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非线性等式约束条件下多种滤波器的性能评估

Performance evaluation of multiple filters under nonlinear equality constraints

  • 摘要: 针对在非线性等式约束条件下目标跟踪精度问题,提出了一种通用的投影式约束滤波方法。基于此框架对扩展卡尔曼滤波(CEKF)、容积卡尔曼滤波(CCKF)及无迹卡尔曼滤波(CUKF)三种算法进行了性能对比分析。通过将非线性限制条件视作不含噪声的虚拟测量值,并将其融入到过滤过程中,利用投影技术实现了状态估计的调整以满足约束要求。仿真结果显示,在一致的约束模型和噪声配置下,CUKF相较于CEKF与CCKF,在位置精度、数值稳定性以及收敛速率方面表现更佳。特别是在面对高度非线性的约束时,CUKF能够更加精确地追踪目标路径,其预测误差始终维持在一个较低水平,显著优于其他两种方法。

     

    Abstract: To address target-tracking accuracy under nonlinear equality constraints, this paper proposes a general projection-based constrained filtering method. Within this unified framework, the constrained extended Kalman filter (CEKF), constrained cubature Kalman filter (CCKF), and constrained unscented Kalman filter (CUKF) are comparatively evaluated. By treating the nonlinear constraints as noise-free pseudo-measurements and incorporating them into the filtering process, a projection technique is employed to correct the state estimates so that they satisfy the constraints. Simulation results demonstrate that, under the same constraint model and noise settings, the CUKF outperforms the CEKF and CCKF in terms of position accuracy, numerical stability, and convergence speed. In particular, when the constraints are strongly nonlinear, the CUKF tracks the target trajectory more precisely, maintaining consistently low estimation errors and achieving markedly better performance than the other two methods.

     

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