We must establish a common denominator for comparison of position estimates given measurements. We have pursued a statistical procedure for doing so. Our objective is to maximize the posterior probability of position given the bearings, $p(x,\; y\; |\; R)$. Position is discretized in intervals of 30 meters, agreeing with the discretization of Digital Elevation Maps. At first, we must specify a prior density for position, $p(x,\; y)$. Currently we use a uniform distributions to signify absence of prior knowledge. Secondly, we must specify the likelihood the bearings (the measurements) given position, $p(R\; |\; x,\; y)$. In practice it is difficult to determine the likelihood of a bearing given position; it is appropriate to decompose this expression in terms of the possible interpretations of the bearings:

$p(R|x,\; y)\; =\; \sum $_{I} p(R|x, y, I) p(I|x, y).

Experience with the mountain detection system has led to the conclusion that, for fixed pose and correspondences, the errors in measuring bearings are fairly independent:

$p(R\; |x,\; y,\; I)\; =\; \prod $_{i=1}^{m} p(r_{i}|I,Γ).