非线性基线长约束条件线性化近似对模糊度解算影响

Abstract

GNSS动态相对定位中常附加非线性的基线长约束进行解算，而LAMBDA方法只能处理无约束或者线性约束的模型，为了应用LAMBDA方法，应对非线性约束条件进行线性化近似。通常附加该约束后，模糊度固定成功率会提高，但对于超短基线有时反而会降低。何种条件下附加线性化近似的基线长约束条件可以提高模糊度固定成功率尚未有定论。本文基于附加基线长约束的GNSS相对定位数学模型，推导基线长约束条件线性化近似余项对浮点解的最大影响值公式，给出基线长约束能否线性化近似的诊断条件。当该条件满足时，线性化近似余项影响可以忽略，附加线性化近似的基线长约束可以改善浮点解解算精度，提高模糊度固定成功率；若不满足，则线性化近似余项影响可能不可以忽略，附加约束会因浮点解有偏不能固定为正确的模糊度，并通过算例验证了相关结论。

Alternate abstract:

Additional nonlinear baseline length constraint is often used for GNSS dynamic relative positioning, but the LAMBDA method can only deal with linear constraint model. So, it is necessary to linearize and approximate nonlinear constraint conditions. Linearized approximate constraint usually increases the success rate of fixing integer ambiguity, but for the ultra-short baseline, the opposite results may be derived. When will the linearized approximate baseline length constraint can improve the success rate of fixing ambiguity? This article attempts to answer these questions. Firstly, the float solution's maximum influence value formula is derived when using linearized approximate baseline length constraint, based on GNSS relative positioning model; Secondly, a discriminant condition is given to determine whether baseline length constraint can be linear approximation. When the condition is met, the influence can be ignored, linearized approximate baseline length constraint can improve the accuracy of float solution and increase the success rate of fixing ambiguity,on the contrast, the influence may not be ignored, linear approximation will result in a biased float solution and the ambiguity cannot be fixed correctly; At last, the foregoing conclusions are verified with some numerical example in this paper.