Multisensor data fusion
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n 1. F 1 (s). y 1. n 2. x. z. F 2 (s). y 2. n k. F k (s). n 1. y k. x. x. z. S 1. x. y 1. S 2. Filter. y. n 2. 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.

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Multisensor Data Fusion

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Multisensor data fusion

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:


Multisensor data fusion

n

y

e

W(s)

F(s)

x

I(s)=1

Optimal Filtration in Scalar Case.

(4)

(5)

Wiener-Hopf Equation:

(6)

(7)


Multisensor data fusion

Wiener Factorization:

(8)

Wiener Separation:

(9)

Optimal Filter:

(10)

Example:

(11)

(12)

(13)


Optimal fusion of 2 sensors

n

W(s)

F(s)

x

y

n1

z

F1(s)

W1(s)

y1

ε

Optimal Fusion of 2 sensors.

(1)

i

(2)

(3)

(4)

(5)

(6)


Multisensor data fusion

Wiener-Hopf equation:

(7)

(8)

(9)

Example: fusion of Doppler and barometric speed sensors:

Barometric:

(10)

(11)

Doppler:

(12)

where:


Discrete kalman filter

Discrete Kalman Filter

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)


Discrete observer

Discrete Observer:

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)


Time dependant kalman filter algorithm

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])

Time-dependant Kalman Filter Algorithm

1

2

3

4

5

6

7


Example fusion of the dead reckon and radio navigation systems

v1

w1

FK

RNS

w2

DRS

yn/n

v2

Example: fusion of the dead reckon and radio-navigation systems


Transmission of information

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:


Angle code converter

Angle-Code Converter


2 modulation of signals

Com. Ch.

LPF

CSG

ym

ym

2. Modulation of Signals


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