Minimum variance estimation of parameters constrained by bounds

This correspondence deals with an extension of minimum variance estimation when the parameter to be estimated is constrained by bounds. It is shown that a particular initial distribution allows finite-dimensional calculation and leads to a nonlinear filter. More precisely, it is shown that a truncated Gaussian distribution is preserved a long time, leading to a finite number of parameters to be computed. Proof of the main theorem is straightforward with significant application such as positive real amplitude estimation. Performance gains are shown on the LORAN-C signal reception example.