The main objective of this dissertation is to develop mean-squared error performance predictions for multiple target tracking. Envisioned as an approximate Cramer-Rao lower bound, these performance predictions allow a tracking system designer to quickly and efficiently predict the general performance trends of a tracking system. The symmetric measurement equation (SME) approach to multiple target tracking (MTT) lies at the heart of our method. The SME approach, developed by Kamen et al., offers a unique solution to the data association problem. Rather than deal directly with this problem, the SME approach transforms it into a nonlinear estimation problem. In this way, the SME approach sidesteps report-to-track associations. Developing performance predictions using the SME approach requires work in several areas: (1) extending SME tracking theory, (2) developing nonlinear filters for SME tracking, and (3) understanding techniques for computing Cramer-Rao error bounds in nonlinear filtering. First, on the SME front, we extend SME tracking theory by deriving a new set of SME equations for motion in two dimensions. We also develop the first realistic and efficient method for SME tracking in three dimensions. Second, we apply, for the first time, the unscented Kalman filter (UKF) and the particle filter to SME tracking. Using Taylor series analysis, we show how different SME implementations affect the performance of the EKF and UKF and show how Kalman filtering degrades for the SME approach as the number of targets rises. Third, we explore the Cramer-Rao lower bound (CRLB) and the posterior Cramer-Rao lower bound (PCRB) for computing MTT error predictions using the SME. We show how to compute performance predictions for multiple target tracking using the PCRB, as well as address confusion in the tracking community about the proper interpretation of the PCRB for tracking scenarios.

<p> In this thesis, we address the problem of sensor management with particular application to using unmanned aerial vehicles (U AV s) for multi target tracking. Also, we present a decision based approach for controlling information flow in decentralized multi-target multi-sensor data fusion.</p> <p> Considering the problem of sensor management for multitarget tracking, we study the problem of decision based control of a group of UAVs carrying out surveillance over a region that includes a number of moving targets. The objective is to maximize the information obtained and to track as many targets as possible with the maximum possible accuracy. Uncertainty in the information obtained by each UAV regarding the location of the ground targets are addressed in the problem formulation. We propose an altered version of a classical Value Iteration algorithm, one of the most commonly used techniques to calculate the optimal policy for Markov Decision Processes (MDPs) based on Dynamic Element Matching (DEM) algorithms. DEM algorithms, widely used for reducing harmonic distortion in Digital-to-Analog converters, are used as a core element in the modified algorithm. We introduce and demonstrate a number of new performance metrics, to verify the effectiveness of an MDP policy, especially useful for quantifying the impact of the modified DEM-based Value Iteration algorithm on an MDP policy. Also, we introduce a multi-level hierarchy of MDPs controlling each of the UAV s. Each level in the hierarchy solves a problem at a different level of abstraction. Simulation results are presented on a representative multisensor-multitarget tracking problem showing a significant improvement in performance compared to the classical algorithm. The proposed method demonstrated robust performance while guaranteeing polynomial computational complexity.</p> <p> Decentralized multisensor-multitarget tracking has numerous advantages over singlesensor or single-platform tracking. In this thesis, we present a solution for one of the main problems in decentralized tracking, namely, distributed information transfer and fusion among the participating platforms. We present a decision mechanism for collaborative distributed data fusion that provides each platform with the required data for the fusion process while substantially reducing redundancy in the information flow in the overall system. We consider a distributed data fusion system consisting of platforms that are decentralized, heterogenous, and potentially unreliable. The proposed approach, which is based on Markov Decision Processes with introduced hierarchial structure will control the information exchange and data fusion process. The information based objective function is based on the Posterior Cramer-Rao lower bound and constitutes the basis of a reward structure for Markov decision processes which are used, together with decentralized lookup substrate, to control the data fusion process. We analyze three distributed data fusion algorithms - associated measurement fusion, tracklet fusion and track-to-track fusion. The thesis also provides a detailed analysis of communication and computational load in distributed tracking algorithms. Simulation examples demonstrate the operation and the performance results of the system.</p> <p> In this thesis, we also present the development of a multisensor-multitarget tracking testbed for simulating large-scale distributed scenarios, capable of handling multiple, heterogeneous sensors, targets and data fusion methods</p>. / Thesis / Doctor of Philosophy (PhD)

