Bayesian Estimation with Distance Bounds

TL;DR

This paper introduces an approximate Bayesian estimator for state estimation with distance bounds, demonstrating its effectiveness in positioning and dead-reckoning applications through performance evaluation and comparison with theoretical bounds.

Contribution

It proposes a novel approximate MMSE estimator for Bayesian state estimation with distance constraints, applicable to positioning and filtering problems.

Findings

Estimator performs well in positioning scenarios

MSE is close to posterior Cramér-Rao bounds

Effective in inequality constrained recursive filtering

Abstract

We consider the problem of estimating a random state vector when there is information about the maximum distances between its subvectors. The estimation problem is posed in a Bayesian framework in which the minimum mean square error (MMSE) estimate of the state is given by the conditional mean. Since finding the conditional mean requires multidimensional integration, an approximate MMSE estimator is proposed. The performance of the proposed estimator is evaluated in a positioning problem. Finally, the application of the estimator in inequality constrained recursive filtering is illustrated by applying the estimator to a dead-reckoning problem. The MSE of the estimator is compared with two related posterior Cram\'er-Rao bounds.