带约束条件的自适应滤波及其在GPS定位中的应用

推导了约束状态下的卡尔曼滤波递推方程,采用不消去状态参数的方法,在卡尔曼滤波的数学模型中增加约束状态方程推导出约束状态下的卡尔曼滤波递推方程.表明采用带约束条件的滤波递推过程与一般卡尔曼滤波递推方程相似,只要对预报值及其协方差增加一项约束条件改正项即可,因此,在滤波计算上不需要做大的修改.还讨论了带约束条件的卡尔曼滤波的自适应算法,说明一般自适应滤波算法同样适用于带约束条件的滤波,因此在应用上非常便利.利用一组GPS动态定位数据中的伪距观测值进行计算分析,并以距离作为一个约束条件,结果显示约束条件对滤波结果的改善程度与约束条件和动态系统本身有关.对于一般卡尔曼滤波中因模型确定误差和动态目标突然加速而导致的滤波发散现象,如果增加约束条件的约束力较小时,同样会出现滤波结果偏离,因此,带约束条件的滤波同样需要考虑滤波的自适应性.

Adaptive Filtering with Constraint for GPS Positioning

This paper has introduced the adaptive Kalman filtering with constraint. The recursive algorithm with constraint has been deduced without eliminating some of state parameters and it shows that only a small modification is needed for the prediction calculation compared with the conventional recursive filtering algorithm. The adaptive filtering with fading memory algorithm will be presented and demonstrates that it can be used almost in the same way as in the conventional filtering. It is assumed in conventional Kalman filtering that a priori statistical information about dynamic noise and observation noise are determined beforehand and they will maintain unchanged during the process of filtering. When such assumption is unreasonable or is changed, i.e. the sudden change of the state of the dynamic system, the filtering system will become unstable or diverging. In this case, the conventional Kalman filtering can not meet with the expected purpose and the adaptive filtering has to be adopted. For the filtering with constraint condition the same problem will also exist. There are many kinds of adaptive filtering algorithms. From a numeric test of DGPS with a fixed distance as a constraint condition, it has been showed that filtering divergence will also be caused by the acceleration of the moving object and can be overcome with adaptive method. Compared with conventional filtering, the accuracy improvement in north and east are about 10% and 0% respectively with constraint , and 26% and 13% respectively with constraint adaptive filtering. The accuracy improvement depends on the type and number of constraint condition. Both indicate that the constraint condition will contribute to the accuracy improvement of the filtering. As a result ,this method can be applied in the GPS navigation and attitude determination with Kalman filtering by utilizing constraint information such as DR data ,fixed distance among the antennas and some other constraint.