In distributed sensor networks, computational and energy resources are in general limited. Therefore, an intelligent selection of sensors for measurements is of great importance to ensure both high estimation quality and an extended lifetime of the network. Methods from the theory of model predictive control together with information theoretic measures have been employed to pick sensors yielding measurements with high information value. We present a novel information measure that originates from a scalar product on a class of continuous probability densities and apply it to the field of sensor management. Aside from its mathematical justifications for quantifying the information content of probability densities, the most remarkable property of the measure, an analog on of the triangle inequality under Bayesian information fusion, is deduced. This allows for deriving computationally cheap upper bounds for the model predictive sensor selection algorithm and for comparing the performance of planning over different lengths of time horizons.
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