Theoretical Analysis on the Filtering Accuracy of the White Noise Equivalence of Colored Measurement Noise

In order to reduce the filtering computational complexity and gain a rapid response, the colored measurement noise is generally equivalent to white noise, but as a result the filtering accuracy is accordingly deteriorated. The analytical solution to the degree of the filtering performance degeneration is presented in the paper. Based on the continuous finite memory optimal filtering theory, the prediction error of the future position of target is analyzed under three cases: 1) measurement noise is colored, 2) measurement noise is white, and 3) the colored measurement noise is equivalent to white noise. Simulations are presented on the shipborned fire control system. The simulation results show that when the colored measurement noise of the firing control system is equivalent to white noise, the degree of filtering accuracy degradation is decided by the damping ratio and the damped frequency of the measurement noise, as well as the filtering time.