In this dissertation, we seek to improve and advance the use of the finite-set statistics (FISST) approach to multitarget tracking. We consider a subsea multitarget tracking application that poses several challenges due to factors, such as, clutter/environmental noise, joint target and sensor state dependent measurement uncertainty, target-measurement association ambiguity, and sub-optimal sensor placement. The specific application that we consider is that of an underwater mobile sensor that measures the relative angle (i.e., bearing angle) to sources of acoustic noise in order to track one or more ships (targets) in a noisy environment. However, our contributions are generalizable for a variety of multitarget tracking applications. We build upon existing algorithms and address the problem of improving tracking performance for multiple maneuvering targets by incorporation several target motion models into a FISST tracking algorithm known as the probability hypothesis density filter. Moreover, we develop a novel method for associating measurements to targets using the Bayes factor, which improves tracking performance for FISST methods as well as other approaches to multitarget tracking. Further, we derive a novel formulation of Bayes risk for use with set-valued random variables and develop a real-time planner for sensor motion that avoids local minima that arise in myopic approaches to sensor motion planning. The effectiveness of our contributions are evaluated through a mixture of real-world and simulated data. / Doctor of Philosophy / In this dissertation, we seek to improve the accuracy of multitarget tracking algorithms based on finite-set statistics (FISST). We consider a subsea tracking application where a sensor seeks to estimate the position of nearby ships using measurements of the relative sensor-ship angle. Several challenges arise in our application due to factors such as environmental noise and limited resolution of measurements. Our work advances FISST algorithms by expanding upon existing methods and deriving novel solutions to mitigate challenges. We address the non-trivial question of improving tracking accuracy by planning of future sensor motion. We show that our contributions greatly improve tracking accuracy by evaluating algorithm performance using a mixture of real-world and simulated data.

This thesis presents a clustering-based approach to decrease the computational cost of data association in multi-target tracking. This is achieved by clustering the sensor tracks using approximate distance functions, thereby decreasing the number of possible associations and the need to calculate expensive statistical distances between tracks. The studied tracking problem includes passive and active sensors with built-in filters. Statistical and non-statistical distance functions were designed to account for the characteristics of the different combinations of sensors. The computational cost and accuracy of these distance functions were evaluated and compared. Analysis is done in a simulated environment with randomly positioned targets and sensors. Simulations show that there are approximate distances with a cost of calculation ten times cheaper than the true statistical distance, with only minor drops in accuracy. Spectral clustering is used on these distances to divide complex association problems into sub-problems. This algorithm is evaluated on a large number of random scenarios. The mean size of the largest sub-problem is 40 % of the original, and the mean number of errors in the clustering is 5 %.

Tracking multiple targets with uncertain target dynamics is a difficult problem, especially with nonlinear state and/or measurement equations. Random finite set theory provides a rigorous foundation to multitarget tracking problems. It provides a framework to represent the full multitarget posterior in contrast to other conventional approaches. However, the computational complexity of performing multitarget recursion grows exponentially with the number of targets. The Probability Hypothesis Density (PHD) filter, which only propagates the first moment of the multitarget posterior, requires much less computational complexity. This thesis addresses some of the essential issues related to practical multitarget tracking problems such as tracking target maneuvers, stealthy targets, multitarget tracking in a distributed framework. With maneuvering targets, detecting and tracking the changes in the target motion model also becomes important and an effective solution for this problem using multiple-model based PHD filter is proposed. The proposed filter has the advantage over the other methods in that it can track a timevarying number of targets in nonlinear/ non-Gaussian systems. Recent developments in stealthy military aircraft and cruise missiles have emphasized the need to t rack low SNR targets. The conventional approach of thresholding the measurements throws away potential information and thus results in poor performance in tracking dim targets. The problem becomes even more complicated when multiple dim targets are present in the surveillance region. A PHD filter based recursive track-before-detect approach is proposed in this thesis to track multiple dim targets in a computationally efficient way. This thesis also investigates multiple target tracking using a network of sensors. Generally, sensor networks have limited energy, communication capability and computational power. The crucial consideration is what information needs to be transmitted over the network in order to perform online estimation of the current state of the monitored system, whilst attempting to minimize communication overhead. Finally, a novel continuous approximation approach for nonlinear/ non-Gaussian Bayesian tracking system based on spline interpolation is presented. The resulting filter has the advantages over the widely-known discrete particle based approximation approach in that it does not suffer from degeneracy problems and retains accurate density over the state space. The filter is general enough to be applicable to nonlinear/non-Gaussian system and the density could even be multi-modal. / Thesis / Candidate in Philosophy

