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

This paper considers the design of univer- sal delayed Kalman fllter for the networked tracking sys- tem with arbitrary random delay. Firstly, an equivalent Weighted summation form of the conventional Kalman fll- ter (WSFKF) is given to provide a novel frame to more efiectively solve the delayed flltering or Out-of-sequence measurements (OOSMs) estimate. In nature, this form makes perfectly use of the properties of o†ine parameters computation for Kalman fllter 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) estima- tor. Secondly, by combing a replacement with global mea- surement prediction and a compensation operation based on the innovation of delayed measurement and adaptive on- line weighted coe-cient matrix, a novel universal delayed Kalman fllter which is applicable to the arbitrary random delay is designed under the WSFKF frame. Compared with the current delayed fllters or OOSMs update meth- ods, the proposed delayed estimator has not only more con- cise algorithm structure and better estimate accuracy but also stronger application range. The example is demon- strated to validate the proposed delayed estimator in this paper.