For an algorithm used for generation of a road map based upon position-samples, I am looking for a method of determining the probability of a sample belonging to an already discovered element of the map. For the sake of simplicity, the element on the map is represented as one point $v$ (a node in the graph), for which the position $\mu_v$ is estimated using the average of all measurements $M_v$ matched to this position. Each measurement comes from a GPS-source, which gives an approximate position ($\mu_m$) and accuracy ($\sigma_m$). The accuracy follows a Gaussian distribution. The distribution $\sigma_v$ for $v$ is assumed Gaussian, for ease of computation.
In the algorithm I use the chance of a measurement and the already estimated node on the map belonging together to determine if a measurement should be merged with the node, or should become a new node on the map. If the chance of belonging together is acceptable, the measurement will be added to the node. If this chance is below a certain threshold (probably 0.05), the measurement will be added to the map generating a new node in the graph.
My question is therefore:
Given $\mu_v$, $\sigma_v$, $\mu_m$, and $\sigma_m$:
What is the chance that $m$ and $v$ are observations of the same phenomenom?