form. The proposed filters for the discrete-time model and continuous-time dynamics with sampled-data measurements respectively are shown to be robust under highly nonlinear and uncertain conditions where standard analytical approximation based filters diverge. Moreover, the LFT based filters are efficient for online implementation. In addition, the LFT framework is applied to extend the closed form solution of the PHD recursion to the nonlinear jump Markov multi-target model.

Multi-target tracking (MTT) methods estimate the trajectory of targets from noisy measurement; therefore, they can be used to handle the pedestrian-vehicle interaction for a moving vehicle. MTT has an important part in assisting the Automated Driving System and the Advanced Driving Assistance System to avoid pedestrian-vehicle collisions. ADAS and ADS rely on correct estimates of the pedestrians' position and velocity, to avoid collisions or unnecessary emergency breaking of the vehicle. Therefore, to help the risk evaluation in these systems, the MTT needs to provide accurate and robust information of the trajectories (in terms of position and velocity) of the pedestrians in different environments. Several factors can make this problem difficult to handle for instance in crowded environments the pedestrians can suffer from occlusion or missed detection. Classical MTT methods, such as the global nearest neighbour filter, can in crowded environments fail to provide robust and accurate estimates. Therefore, more sophisticated MTT methods should be used to increase the accuracy and robustness and, in general, to improve the tracking of targets close to each other. The aim of this master's thesis is to improve the situational awareness with respect to pedestrians and pedestrian-vehicle interactions. In particular, the task is to investigate if the GM-PHD and the GM-CPHD filter improve pedestrian tracking in urban environments, compared to other methods presented in the literature.  The proposed task can be divided into three parts that deal with different issues. The first part regards the significance of different clustering methods and how the pedestrians are grouped together. The implemented algorithms are the distance partitioning algorithm and the Gaussian mean shift clustering algorithm. The second part regards how modifications of the measurement noise levels and the survival of targets based on the target location, with respect to the vehicle's position, can improve the tracking performance and remove unwanted estimates. Finally, the last part regards the impact the filter estimates have on the tracking performance and how important accurate detections of the pedestrians are to improve the overall tracking. From the result the distance partitioning algorithm is the favourable algorithm, since it does not split larger groups. It is also seen that the proposed filters provide correct estimates of pedestrians in events of occlusion or missed detections but suffer from false estimates close to the ego vehicle due to uncertain detections. For the comparison, regarding the improvements, a classic standard MTT filter applying the global nearest neighbour method for the data association is used as the baseline. To conclude; the GM-CPHD filter proved to be the best out of the two proposed filters in this thesis work and performed better also compared to other methods known in the literature. In particular, its estimates survived for a longer period of time in presence of missed detection or occlusion. The conclusion of this thesis work is that the GM-CPHD filter improves the tracking performance and the situational awareness of the pedestrians.

