Evaluation of navigation errors based on ergodic processes

Abstract

The problems of estimation and test of navigation errors are discussed in this paper. Based on Poor's estimation algorithm, the error model of a navigation system is studied from the stochastic process point of view, and the ergodicity of a stochastic process is extended to the ergodicity of a multivariate stochastic process. It is pointed out that Poor's estimation algorithm should be based on the ergodicity of a multivariate stochastic process for practical use and a sufficient condition is given for its application. In addition, Poor's estimation algorithm is extended to the case of any n navigation systems. The hypothesis test problem of a navigation system accuracy is also discussed in this paper. By using the multivariate statistical analysis theory, the hypothesis test problem of the error covariance matrix of every navigation system can be solved by testing the hypothesis of the relative error covariance matrix between two different navigation systems.