Cross approximation-based quadrature filter
Cross approximation-based quadrature filter
复制标题
基于交叉近似的正交滤波器
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Yan Li
中科院分区：
文献类型：
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作者：
Zhong Wang;Yan Li
高斯-厄米特正交滤波器（GHQF）可以达到任意精度和高稳定性，但它的计算量很大。替代的高精度滤波器，例如高阶容积卡尔曼滤波器（CKF）和高阶稀疏网格正交滤波器（SGQF），可以大大降低计算成本，但可能存在稳定性问题。为了兼顾滤波的稳定性和效率，提出了一种基于交叉逼近的正交滤波器。该滤波器可以达到与GHQF相同的精度和稳定性，而计算量要小得多。首先，将GHQF中的张量展开为矩阵，并结合交叉逼近方法，通过对sigma点的一小部分采样得到展开矩阵的低秩表示.其次，利用低秩表示的优势，使用低秩矩阵运算进一步降低计算成本。仿真结果表明，在10维目标跟踪问题中，该滤波器仅对3点GHQF的约3%的sigma点进行采样，而达到了与GHQF相同的性能。
The Gauss-Hermite quadrature filter (GHQF) can achieve arbitrary degree of accuracy and high stability, but it suffers from heavy computational burden. Alternative high accurate filters, such as high-degree cubature Kalman filter (CKF) and high-degree sparse-grid quadrature filter (SGQF), can greatly reduce the computational cost but may have stability concerns. To give consideration to both filtering stability and efficiency, a cross approximation-based quadrature filter is proposed. The filter can achieve the same accuracy and stability as GHQF with much less computational burden. Firstly, tensors in GHQF are unfolded into matrices to incorporate cross approximation method, and low-rank representations of the unfolding matrices are obtained by only sampling a small subset of the sigma points. Secondly, taking advantage of the low-rank representations, the computational cost is further reduced using low-rank matrix operations. Simulation results show that the proposed filter only samples about 3% of the sigma points of 3-point GHQF in a 10-dimension target tracking problem, but achieves the same performance as GHQF.