Performance Ranking of Kalman Filter With Pre-Determined Initial State Prior

The Kalman filter has successful applications in many fields. The applicability of the standard Kalman filter critically hinges on the accurate prior knowledge of all the system model parameters. However, in practical applications, it can be difficult or unrealistic to obtain these parameters, in which case it is a common practice to employ some pre-determined alternatives for the unknown model parameters. This letter investigates the case of unknown initial state priors by assessing how their pre-determined alternatives affect the performance of the Kalman filter. The ranking of three types of mean squared errors is established. It is found that the definiteness of the initial state prior deviation is critical, which determine the ranking of the three types of mean squared errors. Such results provide guideline on the choice of the pre-determined initial state prior. Numerical examples are provided to validate the results.