Injection-Constrained State Estimation

In applications of state estimation involving data assimilation over a spatial region, it is often convenient, and sometimes necessary, to confine the state correction to a prescribed subspace of the state space that corresponds to the measurement location. This is the injection-constrained state-estimation problem, where the injection of the output error is constrained to a specified subspace of the state space. Unlike full-state output-error injection, which is the dual of static full-state feedback, constrained output-error injection is the dual of static output feedback. To address the injection-constrained state-estimation problem, this paper develops the injection-constrained unscented Kalman filter (IC-UKF) and the injection-constrained retrospective cost filter (IC-RCF). The performance of these filters is evaluated numerically for linear and nonlinear state-estimation problems in order to compare their accuracy and determine their suboptimality relative to full-state output-error injection. As a benchmark test case, IC-UKF and IC-RCF are applied to the viscous Burgers equation for state and parameter estimation.

Automated summary

In applications of state estimation, it is often necessary to restrict the state correction to a specific subspace corresponding to the measurement location. This paper presents the injection-constrained unscented Kalman filter (IC-UKF) and the injection-constrained retrospective cost filter (IC-RCF) to address this problem. The performance of these filters is evaluated numerically, and their accuracy and suboptimality relative to full-state output-error injection are compared.