Fixed-lag smoothing with linear equality constraints

The problem of fixed-lag smoothing with linear equality constraint (LEC) is considered. Fixed-lag smoothing algorithms are developed by applying the state-augmentation approach to several popular constrained filtering methods, including model reduction, pseudo measurement, estimate projection and other two LEC filtering methods based on conversion or direct elimination method. After a briefly review, they are extended to address the smoothing problem with LEC. The nonlinear radar measurements in polar coordinate are converted to Cartesian coordinate by applying unbiased measurement conversion method. Thus the nonlinear smoothing problem is converted to a linear one and the proposed smoothing algorithms are formulated for linear system. The performance of the proposed smoothers are evaluated using a comparison against traditional unconstrained fixed-lag smoothing algorithm. Monte-Carlo simulation results are presented to illustrate the effectiveness of fixed-lag smoothing algorithms with LEC, where a significant performance improvement over the unconstrained smoothing algorithm can be observed. And the impact of the lag (time delay) on the performance is discussed. A small lag is recommended in the practical applications.