Analytical solution for a steady-state Kalman filter tracker with random power spectral density process noise

An analytical solution is obtained for a steady-state Kalman filter tracker with a random power spectral density as process noise. Great insight is obtained from these analytic solutions of trackers. Optimal relationships are obtained between the gain variables. A unitless tracking index is defined as the only variable driving the steady-state Kalman filter tracker. This unitless tracking index value is defined as: Λ=√(psd8(ΔT)³/σ_m ²). Optimal gains and minimum covariance are analytically calculated given the tracking index ΛA