optimization of multistatic passive radar geometry

Dottorato di ricerca in Telerilevamento – XXIV ciclo

DIPARTIMENTO DIET - Roma, 26 Ottobre 2010

Valeria Anastasio

Tutor: Pierfrancesco Lombardo

Optimization of Multistatic Passive Radar GeometryOptimization of Multistatic Passive Radar Geometry

Valeria Anastasio

Tutor: Prof. Pierfrancesco Lombaardo

Passive Bistatic Radar (PBR)

Passive Bistatic Radar exploits existing transmitters as illuminators of opportunity to perform target detection and localization.

Advantages:

fraction of direct signal received by SL/BL of the SURV antennastrong clutter/multipath echoes, and echoes from other strong targets at short ranges.

- continuous wave and low power levels long integration time- high sidelobes of the ambiguity function with a time-varying structure

The transmitted waveform is not under control of the radar designer:Drawbacks:

Target echoes can be masked

by:

- low cost - covert operation, low

vulnerability - reduced impact on the

environment

26/10/2010 Valeria Anastasio – Dottorato di Ricerca in Telerilevamento (XXIV ciclo)Multistatic Passive Radar

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Objective of the work

PBR performance can be largely improved through multistatic operation

However, its performance largely depend on the geometric configuration

We aim at optimizing the geometric configuration based on:

CRLB for Passive Multistatic Radar SystemAccount for Pd<1 , i.e. with uncertain observationGeometrical constraints for PBR receiver placement


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Case Study

Sub-Case APd=1 σε=2000m

Sub-Case BPd=1 σε=f(SNR)

Sub-Case C:Pd=f(SNR) σε=2000m

Sub-Case D:Pd=f(SNR) σε=f(SNR)

Optimize the geometric configuration of a multistatic passive radar composed of 2 TXs and 1 RX:

-selecting the best TXs couple among the available ones;-selecting the best receiver position

TX1

TX2

TX3

TX4TX5

TX6

TX7

TX8

TX9

TX10

TX11

TX12

TX13

TX14

TX15

TX16

TX17

AMB


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Case Study - parameters

Considering the following parameters:

Transmitters power Pt=10 kW; Transmitter antenna gain: Gt=0 dB;Wavelength: λ=3 m; Receiver antenna gain: Gr=7 dB;Receiver bandwidth: B=200 kHz;Receiver equivalent noise: NF=30 dB;Time of integration τ=1 s;Radar Cross Section: RCS=1 m2; Propagation loss: L=10 dB;


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The Signal to Noise Ratio can be evaluated in the following manner:

And the measurements accuracy is:

Considering a Swerling I target model, the Detection Probability is:

with

nFrts

nrttn LNRRkT

GGPSNR

nn

nn

223

2

)4( πτσλ

=

nn SNR2B

c=εσ

nSNR11

fand PP += 4fa 10P −=

with n=1,..,N N is the # of bistatic couples

Signal to Noise Ratio & Pd


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CRLB for a Multistatic Passive Radar

Considering N bistatic couples each one performing K range measurements having a Gaussian probability density function:

with expected value:

and variance:

Assuming that all the observation are statistically independent, the joint probability of the NxK measurements:

Where

kn,kn,kBn, ε)y,x(RR += with n=1..N and k=1..K

.

( )( )

( )∑∑

= = =

−−

= =∏∏

N

1n

K

1k2

k,n

2k,nk,Bn RR

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N

1n

K

1kk,n

B e2

1Rp εσ

εσπ

{ }KkNnRR knBB ,..1 ;,..1 ,, ===

{ } )y,x(RRE kn,kBn, =

{ }( ){ } 2n

2kBn,kBn, RERE εσ=−


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Defining the estimation parameters set:

The element (j,h ) Fisher Information Matrix can be written as follows:

The element (j,h) of the FIM can be written as follows:

The variance of the estimation error of the parameter Θj is:

( ){ } { }jj122

jj Jˆ Ej

−Θ =σ=Θ−Θ

CRLB for a Multistatic Passive Radar

]y,x[=Θ

( )( ) ( )( )

Θ∂∂

Θ∂∂

=h

B

j

Bh,j

RplnRplnEJ

( )( ) ( )

∑ ∑= =

Θ∂∂⋅

Θ∂∂

=N

1n

K

1k h

k,n

j

k,n2

nh,j

RR1Jεσ


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Defining a binary variable dn,k as follows:

with k=1..K and n=1..N

The n-th couple can form 2K possible detection/miss sequences and the m-th sequence will be:

with a number of detections and a number of misses

With a probability of occurrence:

