Analytical steady-state solution for a three-state Kalman filter

A closed-form steady-state solution is presented for the discrete Kalman-Buch filter when only position is measured. The procedure is based on a comparison between the Wiener and Kalman approaches. The solution obtained is more straightforward than the one given by S.N. Gupta (see ibid., vol.AES-20, p.839-49, Nov. 1984), which is difficult to handle when the eigenvalues are complex. The results agree perfectly with those obtained by simulation of Kalman's recursive equations extended until the steady-state is reached. The results supply apriori tracking performances and are therefore useful for preliminary design. This approach is also applied to the Singer and Fitzgerald model, because of the latter's physical importance