针对基于GPS/INS组合测量的合作目标相对导航非线性滤波问题，为提高相对导航系统的精确性和可靠性，在考虑相对导航系统模型中存在不确定性及噪声统计特性未知的条件下，基于鲁棒 H∞滤波方法，提出了一种相对导航的鲁棒滤波方法。首先采用近似线性化方法将相对导航系统模型中的非线性函数进行泰勒级数展开，以避免非线性系统鲁棒H∞滤波方法求解HJI不等式困难问题，并采用不确定项来表征泰勒级数展开项中的高阶项，降低线性化误差对相对导航滤波性能的影响；在此基础上，基于鲁棒 H∞滤波方法设计了 GPS/INS 相对导航的鲁棒滤波算法。仿真结果表明，该方法对相对导航系统模型中的不确定性具有很好的鲁棒性，相对位置估计误差小于0.1 m，相对姿态角估计精度为0.0072°，相对位姿估计精度很高。%A robust H∞ filtering was applied to a GPS/INS integrated system to improve the accuracy and reliability of relative navigation system and solve the relative navigation problem with cooperative targets. The relative navigation estimator is performed in two stages: First, the Taylor series expansion method is used to approximate the nonlinear model for the relative navigation system to the first order instead of solving the HJI inequality in the robust nonlinear H∞ filtering. And the high order terms of the nonlinear model are represented by an uncertain term to improve the accuracy of the relative navigation system. Then, the relative navigation estimator is designed based on the robust H∞ filtering. Compared with the relative navigation method based on the EKF or UKF, the proposed estimator doesn’t need to know the exact information or the statistical properties of the noises in the relative navigation model, and the uncertainties in the system model can be also lowered. The numerical simulation demonstrates that the relative estimator performs excellently in the properties of the accuracy and the robustness against the uncertainties. The accuracy for the relative attitude angle estimation is 0.0072°, and the absolute maximum estimation error for the relative position is less than 0.1 m.
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