The Use of Software-Defined Radio Systems in Multilateral Navigation ...

The Use of Software-Defined Radio Systems...

INFOCOMMUNICATIONS JOURNAL

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The Use of Software-Defined Radio Systems in Multilateral Navigation Radio Systems G. M. Mashkov, E. G. Borisov, A. G. Vladyko, and A. I. Gomonova Abstract — The paper describes an optional application of software-defined radio systems technology in multilateral range finding systems for solving tasks of determining the flying objects coordinates. The design feature of the described system is the use of cooperative processing of range measurements aggregate to improve accuracy of object positioning. Keywords — multilateral, range measurements, cooperative processing, mean square error (MSE), and software-defined radio systems (SDR).

I. INTRODUCTION AND PROBLEM DEFINITION The last decade has shown a significant growth in passenger and cargo air traffic, as well as a considerable increase of flights of privately owned aircraft. This leads to growing of air traffic density, overloading of airfield areas and flight routes. Besides, constantly tightened security requirements place higher demand on the accuracy of flying objects positioning in the shortest possible period. That is the reason why the developing of multi-position navigation radio stations is being carried out worldwide nowadays (for range finding only as well as for range finding and multilateration – MLAT together). Multilateral radio systems represent an independent cooperative navigation system of a new type, combining in single unit measurement subsystems, means of communication, data transfer, and computing devices. An example of such system is the MLAT system developed by Czech company Era [1]. Successful achievements in this field have been achieved by the French multinational group “Thales” [2]. The multilateral surveillance system “Mera”, developed by NIIRA JSC [3], is actively used in this country. Multilateral navigation system, developed by Australian company “Locata”, incorporates pinpoint accuracy characteristic, working in the 2.4 GHz frequency range [4]. General requirements for multilateral systems are given in [5]. The need for the emergence of such systems arrived due to the fact that the existing satellite navigation systems (GPS, GLONASS, and prospective European GALILEO system), have the following main disadvantages: low resistance when exposed to electronic interference, low signal value, complexity of working indoors, as well as in areas of dense urban Manuscript received May 12, 2015, revised June 12, 2015. The authors are with the Bonch-Bruevich Saint Petersburg State University of Telecommunications, 22 Prospekt Bolshevikov, Saint Petersburg, Russia (e-mail: [email protected]).

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development, in the mountain gorges, etc. Furthermore, the aforementioned systems lack positioning accuracy in urban areas and to the North of the 60o parallel. The positioning error of GPS/GLONASS can reach over 30 m and more. The main advantages of MLAT systems in comparison with single position systems are the following: the possibility to form spatial view areas of complex configuration with a given overlap ratio, the ability to control and redistribute energy within the system, precise accuracy of flying objects positioning, the ability to measure objects complete velocity vector, etc [6, 7]. II. BASIC PRINCIPLES OF MLAT SYSTEM DESIGN. NI USRP SOFTWARE-DEFINED RADIO SYSTEMS TECHNOLOGY For mass adoption, MLAT systems need to have a low cost of installation with minimum operating costs, small size combined with low power consumption by using different power supply, easy to build up, update and reconfigurable hardware platform. It is necessary to allow the operation of navigation equipment developed in conjunction with the systems used in the management of air traffic, such as ADS-B (Automatic dependent surveillance-broadcast) and their modifications, enabling the pilots in the cockpit and air traffic controllers on the ground point to observe the traffic of aircraft movements with greater accuracy and receive aeronautical information. The instruments of software-defined radio systems could be used as prospective MLAT system transceiver modules. It would allow carrying on the tasks of generating signals of any modulation type, range finding, communication with an object being located, an exchange of information between modules, synchronization of functioning modes of the modules, and optimization of frequencies allocation inside the system etc. Software-defined radio system is a radio communication system in which the functions of the main instruments are implemented by software solutions. These instruments can include filters, amplifiers, modulators or/and demodulators. As soon as these instruments are configurable by software only, there is a possibility of modifying such a system without any significant changes in the hardware configuration. When using SDR, almost the entire volume of work on signal processing is shifted to the software that can run on digital signal processors or special DSP-purpose high-speed PLD. The main reason for such an approach is to create a system that can receive and transmit radio signals in a given frequency range and easily select the desired modulation law [10]. National Instruments Corporation proposes its own solution - NI USRP (NI Universal Software Radio Peripheral). It is a

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The Use of Software-Defined Radio Systems...

