基于贝叶斯压缩感知的CSR稳健参数估计方法

Robust parameter estimation method for CSR based on Bayesian compressed sensing

针对"完全扰动"情况下压缩感知雷达(compressed sensing radar,CSR)观测矢量和感知矩阵严重失配,进而引起参数估计性能急剧下降的问题,提出了一种基于贝叶斯压缩感知(Bayesian compressed sensing,BCS)的稳健参数估计方法。首先构造"完全扰动"情况下CSR参数估计的稀疏线性模型,并从稀疏矢量的最大后验概率(maximum a posteriori,MAP)出发,推导了完全扰动矩阵服从柯西分布时的优化目标函数;随后通过稀疏矢量和尺度参数的交替迭代,求得稀疏矢量的最优解。与现有重构算法及其改进算法相比,该方法能够有效改善CSR系统应对失配误差的稳健性,提高目标成功检测的概率和参数估计的精度。计算机仿真实验验证了该方法的有效性和鲁棒性。

In practical application, the mismatch between measurement vector and sensing matrix caused by corn pletely perturbed observations will result in a sharp decline in the performance of parameter estimation for compressed sensing radar （CSR）. A novel robust parameter estimation algorithm is proposed based on Bayesian compressed sens- ing （BCS）. The completely perturbed sparse linear model is firstly built, and the robust target function is derived with the maximum a posteriori （MAP） of the sparse vector when the completely perturbed matrix obeys Cauchy distribu- tion. Then the optimal solution is achieved through the alternate iteration between the sparse vector and the scale pa- rameter. Compared with most existing recovery algorithm and their derivants, the proposed method effectively im proves the robustness against the foregoing mismatch, increases the target detection probability and reduces the estima- tion error. The effectiveness of the proposed algorithms is demonstrated by computer simulations.