In radioactive source surveying protocols, a number of task-inherent features degrade the quality of collected gamma ray spectra, including: limited dwell times, a fluctuating background, a large distance to the source, weak source activity, and the low sensitivity of mobile detectors. Thus, collected gamma ray spectra are expected to be sparse and noise dominated. For extremely sparse spectra, direct background subtraction is infeasible and many background estimation techniques do not apply. In this paper, we present a statistical algorithm for source estimation and anomaly detection under such conditions. We employ a fixed-hyperparameter Gaussian processes regression methodology with a linear innovation sequence scheme in order to quickly update an ongoing source distribution estimate with no prior training required. We have evaluated the effectiveness of this approach for anomaly detection using background spectra collected with a Kromek D3S and simulated source spectrum and hyperparameters defined by detector characteristics and information derived from collected spectra. We attained an area under the ROC curve of 0.902 for identifying sparse source peaks within a sparse gamma ray spectrum and achieved a true positive rate of 93% when selecting the optimum thresholding value derived from the ROC curve.