The proper computation of the matrix pseudoinverse and its impact in MVRO filtering

Simple nonpathological counterexamples are used to demonstrate the problems inherent in conventional approaches to matrix pseudoinverse calculation for navigation applications. An alternative matrix pseudoinverse algorithm based on the singular-value decomposition (SVD) approach is described, and some sample calculations are carried out. Specific results are presented for a minimum variance reduced-order (MVRO) design methodology for selecting reduced-order filters for navigation applications. The nontrivial block calculations and condition-checking procedures in the MVRO are discussed, and a potential source of error in applying the MVRO to Kalman filter design is identified.