Research on singular value decomposition algorithm for mixed additive and multiplicative error model - Li, Guohong; Xin, Huijuan (Measurement : journal of the International Measurement Confederation, 2026)
•LiDAR data is disturbed by mixed additive and multiplicative errors.•The bias-corrected weighted least squares solution relies on error distribution information.•The SVD algorithm overcomes the reliance on error information for the solution. Extensive research has demonstrated that observational data from techniques such as Electronic Distance Measurement (EDM), Global Positioning System (GPS), Very Long Baseline Interferometry (VLBI), and Light Detection and Ranging (LiDAR) are influenced by both multiplicative and additive errors. Bias-corrected weighted least squares (bcWLS) is the preferred algorithm for processing such observational data. However, to accurately obtain the bcWLS solution, it is necessary to acquire variance information for both multiplicative and additive errors. Currently, it is not possible to separate multiplicative and additive errors from observational data using existing theoretical and technical methods. We introduce the concept of total least squares (TLS) into the mixed additive and multiplicative error model (MAMEM) and propose a singular value decomposition (SVD) algorithm for this model that does not require explicit variance information of the errors. The proposed SVD algorithm was validated for accuracy using a digital terrain model (DTM) case study. Experimental results show that the fitted values obtained by the SVD algorithm are closer to the true values of the observations, thereby mitigating the reliance of the bcWLS solution on detailed error distribution information.