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)

Multiple Object Trajectory Estimation Using Backward Simulation

This paper presents a general solution for computing the multi-object posterior for sets of trajectories from a sequence of multi-object (unlabelled) filtering densities and a multi-object dynamic model. Importantly, the proposed solution opens an avenue of trajectory estimation possibilities for multi-object filters that do not explicitly estimate trajectories. In this paper, we first derive a general multi-trajectory backward smoothing equation based on random finite sets of trajectories. Then we show how to sample sets of trajectories using backward simulation for Poisson multi-Bernoulli filtering densities, and develop a tractable implementation based on ranked assignment. The performance of the resulting multi-trajectory particle smoothers is evaluated in a simulation study, and the results demonstrate that they have superior performance in comparison to several state-of-the-art multi-object filters and smoothers.Comment: Accepted for publication in IEEE Transactions on Signal Processin