Mobile Location Method of Radio Wave Emission Sources

Transcription

1 PIERS ONLINE, VOL. 5, NO. 5, Mobile Location Method of Radio Wave Emission Sources P. Gajewski, C. Zió lkowski, and J. M. Kelner Military University of Technology, Poland Abstract This paper deals with the new location method of radio wave sources, based on the Doppler effect. In this method, position of the radio signal source is calculated on the basis of momentary frequency measurements taken by mobile receiver. Theoretical and simulating analysis of the presented methodology was made before empirical verification process was introduced. General outline of the method on the basis of the Doppler effect and preliminary empirical verification results are presented. 1. INTRODUCTION Over that last decade, the emerging location service of electromagnetic waves sources has found numerous applications in the commercial as well as the military radio systems. In this paper, we concentrate on location service of a subscriber in radio communication networks. Several methods for subscriber location in radio communication nets have been already presented like [1] [5]: access station identification so-called Cell ID or Cell of Origin (CoO), Angle of Arrival (AoA), Time of Arrival (ToA), Time Difference of Arrival (TDoA), Received Signal Strength (RSS), Global Positioning System (GPS). Each of foregoing methods have some advantages and some disadvantages too. Disadvantages of foregoing methods make difficult for practical utilization. These factors have motivated the development of new location methods based on analytic description of the Doppler effect. The analytic description of this problem [6] makes it possible to calculate exactly the value of the received signal parameters especially frequency offset. In this paper, the theoretical basis as well as empirical verification of frequency offset measurement is described. 2. ANALYTIC DESCRIPTION OF THE DOPPLER EFFECT The analytic description of the Doppler effect results from solution of Maxwell equations. In the case of free space, the Faraday and the Ampere equations as well as the property of vector field double rotation are the basis for the following wave equation describing the vector of the electric field strength: 1 2 c 2 t 2 E(x, t) + E(x, t) = µ 0 t i 0(x, t) (1) where x = (x, y, z) is the space co-ordinate, i 0 (x, t) = (i x (x, t), i y (x, t), i z (x, t), ) is the vector of density of current density, = 2 x y z Laplacian. 2 In [8] we have concentrated on two considerations: - the linear antenna system i.e., we assume that the current density vector has the form i 0 (x, t) = (0, 0, i z (x, t)) = i 0 (t) I(z) δ(x) δ(y) (2) - the motion of signal source model in x co-ordinate direction with v velocity. Thus the problem has been reduced to solve the following second orders partial differential equation. 1 2 c 2 t 2 E(x, t) + E(x, t) = µ 0 t [i 0(t) I(z) δ(x vt) δ(y)] (3) The analytic form of the of electric field phase generated by moving transmitter is ([6]): Φ(x, t) = ω 1 t β 1 kx β 1 R 0 (x, t) π 2 (4)

2 PIERS ONLINE, VOL. 5, NO. 5, where R 0 (x, t) = (x vt) 2 + (1 k 2 ) (y 2 + z 2 ), β 1 = ω 1 /c = β/(1 k 2 ), ω 1 = ω 0 /(1 k 2 ) = 2πf 0 /(1 k 2 ), k = v/c. Hence, the Doppler frequency expresses the following dependence ([7]) f D (x, t) = f(x, t) f 0 = k [ 1 k 2 k + x vt ] f 0 (5) R 0 (x, t) The f D (x, t) is linear dependent on the frequency carrier, whereas the dependence on velocity and space co-ordinates has a more complex character. Location calculation are made on the basis of the above formula and the described value of Doppler frequency shifts as a function of movement and coordinates of signal source parameters. The temporal frequency value f(x, t) = f 0 + f D (x, t) measurement over mobile station is the basis of the new method of the subscriber location. 3. NEW LOCATION METHOD OF RADIO SIGNALS SOURCES The illustration of the subscriber location methodology is shown in Figure 1. Measurement of the Doppler frequency offset is base of this method. The Doppler curves for five different locations of subscriber (station) are presented in Figure 2. The diverse courses of the Doppler curves (Figure 2) are characteristic for every subscriber location. It determinates methodology of the frequency offset value using to three-dimensional location. Figure 1: Space structure of the mutually mobile station and five station locations [6]. Figure 2: Doppler curves vs. the mobile station to subscriber vt x distance.

3 PIERS ONLINE, VOL. 5, NO. 5, After elementary transformation of the expression (5) for two moments t 1 and t 2 the formulas described x and z co-ordinates are following ([8] [9]): x = v t 2A(t 1 ) t 2 A(t 2 ), A(t 1 ) A(t 2 ) [ ] 2 v(t1 t (6) 2)A(t 1)A(t 2) A(t 1) A(t 2) z = ± 1 k 2 y 2, where A(t) = 1 F 2 (t) F (t), F (t) = f D(t) 1 k 2 k (7) f 0 k This methodology and also method of bearing and three-dimensional location has been described in patent application [8]. Figure 3: Structure of mobile test stand used in empirical verification. Figure 4: Measuring rout with characteristic points A E and example course of Doppler frequency.