22 2 HF HF transceiver transceiver controlled controlled by by aa computer. computer. The The company company offers offers HF functional transceiver controlled by a computer. The company offers the the functional abilities abilities of of aa graphical graphical development development environenvironthe functional abilitiesconfiguring of a graphical development environment ment NI NI LabVIEW LabVIEW for for configuring SDR SDR platform. platform. Due Due to to the the ment NI LabVIEW for configuring SDR platform. Due to the programmability programmability of of the the measuring measuring equipment, equipment, this this isis aa unique unique programmability of the measuring equipment, this is a unique possibility possibility to to generate generate periodic periodic test test signals, signals, depending depending on on nanapossibility to generate periodic test signals, depending on navigation receiver trajectory, i.e. there is no need vigation receiver trajectory, i.e. there is no needfor forcostly costlytests tests vigation receiver trajectory, i.e. there isThe no needUSRP for costly tests with withparticipation participationof ofair airtraffic trafficcontrol. control. TheNI NI USRPsoftware software with participation of air traffic control. The NI USRP software contains contains aa set set of of functions functions implemented implemented in in the the form form of of virtual virtual contains a set of functions implemented in the form of virtual instruments instruments (VIs (VIs for for LabVIEW) LabVIEW) to to control control one one or or more more platplatinstruments (VIs for LabVIEW) to control one or more platforms forms for for USRP. USRP. At At the the higher higher level, level, NI NI USRP USRP driver driver proproformstofor USRP. At the higher level, NI USRPofdriver proposes use Vis for session opening, configuring hardware, poses to use Vis for session opening, configuring of hardware, poses to use Vis for session operations, opening, configuring of hardware, performance of read/write and session closing. performance of read/write operations, and session closing. performance of read/write operations, andcreation session closing. The The basic basic principle principle of of programming programming isis the the creation of of virtual virtual The basic principle of programming is the creation of virtual objects: objects: aa satellite, satellite, positions positions of of aa receiver receiver and and an an HF HF genegeneobjects: a satellite, positions of a receiver and an HF generator. rator.Each Eachobject objectisisbeing beingoperated operatedby byaa link linkspecially speciallydesigndesignrator.for Each object is being operated by aproperties, link specially designated it in the software. All of the status ated for it in the software. All of the properties, status and and ated for it exercised in the software. All of the properties, status and control control are are exercised by by using using functional functional tools tools incorporated incorporated control are exercised by using functional tools incorporated into intothe theset setof ofbuilt-in built-inlibraries librariesfor forvisualization visualization[11]. [11]. into the set of built-in libraries for visualization [11]. Figure Figure 11 shows shows aa scheme scheme of of the the MLAT MLAT navigation navigation system, system, Figure 1 shows a scheme of the MLATpoints navigation system, consisting consisting of of NN ground-based ground-based transceiver transceiver points (GTP); (GTP); each each consisting of N ground-basedsignal transceiver points (GTP); each point point emitting emitting aa broadband broadband signal on on aa lettered lettered frequency. frequency. point emitting a broadband asignal on a lettered frequency. Onboard Onboard equipment equipment contains contains a multi-channel multi-channel transceiver, transceiver, rereOnboard equipment contains a multi-channel transceiver, receiving signals from GTP, and then relaying them. ceiving signals from GTP, and then relaying them.Each Eachof ofthe the ceiving signals from GTP,receives and then relayingsignals them. Eachtoofthe the spatially spatially separated separated GTPs GTPs receives relayed relayed signals due due to the spatially separated GTPs receives relayed signals due to the request request from from each each position, position, thus thus forming forming range-finding range-finding and and request from each position, thus forming range-finding and summarized summarized range-finding range-finding measurements. measurements. One One of of the the GTPs GTPs isis summarized range-finding measurements. One measurements of the GTPs is nominated nominated as as aa primary primary point point and and takes takes all all the the measurements nominated as a primary point and takes all the measurements from from the the others others (thus (thus implementing implementing cooperative cooperative processing), processing), others (thus implementing cooperative processing), from the calculates calculates estimates estimates of of rectangular rectangular coordinates coordinates and and speed speed of of calculates estimates of rectangular coordinates and speed of their theirchange. change. their change. HH H

TT T

(x (xNN,y ,yNN)) (xN,yN)

RR33 R3

XX X

(x (x11,y ,y11)) (x1,y1) (x (xt,t,yyt)t) (xt, yt)

(x (x33,y ,y33)) (x3,y3)

