The purpose of this paper is 1) to propose a Kalman-filtering-formula based ARMA spectral estimator capable of estimating spectra on line

2)to consider a fast algorithm for recursively calculating the Kalman gain whose computational requirement is proportional to the order of the filter

and 3) to give a consistency theorem for this recursive estimator.Compared with recently developed ARMA spectral estimation approaches--the overdeterminedequation method and the instrumental variable method

this estimator has advantages that the positivity of estimated spectra can be warranteed and parameters of ARMA processes can be identified in real time. Numerical examples show that this estimator provides higher resolution than AR spectral estimation.