Abstract: In order to improve the accuracy and rapidity of localization, the improved smoothed [l0] compressed sensing algorithm will be applied in wireless sensor network localization. First, using the gridding method for sensing area, target localization is converted to compressed sensing issue and applying hyperbolic tangent function as the approximation to the big steep nature in the norm, the problem of minimization of the [l0] norm in the reconstruction can be transformed into a convex optimization problem for the smoothed function. Then, in order to solve the problem of slow convergence and inaccuracy estimation caused by “notched effect” of the gradient method, hybrid optimization algorithm, which combines the advantages of the gradient method and the revised Newton method, is introduced to improve the accuracy and speed of sparse recovery. The numerical simulation results show that the localization performance is improved by the proposed algorithm, comparing with OMP algorithm, BP algorithm and SL0 algorithm under the same condition.

Key words: multi-target localization, SL0, compressed sensing, wireless sensor networks

摘要： 为提高定位的精度与速度，将改进的平滑[l0]（smoothed [l0]，SL0）压缩感知算法应用于无线传感网络（WSN）定位中。首先通过感知区域的网格化，将定位问题转化为压缩感知问题，采用更陡峭的近似双曲正切函数去逼近[l0]范数，将压缩感知重构中的[l0]范数最小化问题转化为求解光滑函数最小值的最优化问题。其次，针对算法中因最速下降法“锯齿现象”导致的收敛速度慢、估计不精确等缺点，引入了混合优化算法，该算法结合了最速下降法和修正牛顿法的优点，提高了重构精度和速度。仿真结果表明，改进的SL0算法相对于匹配追踪（OMP）、基追踪（BP）、SL0算法等在定位精度与实时性上有了明显提高。

关键词: 多目标定位, SL0, 压缩感知, 无线传感网络