A Multipurpose Consider Covariance Analysis for Square-Root Information Filters
Joanna C. Hinks, Mark L. Psiaki · 2012
A new form of consider covariance analysis suitable for application to square-root infor-mation filters 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 filtering to provide generality and compactness. This analysis enables one to investigate the estimation errors that arise when the filter’s dynamics model, measurement model, assumed statistics, or some combination of these is incorrect. Such an investiga-tion can improve filter design or characterize an existing filter’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. I.