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

We present a necessary and sufficient condition for the stability of an α-β-γ filter that can be used even when the values of filter gains α, β and γ are larger than 1. We also present the optimal choice of the α, β, γ combination of an α-β-γ filter. For choice, we use the steady state errors of the predicted position of the α-β-γ 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