Nonlinear Stochastic Modeling for INS Derived Doppler Estimates in Ultra-Tight GPS/PL/INS Integration

GPS, Pseudolites (PL) and Inertial Navigation Systems (INS) exhibit complementary performance characteristics, advantage of which can be taken through integration. System integration can be made at different levels, namely loose coupling, tight coupling and ultra-tight coupling, depending on the desired robustness (vs complexity) of the of the overall system design. In ultra-tight integration, the dynamics of the GPS receiver is compensated by the aiding Doppler derived from the INS. This results in the mitigation of the effect of vehicle dynamics on the carrier tracking loop. Hence, a significant reduction of carrier tracking bandwidth can be achieved, which in turn results in higher anti-jamming performance, improvement in raw measurement accuracy, and increased robustness of the GPS receiver tracking loop. Accurate estimation of Doppler frequency from INS is therefore the pivotal technique for ultra-tight integration. The estimation accuracy is mostly affected by the time-dependent growth of inertial sensor errors, especially the stochastic errors. In order to eliminate the negative effect of these random errors, they must be accurately modelled. Usually the stochastic models are based on the 1 or 2 Gauss-Markov models, where the key to successful implementation depends on how well the noise statistics of the inertial sensors are selected. Or, in other words, whether an accurate inertial sensor error variance can be determined. The RMS method is widely used because of the comparatively simple computation. However, the accuracy of estimation can be further improved. This paper proposes a novel stochastic modelling approach for the inertial sensor errors to improve the quality of the Doppler estimates from the INS. The procedure is based on the Allan Variance method, which is a nonlinear estimation method especially suited for modelling the random errors with higher precision. Simulation tests are preformed and the results show that, compared with the usual RMS estimation model, the proposed stochastic modelling technique effectively improves the accuracy of the Doppler estimates. Consequently, a significant enhancement in the performance of the GPS receiver tracking loop is achievable.