New developments in state estimation for INS/GPS integrated systems

This paper proposes a new filter for INS/GPS integration based on a new interpolation formula known as Discrete Singular Convolution (DSC)-based Generalized Finite Difference. Singular convolutions are essential to many science and engineering problems such as stochastic process analysis. By appropriate approximation of a singular kernel in DSC scheme, the discrete singular convolution can be an extremely efficient, accurate and reliable algorithm for practical applications. The theory of distribution and wavelet analysis form the mathematical foundation of DSC. The objective is to explore the utility of the DSC algorithm for the development of a new filter for INS/GPS integration system. The significance of this paper is that the higher order DSC-based finite difference approximation can be considered by implicitly calculating the DSC-based first and second partial differentiations (Jacobian and Hessian approximation) involved in the second order modified Gaussian Kalman filter (SOKF) scheme. To examine the performance of the proposed filter, dual frequency GPS/INS data are collected onboard a hydrographic surveying vessel owned by the Canadian Hydrographic Service (CHS). The unscented Kalman filter (UKF) is also examined and compared with the developed DSC-based SOKF. It is shown that the accuracy (RMS error) of the developed DSC-based SOEKF state estimator is better than the UKF estimator.