Sequential Monte Carlo methods for dynamic state space models with applications to communications

This dissertation investigates adaptive signal processing methods for time varying systems using new methods called sequential Monte Carlo methods or Particle filtering. Bayesian estimation and detection is applied in problems modeled as Dynamic State Space models, which provide filtering and predictive densities of the unknowns. The goal is to estimate these densities sequentially in time as each new noisy observation arrives. Closed form analytical expression are in general unavailable, except for the linear, Gaussian noise case. Hence, for nonlinear, non-Gaussian models, numerical methods are examined, which provide estimates of the filtering and predictive densities in the form of samples from these densities. Application of these methods are investigated for applications in communications.; A new filter called the Gaussian Particle Filter is proposed, which approximates the filtering and predictive densities as Gaussians similar to the well known extended Kalman filter. It is shown that under Gaussian assumptions, the estimate of the mean converges to the minimum mean square error estimate asymptotically in the number of particles used. Hence, the filter provides improved tracking performance and more reliable estimates of confidence intervals and divergence can be avoided in many nonlinear problems in which the extended Kalman filter and others fail. Most importantly, the filter is applicable in non-additive and non-Gaussian noise models unlike the extended Kalman filter and its variations. For problems where the Gaussian assumption is insufficient, a new class of filters called the Gaussian Sum Particle Filters is proposed, which approximates densities as Gaussian mixtures. These filters are applicable in models with additive noise which can be Gaussian or Gaussian mixture. They provide a new paradigm for sequential problems and are versatile for many applications. Simulations show that these methods have reduced complexity compared to previous particle filtering methods and comparable performance.; In the second part of the dissertation, joint Bayesian sequential estimation and detection in dynamic state space models is investigated. Two joint algorithms based on particle filters are proposed for this task. Applications of these algorithms for joint channel estimation and symbol detection over fading channels are examined. Specifically, three detectors are proposed for flat fading channels. Various complexities which may be otherwise intractable, like nonlinear channel models, non-Gaussian channel noise and a variety of fading distributions including Rayleigh fading can be addressed by these algorithms. The proposed methods are also extendable to frequency selective and nonlinear satellite channels.