Data Driven Joint Sensor Fusion and Regression Based on Geometric Mean Squared Error

This paper explores the problem of estimating a temporal series measured from multiple independent sensors with unequal and stationary measurement errors with unknown variances. By formulating the data fusion problem as a joint Maximum Likelihood estimation of sensor covariances and a fusion rule, a batch data driven method is derived involving a residual covariance determinant minimization of a diagonal matrix. It is shown that yielding useful learning from data with good generalization properties in the joint regression and fusion approach requires the assumption of some structure on the sensor noises and/or on the temporal series to be estimated. An efficient data driven algorithm is proposed to obtain the best linear sensor combiner, whose performance is numerically analyzed and compared with the Cramer-Rao Lower Bound of the estimated parameters.