Model Error Compensation of Double-fading Kalman Filtering to Rectangular Board of Six-axis Force Sensors
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摘要: 六维力传感器能够通过应变片及板梁结构实时检测空间六方向的力信息，但其输出信号不可避免地被噪声干扰所污染。为改善这一现象，同时针对过程噪声模型不精准致使经典卡尔曼滤波器性能差的问题，设计了一种双因子渐消卡尔曼滤波器。算法研究了加性噪声信号的统计特性，建立了矩形板主振型增广状态方程，分析了两种过程噪声模型偏差对滤波性能的影响。在经典卡尔曼滤波器的基础上，基于新息正交性原理，依据Sage开窗估计原理与最小二乘准则，构造了双渐消因子的解析式，阐述了滤波器的工作原理。研究表明：双渐消卡尔曼滤波器稳定性强，能够有效削弱噪声模型偏差的影响；对比抗差卡尔曼滤波器，精度提升38.66%。Abstract: The six-axis force sensors can detect spatial force information in six directions in real time through the strain gauge and plate girder structure, but the output signal is inevitably polluted by the noise signal. In order to improve this phenomenon, a kind of double-fading factors Kalman filter is designed for the problem of poor performance of the standard Kalman filter due to the inaccuracy of the acoustic noise model. The statistical properties of the additive noise signal are studied in this algorithm. The augmented state equation of the principal mode shape of the rectangular plate is established. The influence of the two acoustic noise model deviations on the filter performance is analyzed. Based on the standard Kalman filter and the theory of orthogonality of innovation, according to the Sage window estimation principle and the least squares criterion, the analytic formula of the double-fading factors are constructed. The working principle of filter is described. The simulation results indicate that the proposed algorithm has better stability comparing with robust Kalman filter; it can effectively reduce the effect of model errors come from noise and improve filtering precision to 38.66 percent.
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表 3 四枚应变片中心位置信息
应变片编号 X/mm Y/mm Z/mm 1 16.35 0 -0.75 2 16.35 0 0.75 3 3.65 0 0.75 4 3.65 0 -0.75 
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表 4 固有频率与振型函数
固有频率/Hz 简化振型函数 19 542 W1=0.999 6sin(157x)2 33 856 W2=0.999 8sin(157x)sin(314x) 51 403 W3=0.991 0sin(157x)2 (1-250y)+0.133 9sin(157x)sin(471x)(1-250y)
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表 5 滤波前期算法性能比较
滤波算法 RMSE 精度提升 SKF 0.001 487 7 / RKF 0.000 938 1 36.94% AKF 0.000 938 1 36.94%
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表 6 滤波中期算法性能比较
滤波算法 RMSE 精度提升 SKF 0.002 070 5 / RKF 0.000 942 2 54.49% AKF 0.000 9422 54.49%
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