Derivation of a fixed-lag, alpha-beta filter for target trajectory smoothing

A fixed-lag Kalman smoother is used for target trajectory reconstruction in post mission data analysis from noisy sensor data, where lag is the time difference between the latest available measurement and the smoothed estimate. Based on the steady-state conditions of a Kalman smoother, a derivation of the steady-state gains and the covariance matrix for a fixed-lag, alpha-beta smoother is presented. The equations for the steady state covariance matrices of the alpha-beta filter and the alpha-beta fixed-lag smoother are used to characterize the benefits to state estimation that result from fixed-lag smoothing.