CRLB with Uncertain Observations

= k n k n

time at target the missessensor the if 0, time at target the detectssensor the if,1

d k,n

)(K,n

)(2,n

)(1,n

)(K,n ,...d,d d:S mmmm with m=1,..2K

∑=

=∆K

1k

)(k,n,K,n d m

m mm ,K,n,K,n K ∆−=∆

{ } ( ) llm ,K,n

n

,K,n

n dd)(K,n P1PSPr ∆∆ −⋅=

∆∆


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=

1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1

S


Sensor #1Pd1

RB1=RTX1+RRX

Sensor #2Pd2

RB2=RTX2+RRX

Considering N bistatic couples and K range measurements eachwe will have L=(2K)N possible sequences

lS

with

With K=2 and N=2:


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{ }( )∑ ∑= = =ε

∑Θ∂

∂Θ∂

∂σ

=NK2

1l

N

1n

K

1k

)l(k,n

h

Bn

j

Bn2n

)l(h,j dRR1SPrJ

The CRLB is then the average over the scenario dependent values. The weighted mean of all the possible covariance matrix. The weight will be the probability of occurrence of the particular detection/miss sequence

Assuming the target movement is negligible, the element (j,h) of the Fisher Information Matrix is:

target detected or missed

Sum over the total number of measurements for each sensor: K=2

Sum over all the possible detection/miss sequences



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2D Localization Accuracy

The expression of the 2D accuracy:

Best receiver position

the one that minimizes the maximum estimation error of the target positions on the whole trajectory.

{ } { }221

1112

y2xH JJ −− +=+= σσσ


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A. Pd=1, σε=2000m B. Pd=1, σε=f(SNR)

C. Pd=f(SNR), σε=2000m D. Pd=f(SNR), σε=f(SNR)

Results TX3-TX5


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A. Pd=1, σε=2000m B. Pd=1, σε=f(SNR)

C. Pd=f(SNR), σε=2000m D. Pd=f(SNR), σε=f(SNR)

Results TX12-TX17


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Results

Couple Estimation ErrorPd=1,

σε= 2000m

Estimation ErrorPd=f(SNR), σε= f(SNR)

1-4 1442,2 m 46.1 m

3-5 1450,5 m 65.5 m

1-3 (1-5) 1739,0 m 69.0 m

2-5 (3-6) 1396,2 m 79.8 m

2-4 (4-6) 1475,5 m 82.7 m

3-4 (4-5) 2452,0 m 86.8 m

4-7 (4-9) 1316,1 m 99.6 m

4-15 (4-17) 1308,2 m 186.4 m

12-15 (12-17) 1308,2 m 257.9 m


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Antenna Beam Pattern and geometrical constraints

In order to localize a target on a specific trajectory:The whole trajectory shall be within the receiver main beamThe TX direct signal shall arrive in the back lobe of the RX antenna.The target Doppler frequency shall not be equal to zero.

α: -3dB beamwidth

γ: low level back-lobes angular region

β: two intermediate angular regions


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Main beam steeringAdmissible region: outside the two circles passing for points A and B, and with centre O and O’, such that angles AOB and AO’B are equal to 2α.

Direct signal attenuationAdmissible region: inside the two circles with Centres in Q and Q’, passing for both target (TGT) and transmitter (TX) locations, such that angles TGT-Q-TX=2β and TGT-Q’-TX=2β.

Zero DopplerAdmissible region: (i) the angle between TX-target line and velocity vector has to differ from the angle between RX-target line and velocity vector. (ii) The receiver cannot be placed on the TX-Target line.

Geometrical Constraints


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Geometrical constraints: results

Antenna Beam pattern:-3dB beamwidth: α=90°Low level back-lobes angular region: γ=180°Two intermediate angular regions: β=45°

Transmitters couples that do not allow the receiver placement:1-4; 1-12 (4-8); 4-16; 8-12; 12-16; 4-7 (4-9); 4-15 (4-17).