RR22 R2

00 0

YY Y

Fig.1 Fig.1Layout Layoutof offlying flyingobject objectpositioning positioning Fig.1 Layout of flying object positioning

(x (x22,y ,y22)) (x2,y2)

For For this this case case let let us us write write aa system system of of linear linear algebraic algebraic For this(SLAE), case letwhich us write system of linear algebraic equations takes account the of equations (SLAE), which takesainto into account the number number of equations (SLAE), which takes intomeasurements account the number of direct and N(N-1) -- ,,formdirect хх--NN andsummarized summarized N(N-1) measurements formdirect хmeasurements, - N and summarized N(N-1) measurements - , formi.e.: ing NN22measurements, i.e.: ing ing N2 measurements, i.e.:

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(1) (1) (1)

RˆRˆ11,,RˆRˆ22… …RˆRˆN --primary primarymeasuring measuringthe theslant slantrange; range; Rˆ1 , Rˆ 2 … Rˆ NN - primary measuring the slant range; ˆ ˆ ˆ , … the primary measure summary ˆ ˆ ˆ RR1212 ,RR2121 …RRNN( N( N−−11) ) - the primary measure summaryranges. ranges. Rˆ12 , Rˆ 21 … Rˆ N ( N −1) - the primary measure summary ranges.

2 Equations estiEquations(1) (1) contain contain measurements measurementsrelative relative to to NN22estiestiEquations (1) contain measurements relative to N mated mated parameters parameters that that allow allow us us to to implement implement their their solution solution mated parameters that allow us to implement their solution using usingthe theleast-squares least-squaresmethod method[8,9]: [8,9]: using the least-squares method [8,9]:

[([[((

]]]

−− 11 T ~ TT −1 −1 XX~ W −1AA −1AATΛΛW W −1 HH,, ~ == AA ΛΛW X = AT ΛW −1 A AT ΛW −1 H ,

)) )

(2) (2) (2)

2 where consisting of of zezewhere AA isis the the matrix matrix of of dimension dimension NxN NxN22,, consisting , consisting of zewhere A is the matrix of dimension NxN ros ros and and ones, ones, where where "1" "1" indicates indicates the the presence presence of of corresponding corresponding ros and ones, whereits"1" indicates the presence of corresponding dimension, dimension,and and"0" "0" itsabsence. absence. dimension, and "0" its absence. So, So, for for three-position three-position system, system, this this matrix matrix has has the the following following So, for three-position system, this matrix has the following form: form: form: 11 00 00 11 11 11 11 00 00 (3) (3) 1 0 0 1 1 1 1 0 0 ,, AAТТ == 00 11 00 11 11 00 00 00 00 , (3) Т

A = 0 00 0

1 00 0

0 11 1

1 00 0

1 00 0

0 11 1

0 11 1

0 11 1

0 11 1

--matrix matrixsystem systemcondition, condition,taking takinginto intoaccount accountthe thetotality totalityof of - matrix system condition, taking into account the totality of the theprocessed processedmeasurements; measurements; the processed measurements;

HHТТТ == RˆRˆ11,,RˆRˆ222 line vecvec2RˆRˆN ,,RˆRˆΣ12 ,,RˆRˆˆΣΣ2121,,RˆRˆˆΣΣ1313,,RˆRˆˆΣΣ31312 2RˆRˆˆΣΣNN( (NN−−11) ) -- line - line vecH = Rˆ1 , Rˆ 2 2 Rˆ NN , Rˆ ΣΣ12 R R R , , , Σ 21 Σ13 Σ 31 2 RΣN ( N −1) 12 tor tor of of the the estimated estimated parameters parameters (vector (vector row row of of primary primary meameator of the estimated parameters (vector row of primary measurements); surements); surements);

