Information-Form Fusion of Two Range Measurements

A landmark's range is measured independently by two sensors. Sensor A reports $r_A = 10.0\,\text{m}$ with standard deviation $\sigma_A = 0.5\,\text{m}$; sensor B reports $r_B = 10.6\,\text{m}$ with standard deviation $\sigma_B = 0.3\,\text{m}$. Assuming both measurements are unbiased, Gaussian, and statistically independent, compute the maximum-likelihood (information-weighted) fused range estimate in meters. (This is exactly the scalar version of the information-form update at the core of graph-SLAM and EKF/EIF back-ends.)