L-Band observations at the Green Bank Telescope (GBT) and other radio observatories are often made in frequency bands allocated to aviation pulsed radar transmissions. It is possible to mitigate radar contamination of the astronomical signal by time blanking data containing these pulses. However, even when strong direct path pulses and nearby fixed clutter echoes are removed there are still undetected weaker aircraft echoes present which can corrupt the data. In a previous paper we presented an algorithm to improve real-time echo blanking by forming a Kalman filter tracker to follow the path of a sequence of echoes observed on successive radar antenna sweeps. The tracker builds a history which can be used to predict the location of upcoming echoes. We now present details of a new Bayesian detection algorithm which uses this prediction information to enable more sensitive weak pulse acquisition. The developed track information is used to form a spatial prior probability distribution for the presence of the next echoes. Regions with higher probability are processed with a lower detection threshold to pull out low level pulses without increasing the overall probability of false alarm detection. The ultimate result is more complete removal, by blanking the detected pulse, of radar corruption in astronomical observations.