TX12-TX17 TX3-TX5


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m116H =σ

Localization Accuracy with constraints

TX12-TX17

TX3-TX5

m258H =σ

m512H =σ

m66H =σ


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Real Geography :11°-14°E ; 41°-43°N


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Selected Transmitters

Trasmettitore Latitudine Longitudine

1 Ausonia 41°21’49” 13°13’13”

2 Campocatino 41°49’55” 13°20’9”

3 Formia 41°16’52” 13°40’57”

4 Gaeta 41°12’26” 13°34’39”

5 Guadagnolo 41°54’43” 12°55’48”

6 Monte Cavo 41°45’15” 12°42’36”

7 Monte Favone 41°36’1” 13°37’56”

8 Monte Pilucco 41°19’36” 13°17’20”

9 Roma Monte Mario 41°55’6” 12°26’44”

10 Segni 41°41’47” 13°1’23”

11 Settefrati 42°40’20” 13°51’10”

12 Sezze 41°29’30” 13°4’46”

13 Terminillo 41°27’24” 12°57’35”

14 Velletri 41°41’46” 12°43’9”

15 Città Del Vaticano 41°54’13” 12°27’0”

16 Civitavecchia 42°5’1” 11°47’1”

17 Monte Argentario 42°23’60” 11°10’0”


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Real Geography :11°-14°E ; 41°-43°N


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Coast profile


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A. Pd=1, σε=2000m: TXs :5.Guadagnolo–17.Monte Argentario


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Best Receiver Position:

42° 24’ 51.5” N – 12° 22’ 0.3”E

m5.1339H =σ

Best Receiver Position in Line of Sight:

42° 24’ 24” N – 12° 12’ 10”E

m6.1385H =σ

D. Pd=f(SNR), σε=f(SNR) TXs : 15. Città del Vaticano – 16. Civitavecchia


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Best Receiver Position:

41° 56’ 01.3”N – 12°11’42”E

m7.74H =σ

Best Receiver Position in Line of Sight:

42° 09’ 16” N – 11° 54’ 31”Em1315H =σ

Area di interesse

-1 -0.5 0 0.5 1

x 105

-8

-6

-4

-2

0

2

4

6

8

10

12

x 104

Area Of Interest:Radius 40kmTarget flying at 8000 m of altitude3D localization

Among the available 136 TXs couples, only 14 couples fulfill the constraints


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Surveillance of an Area Of Interest

The whole Area of Interest shall be withinthe receiver main beam


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Admissible receiver positions:

d(RX,C)>d

The TXs direct signals shall arrive in the back lobe of the RX antenna:

Admissible receiver positions:

β>45°& β’>45°

z

x

τU

Transmitter

τu= 85°τ i= 0°


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z

x

ε

δ

Receiver

δ = 1°ε= 86°

TXs elevation beam pattern

RXs elevation beam pattern

TX8 - TX13

x (m)

y (

m)

-1 -0.5 0 0.5 1

x 105

-8

-6

-4

-2

0

2

4

6

8

10

12

x 104

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000TX13 - TX17

x (m)

y (

m)

-1 -0.5 0 0.5 1

x 105

-8

-6

-4

-2

0

2

4

6

8

10

12

x 104

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Monte Pilucco-Terminillo Terminillo-Monte Argentario


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Results: best TXs couples

α=90°γ=180°β: 45°

Conclusions

We derived a version of the CRLB for the localization of a target by amultistatic passive radar for uncertain observationsAn effective procedure has been devised to optimize the geometricconfiguration of a multistatic passive radar, that accounts for

Varying SNR with bistatic range Uncertain observations;Constraints to be fulfilled for proper operation of the PBR receivers

The procedure allows to jointly select the couples of TXs to be used and the optimal receiver position.


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Future worksTarget tracking accuracy thanking into account the uncertainty of the measurementsAnalysis and design of multi receiver systemDesign of a net of Passive Radar Systems in order to monitor and localize the targets flying in the airspace

Essential Biography

A. Farina, B. Ristic, L. Timmoneri, “Cramér–Rao Bound for Nonlinear Filtering With Pd<1 and Its Application To Target Tracking” – IEEE Transaction on Signal Processing, Vol 50, No 8, pp 1916-24, Aug. 2002.M. Hernandez, B. Ristic, A. Farina, L. Timmoneri, “A Comparison of Two Cramér–Rao Bounds for Nonlinear Filtering with Pd<1” – IEEE Transaction On Signal Processing, Vol 52, No 9, pp 2361-70, Sept. 2004.A. Farina, A. Di Lallo, L. Timmoneri, T. Volpi, B. Ristic, “CRLB and ML for parametric estimate new results” – Jan. 2005

PublicationsOptimization of Multistatic Passive Radar Geometry Based on CRLB with Uncertain ObservationsV. Anastasio, F. Colone, A. Di Lallo, A. Farina, F. Gumiero, P. Lombardo– EuRAD 2010


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Multistatic Passive Radar Geometry Optimization for Target 3D Positioning AccuracyF.Gumiero, C.Nucciarone, V. Anastasio, F. Colone, P. Lombardo - EuRAD 2010

optimization of multistatic passive radar geometry

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