<p>Multi-Target Tracking (MTT), where the number of targets as well as their states are time-varying, concerns with the estimation of both the number of targets and the individual states from noisy sensor measurements, whose origins are unknown. Filtering typically produces the best estimates of the target state based on all measurements up to current estimation time. Smoothing or retrodiction, which uses measurements beyond the current estimation time, provides better estimation of target states. This thesis proposes smoothing methods for various estimation methods that produce delayer, but better, estimates of the target states.</p> <p>First, we propose a novel smoothing method for the Probability Hypothesis Density (PHD) estimator. The PHD filer, which propagates the first order statistical moment of the multitarget state density, a computationally efficient MTT algorithm. By evaluating the PHD, the number of targets as well as their individual states can be extracted. Recent Sequential Monte Carlo (SMC) implementations of the PHD filter have paved the way to its application to realistic nonlinear non-Gaussian problems. The proposed PHD smoothing method involves forward multitarget filtering using the standard PHD filter recursion followed by backward smoothing recursion using a novel recursive formula.</p> <p>Second, we propose a Multiple Model PH (MMPHD) smoothing method for tracking of maneuvering targets. Multiple model approaches have been shown to be effective for tracking maneuvering targets. MMPHD filter propagates mode-conditioned PHD recursively. The proposed backward MMPHD smoothing algorithm involves the estimation of a continuous state for target dynamic as well as a discrete state vector for the mode of target dynamics.</p> <p>Third, we present a smoothing method for the Gaussian Mixture PHD (GMPHD) state estimator using multiple sensors. Under linear Gaussian assumptions, the PHD filter can be implemented using a closed-form recursion, where the PHD is represented by a mixture of Gaussian functions. This can be extended to nonlinear systems by using the Extended Kalman Filter (EKF) or the Unscented Kalman Filter (UKF). In the case of multisenor systems, a sequential update of the PHD has been suggested in literature. However, this sequential update is susceptible to imperfections in the last sensor. In this thesis, a parallel update for GMPHD filter is proposed. The resulting filter outputs are further improved using a novel closed-form backward smoothing recursion.</p> <p>Finally, we propose a novel smoothing method for Kalman based Interacting Multiple Model (IMM) estimator for tracking agile targets. The new method involves forwarding filtering followed by backward smoothing while maintaining the fundamental spirit of the IMM. The forward filtering is performed using the standard IMM recursion, while the backward smoothing is performed using a novel interacting smoothing recursion. This backward recursion mimics the IMM estimator in the backward direction, where each mode conditioned smoother uses standard Kalman smoothing recursion.</p> / Thesis / Doctor of Philosophy (PhD)

This thesis gives a unified framework to formulate and solve resource management problems in radar systems. / As a crucial factor in improving radar performance for multiple target tracking (MTT), resource management problems are analyzed in this thesis with regard to sensor platform path planning, beam scheduling, and burst parameter design. This thesis addresses problems to deploy or adapt radar configurations for multisensor-multitarget tracking, including 1) the path planning of movable receivers and power allocation of transmitted signals, 2) the optimal beam steering of high-precision pencil beams, and 3) the pulsed repetition frequency (PRF) set selection and waveform design. Firstly, the coordinated sensor management on the ends of both receivers and transmitters for a multistatic radar is studied. A multistatic radar system consists of fixed transmitters and movable receivers. To form better transmitter-target-receiver geometry and to establish an effective power allocation scheme to illuminate targets with different priorities, a joint path planning and power allocation problems, which determines the moving trajectories of receivers mounted on unmanned airborne vehicles (UAVs) and the power allocation scheme of transmitted signals over a limited time horizon, is formulated as a weighted-sum optimization. The problem is solved with a genetic algorithm (GA) with a novel pre-selection operator. The pre-selection operator, which takes advantage of the receding horizon control (RHC) framework to improve population structures prior to the next generation, can accelerate the convergence of GA. Secondly, the beam steering strategies for a cooperative phased array radar system with high-precision beams are developed. Pencil beams with narrow beamwidth, which are designated to track targets for a phased array radar, offer efficient performance in an energy-saving design, but can cause partial observations. The novel concept of expected Cramér-Rao lower bound (EPCRLB) is proposed to model partial observations. A formulation based on PCRLB is given and solved with a hierarchical genetic algorithm (HGA). An optimal strategy based on EPCRLB, which is effective in performance and efficient in time, is proposed. Finally, a joint pulsed repetition frequency (PRF) set selection and waveform design is studied. The problem tries to improve blind zone maps while preventing targets from falling into blind zones. Waveform parameters are then optimized for the system to provide better tracking accuracy. The problem is first formulated as a bi-objective optimization problem and solved with a multiple-objective genetic algorithm. Then, a two-step strategy that prioritizes the visibility of targets is developed. Numerical results demonstrate the effectiveness of proposed strategies over simple approaches. / Thesis / Doctor of Philosophy (PhD) / This thesis formulates resource management problems in various radar systems. The problems use PCRLB, a theoretically achievable lower bound for estimators, as a metric to optimize, and help the configuration of radar resources in an efficient manner. Effective strategies and improved algorithms are proposed to solve the problems.

