A Blind Sequential Monte Carlo Receiver for OFDM Systems in the Presence of Phase Noise, Multipath fading, and Channel Order Uncertainty

em>IEEE Transactions on Signal Processing, Vol. 56, No.3, March 2008.
Amin Zia, T. Kirubarajan, J.P. Reilly, Derek Yee,
K. Punithakumar, and S. Shirani

Abstract   In most solutions to state estimation problems, e.g., target tracking, it is generally assumed that the state transition and measurement models are known a priori. However, there are situations where the model parameters or the model structure itself are not known a priori or are known only partially. In these scenarios, standard estimation algorithms like the Kalman filter and the extended Kalman Filter (EKF), which assume perfect knowledge of the model parameters, are not accurate. In this paper, the nonlinear state estimation problem with possibly non-Gaussian process noise in the presence of a certain class of measurement model uncertainty is considered. It is shown that the problem can be considered as a special case of maximum likelihood estimation with incomplete-data. Thus, in this paper, we propose an EM-type algorithm that casts the problem in a joint state estimation and model parameter identification framework. The expectation (E) step is implemented by a particle filter that is initialized by a Monte-Carlo Markov chain algorithm. Within this step, the posterior distribution of the states given the measurements, as well as the state vector itself, are estimated. Consequently, in the maximization (M) step, we approximate the nonlinear observation equation as a mixture of Gaussians (MoG) model. During the M-step, the MoG model is fit to the observed data by estimating a set of MoG parameters. The proposed procedure, called EM-PF (expectation–maximization particle filter) algorithm, is used to solve a highly nonlinear bearing-only tracking problem, where the model structure is assumed unknown a priori. It is shown that the algorithm is capable of modelling the observations and accurately tracking the state vector. Additionally, the algorithm is also applied to the sensor registration problem in a multi–sensor fusion scenario. It is again shown that the algorithm is successful in accommodating an unknown nonlinear model for a target tracking scenario.