Robust Kalman Filtering: Handling Outlier Measurements

The standard Kalman filter assumes Gaussian measurement noise. In practice -- especially in financial signal processing or sensor fusion -- you will occasionally see a reading that is wildly off: a data error, a flash crash tick, a sensor glitch. A single such outlier can drag your state estimate far from the truth and take many steps to recover. Describe three distinct approaches to make a Kalman filter robust to outlier measurements. For each approach, explain the core idea, how it modifies the standard filter equations, and when you would choose it.