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In this paper we present several new sequential Monte Carlo (SMC) algorithms for online estimation (filtering) of nonlinear dynamic systems. SMC has been shown to be a powerful tool for dealing with complex dynamic systems. It sequentially generates Monte Carlo samples from a proposal distribution, adjusted by a set of importance weight with respect to a target distribution, to facilitate statistical inferences on the characteristic (state) of the system. The key to a successful implementation of SMC in complex problems is the design of an efficient proposal distribution from which the Monte Carlo samples are generated. We propose several such proposal distributions that are efficient yet easy to generate samples from. They are efficient because they tend to utilize both the information in the state process and the observations. They are all Gaussian distributions hence are easy to sample from. The central ideas of the conventional nonlinear filters, such as extended Kalman filter, unscented Kalman filter and the Gaussian quadrature filter, are used to construct these proposal distributions. The effectiveness of the proposed algorithms are demonstrated through two applications-real time target tracking and the multiuser parameter tracking in CDMA communication systems.

Most wavelet-based reconstruction methods of compressive sensing (CS) are developed under the independence assumption of the wavelet coefficients. However, the wavelet coefficients of images have significant statistical dependencies. Lots of multivariate prior models for the wavelet coefficients of images have been proposed and successfully applied to the image estimation problems. In this paper, the statistical structures of the wavelet coefficients are considered for CS reconstruction of images that are sparse or compressive in wavelet domain. A multivariate pursuit algorithm (MPA) based on the multivariate models is developed. Several multivariate scale mixture models are used as the prior distributions of MPA. Our method reconstructs the images by means of modeling the statistical dependencies of the wavelet coefficients in a neighborhood. The proposed algorithm based on these scale mixture models provides superior performance compared with many state-of-the-art compressive sensing reconstruction algorithms.

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