A necessary and sufficient condition for the stability of an /spl alpha/-/spl beta/-/spl gamma/ filter

We present a necessary and sufficient condition for the stability of an /spl alpha/-/spl beta/-/spl gamma/ filter that can be used even when the values of filter gains /spl alpha/, /spl beta/ and /spl gamma/ are larger than 1. We also present the optimal choice of the /spl alpha/, /spl beta/, /spl gamma/ combination of an /spl alpha/-/spl beta/-/spl gamma/ filter. For choice, we use the steady state errors of the predicted position of the /spl alpha/-/spl beta/-/spl gamma/ filter. More exactly, we use the steady state variance for a constant velocity target under the condition that the steady state errors for a constant jerk (derivative of the acceleration) target are the same.