This paper delves into the domain of nuclear security, leveraging advanced data analytics techniques to pinpoint anomalous patterns within radiation measurements associated with illicit nuclear activities. A major hurdle in this analysis lies in the widespread presence of background radiation, which often obscures signals emanating from illicit radioactive sources. Consequently, accurately estimating and subtracting background radiation from measurements becomes paramount to enhancing the detection of clandestine nuclear activities. In this study, the authors integrate the Dynamic Data Driven Applications Systems (DDDAS) paradigm with the Matrix Profile method for anomaly detection in radiation spectra. The Matrix Profile method is utilized to construct a model from a single radiation measurement acquired from a sensor. This model is refined using a nonlinear approach, while the DDDAS framework is implemented to continuously update the matrix profile with incoming sensor data. The results, drawn from a comprehensive dataset comprising both pristine background and source-influenced measurements, demonstrate significantly improved accuracy in anomaly detection through the adoption of the DDDAS framework.