Solution methods to the nearest rotation matrix problem in ℝ3: A comparative survey

Abstract Nowadays, the singular value decomposition (SVD) is the standard method of choice for solving the nearest rotation matrix problem. Nevertheless, many other methods are available in the literature for the 3D case. This article reviews the most representative ones, proposes alternative ones, and presents a comparative analysis to elucidate their relative computational costs and error performances. This analysis leads to the conclusion that some algebraic closed‐form methods are as robust as the SVD, but significantly faster and more accurate.