Source Number Estimation Algorithm AIC

The AIC (Akaike Information Criterion) algorithm for source number estimation is a signal processing technique based on information-theoretic principles, primarily used to determine the number of signal sources. The AIC criterion selects the optimal source number by balancing model goodness-of-fit and complexity. Its core principle involves finding a trade-off between model accuracy and the number of parameters used. From an implementation perspective, the AIC value is typically computed using the formula: AIC = -2 * log-likelihood + 2 * k, where k represents the number of estimated parameters. Developers often implement this by iterating over candidate source numbers, calculating log-likelihoods from covariance matrices, and selecting the model with the minimum AIC value. However, it is important to note that AIC is not a consistent estimator. This means that even with a large number of snapshots (samples), AIC may still produce significant estimation errors. This characteristic requires special attention in practical applications, particularly when handling high-dimensional data or scenarios demanding high estimation accuracy. Unlike consistent estimators, AIC does not guarantee that the error probability approaches zero as the number of snapshots increases. Therefore, in practical engineering applications, it is essential to combine AIC with other criteria (such as the Minimum Description Length (MDL) criterion) or validate results through multiple experimental trials to enhance the reliability of source number estimation. Code implementations often include comparative analysis between AIC and MDL, where MDL tends to perform better in large-sample scenarios due to its asymptotic consistency properties.