GPS动态定位的自适应卡尔曼滤波算法研究

GPS Dynamic Orientation＇s Adaptive Kalman Filtering Algorithm

将卡尔曼滤波方法应用于GPS定位解算模型中就可以显著减小定位误差，提高定位精度．但在实际系统中系统状态的精确描述是未知的，在动态滤波中可能会遇到滤波发散和计算发散等问题．在分析了GPS定位误差源的基础上，建立动态GPS定位滤波的一般模型，同时采用了Sage自适应和基于“当前”加速度模型的自适应滤波方法，联合对系统状态噪声方差和量测噪声方差进行自适应修正，有效的解决了动态GPS定位中出现因系统噪声和量测噪声未知而导致的滤波发散问题．同时，联合采用矩阵平方根分解和衰减记忆滤波的方法，有效的解决了误差均方差阵在计算过程中因舍入误差而造成的病态或负定而造成的滤波计算发散问题．计算机仿真结果表明，本算法对滤除随机噪声有良好的效果．

With the measurement series for GPS and establishing a kinematics model to describe the motion of the user, the errors will be decreased and the positioning precision will be increased when applying the Kalman filtering in GPS positioning computation model. However, we have so great difficulty in accurately describing the state of the system that we barge up against some problem “such as filtering divergence and computational divergence. The article puts forward a general model base on the foundation of analyzing error＇s reasons, and then, establish a adaptive model base on Sage adaptive and “current” acceleration model, simultaneously solve the filtering divergence in the dynamics filer due to the unknown of the system noise and measurement noise. During the calculation of Kalman filter, using square-root matrix decompounds and faded-memory method to avoid the computational divergence, which is conduced by the accumulate of round off error. At the end of this paper we stimulated the designed arithmetic, the result indicates that the effect of our designed arithmetic is satisfactory.