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Estimation and filtering of Gaussian variables with linear inequality constraints

In practice, a parameter or the state of a system is often subject to constraints. This paper considers the estimation problem for the parameter or the state constrained by a class of linear inequalities. Two sequential methods for optimal parameter estimation in the MMSE sense are obtained. They have an analytic form, which is different from most existing methods. For a dynamic system with constrained state, we model it with density function and provide a suboptimal filter based on reasonable approximations. This filter is applied to an example of tracking a ground moving target and its performance is also examined.