If you have ever wondered how a GPS knows exactly where you are even when the signal is noisy, or how a robot balances itself, the answer is likely the Kalman Filter.
Kalman Filter for Beginners: A Clear Guide with MATLAB Examples The Kalman Filter for Beginners: A MATLAB Tutorial
You can download the MATLAB code used in this example from the following link: It works in real-time (no need to store all past data)
% True State (What actually happens) true_velocity = 2; % Moving 2 meters per second initial_position = 0;The filter assumes that the state of a system follows a linear model and that all noise follows a Gaussian (normal) distribution Prediction Step You can download the MATLAB code used in
The filter calculates a "Kalman Gain" to decide which source to trust more. If your sensor is very noisy, it trusts the prediction more; if your prediction model is uncertain, it trusts the sensor more. 2. The Algorithm Steps The filter loops through these equations at every time step Key Equation (Simplified) Prediction Forecast the next state $\hatx_{k Update Refine forecast with measurement $\hatxk = \hatx{k : State transition matrix (how the system moves). : Measurement matrix (how states relate to sensor data). : Kalman Gain (the "trust" factor). 3. MATLAB Implementation Example