EE-608 Course projectEE-608 Course project

Adaptive Kalman Structure for Adaptive Kalman Structure for Passive Undersea TrackingPassive Undersea Tracking

Pannir Selvam E (05407703)Pannir Selvam E (05407703)

Vikram Mehta (CEP)Vikram Mehta (CEP)

Praveen Goyal (05307810)Praveen Goyal (05307810)

Guided ByGuided By

Prof. U.B. DesaiProf. U.B. Desai

AIMAIM

Estimate submarine rangeEstimate submarine range Use passive sonar Use passive sonar Adaptive Kalman filterAdaptive Kalman filter

Submarine – Ship geometrySubmarine – Ship geometry

Submarine – Ship geometrySubmarine – Ship geometry

B

L

R

Submarine

1, t1

c

BLR

L

cB

c

BLc

BL

22

211

2

1

cos

2

)(sin

sin

sin

L2, t2 3, t3

Propagation of errors – nonlinear transformations

Estimation problemEstimation problem

c

BLR

L

cB

22

211

cos

2

)(sin

Propagation of errors – Taylor seriesPropagation of errors – Taylor series Measurements of Measurements of 11 and and 22 have AWGN have AWGN

Kalman StructureKalman Structure Model Model ’s’s

R - GatedR - Gated

Estimation problemEstimation problem

c

BLR

L

cB

22

211

cos

2

)(sin

Propagation of errors – Taylor seriesPropagation of errors – Taylor series Measurements of Measurements of 11 and and 22 have AWGN have AWGN

Kalman StructureKalman Structure Model Model ’s’s

R - GatedR - Gated

Block diagram of Two Stage Kalman Structure Block diagram of Two Stage Kalman Structure

Time Delays

Correlation

Bearing Function

Bearing Filter

Non Linear Range

Function

Time Delay Filter (2)

Time Delay Filter (1)

Range Filter

Time Delay Process Variance

Adaptive Feedback Loop

B̂ R̂

q

n1 n2

nB

Second Stage

Moving Source

RB

Dynamic model & measurement Dynamic model & measurement equation usedequation used

timeSampling

noiset Measuremen

range unbiased Observed

Noise Process

velocityand range containing State

01

210

111

2

1

T

v

z

a

vx

xz

aT

T

x

x

x

x

k

k

k

k

k

k

k

kk

x

ReferencesReferences

1.1. ““An Adaptive Two Stage Kalman An Adaptive Two Stage Kalman Structure for Passive Undersea Structure for Passive Undersea Tracking” by Mark R Allen and Louis A Tracking” by Mark R Allen and Louis A King, IEEE Transactions on Acoustics, King, IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 16, Speech and Signal Processing, Vol. 16, No. 1, Jan 1988No. 1, Jan 1988

2.2. Misha SchwartzMisha Schwartz

3.3. Adaptive Filter Theory by Simon HaykinAdaptive Filter Theory by Simon Haykin