Have you ever wondered how GPS navigation knows exactly where you are, even when you drive through a tunnel? Or how a drone stays stable in a gusty wind? The secret ingredient in many of these technologies is the .
Equation (Simplified): New State = Predicted State + Kalman Gain * (Measurement - Prediction) MATLAB Example: Estimating a Constant Voltage
What your physics equations say should happen. The Measurement: What your sensors say is happening. The Boat Analogy Imagine you are navigating a boat at night.
MATLAB is the perfect environment to start because it abstracts away the complex matrix math, allowing you to focus on the logic of the filter. Have you ever wondered how GPS navigation knows
Once you master the standard Linear Kalman Filter, you might find that your real-world problem is non-linear (for example, navigating a turning vehicle or tracking a drone moving in 3D space). For non-linear systems, you will need an , which uses calculus (Jacobians) to approximate non-linear functions.
Your relies on dead reckoning: you know your starting point, your speed, and your direction. However, wind and currents introduce drift error over time.
). Because no model is perfect, the uncertainty (variance) of our estimate increases during this step. 2. The Update Step (Measurement Update) Equation (Simplified): New State = Predicted State +
Your comes from a GPS. The GPS gives you your position, but the signal bounces around, making it jumpy and noisy.
% Predict xhat_p = A*xhat; P_p = A*P*A' + Q; % Update K = P_p*H'/(H*P_p*H' + R); xhat = xhat_p + K*(z - H*xhat_p); P = (eye(4) - K*H)*P_p;
% --- True Initial State and Simulate --- x_true = [0; 10]; % [position; velocity] x_true_hist = zeros(2, N); for k = 1:N x_true_hist(:, k) = x_true; x_true = A * x_true + sqrt(Q) * randn(2, 1); % Add process noise end MATLAB is the perfect environment to start because
At its core, a Kalman filter is an optimal, recursive data processing algorithm [1]. It helps you estimate the state of a dynamic system (like position, velocity, or temperature) when your measurements are noisy, or your model is imperfect.
The Kalman Filter is an algorithm that estimates the state of a dynamic system over time, even when the system is noisy or measurements are inaccurate. It is a , meaning it doesn't need to look at the entire history of data to make a prediction; it only needs the estimate from the previous time step and the current measurement. Why do we need it?
extendedKalmanFilter : Used for non-linear systems where physics equations involve curves, trigonometry, or rotations.
Adjust these parameters to experiment: