非线性基线长度约束在北斗测姿中的应用

Application of nonlinear baseline length constraint in BD attitude determination

针对传统无约束LAMBDA(least-squares ambiguity decorrelation adjustment)算法中整周模糊度求解成功率不高的问题,提出一种利用基线约束的整数最小二乘快速求解整周模糊度的方法,并将其应用到北斗姿态测量系统中。该方法利用基线长度作为先验信息,将无约束的整数最小二乘扩展为非线性约束的最小二乘,并采用正交映射方法求解其约束解;同时在模糊度求解过程中,根据搜索空间的特性,先确定其上下界范围,再对模糊度残差范围限定,减少模糊度搜索过程中的候选解,最后采用迭代增加模糊度空间法和约束最小二乘求解对模糊度候选解筛选。实验采用单频北斗接收机实时数据对该算法的有效性进行验证,结果表明,在单频单历元条件下,该算法有效降低计算量,将姿态角求解成功率提高30%左右。

For the low success rate problem of ambiguity resolution in traditional unconstrained attitude determination, the paper presents a novel fast ambiguity determination method based on integer least squares problem and its application in BD attitude determination. Taking baseline length as the prior information, it extends current unconstrained ILS theory to the nonlinearly constrained ease. then approaches its sub-multiple by adopting the orthogonal mapping method. Meanwhile, during the search processing, according to the characteristic of the search space, the upper and lower bound of it was determined, as well as the ambiguity residual is limited. As a result the number of these candidates could be decreased. Finally, by increasing the search space in an iterative way together with the constrained least square, the optimum ambiguity could be obtained. Experimental results with a single frequency BD receiver reveal the effectiveness of the proposed algorithm. In single epoch case, the results show that the method could reduce the computational load, and the success rate has been improved about 30%.