高斯混合概率假设密度滤波具有严密的数学基础，适合跟踪弱信噪比多目标，但其目标分布协方差P和高斯元素裁剪门限T至今未有合理取值规则，影响了跟踪效果，且残差协方差S参与增益计算时需要对其进行逆计算，如果S为非正定，会导致计算发散。针对上述问题，通过概率统计方法推导了参数P和T的取值规则，通过Cholesky和QR分解，确定了参数S的计算规则。仿真比较分析表明：文中提出的目标分布协方差P、裁剪门限T和残差协方差S的计算规则用于雷达组网高斯混合概率假设密度滤波跟踪弱信噪比多目标时，能较高精度地跟踪到所有目标，且没有带来多余计算负担。

Gaussian mixture probability hypothesis density filter(PHDF), which is suitable for tracking weak signal to noise ratio(WSNR) multi target, has rigorous mathematical foundation. But there is no reasonable calculation rules about distribution covariance P and truncation threshold T of Gaussian elements in PHDF as yet, which bring bad influence to PHDF. Because the residual covariance S will be inverse calculated when it is involved in the gain calculation. If S is non positive definite, it would lead to divergence calculation. Probability statistics derivation is used to determine the P and calculation rules. Cholesky and QR decomposition is used to solve the S calculation problem. The simulation comparison demonstrates that PHDF in radar network, using the proposed calculation rules of P, T and S, can precisely track WSNR multi target, containing exist, birth and spawn targets, and bring no extra calculation burden.

TN953

国家自然科学基金资助项目;安徽省自然科学基金资助项目