This paper addresses the problem of estimating the frequenc
ies, amplitudes and phases of the
n
sinusoidal components of a
possibly biased multi-sinusoidal signal. The proposed ada
ptive observer allows the
direct
adaptation of the frequency estimates
with a relatively low dynamic order 3
n
+ 1 (3
n
for an unbiased signal). The stability analysis proves the g
lobal exponential
convergence of the estimation error and the robustness to ad
ditive norm-bounded measurement perturbations.