Generalized Square-Root Information Consider Covariance Analysis for Filters and Smoothers

Abstract

A new form of consider covariance analysis for studying incorrectly modeled square-root information filters and smoothers is presented and demonstrated. The value of this technique is its ability to compute the true estimation error covariance when the estimator has an incorrect dynamic model, an incorrect measurement model, or an incorrect statistical model. The new analysis casts systems with a wide range of possible modeling errors into a special form and exploits square-root techniques to provide both generality and compactness. A consider covariance analysis can improve filter or smoother design or characterize an existing estimator’s true accuracy, and it greatly reduces computational burden compared with alternative Monte Carlo-based methods of analyzing an estimator’s sensitivity to mismodeling. Applicable modeling errors include incorrect initial state covariance, colored or correlated noise statistics, unestimated disturbance states, and erroneous system matrices. Several simple examples are developed to illustrate the application of the new consider analysis to models with a variety of error types, and these examples are independently validated by Monte Carlo simulation.