Interacting Multiple Model-Feedback Particle Filter for Stochastic Hybrid Systems

In this paper, a novel feedback control-based particle filter algorithm for the continuous-time stochastic hybrid system estimation problem is presented. This particle filter is referred to as the interacting multiple model-feedback particle filter (IMM-FPF), and is based on the recently developed feedback particle filter. The IMM-FPF is comprised of a series of parallel FPFs, one for each discrete mode, and an exact filter recursion for the mode association probability. The proposed IMM-FPF represents a generalization of the Kalmanfilter based IMM algorithm to the general nonlinear filtering problem. The remarkable conclusion of this paper is that the IMM-FPF algorithm retains the innovation error-based feedback structure even for the nonlinear problem. The interaction/merging process is also handled via a control-based approach. The theoretical results are illustrated with the aid of a numerical example problem for a maneuvering target tracking application

Constructing reparametrization invariant metrics on spaces of plane curves

Metrics on shape space are used to describe deformations that take one shape to another, and to determine a distance between them. We study a family of metrics on the space of curves, that includes several recently proposed metrics, for which the metrics are characterised by mappings into vector spaces where geodesics can be easily computed. This family consists of Sobolev-type Riemannian metrics of order one on the space $\text{Imm}(S^1,\mathbb R^2)$ of parametrized plane curves and the quotient space $\text{Imm}(S^1,\mathbb R^2)/\text{Diff}(S^1)$ of unparametrized curves. For the space of open parametrized curves we find an explicit formula for the geodesic distance and show that the sectional curvatures vanish on the space of parametrized and are non-negative on the space of unparametrized open curves. For the metric, which is induced by the "R-transform", we provide a numerical algorithm that computes geodesics between unparameterised, closed curves, making use of a constrained formulation that is implemented numerically using the RATTLE algorithm. We illustrate the algorithm with some numerical tests that demonstrate it's efficiency and robustness.Comment: 27 pages, 4 figures. Extended versio

Tracking shocked dust: state estimation for a complex plasma during a shock wave

We consider a two-dimensional complex (dusty) plasma crystal excited by an electrostatically-induced shock wave. Dust particle kinematics in such a system are usually determined using particle tracking velocimetry. In this work we present a particle tracking algorithm which determines the dust particle kinematics with significantly higher accuracy than particle tracking velocimetry. The algorithm uses multiple extended Kalman filters to estimate the particle states and an interacting multiple model to assign probabilities to the different filters. This enables the determination of relevant physical properties of the dust, such as kinetic energy and kinetic temperature, with high precision. We use a Hugoniot shock-jump relation to calculate a pressure-volume diagram from the shocked dust kinematics. Calculation of the full pressure-volume diagram was possible with our tracking algorithm, but not with particle tracking velocimetry.Comment: 10 pages, 8 figures, accepted for publication in Physics of Plasma

Intent Inference and Syntactic Tracking with GMTI Measurements

In conventional target tracking systems, human operators use the estimated target tracks to make higher level inference of the target behaviour/intent. This paper develops syntactic filtering algorithms that assist human operators by extracting spatial patterns from target tracks to identify suspicious/anomalous spatial trajectories. The targets' spatial trajectories are modeled by a stochastic context free grammar (SCFG) and a switched mode state space model. Bayesian filtering algorithms for stochastic context free grammars are presented for extracting the syntactic structure and illustrated for a ground moving target indicator (GMTI) radar example. The performance of the algorithms is tested with the experimental data collected using DRDC Ottawa's X-band Wideband Experimental Airborne Radar (XWEAR)

Implementation of IMMPDAF Algorithm in LabVIEW for Multi Sensor Single Target Tracking

Real time IMMPDAF algorithm has been implemented and tested in LabVIEW. Single aircraft flight profiles have been simulated and the plot data from multiple radars observing the single aircraft are generated with noise as well as clutter. The performance of the algorithm is evaluated using standard procedures. Since it is implemented and tested in LabVIEW, this algorithm can be easily realized in hardware for real time tracking applications