Context. A large portion of all the transportation in the world consists of voyages over the sea. Systems such as Automatic Identification Systems (AIS) have been developed to aid in the surveillance of the maritime traffic, in order to help keeping the amount accidents and illegal activities down. In recent years a lot of time and effort has gone into automated surveillance of maritime traffic, with the purpose of finding and reporting behaviour deviating from what is considered normal. An issue with many of the present approaches is inaccuracy and the amount of false positives that follow from it. Objectives. This study continues the work presented by Woxberg and Grahn in 2015. In their work they used quadtrees to improve upon the existing tool STRAND, created by Osekowska et al. STRAND utilizes potential fields to build a model of normal behaviour from received AIS data, which can then be used to detect anomalies in the traffic. The goal of this study is to further improve the system by adding statistical analysis to reduce the number of false positives detected by Grahn and Woxberg's implementation. Method. The method for reducing false positives proposed in this thesis uses the charge in overlapping potential fields to approximate a normal distribution of the charge in the area. If a charge is too similar to that of the overlapping potential fields the detection is dismissed as a false positive. A series of experiments were ran to find out which of the methods proposed by the thesis are most suited for this application.   Results. The tested methods for estimating the normal distribution of a cell in the potential field, i.e. the unbiased formula for estimating the standard deviation and a version using Kalman filtering, both find as many of the confirmed anomalies as the base implementation, i.e. 9/12. Furthermore, both suggested methods reduce the amount of false positives by 11.5% in comparison to the base implementation, bringing the amount of false positives down to 17.7%. However, there are indications that the unbiased method has more promise. Conclusion. The two proposed methods both work as intended and both proposed methods perform equally. There are however indications that the unbiased method may be better despite the test results, but a new extended set of training data is needed to confirm or deny this. The two methods can only work if the examined overlapping potential fields are independent from each other, which means that the methods can not be applied to anomalies of the positional variety. Constructing a filter for these anomalies is left for future study.