[Show abstract][Hide abstract] ABSTRACT: We consider linear systems whose state parameters are separable into linear and nonlinear sets, and evolve according to some known transition distribution, and whose measurement noise is distributed according to a mixture of Gaussians. In doing so, we propose a novel particle filter that addresses the optimal state estimation problem for the aforementioned class of systems. The proposed filter, referred to as the approximate conditional mean particle filter (ACM-PF), is a combination of the approximate conditional mean filter and the sequential importance sampling particle filter. The algorithm development depends on approximating a mixture of Gaussians distribution with a moment-matched Gaussian in the weight update recursion. A condition indicating when this approximation is valid is given. In order to evaluate the performance of the proposed algorithm, we address the blind signal detection problem for an impulsive flat fading channel and the tracking of a maneuvering target in the presence of glint noise. Extensive computer simulations were carried out. For computationally intensive implementations (large number of particles), the proposed algorithm offers performance that is comparable to other state-of-the-art particle filtering algorithms. In the scenario where computational horsepower is heavily constrained, it is shown that the proposed algorithm offers the best performance amongst the considered algorithms for these specific examples.
Full-text · Article · Jan 2009 · IEEE Transactions on Signal Processing
[Show abstract][Hide abstract] 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 modeling the observations and accurately tracking the state vector. In addition, 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.
Full-text · Article · Apr 2008 · IEEE Transactions on Signal Processing
[Show abstract][Hide abstract] ABSTRACT: In most solutions to state estimation problems like, for example, target tracking, it is generally assumed that the state evolution and measurement models are known a priori. The model parameters include process and measurement matrices or functions as well as the corresponding noise statistics. However, there are situations where the model parameters are not known a priori or are known only partially (i.e., with some uncertainty). Moreover, there are situations where the measurement is biased. 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 problem with uncertain model parameters is considered as a special case of maximum likelihood estimation with incomplete-data, for which a standard solution called the expectation-maximization (EM) algorithm exists. In this paper a new extension to the EM algorithm is proposed to solve the more general problem of joint state estimation and model parameter identification for nonlinear systems with possibly non-Gaussian noise. In the expectation (E) step, it is shown that the best variational distribution over the state variables is the conditional posterior distribution of states given all the available measurements and inputs. Therefore, a particular type of particle filter is used to estimate and update the posterior distribution. In the maximization (M) step the nonlinear measurement process parameters are approximated using a nonlinear regression method for adjusting the parameters of a mixture of Gaussians (MofG). The proposed algorithm is used to solve a nonlinear bearing-only tracking problem similar to the one reported recently with uncertain measurement process. It is shown that the algorithm is capable of accurately tracking the state vector while identifying the unknown measurement dynamics. Simulation results show the advantages of the new technique over standard algorithms like the EKF whose performance degrades rapidly in the presence of uncertain models.
Full-text · Article · Jan 2008 · IEEE Transactions on Signal Processing
[Show abstract][Hide abstract] ABSTRACT: In this paper, an efficient detector is developed to address the blind detection problem for an orthogonal- frequency-division-multiplexing (OFDM) system in the presence of phase noise and unknown multipath fading, even with channel order that is possibly not known and time varying. The proposed maximum a posteriori detector is a combination of the sequential Monte Carlo (SMC) method and the variance reduction strategy known as Rao-Blackwellization. Being blind, the developed detector, does not rely on pilot tones for the detection of the transmitted data. However, as in most work found in the literature, the aforementioned detector, which we call the RB-SMC detector, invokes the assumption of a fixed and known channel order, which may be a limitation in a number of scenarios. Therefore, to relax this assumption, we model channel order uncertainty via a first-order Markov process and subsequently introduce appropriate extensions to the RB-SMC detector, thereby proposing a novel algorithm called the E-RB-SMC detector. The performance of the novel SMC-based detectors are validated through computer simulations. It is shown that the proposed SMC-based detectors achieve near bound performance. In terms of convergence speed, the proposed E-RB-SMC detector also shows the smallest acquisition time amongst the considered algorithms.
Full-text · Article · Oct 2007 · IEEE Transactions on Signal Processing
[Show abstract][Hide abstract] ABSTRACT: We consider partially observed non-Gaussian dynamic state space models in which the process equation consists of a combination of linear and nonlinear states and the process noise for the nonlinear state update is distributed according to a mixture of Gaussians. In this paper, we solve a Bayesian filtering problem. The proposed filter is an efficient combination of the particle filter and the approximate conditional mean filter. Simulation results on a time-varying autoregressive signal demonstrate the effectiveness of the proposed algorithm
[Show abstract][Hide abstract] ABSTRACT: In this paper we address the problem of channel equalization and phase noise suppression in orthogonal frequency division multiplexing (OFDM) systems. For OFDM systems, random phase noise introduced by the local oscillator causes two effects: the common phase error (CPE), and the intercarrier interference (ICI). The performance of coherent OFDM systems greatly depends on the ability to accurately estimate the effective dynamic channel, i.e. the combined effect of the CPE and the time-varying frequency selective channel. The proposed approach uses a pilot tone aided particle filter to track/estimate the effective dynamic channel in the time domain and equalizes in the frequency domain. The particle filter is efficiently implemented by combining sequential importance sampling, principles of Rao-Blackwellization, and strategies stemming from the auxiliary particle filter. Simulation results are provided to illustrate the effectiveness of the proposed algorithm.
[Show abstract][Hide abstract] ABSTRACT: In this paper, we present efficient particle filtering and smoothing algorithms to solve the problem of blind detection in a time-varying frequency selective channel with additive non-Gaussian noise. The proposed algorithms are efficiently implemented via a combination of the optimal importance distribution and the principle of Rao-Blackwellization. The proposed particle smoothing algorithms which results in significantly improved performance, employ the method of delayed sampling, delayed weights, or a combination of the former. Simulation results are provided to illustrate the effectiveness of the proposed algorithms.