RR11 R1

RRNN RN

RˆRˆ1 ==11⋅ ⋅RR1 ++00⋅ ⋅RR2 ++00⋅ ⋅RR3 ++2 2++00⋅ ⋅RR  Rˆ1 = 1 ⋅ R1 + 0 ⋅ R2 + 0 ⋅ R3 + 2 + 0 ⋅ RNN N RˆRˆ212==00⋅ ⋅RR111++11⋅ ⋅RR222++00⋅ ⋅RR333++2 2++00⋅ ⋅RRNN meas. .  Rˆ 2 = 0 ⋅ R1 + 1 ⋅ R2 + 0 ⋅ R3 + 2 + 0 ⋅ RN NNmeas N meas.  Rˆˆ = 0 ⋅ R + 0 ⋅ R + 0 ⋅ R + 2 + 1 ⋅ R 11 + 0 ⋅ R 22 + 0 ⋅ R 33 + 2 + 1 ⋅ R NN = 0 ⋅ R NN  R Rˆ = 0 ⋅ R + 0 ⋅ R + 0 ⋅ R + 2 + 1 ⋅ R Rˆˆ N = 1 ⋅ R1 + 1 ⋅ R 2 + 0 ⋅ R 3 + 2 + 0 ⋅ R N  RΣ12 = 1 ⋅ R1 1 + 1 ⋅ R2 2 + 0 ⋅ R3 3 + 2 + 0 ⋅ RNN  Rˆ ΣΣ12 12 = 1 ⋅ R1 + 1 ⋅ R2 + 0 ⋅ R3 + 2 + 0 ⋅ RN RˆRˆΣΣ2121==11⋅ ⋅RR1 1++11⋅ ⋅RR2 2++00⋅ ⋅RR3 3++2 2++00⋅ ⋅RRNN ˆ  R ˆ Σ 21 = 1 ⋅ R1 + 1 ⋅ R2 + 0 ⋅ R3 + 2 + 0 ⋅ RN 2++00⋅ ⋅RRNN RRˆˆΣΣ1313==11⋅ ⋅RR1 1++00⋅ ⋅RR2 2++11⋅ ⋅RR3 3++2 NN((NN−−11))mmeas eas. . 2 + 0 ⋅ RN RˆRˆ Σ13==11⋅ ⋅RR1++00⋅ ⋅RR2++11⋅ ⋅RR3++2 + 0⋅ R N (N − 1) meas.  RˆΣΣ3131 = 1 ⋅ R1 1 + 0 ⋅ R2 2 + 1 ⋅ R3 3 + 2 + 0 ⋅ RNN RΣ 31 = 1 ⋅ R1 + 0 ⋅ R2 + 1 ⋅ R3 + 2 + 0 ⋅ RN  RˆRˆΣΣNN( N( N−1−)1)==00⋅ ⋅RR1 1++00⋅ ⋅RR2 2++00⋅ ⋅RR3 3++2 2++11⋅ ⋅RRNN( N( N−1−)1)  Rˆ ΣN ( N −1) = 0 ⋅ R1 + 0 ⋅ R2 + 0 ⋅ R3 + 2 + 1 ⋅ RN ( N −1)

σσR2R22 σR

00 00 00 0 0 0 00 σσR2R2 00 00 W W == 0 σ R2 0 0 W = 00 00    0 0  22 00 00 2 2 σσRR∑∑ 0 0 2 σ R2 ∑

(4) (4) (4)

2 2 W containing the the W isis aa precision precision matrix matrix of of dimension dimension NN22 xx NN22 containing x N containing the W is a precision matrix of dimension N variance varianceof ofrange-finding range-findingerrors errorsand andthe thesums sumsof ofthe theranges: ranges: variance of range-finding errors and the sums of the ranges:

11 1 00 0 ΛΛ== 00 Λ= 0 00 0 00 0

00 0 11 1 00 0 00 0 00 0

00 0 00 0 11 1 00 0 00 0

00 0 00 0 00 0    00 0

00 0 00 0 00 0 00 0 11 1

(5) (5) (5)

ΛΛ isis aa diagonal diagonal matrix matrix of of coefficients, coefficients, the the diagonal diagonal element element Λ is a is diagonal to matrix ifofthe coefficients, the diagonal element of of which which is equal equal to one one if the measurement measurement isis present present (or (or isis of which is equal to one if the measurement is present (or is used used for for measurements) measurements) and and equal equal to to zero zero ifif the the measurement measurement for measurements) and equal to zero if the measurement isused not used. is not used. is not used.

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3 Error covariance matrix for the system (2) is defined as [8]

(

)

(

)

K Хˆ = ATW −1 A σ 02 = diag AT A σ 02 , −1

(6)

−1

where σ = σ = σ - is the variance of measurement error of the range-finding parameter. Therefore, for range-finding and summarized rangefinding systems the expression of angle ranges and variances of the measurement errors obtained with (2) and (6) will take the following form: - for three positions systems 2 0

