Linear minimum‐mean‐square error estimation of Markovian jump linear systems with Stochastic coefficient matrices

Abstract

This study presents the state estimation problem of discrete-time Markovian jump linear systems with stochastic coefficient matrices which is motivated by the idea of establishing the general filter framework of the joint state estimation and data association in clutters for tracking the manoeuvering target. According to the orthogonality principle, the linear minimum-mean-square error estimator for this system (abbreviated as LMSCE estimator) is derived recursively and sufficient conditions are given for the stability of the LMSCE estimator. The simulation about tracking the manoeuvering target in clutters shows that the LMSCE estimator obtains much more accurate estimate than the well-known interacting multiple model probabilistic data association filter.

Minimum upper-bound filter of Markovian jump linear systems with generalized unknown disturbances

“…Suppose K opt k+1 exists, and then its existence needs to be testified. After simple derivation, we have From (5), (12) and 18, we have…”

“…First, we demonstrate that the upper-bound S * k+1 satisfying (12) guarantees S * k+1 ≥ S k+1 in (5). Denote Υ k|l := E(ξ k −ξ k|l )(z k −ẑ k|l ) T andφ i,m,k = ϕ i,m,k − ϕ i,m,k .…”

“…By the fact that roundoff errors in solving the above Riccati equation may cause the loss of the symmetry and positive-semidefinition, an array implementation with the better numerical robustness was devel-oped [11]. Recently, the LMMSE estimations of MJLSs are also extended to the cases of stochastic coefficient matrices [12] and randomly delayed measurements [13].…”

“…Thus, from (A.4), it is obvious that (5) can be easily obtained given S * k+1 with structure in (12). Then, we need to proof that (4) and (6) are satisfied when given (11) and (13), respectively.…”

Survey of duality between linear quadratic regulation and linear estimation problems for discrete-time systems

“…Plenty of scholars have shown a great interest in studying the estimation problems for linear systems subject to Markovian jump. In these works, the LMI tool [84] and Riccati equation tool [85] are usually used to settle the estimation problems. The authors in [86] study a stationary LMMSE estimation problem for the linear systems with Markov jump, in which the jump parameters' prior knowledge is unspecified.…”