Hello Aniket,
I understand that you are interested in analysing how the noise varies with the entropy of the state covariance and how the Kalman filters react under the same conditions in a forward collision warning system using sensor fusion in MATLAB. To achieve this, you will need to implement Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and the standard Kalman Filter (KF). You will also need to define the measurement noise and state covariance variables, and then vary them to study the effects.
Here's a conceptual outline of how you might structure your MATLAB code to achieve this:
- Define Your System: You need to define the state transition and measurement models for your forward collision warning system.
- Initialize Filters: Set up the EKF, UKF, and KF with initial state estimates and initial state covariance.
- Vary Measurement Noise and State Covariance: Create a loop or a set of experiments where you systematically vary the "MeasurementNoise" and "stateCov" variables.
- Simulate the System: Run the filters with the varying parameters over a predefined scenario or set of measurements.
- Calculate Entropy: For each variation, calculate the entropy of the state covariance matrix. Entropy can serve as a measure of uncertainty in the state estimate.
- Analyze Results: Compare the performance of the EKF, UKF, and KF under the different noise and covariance conditions.
Here's a skeleton MATLAB code to illustrate the above steps:
% Define the system (this would need to be replaced with your actual system)
stateTransitionModel = ...;
measurementModel = ...;
% Initial state and covariance
initialState = ...;
initialStateCovariance = ...;
% Define the range of measurement noise and state covariance to test
measurementNoiseValues = ...;
stateCovValues = ...;
% Results storage
results = struct();
for i = 1:length(measurementNoiseValues)
for j = 1:length(stateCovValues)
% Set the measurement noise and state covariance
MeasurementNoise = measurementNoiseValues(i);
stateCov = stateCovValues(j);
% Initialize the EKF, UKF, and KF
ekf = ...; % Set up the Extended Kalman Filter
ukf = ...; % Set up the Unscented Kalman Filter
kf = ...; % Set up the standard Kalman Filter
% Simulate the system and update the filters
for t = 1:T % Assume T time steps
% Your code to simulate the system and generate measurements
% Update the filters with the measurements
ekf = ...; % Update EKF
ukf = ...; % Update UKF
kf = ...; % Update KF
end
% Calculate the entropy of the state covariance matrix
entropy_ekf = ...; % Entropy for EKF
entropy_ukf = ...; % Entropy for UKF
entropy_kf = ...; % Entropy for KF
% Store the results for analysis
results(i,j).MeasurementNoise = MeasurementNoise;
results(i,j).stateCov = stateCov;
results(i,j).entropy_ekf = entropy_ekf;
results(i,j).entropy_ukf = entropy_ukf;
results(i,j).entropy_kf = entropy_kf;
end
end
Keep in mind that the actual implementation will be more complex and will require the specific models and update equations for your system. MATLAB's Sensor Fusion and Tracking Toolbox can help you with pre-built functions for EKF and UKF.
To calculate the entropy of a covariance matrix, you can use the following formula, assuming the covariance matrix is "P":
entropy = 0.5 * log(det(2 * pi * exp(1) * P));
Remember to replace the placeholder code with your actual system models, filter initialization, update steps, and to implement the logic for simulating your system and generating measurements.
Hope this helps.