The multi-target tracking problem essentially involves the recursive joint estimation of the state of unknown and time-varying number of targets present in a tracking scene, given a series of observations. This problem becomes more challenging because the sequence of observations is noisy and can become corrupted due to miss-detections and false alarms/clutter. Additionally, the detected observations are indistinguishable from clutter. Furthermore, whether the target(s) of interest are point or extended (in terms of spatial extent) poses even more technical challenges. An approach known as random finite sets provides an elegant and rigorous framework for the handling of the multi-target tracking problem. With a random finite sets formulation, both the multi-target states and multi-target observations are modelled as finite set valued random variables, that is, random variables which are random in both the number of elements and the values of the elements themselves. Furthermore, compared to other approaches, the random finite sets approach possesses a desirable characteristic of being free of explicit data association prior to tracking. In addition, a framework is available for dealing with random finite sets and is known as finite sets statistics. In this thesis, advanced signal processing techniques are employed to provide enhancements to and develop new random finite sets based multi-target tracking algorithms for the tracking of both point and extended targets with the aim to improve tracking performance in cluttered environments. To this end, firstly, a new and efficient Kalman-gain aided sequential Monte Carlo probability hypothesis density (KG-SMC-PHD) filter and a cardinalised particle probability hypothesis density (KG-SMC-CPHD) filter are proposed. These filters employ the Kalman- gain approach during weight update to correct predicted particle states by minimising the mean square error between the estimated measurement and the actual measurement received at a given time in order to arrive at a more accurate posterior. This technique identifies and selects those particles belonging to a particular target from a given PHD for state correction during weight computation. The proposed SMC-CPHD filter provides a better estimate of the number of targets. Besides the improved tracking accuracy, fewer particles are required in the proposed approach. Simulation results confirm the improved tracking performance when evaluated with different measures. Secondly, the KG-SMC-(C)PHD filters are particle filter (PF) based and as with PFs, they require a process known as resampling to avoid the problem of degeneracy. This thesis proposes a new resampling scheme to address a problem with the systematic resampling method which causes a high tendency of resampling very low weight particles especially when a large number of resampled particles are required; which in turn affect state estimation. Thirdly, the KG-SMC-(C)PHD filters proposed in this thesis perform filtering and not tracking , that is, they provide only point estimates of target states but do not provide connected estimates of target trajectories from one time step to the next. A new post processing step using game theory as a solution to this filtering - tracking problem is proposed. This approach was named the GTDA method. This method was employed in the KG-SMC-(C)PHD filter as a post processing technique and was evaluated using both simulated and real data obtained using the NI-USRP software defined radio platform in a passive bi-static radar system. Lastly, a new technique for the joint tracking and labelling of multiple extended targets is proposed. To achieve multiple extended target tracking using this technique, models for the target measurement rate, kinematic component and target extension are defined and jointly propagated in time under the generalised labelled multi-Bernoulli (GLMB) filter framework. The GLMB filter is a random finite sets-based filter. In particular, a Poisson mixture variational Bayesian (PMVB) model is developed to simultaneously estimate the measurement rate of multiple extended targets and extended target extension was modelled using B-splines. The proposed method was evaluated with various performance metrics in order to demonstrate its effectiveness in tracking multiple extended targets.

Today, the main research field for the automotive industry is to find solutions for active safety. In order to perceive the surrounding environment, tracking nearby traffic objects plays an important role. Validation of the tracking performance is often done in staged traffic scenarios, where additional sensors, mounted on the vehicles, are used to obtain their true positions and velocities. The difficulty of evaluating the tracking performance complicates its development. An alternative approach studied in this thesis, is to record sequences and use non-causal algorithms, such as smoothing, instead of filtering to estimate the true target states. With this method, validation data for online, causal, target tracking algorithms can be obtained for all traffic scenarios without the need of extra sensors. We investigate how non-causal algorithms affects the target tracking performance using multiple sensors and dynamic models of different complexity. This is done to evaluate real-time methods against estimates obtained from non-causal filtering. Two different measurement units, a monocular camera and a LIDAR sensor, and two dynamic models are evaluated and compared using both causal and non-causal methods. The system is tested in two single object scenarios where ground truth is available and in three multi object scenarios without ground truth. Results from the two single object scenarios shows that tracking using only a monocular camera performs poorly since it is unable to measure the distance to objects. Here, a complementary LIDAR sensor improves the tracking performance significantly. The dynamic models are shown to have a small impact on the tracking performance, while the non-causal application gives a distinct improvement when tracking objects at large distances. Since the sequence can be reversed, the non-causal estimates are propagated from more certain states when the target is closer to the ego vehicle. For multiple object tracking, we find that correct associations between measurements and tracks are crucial for improving the tracking performance with non-causal algorithms.

