Wenling Li

This paper studies the problem of interacting multiple model (IMM) estimation for jump Markov linear systems with unknown measurement noise covariance. The system state and the unknown covariance are jointly estimated in the framework of Bayesian estimation, where the unknown covariance is modeled as a random matrix according to an inverse-Wishart distribution. For the IMM estimation with random matrices, one difficulty encountered is the combination of a set of weighted inverse-Wishart distributions. Instead of using the moment matching approach, this difficulty is overcome by minimizing the weighted Kullback-Leibler divergence for inverse-Wishart distributions. It is shown that a closed form solution can be derived for the optimization problem and the resulting solution coincides with an inverse-Wishart distribution. Simulation results show that the proposed filter performs better than the previous work using the moment matching approach.

The paper proposed an adaptive filter for jump Markov systems with unknown measurement noise covariance. The filter is derived by treating covariance as a random matrix and an inverse‐Wishart distribution is adopted as the conjugate prior. The variational Bayesian approximation method is employed to derive mode‐conditioned estimates and mode‐likelihood functions in the framework of interacting multiple model. A numerical example is provided to illustrate the performance of the proposed filter.

This paper is concerned with distributed multiple model estimation for jump Markov linear systems with missing measurements over a sensor network. Two independent Markov chains are used to describe the switching of dynamic models and the missing of measurements, respectively. Under the assumption that each sensor can only communicate with its neighbours, a distributed filter is developed by applying the basic interacting multiple model (IMM) approach in the Bayesian estimation framework. To circumvent the difficulty of exponentially growing filters by exchanging local measurements between neighbouring sensors, the mode-conditioned estimates are exchanged instead of local measurements and the covariance intersection method is adopted to fuse mode-conditioned estimates. A multi-sensor manoeuvering target tracking example is provided to verify the effectiveness of the proposed filter.

This article studies the problem of distributed filtering for jump Markov linear systems in a not fully connected sensor network. A distributed consensus filter is developed by applying an improved interacting multiple model approach in which the mode‐conditioned estimates are derived by the Kalman consensus filter and the mode probabilities are obtained in the sense of linear minimum variance. A numerical example is provided to demonstrate the effectiveness of the proposed algorithm for tracking a manoeuvring target in a sensor work with eight nodes.

This study is concerned with the problem of filtering and fixed‐lag smoothing for jump Markov non‐linear systems when the mode information can be extracted from an image sensor. Based on the idea of Rao–Blackwellisation, the authors present a general theoretical framework to derive the recursive estimates by employing the particle filtering method. A suboptimal image‐enhanced Rao–Blackwellised particle filter is proposed, in which the mode state is estimated by using random sampling and the continuous state as well as the relevant likelihood function are approximated as Gaussian distributions. The one‐step fixed‐lag smoothing result is also obtained for such systems with lagged mode observations. Performance comparison of the proposed algorithms with the existing methods is provided through a manoeuvring target tracking simulation study.

In this study, a robust Rao-Blackwellised particle filter (RBPF) is proposed for jump Markov non-linear systems (JMNLSs) with unknown noise statistics. A non-linear filter is presented by applying the unscented transform technique in the H_∞ setting, which is used to update the continuous-state particles in the RBPF framework. Moreover, a way to adaptively adjust the disturbance tolerance level for performance requirement is presented. Simulation results using the proposed approach are also presented.

This study is concerned with risk-sensitive filtering and smoothing for a class of discrete-time jump Markov non-linear systems. Using the so-called reference probability method, the authors present a general theoretical framework to yield recursions for deriving filtered and smoothed estimates through identifying the approximations made by the interacting multiple model (IMM) estimation approach. A suboptimal risk-sensitive filtering algorithm is developed by applying the unscented transform (UT) technique and the one-step fixed-lag smoothing result is also presented for such systems. The effectiveness of the proposed algorithms is demonstrated via a manoeuvering target tracking simulation study.