MORE ON VOLTAGE-PROCESSING TECHNIQUES COMPARISON OF DIFFERENT VOLTAGE LEAST-SQUARES ALGORITHM TECHNIQUES Table gives a comparison for the computer requirements for the different voltage techniques discussed in the previous chapter. The comparison includes the computer requirements needed when using the normal equations given by () with the optimum least-squares weight W given by (). Table indicates that the normal equation requires the smallest number of computations (at least when s m, the case of interest), followed by the Householder orthonormalization, then by the modified Gram–Schmidt, and finally the Givens orthogonalization. However, the Givens algorithm computation count does not. | Tracking and Kalman Filtering Made Easy. Eli Brookner Copyright 1998 John Wiley Sons Inc. ISBNs 0-471-18407-1 Hardback 0-471-22419-7 Electronic 14 MORE ON VOLTAGE-PROCESSING TECHNIQUES COMPARISON OF DIFFERENT VOLTAGE LEAST-SQUARES ALGORITHM TECHNIQUES Table gives a comparison for the computer requirements for the different voltage techniques discussed in the previous chapter. The comparison includes the computer requirements needed when using the normal equations given by with the optimum least-squares weight W given by . Table indicates that the normal equation requires the smallest number of computations at least when s m the case of interest followed by the Householder orthonormalization then by the modified Gram-Schmidt and finally the Givens orthogonalization. However the Givens algorithm computation count does not assume the use of the efficient CORDIC algorithm. The assumption is made that all the elements of the augmented matrix T0 are real. When complex data is being dealt with then the counts given will be somewhat higher a complex multiply requiring four real multiplies and two real adds a complex add requiring two real adds. The Householder algorithm has a slight advantage over the Givens and modified Gram-Schmidt algorithms relative to computer accuracy. Table gives a summary of the comparison of the voltage least-squares estimation algorithms. Before leaving this section another useful least-squares estimate example is given showing a comparison of the poor results obtained using the normal equations and the excellent results obtained using the modified Gram-Schmidt algorithm. For this example obtained from reference 82 339 340 MORE ON VOLTAGE-PROCESSING TECHNIQUES TABLE . Operation Counts for Various Least-Squares Computational Methods Method Asymptotic Number of Operations a Normal equations power method 2 sm 2 1 m 3 Householder orthogonalization sm 2 3 m 3 2 Modified Gram-Schmidt sm2 Givens .