2 R

7 ˆ 2 2 5 5 5 ~ R1 = R1 − Rˆ 2 − Rˆ3 + Rˆ Σ12 + Rˆ Σ 21 + Rˆ Σ13 + 27 27 27 27 27 27 5 ˆ 4 4 RΣ 31 − Rˆ Σ 23 − Rˆ Σ 32 27 27 27 ~ = − 2 Rˆ + 7 Rˆ − 2 Rˆ + 5 Rˆ + 5 Rˆ − 4 Rˆ − R Σ12 Σ 21 Σ13 2 1 2 3 27 27 27 27 27 27 4 ˆ 5 ˆ 5 ˆ RΣ 31 + RΣ 23 + RΣ 32 27 27 27

7 27 2 = diag AT A σ R2 = diag − 27 2 − 27

(

)

2 27 7 27 2 − 27 −

2 27 , 2 2 σR − 27 7 27 −

(

)

2 65 11 65 2 − 65 2 − 65 −

2 65 2 − 65 11 65 2 − 65 −

2 65 2 − 65 σ 2 2 R − 65 11 65 −

(10)

The rectangular coordinates of an object are determined by solving the system of equations 2 2 2 (11) R = ( xt − xi ) + ( yt − xi ) + (ht − hi ) , i = 1 ÷ N , xt , yt , ht - desired object coordinates;

xi , yi , hi - known coordinates of GTPs. The accuracy of estimating the location of an object we define by the dependence: (7)

~ = − 2 Rˆ − 2 Rˆ + 7 Rˆ − 4 Rˆ − 4 Rˆ + 5 Rˆ + R Σ12 Σ 21 Σ13 3 1 2 3 27 27 27 27 27 27 5 ˆ 5 ˆ 5 ˆ RΣ 31 + RΣ 23 + RΣ 32 27 27 27

2 σ RC

σ

2 Σ

2 RC

11 65 2 − 2 T 65 = diag A A σ R = diag 2 − 65 2 − 65

(8)

Where : tr matrix; ∂R1 ∂xt ∂R2 D = ∂xt  ∂RN ∂xt

−1 (12) σ = tr (DTW −1D ) - trace - the sum of diagonal elements of a

∂R1 ∂yt ∂R2 ∂yt

∂R1 ∂ht ∂R2 - conversion matrix. ∂ht

∂RN ∂yt

∂RN ∂ht

III. RESULTS OF CALCULATIONS. SCHEME OF THE EXPERIMENTS

Figures 2 and 3 show, as an example, the values of MSE for the range-finding of the objects driven in a circle with a radius of 200 km around the origin of coordinates. Figure 2 shows the MSE for range-finding for the normal law 11 9 9 9 2 9 4 4 ~ R1 = Rˆ1 + RˆΣ12 + RˆΣ13 + RˆΣ14 − Rˆ 2 + RˆΣ 21 − RˆΣ 23 − RˆΣ 24 − 65 65 65 65 65 65 65 65 of error distribution with σ=20 m at zero expectation value, 2 9 ˆ 4 4 2 4 4 9 ˆ and Figure 3 - for a uniform law of error distribution with a − Rˆ3 + RΣ 31 − RˆΣ 32 − RˆΣ 34 − Rˆ 4 − RˆΣ 43 − RˆΣ 42 + RΣ 41 65 65 65 65 65 65 65 65 maximum error ∆R=± 60 m. - for four positions system:

~ = − 2 Rˆ + 9 Rˆ − 4 Rˆ − 4 Rˆ + 11 Rˆ + 9 Rˆ + 9 Rˆ + R 2 1 2 Σ12 Σ13 Σ14 Σ 21 Σ 23 65 65 65 65 65 65 65 4 ˆ 2 ˆ 9 ˆ 9 ˆ 4 ˆ 2 ˆ 9 ˆ RΣ 24 − R3 − RΣ 31 + RΣ 32 − RΣ 34 − R4 − RΣ 43 + 65 65 65 65 65 65 65 4 ˆ 9 ˆ RΣ 42 − RΣ 41 65 65

(9)

~ = − 2 Rˆ − 4 Rˆ + 9 Rˆ − 4 Rˆ − 2 Rˆ − 4 Rˆ + 9 Rˆ − 4 Rˆ + R 3 1 2 Σ12 Σ13 Σ14 Σ 21 Σ 23 Σ 24 65 65 65 65 65 65 65 65 9 ˆ 9 ˆ 9 ˆ 2 ˆ 9 ˆ 4 ˆ 4 ˆ 11 ˆ + R3 + RΣ 31 + RΣ 32 + RΣ 34 − R4 + RΣ 43 − RΣ 42 − RΣ 41 65 65 65 65 65 65 65 65

