this work focuses on the correction of both the coecient and the right hand side matrices of the inconsistent matrix equations $ax = b$ and $xc = d$ with orthogonal constraint. by optimal correction approach, a general representation of the orthogonal solution is obtained. this method is tested on two examples to show that the optimal correction is eective and highly accurate.

Time-Delay Interferometry (TDI) is the data processing technique that cancels large laser phase fluctuations affecting one-way Doppler measurements made by unequal-arm space-based gravitational wave interferometers. By taking finite linear combinations of properly time-shifted measurements, are removed at any time $t$ and signals can be studied a requisite level precision. In this article we sh...