Kalman Filtering with Equality and Inequality State Constraints

TL;DR

This paper explores methods for incorporating equality and inequality constraints into Kalman Filtering, including nonlinear constraints, with experimental results demonstrating their effectiveness in recursive tracking applications.

Contribution

It introduces approaches for integrating both equality and inequality constraints into Kalman Filters, extending to nonlinear cases and state prediction constraints.

Findings

Constraints improve tracking accuracy

Methods effectively handle nonlinear constraints

Experimental results validate the approaches

Abstract

Both constrained and unconstrained optimization problems regularly appear in recursive tracking problems engineers currently address -- however, constraints are rarely exploited for these applications. We define the Kalman Filter and discuss two different approaches to incorporating constraints. Each of these approaches are first applied to equality constraints and then extended to inequality constraints. We discuss methods for dealing with nonlinear constraints and for constraining the state prediction. Finally, some experiments are provided to indicate the usefulness of such methods.