2 4 4 9 ˆ 2 4 4 9 ~ R4 = − Rˆ1 − RˆΣ12 − RˆΣ13 + RΣ14 − Rˆ 2 − RˆΣ 21 − RˆΣ 23 + RˆΣ 24 − 65 65 65 65 65 65 65 65 2 4 4 9 11 9 9 9 − Rˆ3 − RˆΣ 31 − RˆΣ 32 + RˆΣ 34 + Rˆ 4 + RˆΣ 43 + RˆΣ 42 + RˆΣ 41 65 65 65 65 65 65 65 65

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4 σR,m

β, °

for range-finding system

120

20

150

60

2

30 1

180

10

for range-finding system with cooperative processing 0

100

200

300

0

100

200

210

β, °

330

240

Figure 2 – MSE for range-finding of the object for different methods of measurements processing (for normal distribution)

σ,m

300 270

Figure 4 – MSE for positioning of the object for different methods of measurements processing (1 – for range-finding system, 2 – for range-finding system with cooperative processing

σR,m

30

Fig. 5 shows MSE for positioning of object driven in a circle at a distance of 20 km around the origin of coordinates with GTPs stationed at a distance of 200 km from the origin.

for range-finding system with cooperative processing

β, ° 120

20

150

60

2

30 1

for range-finding system

10

180

0

10

20

210 0

100

200

300

Figure 4 shows MSE for positioning of object driven in a circle with a radius of 200 km around the origin of coordinates with ground transceivers stationed as a distance of 20 km from the origin.

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330

β, °

Figure 3 - MSE for range-finding of the object for different methods of measurements processing (for uniform distribution)

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30 σ,m

240

300 270

Fig. 5 - MSE for positioning of the object for different methods of measurements processing (1 – for range-finding system, 2 – for range-finding system with cooperative processing)

Fig. 6 shows, as an example, the object positioning MSE for normal distribution of range-finding and sums of ranges when the distance to the object relative to the origin is 200 km and the GTSs are located 20 km from the origin.

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5

β, °

120

60

2 150

30 1

50% of positions we see zeros. Meanwhile, using a conventional range-finding system, indirect measurement of rectangular coordinates in not possible to produce. But in the case of cooperative processing it is still possible to measure rectangular coordinates, but with reduced accuracy and, therefore, to provide algorithmic and informational stability of the system. 120

180

0

100 200 300

210

σ,m

β, °

60

150

30

330 180 240

0

300

100 200 300

Fig. 6 - MSE for positioning of the object for different methods of measurements processing (1 – for range-finding system, 2 – for range-finding system with cooperative processing)

Fig. 7 shows, as an example, MSE for positioning of the object at uniform distribution of positioning, range-finding and sums of distances errors when the object is 20 km from the coordinates origin, and GTSs are 200 km from the origin.

β, °

120

60

2

30 1

180

3

330

240

300 270

Fig. 8 - MSE for object positioning for different methods of measurements processing (1 – for range-finding system, 2 – for range-finding system with cooperative processing, 3 - for rangefinding system with cooperative processing at incomplete set of measurements)

The experiment was made on the NI USRP platform base, which contained four instruments, three of which worked as ground base stations, and the fourth imitated an airborne transponder. IV. CONCLUSIONS

0

20

40

210

σ,m 330

240

300 270

Fig. 7 – MSE for object positioning for different methods of measurements processing (1 – for range-finding system, 2 – for range-finding system with cooperative processing)

Fig. 8 shows MSE for the case of σ RΣ = 2 2σ R . And in case of such MSE values, the errors of positioning grow insignificantly (curves 1 and 2 respectively). Let us assume that from one round of measurements to the other round for some reason or another there is a lack of range measurements and sums of ranges do not exist, i.e. in matrix Λ (formula 5) in

30

210

2

σ, m

270

150

1

The aforementioned values of the errors of flying object positioning determination show that cooperative processing of positioning information with respect to the four positional system improves the accuracy of determining the flying object location more than two times in comparison with the conventional range-finding method. In so doing, the high positioning accuracy is achieved by one cycle of data processing within the system. The use of algorithms for filtering trajectory messages will further improve the accuracy of determining the coordinates, without restrictions on the flying object movement hypothesis. This extends the applicability of the proposed options for positioning of maneuvering objects. This work was done with the financial support of the Ministry of Education and Science of the Russian Federation as a part of an applied scientific research on lot ciphered 2014-14579-0112 and related to the program "The development of experimental model of multi-position fast deployment selfcontained radar system ground infrastructure for landing aircraft on unprepared ground” (application cipher “2014-14579-0112-030”).

