Introduction Imagine trying to track the exact position of a moving car using a noisy GPS signal. The GPS might tell you the car is at one location, but your intuition says it should be further along the road. Which do you trust? This fundamental problem of blending noisy measurements with a mathematical model is where the Kalman Filter (KF) excels.
%% Visualizing Kalman Gain and Uncertainty clear; clc; dt = 0.1; F = [1 dt; 0 1]; H = [1 0]; R = 9; % Measurement noise variance Q = [0.1 0; 0 0.1]; --- Kalman Filter For Beginners With MATLAB Examples BEST
% Update (using a dummy measurement) S = H * P_pred * H' + R; K = P_pred * H' / S; P = (eye(2) - K * H) * P_pred; Introduction Imagine trying to track the exact position
% State transition matrix F F = [1 dt; 0 1]; This fundamental problem of blending noisy measurements with
Developed by Rudolf E. Kálmán in 1960, the Kalman filter is a recursive algorithm that estimates the state of a dynamic system from a series of incomplete and noisy measurements. It is widely used in robotics, navigation, economics, and signal processing. For beginners, the math can seem daunting, but the core idea is simple:
%% Run Kalman Filter for k = 1:N % --- PREDICT STEP --- x_pred = F * x_est; P_pred = F * P * F' + Q;