GPS/INS navigation based on adaptive finite impulse response-Kalman filter algorithm

Abstract: Global positioning system (GPS) and inertial navigation system (INS) are widely used in target positioning, vehicle navigation, precision agriculture and other fields. However, due to factors such as satellite signal occlusion, multi-path effect and observation error, the filtering results usually have large errors. Kalman filtering algorithm is generally used in navigation and positioning system to improve positioning accuracy. The performance of kalman filter algorithm depends on the dynamic model of state vector and the random model describing noise characteristics. There are 2 corresponding adaptive kalman filtering algorithms: one is the multiple-model-based adaptive estimation (MMAE); the other is the innovation-based adaptive estimation (IAE). The first method is to combine all models with non-zero model probability by using a set of parallel kalman filters under different dynamic models and statistical information. The second method complete the adaptive filtering directly by calculating the observation noise or process noise covariance matrix based on the change of information sequence. In MMAE and IAE methods, discrete time differential models are usually adopted, such as the constant velocity CV model and constant acceleration CA model, to describe the change process of state variables. However, the state vectors such as position, velocity and attitude are correlated, and it is very difficult to accurately describe the statistical relations of these states. When the prior information is not sufficient, the coupling effect of each filtering state will also cause large errors to the positioning results. Another disadvantage of kalman filter algorithm based on discrete time differential model is that it highly depends on the prior statistical information of process noise and observation noise. Generally, the prior statistical information of process noise and measurement noise depends on the motion process and application scene, which is difficult to be obtained accurately. Insufficient prior statistical information of the filter will reduce the estimation accuracy of the filter state and even lead to the divergence of the filter estimation results. The research of adaptive kalman filter algorithm is mainly focused on the covariance of online calculation process noise or measured noise. In order to improve the accuracy of navigation and positioning, an adaptive kalman filter algorithm based on FIR (finite impulse response) prediction model for white noise background was proposed in this paper. Firstly, the continuous trajectory function of moving target was approximated by an N-order polynomial with arbitrary precision, and the FIR prediction model polynomial was obtained. The FIR prediction model coefficient was obtained by solving a convex quadratic programming problem, and the optimal solution of FIR prediction model coefficient was solved by lagrange multiplier method. The convex quadratic programming taken the polynomial motion law of the target as the constraint condition and the minimum white noise gain as the objective function, and the optimal solution could not only satisfy the constraints of the target's motion state, but also had the effect of de-noising to a certain extent. Finally, the proposed FIR prediction model was combined with kalman filter. Simulation test and the measurement results showed that kalman filtering algorithm based on FIR prediction model had higher estimation accuracy than the traditional kalman filtering algorithm under the same parameter settings, and the simulation experiment results showed that the localization precision was increased by 29.54%, the measured experimental results showed that positioning accuracy in east-west direction increased by 21.71%, positioning error in north-south direction increased by 22.62%. The proposed algorithm could be used for single state estimation before information fusion in loosely coupled GPS/INS, and also for noise reduction in post-processing of GPS receivers.