Optimal Bernoulli point estimation with applications

This paper develops optimal procedures for point estimation with Bernoulli filters. These filters are of interest to radar and sonar surveillance because they are designed for stochastic targets that can enter and exit the surveillance region at random instances. Because of this property they are not served by the minimum mean square estimator, which is the most widely used approach to optimal point estimation. Instead of the squared error loss, this paper proposes an application-oriented loss function that is compatible with Bernoulli filters, and it develops two significant practical estimators: the minimum probability of error estimate (which is based on the rule of ideal observer), and the minimum mean operational loss estimate (which models a simple defence scenario).