Inverse Free Kalman Filter Using Approximate Inverse of Diagonally Dominant Matrices

Conventional Kalman filter (KF) requires matrix inversion. But the pervasive applications of KF cannot at times afford inversion. Especially, embedded implementations do not have the capabilities to compute inverse using methods such as Cholesky decomposition. For large matrices, inversion could be computationally prohibitive even for non-embedded implementations. To address this problem, an inverse free Kalman filter (IFKF) is proposed in this letter. The inverse of innovation covariance matrix required in the update step of the KF is approximated using Taylor series expansion. The approximate inverse has a closed form expression in the elements of the original matrix. Bounds on the error covariance of proposed IFKF are also established. The proposed IFKF does not require any iterations to converge.