Off-grid DOA Estimation Algorithm Based on Taylor-expansion and Alternating Projection Maximum Likelihood
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摘要: 针对最大似然DOA估计算法需要多维搜索、计算量大且面临着在网格估计的问题，该文提出一种基于泰勒展开的离网格交替投影最大似然算法。该方法首先利用交替投影将多维搜索转化为多个1维搜索，获得对应预设大网格的粗估计结果，再利用矩阵求导理论将1维代价函数在粗估计结果处进行2阶泰勒展开，最后，通过对2阶泰勒展开求偏导并令导数等于零，求得离网参数的闭式解。与交替投影最大似然算法相比，该方法突破了搜索网格大小的限制，在保证算法精度的同时，有效减少了算法的在网格计算点数，提升了运算效率。仿真结果证明了该算法的有效性。Abstract: According to the problem that the maximum likelihood DOA estimation algorithm requires multi-dimensional search, is computationally intensive, and there is a problem in grid estimation, an Off-grid alternating projection maximum likelihood algorithm based on Taylor expansion is proposed. Firstly, the alternating projection method is used to transform the multi-dimensional search into multiple one-dimensional searches to obtain the rough estimation results corresponding to the preset large grid. Then, the second-order Taylor expansion of the one-dimensional cost function at the rough estimation results is carried out by using the matrix derivation theory. Finally, by calculating the partial derivative of the second-order Taylor expansion and making the derivative equal to zero, the closed-form solution of the off-grid parameters is obtained. Compared with the alternating projection maximum likelihood algorithm, this method breaks through the limitation of the search grid size. While ensuring the accuracy of the algorithm, it effectively reduces the number of points in the grid calculation of the algorithm while ensuring the accuracy of the algorithm, and improves the operation efficiency. Simulation results show the effectiveness of the algorithm.
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Key words:
- Maximum likelihood algorithm /
- Alternating projection /
- Off-grid /
- Taylor expansion
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