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Multisensor Data FusionPowerPoint Presentation

Multisensor Data Fusion

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Multisensor Data Fusion

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n1

F1(s)

y1

n2

x

z

F2(s)

y2

nk

Fk(s)

n1

yk

x

x

z

S1

x

y1

S2

Filter

y

n2

1. The Filtering Approach:

(1)

Multisensor Data Fusion

(2)

(3)

2. The Compensation Approach:

n

y

e

W(s)

F(s)

x

I(s)=1

Optimal Filtration in Scalar Case.

(4)

(5)

Wiener-Hopf Equation:

(6)

(7)

Wiener Factorization:

(8)

Wiener Separation:

(9)

Optimal Filter:

(10)

Example:

(11)

(12)

(13)

n

W(s)

F(s)

x

y

n1

z

F1(s)

W1(s)

y1

ε

(1)

i

(2)

(3)

(4)

(5)

(6)

Wiener-Hopf equation:

(7)

(8)

(9)

Example: fusion of Doppler and barometric speed sensors:

Barometric:

(10)

(11)

Doppler:

(12)

where:

Discrete observed plant:

x[n+1] = Anx[n] + w[n]{State equation}

y[n] = Cnx[n] + v[n] {Measurements}

M{ww'} = Qn, M{vv'} = Rn, M{wv'} = Nn=0,

(1)

(1a)

Performance index:

State vector prediction:

x[n+1/n] = Anx[n/n];

(2a)

Covariance matrix prediction:

(2b)

Measurement update:

X[n+1/n] = AnX[n/n-1] + Kn/n-1 (y[n] - CnX[n/n-1]);

X[n/n] = X[n/n-1] + Kn (y[n] - CnX[n/n-1])

Y[n/n] = CnX[n/n];

Pn/n-1 = E{(x[n] - X[n|n-1])(x[n] - X[n|n-1])'} (Ric. solution)

Pn/n= E{(x[n] - X[n|n])(x[n] - X[n|n])'} (Updated estimate)

Time update:

(3)

(4)

Covariance Matrices:

(5)

(6)

(7)

P(0),X(0),An,

Cn,Qn,Rn.

Initial data:

z-1

z-1

Measurements

y[n]

X[n/n] = AnX[n/n-1] + Kn (y[n] - CnX[n/n-1])

1

2

3

4

5

6

7

v1

w1

FK

RNS

w2

DRS

yn/n

v2

Dec.

Bin.

Grey

0

0

0

0

0

0

0

y

1

0

0

1

0

0

1

2

0

1

0

0

1

1

x

0

1

3

0

1

1

0

1

0

0

0

1

4

1

0

0

1

1

0

1

1

0

5

1

0

1

1

1

1

6

1

1

0

1

0

1

7

1

1

1

1

0

0

Hd=3

1. Coding of Signals.

Hamming’s distance:

Grey Code.

Example: 3-digit word

Transmission of Information

Encoding:

Truth Table:

Decoding:

Com. Ch.

LPF

CSG

ym

ym