Let us consider a discrete-time state-observation system with the observation \(y(t)=x(t)+v(t),\) where v(t) stands for a stationary linear noise process and x(t) is an unknown state process which is to be estimated. It is assumed that the state process x is a finite linear combination of sine waves with unknown frequencies \(f_ 1,...,f_ m\). The aim of the paper is to investigate the properties of the pseudo- linear regression (PLR) algorithm for the estimation of the unknown frequencies. Let \(A(q^{-1})\) be such a polynomial in a unit delay operator \(q^{-1}\) that \(A(q^{-1})x(t)=0\) for all t. The main result of the paper says that the PLR algorithm is locally convergent to a point close the frequency \(f_ k\) if and only if \(Re\{1/A(\rho \exp (if_ k))\}>0,\) where \(\rho\) is a constant close to one. Moreover the m- dimensional PLR algorithm behaves locally like m separate one-dimensional PLR algorithms for corresponding frequencies.