根据附不等式约束的平差过程,利用概率统计的思想,分析不等式约束对平差结果的影响。结果表明,不同的约束对解的贡献是不同的,其大小取决于约束到其真值的距离。由于不等式约束的非对称性,造成参数验后分布的非对称性,从而使参数估计有偏。这种估计的有偏不同于数学中的压缩型有偏估计,其偏量是由观测误差确定,当观测误差为零时,这种估计的期望是无偏的;不管不等式约束是有效约束还是无效约束,对最后的解的精度都有贡献,并且附不等式约束平差时,其解的方差恒定小于无约束的最小二乘解。最后,以一个简单的算例直观验证了有关的分析和结论%The inequality constraint influence to the results according to the adjustment procedure based on statistics are analyzed.The results show that different constraint has different contribution to the solution.The influence is determined by the distance from the constraints to the true value.The asymmetry of inequality constraints leads to asymmetric of posterior distribution of the estimated parameters,thus the estimator is biased.The biasness of the estimation is not the same as that of shrunken biased estimation.Its discrepancy is determined by the observational errors,if the error is zero,the expectation of the estimation is unbiased.It does not matter whether the constraint is active or inactive;they will contribute to the adjustment.The variance of parameter with inequality constrained model is definitely smaller than that of unconstrained model.Finally,a simple example was given to prove some related analysis and conclusions.
展开▼
