Generalized linear minimum mean-square error estimation with application to space-object tracking

The linear minimum mean-square error (LMMSE) estimation has been shown to provide a good tradeoff between the computational requirement and estimation accuracy in nonlinear point estimation. However, the best estimator within the linear class may not be adequate to provide acceptable accuracy when dealing with a highly nonlinear problem. A generalized LMMSE (GLMMSE) estimation framework searches for the best estimator among all the estimators that are linear in a vector-valued function (namely, measurement transform function) of data. The measurement transform function may convert or augment the original measurement model. In this work, general guidelines for designing the GLMMSE estimator are discussed based on a numerical example. With a properly designed measurement transform function, GLMMSE estimation should perform no worse than LMMSE estimation if the moments involved can be computed exactly. We apply the GLMMSE estimation to a space-object tracking problem and its performance is compared with the conventional LMMSE estimator.