Non-negative least squares variance component estimation of mixed additive and multiplicative random error model

In the variance component estimation (VCE) of geodetic data, the problem of negative VCE is likely to occur. In the ordinary additive error model, there have been related studies to solve the problem of negative variance components. However, there is still no related research in the mixed additive and multiplicative random error model (MAMREM). Based on the MAMREM, this paper applies the non-negative least squares variance component estimation (NNLS-VCE) algorithm to this model. The correlation formula and iterative algorithm of NNLS-VCE for MAMREM are derived. The problem of negative variance in VCE for MAMREM is solved. This paper uses the digital simulation example and the Digital Terrain Mode (DTM) to prove the proposed algorithm's validity. The experimental results demonstrated that the proposed algorithm can effectively correct the VCE in MAMREM when there is a negative VCE.