Result analysis of Kaiman filter for unobservable systems

As a set of filtering algorithms for recursive computing the optimal estimation of system states, Kalman filtering is widely used in many fields such as control systems and signal processing. However, in practical application, it is a problem whether the observability of the system will affect the filtering result of system states, which needs to be considered and paid attention to. In this paper, the incomplete observable system is decomposed into observable and unobservable parts, and the optimal estimation result of the corresponding state vectors is obtained by Kalman filter. The linear state space model with 3-dimensional state vector and 2-dimensional observation vector is selected as the simulation model, many different initial values of the filtering state are set for simulation calculation and comparative analysis. Simulation results show that the unobservable state vector cannot be accurately estimated using Kalman filtering, and the deviation of the initial value between the filtering state and the real state will affect the Kalman filtering result, and the larger the deviation of the initial value, the larger the initial deviation between the filtering result and the real state.