A stability condition and steady state errors of an /spl alpha/-/spl beta/-/spl gamma/ filter for radar tracking

We present the necessary and sufficient condition that an /spl alpha/-/spl beta/-/spl gamma/ filter is stable. We also show that there exist two different stable /spl alpha/-/spl beta/-/spl gamma/ filters one of which is derived from Kalman filter equations and another from fading memory filter equations. We derive equations of the steady state variances of an /spl alpha/-/spl beta/-/spl gamma/ filter for a constant velocity target. We also present the necessary and sufficient condition that these variances become positive. Furthermore, we show that this condition is equivalent to the stability condition.