New Method by only TOA for Multi-station Passive Location in Uncommon-view

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International Journal of Information and Computer Science (IJICS) Volume 4, 2015 doi: 10.14355/ijics.2015.04.012

New Method by only TOA for Multi-station Passive Location in Uncommon-view Feng Qi, Li Tingjun, Wang Qinjian, Zhang Haibo, Zhang Yang Naval Aeronautical and Astronautical University, Yantai 264001, China Litingjun99@126.com Abstract For the performance that almost all the methods of the multiple stations passive location will be invalid in the uncommon-view, this paper proposes a new method using only the time of arrival (TOA) in this situation. This paper produces the TOA train of every net point and the one that is most like of the real train is the excellent. Then the paper analyzes how the components affect the location precision such as the TOA-error, the distribution of the stations, the distances between the substations and the main-station and the observation time. The result of the emulation proves that without the error of station address and the synchronous the location can realize the CRLB almost.

Keywords Uncommon-view; TOA Process; Passive Location

Introduction The technology of the multiple stations passive location can look for information on the location of the non-cooperative target of fast, accurate, and concealment. It has been one of extensive research hotspot issues in electronic warfare [1, 2]. For example, reference [3] put forward multiple observers system with TDOA and FDOA combined localization algorithm and precision analysis, which we only know height information; reference [4] studied multi-platform time and position tracking algorithm and precision of the positioning system analysis, calibration of time and space and platform configuration affects positioning of classic.

Almost researches proceed by common-view at present, but common-view is difficult to meet the prerequisites in actual. Physical obstacles block the signal propagation path with the target radiation source and observation station. Based on the ideas, this paper puts forward a new geolocation method with only the TOA under the uncommon-view condition.

For realizing only by TOA information location in uncommon-view, this paper puts forward a guess: for pulse train signal of the target radiation source, no matter what kind of way PRI changes, it exists a fixed inward counting circle Tp , meets t= t0 + N i T p i

(1)

In the formula, t0 expresses time of the first pulse. ti expresses time of the i th pulse. N i is counting integer in the source of radiation, and Tp expresses inherent interval with the first pulse and the i th pulse.

Uncommon-view Mathematical Model by Only TOA Location Supposing there are M observation stations in the observation area. The location of Target radiation source is X .

Every station can receive j = 1, 2, , m j pulses, the location of the m th station receiving j th pulse is S m, j , the time

tm, j can be expressed as tm , j = t0 +

1 1, 2, , M , j = 1, 2, , m j X − S m, j + N m, j Tp + δ m, j , m = c

(2)

In the formula, c is the speed of electromagnetic wave in the air, δ m, j is the measuring error of TOA. Supposing it

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International Journal of Information and Computer Science (IJICS) Volume 4, 2015

(

obeys N 0, σ m2 , j

)

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zero mean Gaussian model, and the measuring error of TOA in different pulses has no

relationship.

We can know from the formulas above, tm, j expression has six unknown quantities: t0 , X, Tp , N m, j , the question has turned in how to evaluate the location of Target radiation source X by measuring sequence of TOA, tm, j .

Uncommon-view Location Algorithms by Only TOA Position Iterative Estimation Get tm, j Taylor expansion at target initial value, give up the secondary and higher item available.

tm , j

(

)

ˆ 1 ˆ 1 X − S m, j =t0 + X − S m, j + ˆ −S c c X m, j

T

( X − Xˆ ) + N

m, j Tp

+ δ m, j

(3)

clear up

( Xˆ − S )

T

ctm, j

ˆ −S − X m, j +

m, j

ˆ −S X m, j

( Xˆ − S )

T

ˆ = ct + X 0

m, j

ˆ −S X m, j

X + cN m, j Tp + cδ m, j

(4)

Make r0 = ct0 , so Formula (4) can be expressed by matrix form (5)

= b Gθ + ε

Indeed,

( Xˆ − S ) +

T

m, j

ˆ −S bm, j = ctm, j − X m, j   1   G =    1 

ˆ −S X m, j

( Xˆ − S )

T

1,1

ˆ X

ˆ -S X 1,1 

cN1,1 

( Xˆ - S )

T

M ,m j

ˆ -S X M ,m

ˆ cN X M ,m

j

j

T

ˆ, X      ,    

(6)

T

b = ε c δ1,1= θ  r0 , x, y, z , Tp  . = b , b , , bM , m  , , δ1,2 , , δ M , m  ,  1,1 1,2    j

T

j

Formula (5) shows meeting the linear relationship between b and θ . Because of Theorem Gauss-Markov, if rank (G ) = 5 (Different pulse position in the pulse train then N m, j is different, so that the number of pulse is greater than 5, which is easy to meet), parameter vector θ exits optimal unbiased method, and is expressed as,

(

θˆ = G T Q -1G

)

-1

(7)

Q -1G T b

In the formula, Q is covariance matrix of measurement error vector ε . According to mathematical model in

