Fusion method for physical systems based on physical laws

We considers a physical system described by a set of parameters. Each parameter is either measured by a number of sensors or estimated by a set of computer programs that use sensor measurements. As a result, the resultant parameter values could be widely varying. We propose a fusion method that combines the measurements and estimators based on the physical laws that relate the parameters. In comparison with the traditional fusion problems, there is no training set that provides the actual parameter values. Furthermore, since every parameter is measured or estimated, there are no parameters whose actual values are known. We propose a fuser based on the least violation of the physical laws that relate the parameters. Under certain smoothness conditions on the physical law, we show the asymptotic convergence of our method, and also derive distribution-free performance bounds based on finite samples. We illustrate the effectiveness of this method for a practical problem of fusing well-log data in methane hydrate exploration. For this problem, the data fusion method resulted in an order-of-magnitude improvement in the accuracy compared to the best set of estimators for the key parameter of porosity.