Adaptive DDF Algorithm for SINS/GPS Integration System
Wei Gao, Jingchun Li, Ya Zhang, Zicheng Wang, Harbin Institute of Technology, China
Location: Big Sur
The integration of SINS and GPS are widely used for positioning and attitude determination applications. The Kalman filter is the most common method for the state estimation of the SINS/GPS integration system if the integration navigation system is a linear system. However, the error equation of SINS may be nonlinear in some situations, such as the initial alignment process with large misalignment angle, in which the nonlinear filter should be used to improve the navigation accuracy of the nonlinear SINS/GPS integration system. Generally, the extended Kalman filer (EKF) is the common employed nonlinear filter. But the complicated derivate operations and the higher-order truncation errors have greatly limited the applications of EKF for the nonlinear estimation.
To solve the nonlinear estimation problem, furthermore, a nonlinear filter called divided difference filter (DDF) is employed in this paper for the SINS/GPS integration system. Specially, the DDF algorithm adopts a polynomial approximation of the nonlinear transformation called divided difference transformation (DDT) to obtain the means and covariances of the filter. Besides, the application of DDT makes DDF algorithm suitable to various kinds of state estimation of dynamic systems, without the derivate operations and the limitations on the continuous differentiability of the system model. The estimation result of the DDF algorithm can be the second-order Taylor approximation and even close to a higher-order Taylor approximation with a sensible choice of interval length.
However, the performance of the DDF algorithm highly depends on the correct model parameters and noise covariances. The fixed covariance parameters of the process and measurement noise in the filter are determinant for the estimation accuracy, as these noise covariances affect the weight between the estimated value and new measurements from GPS. Generally, in practical SINS/GPS integration system, the actual noise statistics are also hard to obtain for lack of a priori information. Moreover, the statistics of the measurement noise may change with the environment as GPS signals are easily to be disturbed by electromagnetic interferences, maneuvers and other factors. All of them will bring in measurement noise uncertainty for the state estimation, and degrade the performance of the DDF algorithm.
For the estimation problems of measurement noise uncertainty, several adaptive Kalman filtering algorithms have been investigated over the recent decades. In general, these adaptive filtering algorithms can be broadly classified into four categories: Bayesian, maximum likelihood method, innovation correlation method and innovation covariance matching (ICM) method. Particularly, the basic idea behind the ICM method is to make the theoretical innovation covariance consistent with the actual covariance, diminishing their deviations. Therefore, an adaptive DDF algorithm based on the ICM method is proposed to solve the estimation problem of measurement noise uncertainty in the nonlinear SINS/GPS system.
Firstly, as measurement model is linear in SINS/GPS integration system, an improved nonlinear DDF algorithm is derived in the structure of Gaussian filter. Secondly, because of the measurement noise uncertainty, the theoretical innovation covariance, which is computed from the filter with initial fixed measurement noise covariance, can not reflect the actual changes of the SINS/GPS system. In order to diminish these deviations, based on the idea of the ICM method, a scaling factor is calculated to correct the covariance of the measurement noise in real time. Moreover, to verify the performance of the proposed adaptive DDF algorithm, simulations in the SINS/GPS integration system with time-varying measurement noise are implemented. The results demonstrate that the proposed adaptive DDF algorithm significantly improves the positioning and attitude accuracy of the SINS/GPS integration system under the time-varying GPS measurement noise.