A good mental model for understanding Kalman Filtering is to think of it as a system that combines two sources of information - predictions and measurements - to estimate the true state of a system. Imagine you are driving a car in a dense fog, and you have to estimate your position using limited visibility.

First, you make a prediction of your current position based on your previous knowledge and the car's dynamics. This prediction is not precise, as it is affected by uncertainties like measurement errors and external disturbances.

Then, you take a measurement of your actual position using a sensor, such as a GPS or an accelerometer. This measurement is also imperfect and can contain noise or errors.

The Kalman Filter acts as your mental processor, continuously updating and refining your estimated position based on the prediction and the measurement. It weighs the accuracy and reliability of both sources of information to produce an optimal estimate of your true position.

Think of the Kalman Filter as a feedback loop. It compares the prediction with the measurement and adjusts the estimate accordingly. It takes into account the uncertainties associated with predictions and measurements, assigning higher weights to more reliable information.

With each iteration, the Kalman Filter refines your estimate, providing a more accurate representation of the true state of the system. It dynamically adapts to changing conditions, improving the estimation as new measurements and predictions become available.

By integrating predictions and measurements in an optimal way, the Kalman Filter provides a powerful mental model for estimating and tracking the state of dynamic systems, even in the presence of uncertainties and noise.

Further reading