4 PIERS ONLINE, VOL. 5, NO. 5, EMPIRICAL RESULTS AND DISCUSSION Measurement station (Figure 3) consisted of: MagTel GSM Car Antena, Compact Receiver Rhode- Schwarz ESMC R1, Universal Frequency Counter Agilent (HP) 53132A, a notebook with implemented Frequencer software. Data from the frequency meter were sent to computer by USB-GPIB Interface Agilent 82357A. Receiver and frequency meter were additionally stabilized with Rubidium Frequency Standard Stanford Research System FS725. All the elements of the test stand were situated in a car vehicle. Battery and voltage converter were used to supply power to these elements. In experiment, source (target) was situated in position relative the begin of the right-handed cartesian co-ordinate system in point B. On rout section A B vehicle with receiver was speeded up to 36 km/h, on section B D vehicle moves with constant velocity 36 km/h (in this interval were made momentary frequency measurements) and on section D E vehicle stopped. The vehicle average velocity on rout section B D was calculated on the basis of the riding time measurements. In order to precision valuation of this location methodology following new quality measure r, further called location error, was determined [7] [9]. Average values of the source co-ordinates (Table 1) were calculated on the basis of Doppler frequency courses. The obtained results shows that the Doppler frequency offset value could be used for radio signal sources location. Table 1: Results of measuring and calculation. 5. CONCLUSION The experiment results give possibility to do initial opinion of location method precision. Possibility of these results comparison with different location methods is basis of this opinion. This comparison permits to infer about large effectiveness of the new method. Errors estimation of individual coordinates x, z and location errors r in presented method were below 1 m (Table 1). It is needed to emphasize, that this method is dedicated first of all to location in open area, where it occurs so-called: down-to-earth space propagation or free space propagation. The measuring rout in this experiment could be classified as suburban terrain. On this stage of empirical verification, the test rout was choice by possibilities of test realization. The measuring rout in section B D was chosen to conditions which were reminding down-to-earth space propagation (direct visibility of antennas on whole measuring rout section). There are buildings beside the section B D, which cause the signals reflections. It is visible in disturbance of the Doppler frequency course on sections A B and D E (Figure 4). This empirical test is initial usefulness verification of this new location method. Many tests in different space conditions should be conducted, to get the full information of method effectiveness.

5 PIERS ONLINE, VOL. 5, NO. 5, ACKNOWLEDGMENT This work was supported in part by the Polish Ministry of Science and Higher Education under Grant N N and by the Department of Electronics, Military University of Technology under Grant PBW 506. REFERENCES 1. Küpper, A., Location-based Services, John Wiley & Sons Ltd., Chichester, UK, Aug An Introduction to Mobile Positioning, Mobile Lifestreams Limited, Gupta, I. J., Stray signal source location in far-field antenna/rcs ranges, IEEE Antennas and Propagation Magazine, Vol. 46, No. 3, 20 29, Jun Zhao, Y., Standardization of mobile phone positioning for 3G systems, IEEE Communications Magazine, Vol. 40, No. 7, , Jul Vossiek, M., L. Wiebking, P. Gulden, J. Weighardt, C. Hoffmann, and P. Heide, Wireless local positioning, IEEE Microwave Magazine, Vol. 4, No. 4, 77 86, Dec Gajewski, P., J. M. Kelner, and C. Zió lkowski, Subscriber location in radio communication nets, Journal of Telecommunications and Information Technology, No. 2/2008, 88 92, Apr. Jun Rafa, J. and C. Zió lkowski, Influence of transmitter motion on received signal parameters Analysis of the Doppler effect, Wave Motion, Vol. 45, No. 3, , Jan Zió lkowski, C., J. Rafa, and J. M. Kelner, Sposób namiaru i lokalizacji źródel przestrzennych fal radiowych z wykorzystaniem efektu Dopplera (Method of direction finding and location of the space radio wave sources using Doppler effect), Polish patent application No. P381154, Warsaw, Poland, Nov. 27, 2006; Biuletyn Urzedu Patentowego (Polish Patent Office Newsletter), Vol. XXXVI, No. 12(899)/2008, 24, Jun. 9, 2008 (in Polish). 9. Kelner, J. M., C. Zió lkowski, and L. Kachel, The empirical verification of the location method based on the Doppler effect, Proceedings 17th International Conference on Microwaves, Radar and Wireless Communications MIKON 2008, Vol. 3, , Wroc lw, Poland, May 19 21, 2008.