文档介绍：Reliability Analysis in Kalman filtering
Jian-Guo Wang
Faculty of Science and Engineering, York University, ******@
Abstract
This manuscript centers on the reliability theory and its applications in Kalman filtering. Especially, it delivers a distinct derivation of the redundancy contribution - the key element of reliability theory for the Kalman filter algorithm that has not prehensively discussed in literature at present. A distinction is made between the system innovation vector and the measurement (or pseudo measurement) residual vector. This allows to directly analyse the observation vector and the process noise vector. Particular attention is paid not only to the theoretical fundamentals of the reliability, and also to the introduction of some practical applications about the use of the redundancy contribution in Kalman filtering. The manuscript aims at assisting readers in prehensive understanding of reliability analysis in Kalman filtering.
Keywords: Kalman filter, stochastic information, quality control, internal reliability, external reliability, redundancy contribution, controllable value, minimal detectable outlier.
1 Introduction
Quality control is a system of maintaining standards in manufactured products by testing and inspection [Barber, 1998]. It belongs to one of the paramount tasks to the applications with Kalman filter just as its importance to the traditional geodetic applications. Specifically, the term quality prises of reliability and precision [Salzmann and Teunissen, 1989]. The former describes the ability of the redundant observations to check model errors, or is concerned with the effects of possible misspecifications of the model on the estimation results, whilst the latter measures the spread of the estimation results due to the stochastic model and is represented by a covariance matrix.
The measures for quality control have been affirmatively developed together with the development of the theory of Kalman filter and m