Multiple Model Adaptive Estimator Target Tracker for Maneuvering Targets in Clutter

The task of tracking a target in the presence of measurement clutter is a two-fold problem: one of handling measurement association uncertainty (due to clutter), and poorly known or significantly varying target dynamics. Measurement association uncertainty does not allow conventional tracking algorithms (such as Kalman filters) to be implemented directly. Poorly known or varying target dynamics complicate the design of any tracking filter, and filters using only a single dynamics model can rarely handle anything beyond the most benign target maneuvers. In recent years, the Multiple Hypothesis Tracker (MHT) has gained acceptance as a means of handling targets in a measurement-clutter environment. MHT algorithms rely on Gaussian mixture representations of a target\u27s current state estimate, and the number of components within these mixtures grows exponentially with each successive sensor scan. Previous research into techniques that limit the growth of Gaussian mixture components proved that the Integral Square Error cost-function-based algorithm performs well in this role. Also, multiple-model adaptive algorithms have been shown to handle poorly known target dynamics or targets that exhibit a large range of maneuverability over time with excellent results. This research integrates the ISE mixture reduction algorithm into Multiple-Model Adaptive Estimator (MMAE) and Interacting Mixed Model (IMM) tracking algorithms. The algorithms were validated to perform well at a variety of measurement clutter densities by using a Monte Carlo simulation environment based on the C++ language. Compared to single-dynamics-model MHT trackers running against a maneuvering target, the Williams-filter-based, multiple-model algorithms exhibited superior tracking performance

A Gaussian Mixture PHD Filter for Jump Markov System Models

The probability hypothesis density (PHD) filter is an attractive approach to tracking an unknown and time-varying number of targets in the presence of data association uncertainty, clutter, noise, and detection uncertainty. The PHD filter admits a closed-form solution for a linear Gaussian multi-target model. However, this model is not general enough to accommodate maneuvering targets that switch between several models. In this paper, we generalize the notion of linear jump Markov systems to the multiple target case to accommodate births, deaths, and switching dynamics. We then derive a closed-form solution to the PHD recursion for the proposed linear Gaussian jump Markov multi-target model. Based on this an efficient method for tracking multiple maneuvering targets that switch between a set of linear Gaussian models is developed. An analytic implementation of the PHD filter using statistical linear regression technique is also proposed for targets that switch between a set of nonlinear models. We demonstrate through simulations that the proposed PHD filters are effective in tracking multiple maneuvering targets

A batch algorithm for estimating trajectories of point targets using expectation maximization

In this paper, we propose a strategy that is based on expectation maximization for tracking multiple point targets. The algorithm is similar to probabilistic multi-hypothesis tracking (PMHT) but does not relax the point target model assumptions. According to the point target models, a target can generate at most one measurement, and a measurement is generated by at most one target. With this model assumption, we show that the proposed algorithm can be implemented as iterations of Rauch-Tung-Striebel (RTS) smoothing for state estimation, and the loopy belief propagation method for marginal data association probabilities calculation. Using example illustrations with tracks, we compare the proposed algorithm with PMHT and joint probabilistic data association (JPDA) and show that PMHT and JPDA exhibit coalescence when there are closely moving targets whereas the proposed algorithm does not. Furthermore, extensive simulations c comparing the mean optimal subpattern assignment (MOSPA) performance of the algorithm for different scenarios averaged over several Monte Carlo iterations show that the proposed algorithm performs better than JPDA and PMHT. We also compare it to benchmarking algorithm: N-scan pruning based track-oriented multiple hypothesis tracking (TOMHT). The proposed algorithm shows a good tradeoff between computational complexity and the MOSPA performance

Human detection and tracking via Ultra-Wideband (UWB) radar

This paper presents an algorithm for human presence detection and tracking using an Ultra-Wideband (UWB) impulse-based mono-static radar. UWB radar can complement other human tracking technologies, as it works well in poor visibility conditions. UWB electromagnetic wave scattering from moving humans forms a complex returned signal structure which can be approximated to a specular multi-path scattering model (SMPM). The key technical challenge is to simultaneously track multiple humans (and non-humans) using the complex scattered waveform observations. We develop a multiple-hypothesis tracking (MHT) framework that solves the complicated data association and tracking problem for an SMPM of moving objects/targets. Human presence detection utilizes SMPM signal features, which are tested in a classical likelihood ratio (LR) detector framework. The process of human detection and tracking is a combination of the MHT method and the LR human detector. We present experimental results in which a mono-static UWB radar tracks human and non-human targets, and detects human presence by discerning human from moving non-human objects

Advanced signal processing techniques for multi-target tracking

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

Bayesian Sample Size Determination for Single-Particle Tracking of Pathogens in Biological Fluids

Single-particle tracking (SPT) experiments measure 2-dimensional particle position with a high-resolution digital camera, capturing microsecond motion. SPT has allowed novel investigation of membrane dynamics, enzymology, subdiffusion processes in proteins, and serves as a burgeoning application of statistical modelling. While particle tracking statistical methodology has shown great promise, the literature is comparatively scarce for methods that determine the necessary number of particles to track to assess a relevant scientific hypothesis. This work addresses this gap by providing a Bayesian sample size determination (SSD) algorithm. Namely, this work proceeds in two-stages, (1) model training and (2) the SSD algorithm. A single-trajectory location-scale model incorporating fractional Brownian motion is fit using maximum likelihood estimation for each 2-dimensional SPT trajectory. Subsequently, a multiple-trajectory hierarchical model is fit to capture different particle dynamics caused by fluid heterogeneity. A Bayesian SSD algorithm follows to evaluate scientific relevance based on population-level mean-squared displacement. The performance of the SSD algorithm is first studied under a simulation environment. Three simplified SSD algorithms are presented to accelerate computation. Following this, experimental data of 3,707 fluorescently labelled herpes-simplex virus trajectories are studied across five separate antibody concentrations ranging 0-1000 mg/L. A detailed analysis on the practical use of the SSD algorithm provides insight into virus dynamics as a function of antibody concentration