等式约束最小二乘在“北斗”姿态测量中的应用

针对传统无约束的姿态测量中整周模糊度求解成功率不高的问题，提出利用等式约束快速求解整周模糊度的算法，并将其应用于“北斗”姿态测量。该算法充分利用基线的先验信息，在整周模糊度的求解过程中加入等式约束，同时利用拉格朗日乘子法求解约束整数最小二乘问题，提高了姿态测量中整周模糊度和姿态角的求解成功率。采用静态测试和动态测试验证该算法，结果表明在“北斗”单历元条件下，整周模糊度及姿态角的求解成功率提升30%左右。

Application of equality constrained least squares in BDS attitude determination

For the low success rate problem of ambiguity resolution in traditional unconstrained attitude determination,this paper proposes an algorithm that uses quadratic equality constraint to fast determine integer ambiguity,and applies it to Beidou Navigation Satellite System(BDS) attitude determination.This algorithm makes full use of a priori information baseline,adds equality constraints in the process of solving the ambiguity,and takes advantage of the Lagrange multiplier method for solving constrained integer least squares problems,thus improving the success rates of integer ambiguity resolution and attitude angle resolution.Static tests and dynamic tests validate that the algorithm can dramatically improve the success rates of integer ambiguity resolution and BDS attitude determination by about 30% under the condition of the BDS single epoch.