Partial-Update Schmidt–Kalman Filter

The Schmidt–Kalman (or "consider" Kalman filter) has often been used to account for the uncertainty in so-called "nuisance" parameters when they are impactful to filter accuracy and consistency. Usually such nuisance parameters are errors in environment or sensor models or other static biases where actively estimating their value is not required. However, there are times that it is desired or necessary to estimate the nuisance terms themselves. This paper introduces an intermittent form of the Schmidt–Kalman filter, where (within the same filter) nuisance terms are sometimes treated as full filter states and estimated, and other times they are only considered. Similarly, more generic partial-update forms of the Schmidt–Kalman filter are introduced, where only a portion of the traditional full filter update is applied to select states. These modifications extend the Schmidt filter concept for use on problematic static biases and even time-varying states, allowing them to be estimated while still maintaining filter consistency in cases where extended Kalman filter implementations do not. The new filters are shown to be unbiased and consistent analytically, and they are demonstrated in simulation on a classic one-dimensional system and a six-degree-of-freedom inertial measurement unit–camera calibration example.