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摘要:
确定采样型滤波算法中的容积卡尔曼滤波（CKF）算法滤波性能优良，但是却难以克服目标模型不确定性或者目标状态突变带来的影响。构造强跟踪CKF能有效改善算法的自适应性，但是在求解渐消因子时大大增加了计算量。为此，提出一种低复杂度自适应CKF算法，通过设立基于新息的自适应修正判决准则和修正方式，直接对状态预测值进行修正，使滤波算法能及时跟上目标真实状态，以提高滤波精度。使用浮点操作数计算并分析了CKF算法、强跟踪CKF算法及所提算法的复杂度，同时将3种算法应用在建模不准确的目标跟踪中，并进行仿真验证。仿真结果表明：在目标建模不匹配的情况下，低复杂度自适应CKF算法和强跟踪CKF算法都能保持较好的滤波精度和数值稳定性，同时所提算法在算法复杂度上有明显改善。
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关键词:
- 容积卡尔曼滤波(CKF) /
- 目标模型不确定性 /
- 强跟踪滤波器 /
- 自适应修正 /
- 算法复杂度
Abstract:Cubature Kalman filter (CKF) with good filtering performance is one of the deterministic sampling filtering algorithms, but it is not able to overcome the impact caused by the target model uncertainty or the mutation of the target state. Constructing strong tracking CKF can effectively improve the adaptability of the algorithm, but the computation is greatly increased when solving the fading factor. A low-complexity adaptive CKF algorithm is proposed to solve the above problems. By establishing adaptive judgment criteria and amending method based on innovation sequence, the predicted state value is directly amended, so that the filtering algorithm can keep up with the real state of the target in time, and thus improve the filtering accuracy. The complexity of CKF, strong tracking CKF and the proposed algorithm are calculated and analyzed by using floating point operations. At the same time, the above three algorithms are applied to target tracking with inaccurate modeling, and are verified through simulation. The simulation results show that both the proposed algorithm and the strong tracking CKF algorithm can maintain better filtering accuracy and numerical stability in the case of mismatched target modeling, and the proposed algorithm has obvious improvement in algorithm complexity.
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表 1 三种算法复杂度计算结果
Table 1. Computational results of complexity of three algorithms
算法 算法复杂度/flops CKF 20n3/3+10n2+10n2l+8nl2+2nl+l3+3l2+l 强跟踪CKF 26n3/3+10n2+16n2l+10nl2-nl+l3+8l2+3l 低复杂度自适应CKF 20n3/3+11n2+10n2l+8nl2+2nl+l3+3l2+3l+n 
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表 2 不同算法平均均方根误差对比
Table 2. Comparison of mean RMSE among different algorithms
算法 平均RMSE/m x轴位置 y轴位置 CKF 35.732 5 35.062 5 强跟踪CKF 8.416 2 8.389 1 低复杂度自适应CKF 8.405 5 8.384 5
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表 3 不同算法运行时间对比
Table 3. Comparison of running time among different algorithms
算法 平均运行时间/(10-2s) 运行时间增加百分比 CKF 2.677 6 0 强跟踪CKF 3.468 3 29.53 低复杂度自适应CKF 2.712 1 1.29
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