Fixed-lag alpha-beta filter for target trajectory smoothing

A fixed-lag Kalman smoother can be used for target trajectory reconstruction in postmission data analysis from noisy sensor data, where lag is the time difference between the time of the latest available measurement (or the latest measurement used for estimation) and the time of the smoothed estimate. Based on the steady-state conditions of a Kalman smoother, a recursive method for calculating the steady-state gains and covariance matrix of a fixed-lag alpha-beta smoother is derived and presented. The equations derived for the alpha-beta fixed-lag smoother were verified using a Kalman smoother in steady-state, and the results are used to characterize the benefits achieved with fixed-lag smoothing.