基于最小二乘的时差定位算法

TDOA Location Algorithms Based on the Least Squares

时差测量方程是非线性双曲线方程,可以通过引入中间变量将其转化为线性方程,对近年来国内外学者关于这种方法的时差定位算法进行了总结。当已知测量误差的先验信息时,可以采用两步加权最小二乘法和约束加权最小二乘法,当测量误差的先验信息未知时,还可以采用约束总体最小二乘的方法。在求解约束最小二乘问题时,采用常规的拉格朗日法计算复杂、运算量大,而采用高斯-牛顿法不仅可以大为降低运算量,还能提高解的精度和稳定性。此外,对约束加权最小二乘法和约束总体最小二乘法之间的关系进行了探讨,得到了它们等价性的条件。

Time difference of arrival（TDOA） defines a nonlinear hyperbola equation, which can be transformed into a linear equation by introducing an intermediate variable. Some TDOA algorithms using this technique are summarized. When the knowledge of measurement errors is available, two-step weighted least squares method and constrained weighted least squares method are appropriate. Otherwise, constrained total least squares method is another option. Lagrange method can he used to find the solution of constrained least squares problem, but suffering from large calculation. The Gauss-Newton method can greatly reduce the cal culation and improve the accuracy and stability of the solution. What＇s more, the relationship between con- strained weighted least squares and constrained total least squares is discussed and the equivalent condition is obtained.