部分参数加权平差的教学内容扩展

Teaching expansion of parameter adjustment with partial parameters weighted

部分参数加权平差方法具有十分重要的理论意义和实用价值,尤其在测量平差程序实践中广泛应用。现有教材及文献关于部分参数加权平差解算公式的推导,均是将具有先验信息的参数连续排列在参数向量的前部或后部(称为参数有序),但实际编程中,常将有先验信息的参数在参数向量中混乱排列(称为参数无序)。为此,本文推导了参数无序时部分参数加权平差的解算公式(简称为严密解法),并阐述了结合无限权法(权无穷大或小)和全部参数加权平差解法的部分参数加权平差的实用解法(简称为实用解法)。通过模拟算例,验证了严密解法的正确性和实用解法的可行性,并指出实用解法具有较好的灵活性,更适于实际应用。

The method of parameter adjustment with partial parameters weighted has very important theoretical significance and practical value,especially in the practice of survey adjustment programming.The solution derivation of this method in existing textbooks and literature is to continuously arrange the parameters with prior information in the front or rear of the parameter vector(called parameter ordered).But in practical programming,parameters with prior information are always arranged in the parameter vector in disorder or randomly(called parameter disordered).Therefore,the solution formula of parameter adjustment with partial parameters weighted in case of parameter disordered(called the rigorous solution)is deduced in this paper.Combined with the infinite weight method(the weight is infinite or infinitesimal)and the solution of all parameter weighted adjustment,the practical solution of parameter adjustment with partial parameters weighted(called the practical solution)is described also.Finally,through a simulation example,the correctness of the rigorous solution and the feasibility of the practical solution are verified,and the practical solution has better flexibility is pointed out which means more suitable for practical application.