Abstract
To further improve the filtering accuracy in nonlinear estimation systems, a nonlinear filter, called the orthogonal simplex Chebyshev-Laguerre cubature Kalman filter (OSCL-CKF), is proposed. The filter is built within the cubature Kalman filter framework, which transforms the multidimensional, Gaussian weighted integral into a spherical-radial coordinate system. In the spherical integral, an orthogonal method is introduced to the third-degree spherical simplex rule, and then the nonlocal sampling effects can be reduced by tuning the high order interference terms. In the radial integral, the quadrature points and corresponding weights are determined according to the Chebyshev-Laguerre (CL) equation, which enables the nonlinear filter to improve the precision by the order of the CL polynomial. Numerical results show that the proposed filter outperforms the conventional algorithms.
Highlights
Nonlinear estimation systems generally exist in civilian and military fields, such as target tracking systems, navigation systems, and communication systems
A multistatic radar based on nonlinear filter localizes a moving target within a small surveillance area [1]; a nonlinear-filter-based autonomous vehicle navigation system provides good positioning performance for vehicles [2]; the improved control systems based on nonlinear filter are adopted in wireless communication systems [3,4,5,6]
In order to regulate the effect of the high order terms, the stochastic orthogonal method [22] is introduced to the third-degree spherical simplex rule, which improves the accuracy of the cubature Kalman filter (CKF) with only two more sample points
Summary
Nonlinear estimation systems generally exist in civilian and military fields, such as target tracking systems, navigation systems, and communication systems. Jia [20] proposed the fifth and higher-degree CKF to further improve the accuracy, but the number of sample points increases rapidly with the increase of the algebraic degree or the state dimension. Compared with the high-degree CKF, the high-degree simplex cubature Kalman filter (SCKF) [21] uses fewer sample points and shows higher accuracy. In order to regulate the effect of the high order terms, the stochastic orthogonal method [22] is introduced to the third-degree spherical simplex rule, which improves the accuracy of the CKF with only two more sample points. Compared with the standard CKF, the proposed filter is more flexible because the accuracy can be further improved with the increase of CL polynomial order.
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