(

)

Chapter One, we can get that the error δ m, j obey the zero mean Gaussian distribution N 0, σ m2 , j , and the TOA measure error of different pulse has norelationship. So that,

(

2 2 Q = c 2 diag σ 1,1 , σ 1,2 , , σ M2 , m j

)

(8)

If TOA measurement error of every pulse is equal, then σ= σ 1,1= σ 1,2=  = σ M , m , so that error vector covariance j

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International Journal of Information and Computer Science (IJICS) Volume 4, 2015

matrix Q can be expressed as Q = c 2σ 2 I , indeed, I is unit matrix. The optimal unbiased solution of parameter vector θˆ can be come down to:

(

θˆ = G T G

)

-1

(9)

G Tb

The above process can be iterative times to the parameter vector θˆ convergence, so that the target location ˆ = θˆ ( 2 : 4 ) . is X However, iteration can convergence mainly depend on the selection of target initial position. So, in order to ensure convergence, the grid search method can be used. According to the estimate of the target distance and wave direction angle estimation, we can structure grid area Z . For each grid point is estimated according to the process.

Each grid point and calculate the cost function J Tp , optimal target location estimation is shown as,

( )

  tm' , j − t0  tm' , j − t0 = J Tp − ∑  Tp  Tp m, j    ˆ = arg min J T X

( )

( p)

X∈Z

   

2

(10)

Simulated Analysis To checkout new method by only TOA for multi-station passive location in uncommon-view condition, this chapter uses MATLAB to make digital simulation. Simulation environment is: The location of the target source is X=[0, 600km, 5km], target speed is 300m/s, The observatory is located in the origin of coordinates, the remaining three station locations are [-15km, 0, 0]，[15km, 0, 0] and [0, -15km, 1km].

The simulation source signal characteristics are: each pulse can only be one or two stations to receive; each station can realize online measurement of pulse arrival time at the same time, but you can't get jet lag information matching. Signal average repetition frequency is 1 kHz, repetition frequency shake is 30%, radiation source emission pulse number is 1000, pulse loss rate is 50% then only 50% pulse can be received by four stations to process location. The observation time is about 1s, target motion distance is 300m about observation time.

Assume that the goal of initial position error is about 30km, corresponding to the accuracy of positioning error of 5%. TOA measurement error is different and has no observation location error measuring TOA only under the condition of the change of position error as shown in figure 1. If considering observation position measurement error, assuming observatory site 15 m absolute position error, the relative position error of 1km, the positioning error curve along with the change of TOA measurement error is shown in figure 2.

2

2

10

10

1

1

10

rmse(km)

rmse(km)

10

0

10

-1

-1

10

10

CEP CRLB 0.5%R

-2

10

0

10

0

10

2

1

10

10

-2

3

10

TOA Error(ns)

FIG. 1 EFFECT OF TOA MEASUREMENT ERROR

CEP CRLB 0.5%R

10

0

10

2

1

10

10

3

10

TOA Error(ns)

FIG. 2 LOCATION ERROR WITH THE POSITIONING ERROR

From Figure 1, without considering observation location error and system clock synchronization error, the positioning error is close to CRLB. When the standard deviation of TOA error is 35ns, the simulation statistics can

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International Journal of Information and Computer Science (IJICS) Volume 4, 2015

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be 3km of circular error probability, positioning accuracy is up to 0.5%.

As shown in figure 2, with small TOA measurement error, the position error is larger; as TOA measurement error increases, the effect on location error is not obvious.

Conclusion For more than under the condition of not depending on the uncommon-view station passive location method mostly failure problem, the paper puts forward an uncommon-view passive location method only by TOA information. The simulation results show that without considering the site error, the algorithm localization accuracy is very close to the CRLB offline, and site error only has significant effects in TOA measurement error is small.

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[1]

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[2]

Shan Yuehui, Sun Zhongkang, Huang Fukan. The Developing Passive Location Technology [J], Aerospace Electronic WarfareďźŒ2002 (3):36-42.

[3]

Ho K C, Chan Y T. Geolocation of a Known Altitude Object from TDOA and FDOA Measurements [J]. IEEE Transactions on Aerospace and Electronic Systems, 1997, 33(3):770-783.

[4]

Wang Han. Research on Some Critical Technology of TDOA Passive Location System of Airborne Multi-Platforms [D].

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[5]

Fogel E, Gavish M. Parameter estimation of quasi-periodic sequences [C]. IEEE ICASSP, 1988: 2348-2351.

[6]

Ye Haohuan, Liu Zheng, Jiang Wenli. Maximum-likelihood pulse repetition interval estimation based on adaptive periodgram peak searching [J]. Journal of Astronautics, 2012, 33(5): 635-641.

[7]

Casey S D, Sadler B M. Modifications of the Euclidean algorithm for isolating periodicities from a sparse set of noisy measurements [J]. IEEE Trans Signal Process 1996, 44(9): 2260-2272.

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