三维AoA目标跟踪的二次约束卡尔曼滤波算法

在基于到达角(angle of arrival, AoA)的三维目标跟踪中, 伪线性卡尔曼滤波具有稳定性高和计算复杂度低的优点, 但是严重的偏差问题使其跟踪精度迅速下降。针对该问题, 提出一种二次约束卡尔曼滤波(quadratic constraint Kalman filter, QCKF)算法。首先引入涉及所有观测噪声项的增广矩阵, 然后建立与线性卡尔曼滤波等价的目标函数并且附加含有二次项的约束条件, 以此降低偏差影响, 实现更准确的状态更新。QCKF算法采用广义特征值分解求解约束优化问题, 无法直接通过状态更新表达式推导其协方差矩阵, 因此利用约束条件以及矩阵扰动方法完成协方差矩阵更新。仿真分析表明, QCKF算法相较于其他非线性滤波算法具有更优的跟踪性能, 不仅在低噪声条件下可达到后验克拉美罗下界, 而且当噪声严重时能够显著降低跟踪误差, 并且计算开销不高。

Quadratic constraint Kalman filter algorithm for three dimensional AoA target tracking

In the three-dimensional target tracking with angle of arrival (AoA) measurements, pseudo-linear Kalman filter has the advantages of high stability and low computational complexity. However, PLKF suffers from severe bias problem which causes its tracking accuracy to degrade rapidly. In view of this problem, a quadratic constraint Kalman filter (QCKF) is proposed. Firstly, an augmented matrix involving all measurement noise terms is introduced. Then, an objective function equivalent to linear Kalman filter is established, and a constraint containing quadratic terms on the objective function is imposed to reduce the bias effect and achieve more accurate state update. QCKF algorithm solves the constraint optimization problem by generalized eigenvalue decomposition, and its covariance matrix cannot be derived directly through the state update expression. Thus, the covariance matrix is updated by utilizing the constraint conditions and the matrix perturbation method. Simulation analysis shows that QCKF algorithm achieves better tracking performance than other nonlinear filter algorithms. QCKF attains the posterior Cramer Rao lower bound over the mild noise region and significantly reduces the tracking error under heavy noise. Moreover, its computational overhead is relatively low.