Universal Delayed Kalman Filter with Measurement Weighted Summation for the Linear Time Invariant System

This paper considers the design of universal delayed Kalman filter for the networked tracking system with arbitrary random delay. Firstly, an equivalent Weighted summation form of the conventional Kalman filter (WSFKF) is given to provide a novel frame to more effectively solve the delayed filtering or Out-of-sequence measurements (OOSMs) estimate. In nature, this form makes perfectly use of the properties of offline parameters computation for Kalman filter and weighted summation of initial state estimate and the ordered measurements, which are respectively from Linear time invariant (LTI) system and Linear minimum mean square error (LMMSE) estimator. Secondly, by combing a replacement with global measurement prediction and a compensation operation based on the innovation of delayed measurement and adaptive online weighted coefficient matrix, a novel universal delayed Kalman filter which is applicable to the arbitrary random delay is designed under the WSFKF frame. Compared with the current delayed filters or OOSMs update methods, the proposed delayed estimator has not only more concise algorithm structure and better estimate accuracy but also stronger application range. The example is demonstrated to validate the proposed delayed estimator in this paper.