Practical Kalman Filter Software Performance Testing & Validation

Several tests are described which can be used for any Kalman-type filter/smoother computer program. These tests are demonstrated by a case history on a large dimensional Kalman filter/smoother program which implements a 34-state inertial navigation system dynamic error model. The execution of a large dimensional Kalman filter/smoother (KFS) on real measurement data does not represent a software test of the KFS since the right answer (the correct underlying state vector) is unknown; only ``reasonableness checks'' are actually possible. Simulated test data were used to exercise the KFS program in a Monte Carlo sense and its outputs evaluated using heuristic plot comparisons as well as rigorous statistical tests. Direct tests on the accuracy of the transition matrix, discrete process noise matrix, and covariance matrix calculations have been derived and demonstrated. Methods for testing properties of the Kalman filter innovations sequence are also covered. The approach and required auxiliary software that generates the test data can be employed to perform suboptimal modeling sensitivity studies and for evaluating analysis methods that depend on KFS estimates.