Use the physical model to project the state forward in time. Update: Use the new sensor data to correct the prediction. MATLAB Example: Tracking a Simple Moving Object
The Kalman filter is a recursive algorithm that estimates the state of a system from noisy measurements. It uses a combination of prediction and measurement updates to estimate the state of the system. The algorithm is based on the following assumptions:
These examples demonstrate the basic concept of the Kalman filter algorithm and its application to simple problems. Use the physical model to project the state forward in time
A common beginner example is estimating a constant voltage, where the sensor is noisy. % --- Kalman Filter for Constant Voltage Measurement --- % Based on Phil Kim's "Kalman Filter for Beginners" % 1. Simulation Parameters ; true_v = - % True voltage v_noisy = true_v + randn( % Noisy measurements % 2. Initialize Kalman Filter Variables % Initial guess % Initial estimation error covariance (uncertainty) % Process noise covariance (constant, so very low) % Measurement noise covariance (std^2) % To store results estimates = zeros( % 3. Kalman Filter Loop % Prediction x_pred = x; P_pred = P + Q;
% Update K = P_pred*H'*inv(H*P_pred*H' + R); x_est = x_pred + K*(z(i) - H*x_pred); P_est = (1 - K*H)*P_pred; It uses a combination of prediction and measurement
Every theoretical chapter is paired with a clean, unoptimized MATLAB script. This allows beginners to see exactly how equations translate into code variables. The Core Kalman Filter Loop
It produces the best possible estimate (in a specific mathematical sense) when the system model is accurate and noise is Gaussian. % --- Kalman Filter for Constant Voltage Measurement
Understanding the Kalman Filter: A Beginner's Guide with MATLAB Examples
The Kalman filter has various applications, including:
% State vector [position; velocity] dt = 0.1; % time step F = [1 dt; 0 1]; % state transition matrix H = [1 0]; % we measure only position Q = [0.01 0; 0 0.01]; % process noise R = 0.5; % measurement noise