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# Results of the mle, Dmle, D o mle and D ? mle estimators when only independent and uncorrelated noise is present at the input and output of the system. (a) General variance; (b) mean execution time.

Source publication

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...

## Contexts in source publication

**Context 1**

... Scenario: Independent and Uncorrelated Noise. In this scenario only independent and uncorrelated noise are present at the inputs and outputs of the system. The Figure 2 shows the general variance on the parameters for the different estimators (Figure 2a) and the execution time (Figure 2b). For low levels of noise at the input the estimators generate similar results. However, when the SNR of the input becomes lower (high presence of noise) and the SNR at the outputs grow, the estimators using complementary output equations (D o mle and D ? mle) show better results than the Dmle estimator. In fact the results of the D o mle and D ? mle are superimposed on the mle ...

**Context 2**

... Scenario: Independent and Uncorrelated Noise. In this scenario only independent and uncorrelated noise are present at the inputs and outputs of the system. The Figure 2 shows the general variance on the parameters for the different estimators (Figure 2a) and the execution time (Figure 2b). For low levels of noise at the input the estimators generate similar results. However, when the SNR of the input becomes lower (high presence of noise) and the SNR at the outputs grow, the estimators using complementary output equations (D o mle and D ? mle) show better results than the Dmle estimator. In fact the results of the D o mle and D ? mle are superimposed on the mle ...

**Context 3**

... Scenario: Independent and Uncorrelated Noise. In this scenario only independent and uncorrelated noise are present at the inputs and outputs of the system. The Figure 2 shows the general variance on the parameters for the different estimators (Figure 2a) and the execution time (Figure 2b). For low levels of noise at the input the estimators generate similar results. However, when the SNR of the input becomes lower (high presence of noise) and the SNR at the outputs grow, the estimators using complementary output equations (D o mle and D ? mle) show better results than the Dmle estimator. In fact the results of the D o mle and D ? mle are superimposed on the mle ...

**Context 4**

... mean execution time for the different estimators is shown in the Figure 2b. According with the results, the Dmle estimator requires less time while the mle estimator expend at least one order of magnitude more. The D o mle and the D ? mle estimators present execution times lower than the half required for the mle being lower for the estimator where the output-output relations are explicit. 2nd Scenario: Independent Uncorrelated and Correlated Noise. Similar than the first scenario uncorrelated noise has been added into the inputs and outputs of the system, but in addition, one unknown excitation is set, which will generate correlated noise in the system. The result shows, as in the previous case, that at high levels of noise at the input, the outputs relations improve the identification of the system reducing the associated variance when is compared with the Dmle implementation. ...