中文摘要：

为了研究多项式卡尔曼滤波器在车辆定位中的应用特性,分析阶数对多项式卡尔曼滤波器估算精度的影响以及评估多项式卡尔曼滤波器的工作性能,该文通过多项式拟合对非线性系统建模,构建多项式卡尔曼滤波器并进行车辆多传感器融合定位试验验证。首先分析了多项式的阶数对多项式卡尔曼滤波器的影响和多项式卡尔曼滤波器的工作性能评价方法;其次,在车辆定位常用的里程计航位推算公式的基础上分别使用0阶、1阶和2阶多项式对车辆纵向速度和航向角进行拟合,建立0阶、1阶和2阶多项式卡尔曼滤波器。在Pioneer 3-AT移动机器人平台上进行试验,多项式卡尔曼滤波器融合信息来源于里程计和AHRS传感器,RTK-GPS测量轨迹作为参考轨迹;同时将卡尔曼滤波理论误差和实际误差进行对比分析,验证了多项式卡尔曼滤波器的工作性能。试验结果显示,所建立的多项式卡尔曼滤波器的实际误差均在超过68%的滤波时间里处于理论误差范围内,验证了滤波器的工作性能正常。0阶多项式卡尔曼滤波器定位精度在X、Y轴方向上分别比里程计航位推算法提高63%和77%;1阶的定位精度优于0阶,2阶的定位精度优于0阶但劣于1阶,说明更高阶的多项式对里程计航位推算公式的车辆纵向速度和航向角拟合,对提高定位精度并无重要作用。该文研究对构建多项式卡尔曼滤波器,评估多项式卡尔曼滤波器的工作性能,以及多项式卡尔曼滤波器在车辆定位的实践应用提供参考。

英文摘要：

In order to study the application of polynomial Kalman filter（PKF） in the vehicle location,and to analyze state estimation accuracy of PKF affected by the order of polynomial and evaluate the performance of the PKF,in this paper,by adopting polynomial fitting method in system model of kalman filter to model nonlinear system,three PKFs were established and applied for vehicle localizaiton experiment with mulitiple sensors fusion.Firstly,previous researches on PKF in tracking accuracy affected by the order of polynomial and in performance evaluation were introduced.Then,zero-order,first-order and second-order PKF were establish using corresponding order of polynomial to fit the longitudinal velocity and heading of encoder dead-reckon model.Experiment was conducted on Pioneer3-AT moble robot platform with Encoder and AHRS used as sensor data input,measurement of RTK-GPS was as reference trajectory.Also,the theorectical error and actual error of the PKF were compared to evaluate the performance of the three PKFs.The experiment result showed that the actual error of the three PKFs were within the theorectical error bounds in more than 68% filtering time which indicated normal status of the filters.The localization accuracy of zero-order PKF were increased by 63% and 73% in X,Y axis respectively compared with encoder dead-reckon method.Localization accuracy of first-order PKF was better than zero-order,and second-order was better than zero-order but worse than first-order,which showed that polynomial fitting the longitudinal velocity and heading of encoder dead-reckon model using higher order could not contribute to even better localization accuracy.This paper provides references for the construction and performance evaluation of PKF,as well as its practical implementation on vehicle localization.