The SUT method for precision estimation of mixed additive and multiplicative random error model

doi:10.11947/j.AGCS.2022.20200514

Abstract

Abstract: The existing parameter estimation method of mixed additive and multiplicative random error model can achieve second-order precision, but the precision estimation method can only achieve first-order precision. If the traditional Taylor series expansion approximate function method is used to obtain the second-order precision information of parameter estimations, it will inevitably require complicated derivation operation due to the complex nonlinear relationship between parameter estimations and observations in the mixed additive and multiplicative random error model. Aiming at this problem, this paper uses the scaled unscented transformation method, which does not require derivative operation and understand the composition of nonlinear function, to obtain the second-order precision information of parameter estimations. The results of experiments show that using the SUT method to solve the mixed additive and multiplicative random error model can effectively avoid complicated derivation operation, and the obtained parameter estimations and covariance matrix can both achieve second-order precision, thus verifies the feasibility and advantages of the proposed method in this paper.

Key words: mixed additive and multiplicative random error model, weighted least squares, nonlinear function, SUT method, precision estimation

CLC Number:

P207

WANG Leyang, CHEN Tao. The SUT method for precision estimation of mixed additive and multiplicative random error model[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(11): 2303-2316.

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