Research News: Optimal Bernoulli Point Estimation with Applications
Alexey Narykov, Post Doc researcher at the Signal Processing Group, provides an overview of his research paper 'Optimal Bernoulli Point Estimation with Applications' which he'll present at SSPD Conference, 13/14 September 2022, IET, Savoy Place, London.
Summary
The output of a Bayesian filter contains a perception of the time-evolving state of the uncertain world in the form of the posterior probability density function. To be useful for an application, this perception may need to be cleared of uncertainty and replaced by an optimal estimate of the true state of the world. In this paper we propose to explicitly model an application that relies on the information from a Bayesian filter and use this model to formulate a criterion for extracting a point estimate from the posterior.
Importance of the research
Bayesian filter is an element of a sensor processing chain that transforms sensor data into an optimal point estimate that supports a specific application. Historically, the research has been focused on computing the correct filtering posterior, i.e., ensuring that is exact and complete, while optimal point estimation has seen significantly less attention. In fact, the approach has been to rely on any optimal criterion that is simply computable, e.g., the minimum mean squared error, as employing the criterion that truly matches the application wouldn’t be seen as feasible. However, this approach cannot be followed anymore since those simple criteria are not compatible with modern Bayesian filters, such as the Bernoulli filter considered in this article. As a result, most filters rely on estimation algorithms that are neither optimal in any pre-specified sense, nor support any specific applications. In this work, we wish to promote an alternative approach and develop case studies that are not just optimal but support some selected applications.
What comes next?
This paper is focused on producing point estimates with the Bernoulli filter, which is a filter that describes an uncertain world containing at most one moving target. In the future, we plan to extend this approach to filters maintaining a description of time-varying number of targets.
A preprint of this paper is available here and the poster can be found here.
Link to Sensor Signal Processsing for Defence Conference.