Fusion of Quantized and Unquantized Sensor Data for Estimation

This letter investigates the usefulness of quantized data for estimation problems in which unquantized data is already available. A worst case scenario is considered in which a fusion center has access to continuous and binary-valued measurements of the same uniformly distributed parameter observed in Gaussian noise. The difference in mean squared error between a minimum mean squared error estimate using unquantized data and a minimum mean squared error estimate using both quantized and unquantized data is used to quantify the value of fusing the two kinds of data. Discussion of the Cramér-Rao Bound predicts how noise in the quantized data affects the reduction in estimate mean squared error from fusing the data types. It is then determined that the maximum reduction in estimate mean squared error from fusion can be approximated as a rational function of the ratio of the standard deviations of the measurement noise in the two data types. Finally, similarities between the approximation to the reduction in estimate mean squared error for the most favorable uniform prior width and a closed form expression based on the Cramér-Rao Bound are discussed.