We have been studying information theoretic measures, entropy and mutual information, as performance bounds on the information gain given a standard suite of sensors. Object pose is described by a single angle of rotation using a Lie group parameterization; observations are simulated using CAD models for the targets of interest and simulators such as the PRISM infrared simulator. Variability in the data due to the sensor by which the scene is remotely 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 target pose. Given observations from multiple sensors, data fusion is automatic in the posterior density. Here, we consider the mutual information between the target pose and remote observation as a performance measure in the pose estimation context. We have quantitatively examined target thermodynamic state information gain dependency of FLIR systems, the relative information gain of the FLIR and video sensors, and the additional information gain due to sensor fusion. Furthermore, we have applied to the Kullback-Leibler distance measures to quantify information loss due to thermodynamic signature mismatch.