New Kalman filter and smoother consistency tests

摘要

We derive three new tests that can be applied to a Kalman filter to check for inconsistencies. The Filter Residual Test can detect observations that are outliers but would be missed by a basic residual test because the uncertainty of the expected observation is large relative to the uncertainty of the observation. The Smoother Residual Test uses the output from a Modified Bryson-Frazier (MBF) smoother to detect observations that are outliers. The Smoother State Test compares the state estimates from the filter and MBF smoother to detect model inconsistencies, in particular insufficient process noise.