Estimating Position of an Aircraft using Kalman Filter
This example shows how to use the Kalman filter in an application that involves estimating the position of an aircraft through a model for RADAR measurements. A user interface (UI) allows the user to control various parameters while the simulation is running. A MEX-file is also generated from the MATLAB code for accelerating the speed of execution in the same application. A speed comparison between the MATLAB function and the generated MEX-file is presented at the end.
Kalman filter is often used in tracking and navigation applications. In this example, we aim to simulate the tracking of an aircraft through a RADAR. The position of an aircraft can be estimated from noisy RADAR measurements using a Kalman filter. The scenario is depicted below:
Four states related to the position of the aircraft are used to describe the system: x-coordinate (), rate of change of x-coordinate (), y-coordinate () and rate of change of y-coordinate (). The system is, therefore, modeled as:
where the noise is independent, white and Gaussian
Kalman Filter System Object
The Kalman filter System object used in this example was created using the procedure described in System Design in MATLAB Using System Objects. The implementation is available in dsp.KalmanFilter. For the algorithm and properties of the Kalman filter, refer to the documentation for dsp.KalmanFilter.
Model for Generation of RADAR Measurements
A model simulates acceleration values for the aircraft and uses that to generate the position and velocity data in Cartesian coordinate system. To create inaccurate measurements by the RADAR antenna, noise is added to the data.
Using the Kalman Filter in MATLAB
The core algorithm of this example application applies Kalman filter to noisy RADAR measurements. It performs the following sequence of tasks:
- Initialize the Kalman filter System object
- Assign its properties based on the aircraft-RADAR system
- Generate noisy RADAR measurement and pass it to the Kalman filter System object.
The function aircraftPositionEstimateExampleApp wraps around the above algorithm and iteratively calls it, providing continuous tracking of the aircraft. It also plots the trajectory of the aircraft to compare the three: True position, noisy measurement of the position and Kalman filtered estimate of the position. The plots are created only when the plotResults input to the function is true.
Click here to call aircraftPositionEstimateExampleApp and plot the results on TimeScopes. Note that the simulation will be run for as long as the user does not explicitly stop it.
The plots below are the output of running the above simulation for 2000 time-steps:
The mitigation effect of Kalman filter over the noise can be seen through the above plots.
The function aircraftPositionEstimateExampleApp launches a User Interface (UI) designed to interact with the simulation. The UI allows you to tune parameters and the results are reflected in the simulation instantly. For example, moving the slider for the 'Thrust in X-Position' to the right while the simulation is running, will increase the acceleration of the aircraft along the X-direction. You will notice the corresponding plot in the TimeScope get steeper, to reflect this change.
There are also three buttons on the UI - the 'Reset' button will reset the states of the Kalman filter to their initial values and the 'Pause Simulation' button will hold the simulation until you press on it again. The simulation may be terminated by either closing the UI or by clicking on the 'Stop simulation' button. The interaction between the UI and the simulation is performed using UDP. Using UDP enables the UI to control either the simulation or, optionally, a MEX-file (or standalone executable) generated from the simulation code as detailed below. If you have a MIDI controller, it is possible to synchronize it with the UI. You can do this by choosing a MIDI control in the dialog that is opened when you right-click on the sliders or buttons and select "Synchronize" from the context menu. The chosen MIDI control then works in accordance with the slider/button so that operating one control is tracked by the other.
Generating and Using the MEX-File
MATLAB Coder can be used to generate C code for the function containing the algorithm. In order to generate a MEX-file for your platform, execute the script HelperAircraftKalmanFilterGenMEX. This will create the MEX-file in the current directory, so make sure that it is writable.
By calling the wrapper function aircraftPositionEstimateExampleApp with 'true' as an argument, the generated MEX-file can be used for the simulation instead of MATLAB code. In this scenario, the UI is still running inside the MATLAB environment, but the main processing algorithm is being performed by a MEX-file. Performance is improved in this mode without compromising the ability to tune parameters.
Click on this to call aircraftPositionEstimateExampleApp with 'true' as argument to use the MEX-file for simulation. Again, the simulation will be run till the user explicitly stops it from the UI.
Creating MEX-Files often helps achieve faster run-times for simulations. The function HelperCompareSpeedKalmanFilter first measures the time taken by the MATLAB function that uses the System object without any plotting, and then measures the time for the run of the corresponding MEX-file. When you run the function, you can observe the magnitude of improvement in speed of execution on the Command Window output.