Equivalence between voltage-processing methods and discrete orthogonal Legendre polynomial (DOLP) approach

There are three methods for solving the least-squares estimation (LSE) problem. (1) the power method; (2) the voltage-processing method (square-root method); and (3) the discrete orthogonal Legendre polynomial (DOLP) method. The first involves a matrix inversion and is sensitive to computer round-off errors. The second and third do not require a matrix inversion and are not as sensitive to computer round-off errors. It is shown that the voltage-processing LSE methods (Givens, Householder, and Gram-Schmidt) become the discrete orthogonal Legendre polynomial (DOLP) LSE method when the data can be modeled by a polynomial function and the times between measurements are equal. Furthermore, when the data can be modeled by a polynomial function and the time between measurements are equal, the DOLP is the preferred method because it does not require an orthonormal transformation and it does not require the back-substitution method