Steady-state solution for a three-state Kalman filter using range, range rate and range acceleration measurements

A closed-form steady-state solution is derived for a three-state Kalman filter which estimates the range, range rate and range acceleration when range, range rate and range acceleration are measured. For simplifying the expressions of the solution, a new normalization of the steady-state error covariance is introduced. Minimum values of the normalized steady-state error variances of a three-state Kalman filter are obtained. The solutions can be applied to tracking filter performance prediction and constant gain filter design.