EKF Consistency, Linearization Error, and Choosing Between EKF and UKF

A mobile robot estimates its 2D pose $(x, y, \theta)$ by fusing wheel odometry (process model) with range-and-bearing measurements to known landmarks using an Extended Kalman Filter (EKF). In testing, the filter's reported $3\sigma$ covariance ellipses are far smaller than the actual error, the estimate occasionally diverges during sharp turns, and the Normalized Estimation Error Squared (NEES) consistently exceeds its chi-square upper bound.

Explain (a) the mechanism by which EKF linearization produces this overconfident / inconsistent behavior, especially for the heading state and the nonlinear bearing measurement; (b) concrete techniques to diagnose and mitigate it; and (c) under what conditions you would switch to an Unscented Kalman Filter (UKF) instead, including how the UKF differs mathematically and what it does and does not fix.