Design analysis for the two-stage alpha, beta, gamma estimator

The transfer functions and variance reduction ratios of the two-stage α, β, γ-bar estimator are compared with those of the standard α, β and α, β, γ filters. In the two-stage α, β, γ-bar estimator, position and velocity are tracked in the first stage, a standard α, β filter, and the acceleration is tracked in the second stage, which is a standard, single-gain γ-bar filter. The output of the acceleration filter can be used to adjust the estimates of the α, β filter when a bias is detected in its tracking residuals. The transfer functions for the position, velocity, and acceleration estimates of the two-stage α, β, γ-bar estimator are derived, along with the variance reduction ratios