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The performance loss due to using the optimal independent test is higher compared to the mGLRT as the correlation increases.
If the observations are statistically independent, the fusion center could save on computations by using the optimal independent test.
On the other hand, using the optimal independent test results in a degradation in performance especially for low false alarm probabilities.
In a scenario where the fusion center could estimate the covariance matrix of the sensors' observations, the fusion center could choose between either using the optimal independent test or resorting to the mGLRT.
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Moreover, predicting or estimating the dependent variable using the optimal combination of multiple independent variables is more effective and realistic than using only one independent variable (Hu et al. 2013).
Following optimisation of the k nearest neighbours and the Support Vector Machine algorithms using the training set, we tabulated the output obtained for the independent test set using the optimal model in terms of the number of samples correctly predicted and the number of samples incorrectly predicted.
Then, stretch using the optimal.
The reason is that the fusion center using the mGLRT uses the correlation information and thus gets better performance, unlike the optimal independent test which assumes that the sensor observations are independent.
Analytically comparing mGLRT to the optimal independent test is difficult.
Also, the optimal independent test appears to be optimal for correlated observations when the correlation matrix is symmetric.
Therefore, in this section, we compare the proposed mGLRT to the optimal independent test through simulations.
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