Sigma-Point Kalman Filtering for Tightly Coupled GPS/INS Integration

ABSTRACT This paper describes the design and implementation of a tightly coupled integration of the Global Positioning System (GPS) and Inertial Navigation System (INS) based on the sigma-point Kalman filtering (SPKF) method. The SPKF uses a set of sigma points to completely capture the first and second order moments of the apriori random variable. In contrast to extended Kalman filtering (EKF), the SPKF has a simpler implementation as it does not require the Jacobian matrices – the computation of which may lead to analytical or computational problems in some applications. The integrated system uses the GPS pseudorange and Doppler measurements to estimate the INS errors so that the compensated INS solution is better than either a GPS or INS standalone solution. Unlike typical SPKF-based designs, using the navigation parameters as the components of the state vector and the system implies that the INS mechanical equation is the process model in which nonlinearities arise. However, the design described in this paper inherits the traditional GPS/INS integration philosophy and uses the navigation errors as the components of the state vector. Therefore it blends the INS error model and the nonlinear observation model (e.g. the nonlinear range and range-rate equations). This design provides greater flexibility for software implementation, e.g. operation switching between different filtering methods. Theoretical analysis shows that for GPS/INS integration the second-order effect on the accuracy of the EKF solution is so small that the EKF and SPKF give almost the same solutions in