abstract: The tracking of multiple targets becomes more challenging in complex environments due to the additional degrees of nonlinearity in the measurement model. In urban terrain, for example, there are multiple reflection path measurements that need to be exploited since line-of-sight observations are not always available. Multiple target tracking in urban terrain environments is traditionally implemented using sequential Monte Carlo filtering algorithms and data association techniques. However, data association techniques can be computationally intensive and require very strict conditions for efficient performance. This thesis investigates the probability hypothesis density (PHD) method for tracking multiple targets in urban environments. The PHD is based on the theory of random finite sets and it is implemented using the particle filter. Unlike data association methods, it can be used to estimate the number of targets as well as their corresponding tracks. A modified maximum-likelihood version of the PHD (MPHD) is proposed to automatically and adaptively estimate the measurement types available at each time step. Specifically, the MPHD allows measurement-to-nonlinearity associations such that the best matched measurement can be used at each time step, resulting in improved radar coverage and scene visibility. Numerical simulations demonstrate the effectiveness of the MPHD in improving tracking performance, both for tracking multiple targets and targets in clutter.
Dissertation/Thesis
M.S. Electrical Engineering 2011

abstract: Neural activity tracking using electroencephalography (EEG) and magnetoencephalography (MEG) brain scanning methods has been widely used in the field of neuroscience to provide insight into the nervous system. However, the tracking accuracy depends on the presence of artifacts in the EEG/MEG recordings. Artifacts include any signals that do not originate from neural activity, including physiological artifacts such as eye movement and non-physiological activity caused by the environment. This work proposes an integrated method for simultaneously tracking multiple neural sources using the probability hypothesis density particle filter (PPHDF) and reducing the effect of artifacts using feature extraction and stochastic modeling. Unique time-frequency features are first extracted using matching pursuit decomposition for both neural activity and artifact signals. The features are used to model probability density functions for each signal type using Gaussian mixture modeling for use in the PPHDF neural tracking algorithm. The probability density function of the artifacts provides information to the tracking algorithm that can help reduce the probability of incorrectly estimating the dynamically varying number of current dipole sources and their corresponding neural activity localization parameters. Simulation results demonstrate the effectiveness of the proposed algorithm in increasing the tracking accuracy performance for multiple dipole sources using recordings that have been contaminated by artifacts.
Dissertation/Thesis
Masters Thesis Electrical Engineering 2014

In this work, we propose three control strategies from different perspectives to solve the alignment problem for different optical wireless communication (OWC) systems. • Experimental modeling based strategy: we model and analyze the vibration effects on the stationary OWC system (e.g. urban free-space optical (FSO) communication system in our case). The proposed Bifurcated-Gaussian (B-G) distribution model of the receiver optical power is derived under different vibra- tion levels and link distances using the nonlinear iteration method. Besides, the UFSO channel under the effects of both vibration and atmospheric turbulence is also explored under three atmospheric turbulence conditions. Our proposed B-G distribution model helps to easily evaluate the link performance of UFSO systems and paves the way for constructing completed auxiliary control subsys- tems for robust UFSO links. • Extremum seeking control based strategy: we propose an extremum seeking control (ESC) based strategy for the mobile OWC system. Our proposed ap- proach consists of coarse alignment and fine alignment. The coarse alignment using feedback proportional-derivative (PD) control is responsible for tracking and following the receiver. For fine alignment, the perturbation-based extremum seeking control (ESC) is adopted for a continuous search for the optimal posi- tion, where the received optical power is maximum in the presence of distur- bance. The proposed approach is simple, effective, and easy to implement. • Time scale theory based strategy: we design a time scale based Kalman filter for the intermittent OWC system. First, the algorithm of Kalman filter on time scales is presented, followed by several numerical examples for interpretation and analysis. The design of Kalman filter on time scales for our simulated vibrating OWC system is then discussed, whose results are analyzed thoroughly and further validated by a reference system. The proposed strategy has great potential for solving the problem of observer design in the case of intermittent received signals (non-uniform measurements) and paves the way for further controller design. The three proposed control strategies directly or indirectly solve the beam align- ment problem for optical communication systems, supporting the development of robust optical communication link.