Principles of Principles of Radar Target TrackingRadar Target Tracking

Jay Bhalodi, Jeff Cao, Lily Healey, Jay Bhalodi, Jeff Cao, Lily Healey, Wendy Lin, Tuling Ma, Zara Mannan, Wendy Lin, Tuling Ma, Zara Mannan,

Brandon Millman, Zachary Purdy, Brandon Millman, Zachary Purdy, Divya Sharma, Mimi XuDivya Sharma, Mimi Xu

The Corporations

CheetahTrack

Jay Bhalodi, Lily Healey, Wendy Lin, Tuling Ma, Mimi Xu

TRACJeffrey Cao, Zara Mannan, Brandon Millman, Zachary Purdy, Divya Sharma,

Government Agent

Consultant

Randy Heuer

Zachary Vogel

Problem and SolutionProblem and Solution

Solution: Kalman Filter

Updates to better approximate noise

Problem: Noise

Inaccuracies in measurement data

Account for noise to better predict

Kalman Filter: Background

Derived by R.E. Kalman

Published A New Approach to Linear Filtering and Prediction Problems in the Journal of Basic Engineering in 1960

Kalman Filter used extensively in fields of navigation and tracking

Kalman Filter Model

kkk

kkk

rHxy

qxx

1

=

The foundation of the Kalman filter lies in its model of both the target’s movement and the actual measurement of the position.

Kalman Theory

The Kalman Filter is a two-step algorithm :

First the algorithm “predicts” the target’s next expected location

Then update predictions based on new measurements

PREDICT UPDATE

Predict Step

1

Q 1

Predicts using transition matrix and current velocity value

Advances state covariance matrix for update step

Update Step

1

11

RHHPHPK Tkk

Tkkk

11ˆˆˆ kkkkkkkk xHyKxx

1 kkkkk PHKIPCalculatesKalman Gain Matrix

Updates position matrix based on weighting factor and residual

Recalculates state covariance matrix for predict step

ImplementationImplementation

Modular - easy to modify

Different class for filter and each matrix

Java - Efficient due to object-oriented nature

ImplementationImplementation

JAMA Matrix LibraryJava Libraries

JAMA Matrix Library

Vector Class

National Institute of Standards and Technology (NIST)

Residuals- difference between our results and real data

Adaptations

Adapted filter to different challenging environments:

Polar Conversions

Two Radars

Collision Avoidance

Maneuvering Targets

Intercepting Targets

r

α

θ

Polar Conversions

sin

cos2

ry

rx

Real life applications-Range and Bearing

Transformed coordinate system

Updating the R Matrix

222222 sincos rrx

222222 cossin rry

2222 2sin2

1rrxy

yxy

xyxR

22

22

Error of range and bearing

not along the xy plane

Multiple Radars

Added update method to recalculate state transition (Φ) matrix

Two changes:

multiple data-input sources

variable time

Implementation:

Tagged data to later reconcile to single reference frame

Collision Avoidance

Some Changes:

Track two targets

Within 12 mi, predict paths

Within 1 mi, prompt for evasive action

Collision Avoidance (cont.)

Sequence of Steps:

Run filter for each target

Check distance each iterationCheck distance each iteration

If less than 12 miles:

Solve for timeSolve for time

Predict if they will come within 1 mi of each other

(40)

01)()22()( 222 yxvvtvvt xyyx

Maneuvering Targets

The Change:

Target no longer follows one linear path and may maneuver

The Steps:

•Detect•Count•Reset

Res

idua

ls

Intercepting Targets

βTarget

Point of Interception

Interceptor

τ

α

N

D

B A

γ

E

• Use Law of Sines to find α

• and β can be found using

BA

sinsin

sin)(sin 1

B

A

I

T

I

T

v

v

tv

tv

B

A

yx

yx

TT

TTTITI

vvD

vvyyxx

,

,,(cos 1

B

A

Intercepting Targets

22 )()( ITIT yyxxD

)(cos 1

D

yy IT

)(cos 1

D

yy IT

βTarget

Point of Interception

Interceptor

τ

α

N

D

B A

γ

Further Applications

Real Time Radar Tracking

Variable Altitudes

Acceleration

Conclusion

• Exposure to and successful implementation of Kalman Filter

• Many adaptations for our tracking system

• Overall, successful and effective

THANK YOU! Randy Heuer and Zachary VogelRandy Heuer and Zachary Vogel Dr. MiyamotoDr. Miyamoto Paul and CounselorsPaul and Counselors Course and Lab TeachersCourse and Lab Teachers

Thank you

Jewish Communal Fund

John and Laura Overdeck

NJGSS Alumnae and Parents, 1984 - 2008

Novartis

Schering-Plough Foundation

The Dorr Foundation

The Edward W. and Stella C. Van Houten Memorial Fund

The Jennifer A. Chalsty Foundation

Any Questions?Any Questions?

ReferencesReferences[1] Blackman SS. 1986. Multiple-Target Tracking with Radar Applications. Artech House, Inc.

[2] Atwood B. 2003. Covariance and GLAST. <http://www-glast.slac.stanford.edu/software/AnaGroup/WBA072003-Covariance.pdf>. Accessed 2008 July 21.

[3] [IEEE] Institute of Electrical and Electronics Engineers. 2003 Jan 23. Rudolf E. Kalman, 1930-. IEEE History Center. <http://www.ieee.org/web/aboutus/history_center/biography/kalman.html>. Accessed 2008 July 21.

[4] Kalman, R. E. 1960. A New Approach to Linear Filtering and Prediction Problems. ASME Journal of Basic Engineering 1960 March.