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REFERENCES REFERENCES [1] Viktor Sotona, ATM Solutions. (2011, Sept.). Implementation of [1] MLAT/ADS-B Viktor Sotona, ATM Solutions. (2011, Sept.). Implementation Systems. Presented at ICAO/FAA Workshop onofADS-B MLAT/ADS-B Systems. Presented atAvailable: ICAO/FAA Workshop on ADS-B and Multilateration Implementation. and Multilateration Implementation. Available: http://www.icao.int/NACC/Documents/Meetings/2011/ADSBMLT/Day http://www.icao.int/NACC/Documents/Meetings/2011/ADSBMLT/Day 01-05-ERA-Sotona.pdf 01-05-ERA-Sotona.pdf [2] Thales Air Systems Gmbh. (2012, Nov.). Ground Stations and [2] multilateration. Thales Air Systems Gmbh.at(2012, Nov.). Seminar. Ground Stations and Presented Asia-Pacific Available: multilateration. Presented at Asia-Pacific Seminar. Available: http://www.icao.int/APAC/Meetings/2012_SEA_BOB_ADSB_WG8/SP http://www.icao.int/APAC/Meetings/2012_SEA_BOB_ADSB_WG8/SP 03_Thales%20ADS-B%20Multilateration.pdf 03_Thales%20ADS-B%20Multilateration.pdf [3] VNIIRA. Saint-Petersburg, Russia. Product: Multilateration System [3] “Mera”. VNIIRA.InSaint-Petersburg, Product: Multilateration System russian language.Russia. Available: “Mera”. In russian language. Available: http://www.vniira.ru/ru/products/790/811/1179?text=basic-purpose http://www.vniira.ru/ru/products/790/811/1179?text=basic-purpose [4] Stephen Shankland. Locata wants to fill holes in GPS location, [4] navigation. Stephen Shankland. Locata wants tohttp://www.cnet.com/news/locatafill holes in GPS location, (2012, Dec.). Available: navigation. (2012, Dec.). Available: http://www.cnet.com/news/locatawants-to-fill-holes-in-gps-location-navigation/ wants-to-fill-holes-in-gps-location-navigation/ [5] ICAO. Multilateration. Concept of use. (2007, Sept.). Available: [5] http://www.icao.int/APAC/Documents/edocs/cns/mlat_concept.pdf ICAO. Multilateration. Concept of use. (2007, Sept.). Available: http://www.icao.int/APAC/Documents/edocs/cns/mlat_concept.pdf [6] V.S. Kondratiev, Multipositional radio systems. Moscow, Russia: [6] Radio V.S. Kondratiev, Multipositional systems. 246-251. Moscow, Russia: and communications, 1986,radio pp. 178-200, RadioCheryak. and communications, 1986, pp. 178-200, 246-251. [7] V.S. Multipositional radiolocation. Moscow, Russia: [7] Radio V.S. Cheryak. Multipositional radiolocation. and communications, 1993, pp. 7-42. Moscow, Russia: RadioBorisov, and communications, 1993, 7-42. [8] E.G. G.M. Mashkov, L.S. pp. Turnetskiy, [8] “Accuracy E.G. Borisov, G.M. in Mashkov, L.S. increase determing anTurnetskiy, object’s coordinates while co“Accuracyprocessing increase inisdeterming object’s coordinates while cooperative applied in an multipositional radiolocation system”, operative processing is 4-9, applied in 2013. multipositional radiolocation system”, Radiotechnics №5, pp. May, Radiotechnics pp. 4-9,anMay, 2013.coordinates in three positional The method for№5, determing object’s The methodradiolocation for determingsystem, an object’s coordinates threeMashkov. positional rangefinder by E.G. Borisov,inG.M. rangefinder radiolocation by E.G. Borisov, G.M. [Online]. Mashkov. (2014, May 10). Patent RFsystem, № 2515571МПК G01S13/46 (2014, Mayhttp://www.freepatent.ru/patents/2515571 10). Patent RF № 2515571МПК G01S13/46 [Online]. Available: Available: [9] J. Mitola II,http://www.freepatent.ru/patents/2515571 Z. Zvonar. Software Radio Technologies. [9] New J. Mitola II,WileyZ. Zvonar. Radiopp. Technologies. York: IEEESoftware Press, 2001, 40-47. New York: IEEE Press, 2001, pp. 40-47. [10] J. Mitola II. WileySoftware Radio Architecture: Object-oriented Approaches [10] to J. Mitola II.System. Software Radio Architecture: Approaches Wireless New York: John WileyObject-oriented & Sons, 2000, pp. 384-436. to Wireless System. New York: John Wiley & Sons, 2000, pp. 384-436.

