RECONCILING STEADY-STATE KALMAN AND ALPHA-BETA FILTER DESIGN

The deterministic design of the “Alpha-Beta” filter and the stochastic design of its Kaiman counterpart are placed on a common basis. The first step is to find the continuous-time filter architecture which transforms into the alpha-beta discrete filter via the method of “impulse invariance.” This yields relations between filter bandwidth and damping ratio and the coefficients, α and β. In the Kaiman case, these same coefficients are related to a defined stochastic signal-to-noise ratio and to a defined normalized tracking error variance. These latter relations are obtained from a closed form, unique, positive-definite solution to the matrix Ricatti equation for the tracking error covariance. A nomograph is given, relating the stochastic and deterministic designs. © 1990 IEEE