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New α - β filters in terms of steady state velocity

In this paper, we present α - β filters that are obtained by minimizing the product of the steady state variance of the estimated velocity for a constant velocity target and the nth (n is a non-negative integer) power of the steady state estimated velocity error for a constant acceleration target under the condition that the steady state position error for a constant acceleration target is constant. We assume that only position measurements are received from a sensor.