| In this thesis we are concerned with the nonlinear filtering problems associated with many highly-complex dynamic systems using Bayesian Monte Carlo methods. We study some issues related to the Bayesian Monte Carlo methods and their performance evaluation in communication systems.; The first issue that is addressed is the improvements for SMC methods. Employing the wavelet decomposition on the random process which cannot be modelled with a linear dynamic model (i.e., ARMA model), we extend the SMC method to deal with more complex applications, such as blind detection in flat-fading or frequency-selective fading channels in wireless communications.; Dynamic systems usually exhibit strong memory effects, i.e., future observations can reveal substantial information about the current state. In order to take the advantage of the properties, we develop two novel sampling scheme for delayed estimation, namely, delayed-pilot sampling schemes and hybrid scheme. Simulation results show that the new techniques can achieve similar performance as the delayed-sample method, but with a much lower computational complexity.; We also study the multilevel mixture Kalman filter to reduce the complexity of the mixture Kalman filter. Multilevel mixture Kalman filter mainly makes use of the multilevel or hierarchical structure of the space from which the indicator variables take values. Such a multilevel sampling scheme can be also used in conjunction with the delayed estimation method, such as the delayed-sample method, resulting in delayed multilevel mixture Kalman filter. Examples in digital communications are provided to demonstrate the performance of the proposed multilevel mixture Kalman filter.; The efficiency of SMC methods are closely related with the proposal distribution. Based on this point, we develop several efficient Kernel-based sequential Monte Carlo methods. In the methods, we represent the discrete samples with Gaussian Kernels, whose adaptive bandwidth are adaptively constructed with conventional nonlinear filters, such as extended Kalman filter, unscented Kalman filter and the Gaussian quadrature filter.; Finally, a general framework for quasi-Monte Carlo particle filter is proposed. Novel extensions to the proposed quasi-Monte Carlo particle filter are also provided based on the deterministic filtering and adaptive importance sampling scheme. (Abstract shortened by UMI.)... |
