A Fast Algorithm for a Class of Nonlinear Systems in Signal Processing
信号处理中一类非线性方程组的快速求解

In signal processing of sonar and radar, we meet a class of nonlinear systems with alterable dimensions, and every equation in the system is a mixed trigonometric polynomial. Because this class of systems have many solutions, and its corresponding least square problems have many local minimal solutions, the classic iteration methods, e.g. Newton's method, can not be applied to find the solutions. On the other hand, if this class of systems is transformed into polynomial systems, and then homotopy methods or symbolic methods is used to solve them, then the solutions can not be found in a short time due to the high complexity. And unfortunately, if the dimension of the problems is very large, this class of systems even can not be solved by the above methods. Combining the hybrid methods presented for mixed trigonometric polynomial systems and the coefficient-parameter homotpy keeping the symmetry of the target system, an effective solving method is presented.