Square Root Partial-Update Kalman Filter

The Partial-Update Kalman Filter is a recent development that, in a very simple fashion, extends the uncertainty and nonlinearities which the extended or unscented Kalman filters are able to tolerate. However, to date its application has been limited to filters using a full covariance matrix representations or through a wasteful mapping between square root and full covariance representations. In this paper, the Square Root Partial-Update Kalman Filter is developed and demonstrated. This new approach benefits from both the numerical stability inherent in the square root filter and the robustness of the partial update while operating directly on the square root representation of the uncertainty. The paper details the algorithm and implementation and provides a nonlinear filtering example to demonstrate the increased robustness of the partial update form of the square root filter.