Test Statistics in Kalman Filtering

Many estimation problems can be modeled using a Kalman filter. One of the key requirements for Kalman filtering is to characterize various error sources, essentially for the quality assurance and quality control of a system. This characterization can be evaluated by applying the principle of multivariate statistics to the system innovations and the measurement residuals. This manuscript will systematically examine the test statistics in Kalman filter on the ground of the normal, 2χ-, t- and F- distributions, and the strategies for global, regional and local statistical tests as well. It is hoped that these test statistics can generally help better understand and perform the statistical analysis in specific applications using a Kalman filter.