Principles of Radar Target Tracking The Kalman Filter: Mathematical Radar Analysis

Problems with Radar Radar can’t measure velocity Radar has measurement error: “noise”

Purpose of Kalman Filter Transform data input from radar trackers into usable form Reduce measurement error (“noise”) of target’s position and velocity Predict future state of target using previous state estimate and new data Lightweight, robust, and expandable program

Rudolph Kalman Rudolph E. Kalman was the “inventor” of the Kalman Filter Began research on control theory in 1958 Blended earlier works Worked with partner R.S. Bucy

Overview of Kalman Filter Initialize Matrices Read Data Predict Update Output Results Finish Correct Measurement Covariance

Introduction to Project Part 1 2 Team Scenario, competing for government contract Similar Projects Individual Programs, Analyses, Graphs required Part 2 Teams Merge Written Component

Problems Getting Started Problems New programming language Unfamiliar algorithm Matrix Algebra Solutions Looked at help files and API’s Teamwork in research Matrix library

Kalman Model State Model Measurement Model

Steps of Kalman Filter Predict

Steps of Kalman Filter Correct

Programming Made using Visual Basic.NET Read data file Convert coordinates Predict location Output to Excel Graph flight path

Case Studies: Basic Kalman Filter Filter noise from a basic, linear data Limited functionality, based solely on Cartesian coordinates Built to be expandable, adaptable Challenges First experience with Kalman Filter tracking

Case Studies: How to Read Graphs Data Analysis Comparison of raw data, estimated state, and truth Filter takes noisy data and projects a path close to the truth Position Residual Comparison of mean squared error Estimate v. Truth should decrease as filter gains accuracy relative to the Raw Data v. Truth

Case Studies: Basic Filter

Case Studies: Filter with Polar Coordinates Data inputted in range and bearing Challenges Transformation of measurement data from Polar to Cartesian coordinates Error ellipse based on accuracy of range and bearing σrσr σθσθ

Case Studies: Filter with Polar Coordinates Filter incorporates past and current data Increased accuracy with more data Position Residual (Estimate v. Truth) should decrease relative to noise

Case Studies: Filter with Polar Coordinates

Case Studies: Multiple Targets Code rewrite necessary Object-oriented rather than structured programming Handles each target individually and allows the same steps to be used for each target

Case Studies: Multiple Targets

Case Studies: Collision Avoidance Use data on multiple targets Predict collisions based on probable courses Alert target aircraft if within a certain range

Case Studies: Collision Avoidance

Case Studies: Maneuver Detection Comparison of projected path and measured data When target deviates from projected course, reinitialize tracking Additional coding necessary

Case Studies: Maneuver Detection

Case Studies: Interceptor Includes maneuver detection algorithms Direct interceptor towards earliest projected interception Reinitialize tracker and plane’s course after maneuvers

Case Studies: Interceptor

Conclusion Visual Basic.NET successfully handled the Kalman equations Kalman Filter successfully reduced noise in all scenarios Position Residual graphs confirms that the filter gains accuracy over time Basic Filter proved expandable and advanced features were successfully incorporated in later scenarios

Thank You

References [IEEE] Institute of Electrical and Electronics Engineers Jan 23. Rudolf E. Kalman, IEEE History Center. Accessed 2006 Aug 3. alman.html Department of Computer Science at University of North Carolina Jan 31. Rudolph Emil Kalman. Accessed 2006 Aug 3. Blackman, Samuel S Multiple-Target Tracking with Radar Applications. Artech House, Inc. Norwood, MA. Bishop G, Welch G An Introduction to the Kalman Filter.. Accessed 2006 Aug 3. Anas SA Jan 18. Matrix operations library.NET.