The Analytical Collocation of the Error Distribution

It is well known that the error for the observational data always exists and the elimination of the error is one of the main task for the survey data processing.To obtain the best estimated results,the error processing should obey the optimal estimated principle,such as the Least Square(LS) principle,but the optimal estimated principle determined should be based on the property and the distribution type of the observational error,so the distribution type of the observational error must be first established before the observational data processing.Traditionally,the distribution type of the error has been determined using the distribution collocation test method or figure method by magnitude of errors,but it is difficult to obtain the specific distribution of the error,therefore,the suitable method to determine the error distribution must be found.To obtain the more reasonable method,the authors have proposed that the error distribution be collocated using the exponential distribution.The exponential distribution is a general distribution that can describe the arbitrary sequential distribution while the distribution parameter p is different.The property and the characteristic for the exponential distribution have been discussed in this paper.The analytical collocation method that determines the specific distribution of error has been proposed first by the authors.The main idea for the analytical collocation is that the known parameter A,C of the exponential distribution and the distribution parameter p are determined using the error interval value and the frequency for the special error interval,and the computational formulae have been derived in detail,so that the explicit expression for the error distribution can be described by the parameter A,C of the exponential distribution and the distribution parameter p.Finally,the two numerical examples have been calculated and analyzed.The experiment results show that the analytical collocation method of the error distribution is very convenient and feasible,and the computational results are identical with conventional methods obtained by the references.