Target Tracking a Non-Linear Target Path

Using Kalman Predictive Algorithm

byJames Dennis Musick

Agenda

• Introduction

• Problem Definition

• Centroid Algorithm

• Kalman Filter

• Target Discrimination

• Conclusion

• Future Work

Introduction

• In the field of biomechanical research there is a subcategory that studies human movement or activity by video-based analysis

• Markers used– Optical

– RF

– Passive reflective

– Etc…

• Video based motion analysis

• 2D Analysis

• 3D analysis

• Golf swing example

Problem Definition

• In order to track the following have to be accomplished– Centroid calculation– Prediction– Discrimination

Problem Definition cont.

• Trials used– Walking Trial– Jumping Trial– Waving Wand Trial– Increasing complexity

Centroid Algorithm• Introduction

• Scanning scheme

Centroid Algorithm cont.

• 640 x 480– ~ 307200 pixels

• 8-bit Gray-scale

• Block diagramThreshold X/Y

address location

Target Discrimination Buffer

Logic control and centroid calculation

Centroid ValueMemory

Centroid Algorithm cont.

• Threshold

Centroid Algorithm cont.

• x/y addressing

Centroid Algorithm cont.

• Target Pixel Discrimination Buffer – x_sum, y_sum, LS_target, RS_target,

Bot_target, target_pixel_num

Centroid Algorithm cont.

• Logic Control and Centroid Calculation

}iin target pixels{

}iin target pixels{

}iin target pixels{

}iin target pixels{ ,),(

kk

kk

kk

kk

iii n

y

n

x

Cyx

Centroid Algorithm cont.

• Centroid Memory Buffer – Once a target is completed (defined as no pixels within

the search criteria at the row just below the target), then the centroid data is stored in a memory array until the data is read out at the end of the number of pictures that are being analyzed.

– The array would be structured in the following manner if there were three targets in each of 5 pictures:

• Target_Centroid_Array = (xy,Target #, Picture #) => (1:2, 1:3, 1:5).

Centroid Algorithm cont.

• Examples

Centroid Algorithm cont.

• Performance and Limitations – Three targets simultaneous– Total number

Centroid Algorithm cont.

• Measurement Uncertainty

• Correct (3.5,4) Correct (3.5,3)

• Blue missing (3.5,4) Red missing (3.8,3.17)• Red missing (3.64, 4.21)

Kalman Filter

• Introduction – State Space representation

kkk xTxx 1

Velocityxk

k

k

k

k

x

xT

x

x

10

1

1

1

Kalman Filter cont.

kkkk xT

xTxx 2

1 2 wk ux

T

2

2

wkkk uxTxx 1 Velocityxk onAcceleratixk

wkk BuApp 1

vkk DuCps ),0(~ 2ww Nu ),0(~ 2

vv Nu

Kalman Filter cont

Kalman Filter cont

Kalman Filter cont

• Target Models:– Noisy Acceleration model

Kalman Filter cont

• Target Models:– Noisy Jerk model

Kalman Filter cont

• Selection of update time:• T = 1

Kalman Filter cont• b

Kalman Filter cont• Operation of the Kalman Filter

Kalman Filter cont• Operation of the Kalman Filter

Kalman Filter cont• Operation of the Kalman Filter

Kalman Filter cont• Operation of the Kalman Filter

Kalman Filter cont• Operation of the Kalman Filter

Kalman Filter cont• Operation of the Kalman Filter

Target Discrimination

• Introduction– Goal

Target Discrimination

• Example

Target Discrimination

• Example cont

Target Discrimination

• Operation of algorithm

Target Discrimination

• Operation of algorithm cont

Target Discrimination

• Operation of algorithm cont

Jumping Trial

Target Discrimination

• Operation of algorithm cont

Target Discrimination

• Occluded targets

Conclusion

• Centroid algorithm

• Kalman filter– Model

• Discrimination

Future Work

• Hardware implementation

• 3D application

• Other biomechanical target discrimination (segmentation, etc.)

• Other tracking application (space, robotics, etc.)