We have been studying information theoretic measures, entropy and mutual information, as performance metrics for object recognition given a standard suite of sensors. Our work has focused on performance analysis for the pose estimation of ground-based objects viewed remotely via a standard sensor suite. Target pose is described by a single angle of rotation using a Lie group parameterization: O (epsilon) SO(2), the group of 2 X 2 rotation matrices. Variability in the data due to the sensor by which the scene is observed is statistically characterized via the data likelihood function. Taking a Bayesian approach, the inference is based on the posterior density, constructed as the product of the data likelihood and the prior density for object pose. Given multiple observations of the scene, sensor fusion is automatic in the joint likelihood component of the posterior density. The Bayesian approach is consistent with the source-channel formulation of the object recognition problem, in which parameters describing the sources (objects) in the scene must be inferred from the output (observation) of the remote sensing channel. In this formulation, mutual information is a natural performance measure. In this paper we consider the asymptotic behavior of these information measures as the signal to noise ratio (SNR) tends to infinity. We focus on the posterior entropy of the object rotation angle conditioning on image data. We consider single and multiple sensor scenarios and present quadratic approximations to the posterior entropy. Our results indicate that for broad ranges of SNR, low dimensional posterior densities in object recognition estimation scenarios are accurately modeled asymptotically.