Continuous‐time Kalman filtering on the orthogonal group O(n)

Summary This paper presents a continuous‐time O(n)‐constrained Kalman‐like filter. O(n) is the group of n × n orthonormal matrices. The O(n)‐constrained Kalman‐like filter is derived by posing a constrained optimization problem. The solution involves a projection of the unconstrained Kalman state estimate derivative onto the tangent space of O(n). Using this filter, an extended O(n)‐constrained Kalman‐like filter is developed for nonlinear systems where a portion of the states evolve on O(n). A numerical example demonstrates the effectiveness of the extended O(n)‐constrained Kalman‐like filter.