1. Principles of Radar Tracking
Utilizing the Kalman Filter

2. Radars Aren’t Perfect Radars give noisy data.
Radars give noisy data.
We need more accurate data.
Position
Velocity
Kalman Filter

3. Why Kalman? Invented by Rudolf Kalman Simple Low Memory Requirement
Invented by Rudolf Kalman
Simple
Low Memory Requirement
Fast
Versatile

4. The Different Cases Case 1: 1 Dimensional Cartesian
Case 1: 1 Dimensional Cartesian
Case 2: 2 Dimensional Cartesian
Case 3: 2 Dimensional Polar
Case 4: Polar with 2 Radars
Case 5: Polar with maneuvering target

5. You like Linear Algebra? Then you’ll like Kalman Filters
Designed to track targets in a linear motion
Series of equations: Algorithm
Measurement
Simple Right?
Predict
Update

6. I take a look at my… The Variable Matrices Initial Conditions
Initial Conditions
Initial Prediction
Initial State Covariance Matrix
The Variable Matrices
x(k) – State Vector
Q – Driving Noise Covariance
H – Observation Model
Φ – State Transition Model
P – State Covariance
y(k) - Measurement

7. Prediction Equations
x(k+1|k) = Φx(k|k)
P(k+1|k) = ΦP(k|k)ΦT + Q

8. Yet Two More Variables
K - Kalman Gain Matrix
R – Measurement Noise

9. Update Equations K(k) = P(k|k-1)HT[HP(k|k-1)HT + R]-1
K(k) = P(k|k-1)HT[HP(k|k-1)HT + R]-1
x(k|k) = x(k|k-1) + K(k)[y(k) – Hx(k|k-1)]
P(k|k) = [I – K(k)H]P(k|k-1)

10. Program Layout Visual Basic .NET console application Classes Data
Visual Basic .NET console application
Classes
Data
Operations
Inheritance
Bicycle
Properties:
Color
Gear
Size
Methods:
setGear()
pedal()
brake()
steer()

11. Datum Holds two pieces of information: time (Double) coords (Matrix)
Holds two pieces of information:
time (Double)
coords (Matrix)
Datum
Properties:
time
coords

12. The KFilter Class MatLib library 2D arrays of doubles predict(time)
MatLib library
2D arrays of doubles
predict(time)
update(y)
reset(initial, P)

13. File I/O FileReader PolarFileReader PolarMultiReader CommaWriter
FileReader
hasNext()
nextDatum()
PolarFileReader
PolarMultiReader
CommaWriter
WriteLine()
Close()

14. Other Functions Initialization Functions: Nsig() initialize() makeP()
Initialization Functions:
initialize()
makeP()
makeQ()
makeR()
Hmat()
PhiMat()
Nsig()

15. Putting It All Together
Initialize
Read data
Predict
Calculate R
Update
Write Output
Check for more data
Finish

16. Case 1 Results

17. Case 2 Results

18. Case 3 Results

19. Case 4 Results

20. Case 5 Results

21. Performance Improvement

22. Conclusion Improved predictions over time Adaptable
Improved predictions over time
Adaptable
Successful project!

23. Team Project 6
Mr. Heuer, Joe Kelly, Ankur Bakshi, Vikram Modi, Karl Strohmaier, Luke Anderson, David Kim, Kareem Elnahal, Alex Shnayder, Adam Pantel, Andrew “Tony” Weintraub, Alex Sood, and Joe Park
Thank You!