In modal identification, the value of the model parameters and the associated uncertainty depends on the quality of the measurements. The maximum likelihood estimator ($mle$) is a consistent and efficient estimator. This means that the value of the parameters trends asymptotically close to the true value, while the variance of such parameters is the lowest possible with the associated data. The $mle$ implementation and application can be complex and generally need strong computational requirements. In applications where the number of inputs and outputs are elevated (as in modal analysis) is common to reduce the covariance matrix to a diagonal one where only the variances are considered. This implementation is still consistent but not efficient. However, it generates acceptable results.
The current work shows that using efficiently the output information as complement to the input--output relations, it is possible to improve the model identification reaching similar levels than the $mle$, while reducing the execution time and the computational load.