We consider the estimation procedure of the multiple sinusoidal model
for signals, when the damping factor is not present. The solution in t
he general case depends on the roots of a polynomial, whose coefficien
ts are estimated from the observed data. When the damping factor is ab
sent, the coefficients exhibit a certain symmetry. It reduces in estim
ating almost half of the total number of unknown parameters. Under the
se symmetric constraints modified methods have been developed to estim
ate the coefficients. It is observed that the standard errors for the
modified methods are closer to the Cramer-Rao lower bound than before
in almost all the situations. It is also observed that the computation
al cost of the modified maximum likelihood method is lower than the or
dinary one. The modified maximum likelihood estimates can be obtained
by an iterative process. Theoretical justification has been provided f
or the convergence of the iterative process.