Iterated Orthogonal Simplex Cubature Kalman Filter for Target Tracking

Abstract

In this paper, an iterated orthogonal simplex cubature Kalman filter (IOSCKF) for target tracking is proposed. The Gaussian weighted integral is decomposed into two parts, including the spherical integral and radial integral. The former is calculated approximately by the spherical simplex rule, while the latter is computed using the second-order Gauss-Laguerre quadrature rule. The above two rules are combined, and the simplex cubature rule is derived. The cubature points, which are extracted from the proposed rule, are transformed using the given orthogonal matrix to reduce the high order error terms. The transformed points and weights are embedded into the nonlinear Kalman filter framework. The measured value is used iteratively to correct the measurement update using the Gauss-Newton iteration until the termination condition is satisfied, and the IOSCKF is achieved. For target tracking with linear state equation, the time update is reduced to that of conventional Kalman filter, and the simplified IOSCKF (SIOSCKF) is obtained. The simulation results show that IOSCKF can achieve higher accuracy, and the simplified form SIOSCKF could provide the same accuracy as IOSCKF with less computational complexity.