<p> Particle filters are being used in a number of state estimation applications because of their capability to effectively solve nonlinear and non-Gaussian problems. However, they have high computational requirements and this becomes even more so in the case of multitarget tracking, where data association is the bottleneck. In order to perform data association and estimation jointly, typically an augmented state vector, whose dimensions depend on the number of targets, is used in particle filters. As the number of targets increases, the corresponding computational load increases exponentially. In this case, parallelization is a possibility for achieving real-time feasibility in large-scale multitarget tracking applications. In this paper, we present an optimization-based scheduling algorithm that minimizes the total computation time for the bus-connected heterogeneous primary-secondary architecture. This scheduler is capable of selecting the optimal number of processors from a large pool of secondary processors and mapping the particles among the selected ones. A new distributed resampling algorithm suitable for parallel computing is also proposed. Furthermore, a less communication intensive parallel implementation of the particle filter without sacrificing tracking accuracy using an efficient load balancing technique, in which optimal particle migration among secondary processors is ensured, is presented. Simulation results demonstrate the tracking effectiveness of the new parallel particle filter and the speedup achieved using parallelization.</p> / Thesis / Master of Applied Science (MASc)

Data association problem for multitarget tracking is determination of the relationship between targets and the incoming measurements from sensors of the target tracking system. Performance of a multitarget tracking system is strongly related to the chosen method for data association and target tracking algorithm. Incorrect data association effects state estimation of targets. In this thesis, we propose a new multi-scan data association algorithm for multitarget tracking systems. This algorithm was implemented by using MATLAB programming tool. Performances of the new algorithm and JPDA method for multiple targets tracking are compared. During simulations linear models are used and the uncertainties in the sensor and motion models are modeled by Gaussian density. Simulation results are presented. Results show that the new algorithm&#039 / s performance is better than that of JPDA method. Moreover, a survey over target tracking literature is presented including basics of multitarget tracking systems and existing data association methods.

Autonomous driving systems are rapidly improving and may have the ability to change society in the coming decade. One important part of these systems is the interpretation of sensor information into trajectories of objects. In this master’s thesis, we study an energy minimisation method with radar and camera measurements as inputs. An energy is associated with the trajectories; this takes the measurements, the objects’ dynamics and more factors into consideration. The trajectories are chosen to minimise this energy, using a gradient descent method. The lower the energy, the better the trajectories are expected to match the real world. The processing is performed offline, as opposed to in real time. Offline tracking can be used in the evaluation of the sensors’ and the real time tracker’s performance. Offline processing allows for the use of more computer power. It also gives the possibility to use data that was collected after the considered point in time. A study of the parameters of the used energy minimisation method is presented, along with variations of the initial method. The results of the method is an improvement over the individual inputs, as well as over the real time processing used in the cars currently. In the parameter study it is shown which components of the energy function are improving the results. / Mycket resurser läggs på utveckling av självkörande bilsystem. Dessa kan komma att förändra samhället under det kommande decenniet. En viktig del av dessa system är behandling och tolkning av sensordata och skapande av banor för objekt i omgivningen. I detta examensarbete studeras en energiminimeringsmetod tillsammans med radar- och kameramätningar. En energi beräknas för banorna. Denna tar mätningarna, objektets dynamik och fler faktorer i beaktande. Banorna väljs för att minimera denna energi med hjälp av gradientmetoden. Ju lägre energi, desto bättre förväntas banorna att matcha verkligheten. Bearbetning sker offline i motsats till i realtid; offline-bearbetning kan användas då prestandan för sensorer och realtidsbehandlingen utvärderas. Detta möjliggör användning av mer datorkraft och ger möjlighet att använda data som samlats in efter den aktuella tidpunkten. En studie av de ingående parametrarna i den använda energiminimeringsmetoden presenteras, tillsammans med justeringar av den ursprungliga metoden. Metoden ger ett förbättrat resultat jämfört med de enskilda sensormätningarna, och även jämfört med den realtidsmetod som används i bilarna för närvarande. I parameterstudien visas vilka komponenter i energifunktionen som förbättrar metodens prestanda.