Linear Unbiased State Estimation with Random One-Step Sensor Delay

Abstract

Sensor delay and observation uncertainty often occur in modern computerbased systems, e.g., when the measurement is transmitted to a remote controller through a network medium. In this paper, we revisit the Kalman filter design problem for a stochastic dynamic system with random one-step sensor delay, and derive the optimal unbiased state estimation algorithm. Both full-and reduced-order filters are studied, and the results compare favorably with those of the existing algorithms in examples via simulation.

Decentralized Optimal Fusion Filtering for Multi-Sensor Multi-Delay Singular Systems

“…From (28), noticing w(t) ⊥α i (t − k|t) and v i (t + 1) ⊥α i (t − k|t), we have (19). From (14), we havẽ…”

Multi-sensor Optimal Information Fusion Estimation under One-step Random Sensor Delay

“…In paper [1], [2], we studied filter design problem for one sensor system. Based on [1], [2], this paper will consider multi-sensor fusion problem, and present multi-sensor fusion estimation.…”

“…This paper presents a generalization of our previous work [1], [2] which is the improvement on [3], [4],and gives the new full-order and reduced-order linear unbiased estimators. [1], [2] considered the linear unbiased state estimation under one-step random sensor delay, while this paper will study multiplesensor fusion estimation under the same conditions, that is, For every single sensor subsystem, applying the optimal linear estimator given in our previous work [2], respectively, the local optimal estimators are obtained, which then are fused to yield the optimal global estimation, according to information fusion criterions weighted by matrices, vectors or scalars [7], [8].The three fusion criterions range from matrices to vectors to scalars in precision, but the order is reverse in view of real applications and computational complexity.…”

“…Up to now, there are few works dealing with filtering problem under random sensor delay [1]- [4]. [1], [2] is our previous work, which compensates for the deficiency existing in [3], [4]. Moreover, filtering problem considered in these literature is based on single sensor.…”

“…[1], [2] considered the linear unbiased state estimation under one-step random sensor delay, while this paper will study multiplesensor fusion estimation under the same conditions, that is, For every single sensor subsystem, applying the optimal linear estimator given in our previous work [2], respectively, the local optimal estimators are obtained, which then are fused to yield the optimal global estimation, according to information fusion criterions weighted by matrices, vectors or scalars [7], [8].The three fusion criterions range from matrices to vectors to scalars in precision, but the order is reverse in view of real applications and computational complexity. This paper considers the fusion algorithm weighted by scalars which has convenient application, and the precision of multisensor fusion estimation is superior to that based on each single sensor via simulation example.…”