A necessary and sufficient condition for the stability of an α-β-γ filter

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