A Multipurpose Consider Covariance Analysis for Square-Root Information Smoothers

A new form of consider covariance analysis suitable for application to square-root information lters with a wide variety of model errors is presented and demonstrated. A special system formulation is employed, and the analysis draws on the algorithms of square-root information ltering to provide generality and compactness. This analysis enables one to investigate the estimation errors that arise when the lter’s dynamics model, measurement model, assumed statistics, or some combination of these is incorrect. Such an investigation can improve lter design or characterize an existing lter’s true accuracy. Areas of application include incorrect initial state covariance; incorrect, colored, or correlated noise statistics; unestimated states; and erroneous system matrices. Several simple, yet practical, examples are developed, and the consider analysis results for these examples are shown to agree closely with Monte Carlo simulations.