Beyond Divergence: Failure Modes of the Classical Extended Kalman Filter in a Unified Nonlinear Tracking Model

The extended Kalman filter (EKF) remains one of the most widely used tools for state estimation, tracking, forecasting, and data assimilation in nonlinear stochastic dynamical systems. This paper does not propose a replacement for the EKF or a modification of the filter itself. Instead, it investigates how the classical EKF may fail when used as a default estimation tool in a unified but practically interpretable nonlinear tracking problem. A stochastic moving-target observation model with angular and range measurements from two identical independent radar channels co-located at the origin of the coordinate system is used as the test environment. To the standard EKF scheme, we add only the technique of linear pseudomeasurements: the EKF is kept in its classical recursive form, and only the observation representation is changed, while the filtering algorithm itself remains unchanged. Within this framework, several systematic model modifications are considered: inaccurate state initialization, absence of prior information about the mean motion parameter, jump-like changes of motion parameters, and incorrect specification of observation-noise characteristics. The experiments show that EKF instability is not limited to explicit divergence. It may also appear as hidden degradation of estimation quality, coordinate-selective failure, physically counterintuitive accuracy behavior, and cases in which the filter remains formally bounded but performs worse than a simple direct estimate based on current measurements. In several experiments, unstable behavior becomes visible only when the Monte Carlo sample size is increased. The results provide a classification of qualitatively different EKF failure modes and support practical diagnostic criteria for testing EKF applicability in nonlinear observation models.