On the Effect of Linearization and Approximation of Nonlinear Baseline Length Constraint for Ambiguity Resolution

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.