Hlinomaz, Peter Vladimir, Ph.D., Engineering Ph.D. Program, Wright State University, 2008. Study of Multi-Modal and Non-Gaussian Probability Density Functions in Target Tracking with Applications to Dim Target Tracking
The majority of deployed target tracking systems use some variant of the Kalman filter for their state estimation algorithm. In order for a Kalman filter to be optimal, the measurement and state equations must be linear and the process and measurement noises must be Gaussian random variables (or vectors). One problem arises when the state or measurement function becomes a multi-modal Gaussian mixture. This typically occurs with the interactive multiple model (IMM) technique and its derivatives and also with probabilistic and joint probabilistic data association (PDA/JPDA) algorithms. Another common problem in target tracking is that the target’s signal-to-noise ratio (SNR) at the sensor is often low. This situation is often referred to as the dim target tracking or track-before-detect (TBD) scenario. When this occurs, the probability density function (PDF) of the measurement likelihood function becomes non-Gaussian and often has a Rayleigh or Ricean distribution. In this case, a Kalman filter variant may also perform poorly. The common solution to both of these problems is the particle filter (PF). A key drawback of PF algorithms, however, is that they are computationally expensive. This dissertation, thus, concentrates on developing PF algorithms that provide comparable performance to conventional PFs but at lower particle costs and presents the following four research efforts.
1. A multirate multiple model particle filter (MRMMPF) is presented in Section-3. The MRMMPF tracks a single, high signal-to-noise-ratio, maneuvering target in clutter. It coherently accumulates measurement information over multiple scans via discrete wavelet transforms (DWT) and multirate processing. This provides the MRMMPF with a much stronger data association capability than is possible with a single scan algorithm. In addition, its particle filter nature allows it to better handle multiple modes that arise from multiple target motion models. Consequently, the MRMMPF provides substantially better root-mean-square error (RMSE) tracking performance than either a full-rate or multirate Kalman filter tracker or full-rate multiple model particle filter (MMPF) with a same particle count.
2. A full-rate multiple model particle filter for track-before-detect (MMPF-TBD) and a multirate multiple model particle filter for track-before-detect (MRMMPF-TBD) are presented in Section-4. These algorithms extend the areas mentioned above and track low SNR targets which perform small maneuvers. The MRMMPF-TBD and MMPF-TBD both use a combined probabilistic data association (PDA) and maximum likelihood (ML) approach. The MRMMPF-TBD provides equivalent RMSE performance at substantially lower particle counts than a full-rate MMPF-TBD. In addition, the MRMMPF-TBD tracks very dim constant velocity targets that the MMPF-TBD cannot.
3. An extended spatial domain multiresolutional particle filter (E-SD-MRES-PF) is developed in Section-5. The E-SD-MRES-PF modifies and extends a recently developed spatial domain multiresolutional particle filter prototype. The prototype SD-MRES-PF was only demonstrated for one update cycle. In contrast, E-SD-MRES-PF functions over multiple update cycles and provides comparable RMSE performance at a reduced particle cost under a variety of PDF scenarios.
4. Two variants of a single-target Gaussian mixture model particle filter (GMMPF) are presented in Section-6. The GMMPF models the particle cloud as a Gaussian finite mixture model (FMM). MATLAB simulations show that the GMMPF provides performance comparable to a particle filter but at a lower particle cost.