JUNE 2015 •

VOLUME VII

• NUMBER 2

Georgiy M. Mashkov was born in 1954, in Georgiy M. Mashkov was born in 1954, in Uzlovaya, a town and the administrative cenUzlovaya, a townDistrict and theinadministrative center of Uzlovsky Tula Oblast, Ruster of Tula Oblast, Russia. HeUzlovsky obtained District a RadioinEngineer degree in sia. Hea Candidate obtained aofRadio Engineer in 1977, Sciences degreedegree in 1984, 1977, a Candidate of Sciences degreedegree in 1984, and a Doctor of Technical Sciences in and a Doctor of Technical Sciences in 1993. Dr Mashkov is the author of degree over 150 1993. Dr publications, Mashkov is the author 26 of of over 150 scientific including invenscientific including 26he of isinventions and publications, useful models. Currently first tions Rector and useful models. he is first Vice (Vice RectorCurrently for Academic AfViceState Rector (Vice Rector for Academic Affairs) of Saint-Petersburg University of Telecommunications fairs) ofafter Saint-Petersburg University of Telecommunications Named Professor M.State A. Bonch-Bruevich, Saint-Petersburg, Named His after M. interests A. Bonch-Bruevich, Russia. areaProfessor of scientific include MLAT,Saint-Petersburg, and methods of Russia. His area of scientific includeinformation MLAT, andofmethods of mathematical processing of interests measurement different mathematical physical nature.processing of measurement information of different physical nature. Evgeny G. Borisov was born in 1967 Evgeny G. Borisov was born 1967 in Novosibirsk. He obtained theindegree in Novosibirsk. He obtained the degree of a Radio Engineer in 1990 and a of a Radio Engineer Sciences in 1990 degree and a Candidate of Technical Candidate of Technical degree in 2000. Presently he isSciences a leading rein 2000. ofPresently he is a leading researcher Saint-Petersburg State UnisearcherofofTelecommunications Saint-Petersburg State University Named versity of Telecommunications Named after Professor M. A. Bonch-Bruevich, Professor M.author A. Bonch-Bruevich, Saint-Petersburg, Russia.. Drafter Borisov is the of three moSaint-Petersburg, Russia.. Dr Borisov the author monographs, more than 120 articles, and 25is patents. Areaofofthree scientific nographs,include more than 120 integration articles, andof25positioning patents. Area of statistical scientific interests MLAT, data, interests include synthesis of radio MLAT, systems. integration of positioning data, statistical synthesis of radio systems. Andrey Vladyko obtained his CanAndreyofVladyko his Candidate Science obtained degree from the didate of Science degree from the Komsomolsk-on-Amur State TechKomsomolsk-on-Amur nical University, RussiaState in Tech2001. nical University, in 2001. Presently he is HeadRussia of the Office of Presently he Head of the Office of Research andis Research Training at Research and ResearchSaint-PetersTraining at The Bonch-Bruevich The Bonch-Bruevich Saint-Petersburg State University of Telecommunications, Saint-Petersburg, RusburgHis State University Telecommunications, sia. major interestsofinclude control systems,Saint-Petersburg, soft computing, Rusnetsia. His majormanagement. interests include control is systems, soft IEEE. computing, network security Dr. Vladyko a Member, work security management. Dr. Vladyko is a Member, IEEE. Anna Gomonova was born in Saint-PetersAnna Russia Gomonova wasShe bornobtained in Saint-Petersburg, in 1991. her BSc burg,MSc Russia in 1991. She obtained her from BSc and degrees in radio engineering and MSc degreesState in radio engineering from Saint-Petersburg Electrotechnical UniSaint-Petersburg versity, Russia inState 2014.Electrotechnical Presently she isUnian versity, Russia 2014. Presently she is an engineer at The in Bonch-Bruevich Saint-Petersengineer The Bonch-Bruevich Saint-Petersburg StateatUniversity of Telecommunications, burg State University of Telecommunications, Saint-Petersburg, Russia. Her major interests Her major interests include MLAT, digital Saint-Petersburg, signal processing, Russia. software-defined radio. include MLAT, digital signal processing, software-defined radio.

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