Efficient High Degree Cubature Kalman Filters with Reduced Dimension Update

Cubature Kalman Filters (CKF) and other related techniques based on evaluation of non-linear functions at so-called “sigma-points” are a popular and effective modern non-linear state estimation technique. For problems with more severe non-linearity, it is possible to make use of higher degree rules that involve evaluation of the function at increasingly many points. The number of points required for higher degree rules may grow rapidly with the state dimension (sometimes exponentially). This paper introduces a technique by which a cubature rule in the dimension of the measurement may be used for the filter update step rather than a rule in the dimension of the state. This introduces a large potential savings in terms of functional evaluations when the state dimension is large.