Machine Learning Driven Analytics for National Security Operations: A Wavelet–Stochastic Signal Detection Framework

Detectingsignals in noisy, dynamic systems is crucial in national security, surveillance systems, radar detection, and security communications networks. This study aimsto achieve a mathematically sound signal anomaly detection framework, which incorporates Discrete Wavelet Transform (DWT) with stochastic noise modellingto facilitate robust feature extraction and denoising at a time-frequency scale. The received signal is modelled as a sum of a wantedsignal and a random noise, consideredGaussian or first-orderMarkovian. Signal components at different scales can be isolated by signal decomposition using multi-resolution wavelets,and probabilistic filtering methods can be deployed to suppress noise,such asGaussian smoothing or ensemble averaging. The wavelet coefficients are then used to generate high-dimensional feature vectors through statistical descriptors like energy, entropy, kurtosis and RMS. Supervised machine learning models can then be trained onthese features,such as Support Vector Machine (SVM), Long Short-Term Memory (LSTM), and the eXtreme Gradient Boosting (XGBoost) model. It is tested on the publicly accessible Wavelet Transform to the TimeSeries Anomaly Detection dataset, which indicates its effectiveness because it has an accuracy of 91.2% and anAUC of 0.94 with XGBoost. Theoretical validation incorporates stochastic denoising,bounded mean-square error convergence proofs and proofs of convergence of the wavelet transform. The paper makes a new contribution tophysical-signal processing and machine learning in favourof theoretical firmness and computational precision. The findings support the framework's applicabilityto high-gain, real-timenational security applications andcomplying with standards of rigorous computational analysis and mathematical modellingdemanded by the discipline.