Search

Abstract: This paper is motivated by the filtering estimation for a class of nonlinear stochastic systems in the case that the measurements are randomly delayed by one sampling time. Through presenting Gaussian approximation about the one-step posterior predictive probability density functions (PDFs) of the state and delayed measurement, a novel Gaussian approximation (GA) filter is derived, which recursively operates by analytical computation and Gaussian weighted integrals. The proposed GA filter gives a general and common framework since: (1) it is applicable for both linear and nonlinear systems, (2) by setting the delay probability as zero, it automatically reduces to the standard Gaussian filter without the randomly delayed measurements, and (3) many variations of the proposed GA filter can be developed through utilizing different numerical technologies for computing such Gaussian weighted integrals, including the previously existing EKF and UKF methods, as well as the improved cubature Kalman filter (CKF) in our paper using the spherical–radial cubature rule. The performance of the new method is demonstrated with a simulation example of the high-dimensional GPS/INS integrated navigation. [Copyright &y& Elsevier]

Abstract: This paper proposes a Gaussian approximation recursive filter (GASF) for a class of nonlinear stochastic systems in the case that the process and measurement noises are correlated with each other. Through presenting the Gaussian approximations about the two-step state posterior predictive probability density function (PDF) and the one-step measurement posterior predictive PDF, a general GASF framework in the minimum mean square error (MMSE) sense is derived. Based on the framework, the GASF implementation is transformed into computing the multi-dimensional integrals, which is solved by developing a new divided difference filter (DDF) with correlated noises. Simulation results demonstrate the superior performance of the proposed DDF as compared to the standard DDF, the existing UKF and EKF with correlated noises. [Copyright &y& Elsevier]

For identifying the parameters in finite impulse response (FIR) systems via the quantized output, existing expectation maximization (EM) methods are involved with the intractable integrals. To overcome the above shortcoming, this paper proposes an approach referred to as explicit EM (EEM). First, we fit the quantized output data by a linear Gaussian regression distribution with some compensation parameters. As a result of the linear Gaussianity, the posterior of the excited output can be explicitly computed, so that EEM has the less computation burden than the existing EMs. Second, through optimizing these compensation parameters by resorting to variational Bayesian inference, the intrinsic distribution of the quantized output can be well fitted with guaranteed identification accuracy. Third, the linear Gaussian regression distribution is independent of the specific quantization function form, which enables EEM applicable for different quantization forms. Finally, the simulation demonstrates the feasibility and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

A recent comment (Chang, 2014) theoretically demonstrated that for the linear system with the correlated process and measurement noises, the GASF framework proposed in the paper Wang et al. (2012) was equivalent to the conventional de-coupling filtering framework. In this note, we would further show that such equivalence between the two frameworks can be justified in a more general way, even for the nonlinear system. [ABSTRACT FROM AUTHOR]

This paper proposes a general framework solution of Gaussian filter (GF) for both linear and nonlinear dynamic systems with correlated noises at the same epoch. Detailed discussions and simulation comparisons with existing Gaussian approximation recursive filter and existing de-correlating GF are provided, which show advantages of estimation accuracy of the proposed method in some applications. [ABSTRACT FROM AUTHOR]

This paper addresses the state estimation problem for dynamic systems subject to uncertain constraints, i.e., all possible constraints are described by a finite set, and only one constraint is satisfied at each moment. For this typical hybrid system estimation problem with coupled discrete constraint modes and continuous states, we design a mode separability-based state estimation (MSSE) framework. Based on the measurement model over a window, the hypothesis testing is performed to detect whether the mode changes firstly. Then the maximum-likelihood criterion is used to estimate the mode change sequence once detecting the change. Next, to consider the possible impact of the decided modes on the state estimation, a metric of mode separability is proposed to evaluate the separability of the recognized modes, and two different state estimation methods are introduced. Specifically, if the recognized modes are separable from the others, the state estimates are obtained by a recursive mode-based constraint Kalman filter (MCKF) which is proved that the estimation error is bounded in mean square. Otherwise, the estimation results output the fused state estimates (FSE) of the inseparable modes. Finally, simulation results of road-constrained vehicle tracking are provided to demonstrate the effectiveness of the proposed framework. [ABSTRACT FROM AUTHOR]