Mildly non-linear motion tracking (tracking aircraft turn rates). unscentedKalmanFilter(stateFcn, measureFcn)
Click New Script , paste either code block from above, and save it as kalman_1d.m or kalman_2d.m .
: A widely recommended practical guide that starts with simple recursive filters and moves to tracking examples like estimating velocity from position . Find details on the MathWorks Book Page .
Now, imagine you have a mathematical model that predicts where the car should be based on its last known velocity. If you blend this prediction with the noisy GPS measurement, you get a result that is better than either source alone. That is the magic of the .
K=Pk−Pk−+Rcap K equals the fraction with numerator cap P sub k raised to the negative power and denominator cap P sub k raised to the negative power plus cap R end-fraction (We calculate the Kalman Gain, . If sensor noise approaches 1.) kalman filter for beginners with matlab examples download
(Measurement Noise): Tells the filter that your sensor is terrible (e.g., a cheap GPS module under thick tree cover). The filter will ignore the rapid sensor spikes and lean heavily on smooth physics predictions. 7. Next Steps and Download Directions
The Kalman filter is a powerful recursive algorithm that estimates the state of a dynamic system from a series of noisy measurements
% 1D Kalman Filter Implementation for Constant Voltage Tracking clear; clc; close all; % 1. Simulation Parameters nSamples = 100; trueVoltage = 1.2; % True constant voltage measuredNoiseStd = 0.2; % Standard deviation of measurement noise % Generate fake noisy sensor data rng(42); % Set random seed for reproducibility measurements = trueVoltage + measuredNoiseStd * randn(1, nSamples); % 2. Kalman Filter Initialization Q = 1e-5; % Process noise covariance (assumed very low since voltage is constant) R = measuredNoiseStd^2; % Measurement noise covariance xtilde = 0; % Initial state guess (0V) P = 1; % Initial error covariance guess % Allocations for plotting estimatedHistory = zeros(1, nSamples); % 3. Kalman Filter Loop for k = 1:nSamples % --- Predict Phase --- % State doesn't change over time (A = 1, B = 0) xtilde_minus = xtilde; P_minus = P + Q; % --- Update Phase --- % Measurement directly maps to state (H = 1) K = P_minus / (P_minus + R); % Kalman Gain xtilde = xtilde_minus + K * (measurements(k) - xtilde_minus); P = (1 - K) * P_minus; % Save result estimatedHistory(k) = xtilde; end % 4. Visualization figure('Position', [100, 100, 800, 400]); plot(1:nSamples, measurements, 'r.', 'MarkerSize', 10); hold on; plot(1:nSamples, estimatedHistory, 'b-', 'LineWidth', 2); yline(trueVoltage, 'g--', 'LineWidth', 2); xlabel('Sample Iteration'); ylabel('Voltage (V)'); title('1D Kalman Filter: Constant Voltage Tracking'); legend('Noisy Measurements', 'Kalman Filter Estimate', 'True Value'); grid on; Use code with caution. Explanation of the 1D Results
The filter operates recursively in a continuous loop: it predicts the next state, receives a noisy measurement, and then updates its prediction based on which source is mathematically more reliable. 2. The Math Simplified: The Two-Step Cycle Find details on the MathWorks Book Page
), it becomes progressively more confident and smoother over time.
: A priori state estimate (our best guess before looking at sensors). Pk−cap P sub k raised to the negative power
When you run this script, you will observe the red dots (noisy sensor data) bouncing wildly between 0.8V and 1.6V. The blue line (Kalman Filter estimate) rapidly converges toward the true 1.2V mark within the first 10 iterations. Because the filter tracks its own tracking error covariance (
to support a 2D tracking environment (GPS Latitude and Longitude coordinate streams). That is the magic of the
To run these scripts locally on your machine, you can download them directly via the links below, or save them manually from the code blocks above. Download 2D Trajectory Tracking Script (kalman_2d_demo.m)
This MATLAB script simulates a vehicle moving in a straight line. The vehicle has a constant velocity, and a noisy sensor measures its position.
Kalman Filter for Beginners with MATLAB Examples Imagine you are trying to track the position of a car using GPS. The GPS gives you a position, but it's noisy—sometimes the car appears to be in the middle of a building or on the wrong side of the street. You also know how fast the car is moving, so you can guess where it should be.
+---------------------------------------+ | | | Initial State | | | | v v | +---------------------------------------+ | | Predict Step | | | 1. Estimate the next state | | | using system physics. | | | 2. Estimate the new uncertainty. | | +---------------------------------------+ | | | v | +---------------------------------------+ | | Update Step | | | 1. Calculate the Kalman Gain | | | (who to trust more). | | | 2. Correct the state estimate | | | using the new measurement. | | | 3. Correct the uncertainty. | | +---------------------------------------+ | ^ | | | +---------------------------------------+