PaperOn The Site Error of Wide Band

Magnetic Direction Finder

Member Yukihiro Miyake (Franklin Japan Co.)Member Masaru Ishii (University of Tokyo)

Member Tatsuo Kawamura (Shibaura Institute of Technology)

Member Noriyasu Honma (Tohoku Electric Power Co.)

A wide band magnetic direction finder is an element of the magnetic direction finding system, which is now widely used for lightning location. A magnetic direction finder exhibits systematic errors in the measurement of the bearing and the intensity of the incoming electromagnetic wave, and they are often called "site errors". Two magnetic direction finding systems, having three direction finders each, were installed in Niigata area. The differences between two direction finders installed within several tens of meters, in the observed bearings and the amplitudes of electromagnetic waves associated with lightning return strokes, were measured. The results are explained by the theory of the quadrantal error, which is caused by nearby objects which scatter electromagnetic fields. A method to estimate site errors is

proposed, and its application to the observed data draws the same conclusion, regarding the causes of the site errors at all of the three sites, as that based on the direct measurement of the differences of site errors.

Key Words : Lightning, Lightning Location, Direction Finding, Site Error

1. Introduction

In recent years, real-time lightning location systems have been operated at many places in the world. The most common system in the real-time use is the magnetic direction finder network, and a magnetic direction finder is designed based on the radio direction finding technology[l]. A magnetic direction finder senses the magnetic component of electromagnetic field originating from a lightning discharge by a crossed-loop antenna, and the bearing and the amplitude of the incoming electromagnetic wave is determined from the output signals of the two antenna loops.

Usually, a magnetic direction finder exhibits systematic errors in the observed bearings and signal amplitudes due to the topography and/or objects surrounding the direction finder. By careful selection of the site and installation of the antenna, such systematic errors can be minimized. As the systematic errors differ from site to site depending on their origins, they are called site errors. They are dependent on the azimuth, and several methods to estimate the site error in the bearing have been proposed[2]-[4]. A different method is employed to evaluate the site error of the bearing, and its effectiveness is tested through comparison with directly measured evidences of site errors.

2. Observation

Two independent magnetic direction finder networks were installed in Niigata area facing to the Sea of Japan. One of the systems (A-system) was put into operation in

Fig. 1 Location of the three sites where magnetic direction finders are installed. The

mean distance between sites is about 60 km.

1984, and the other (B-system) began operation in 1986. Each system consisted of three medium gain direction finders, which were placed about 60 km apart each other. Direction finders of B-system were installed at the same sites as those of A-system, and at each site, the two

crossed-loop antennas of the two systems were set ten to

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several tens of meters apart. Figure 1 shows the location of the direction finder stations.

A direction finder of these two systems received wide band electromagnetic signals in the frequency range from lkHz to 0.3MHz, and selected signals from lightning return strokes based on the waveform discrimination. The bearing, the polarity of the stroke, the peak amplitude of the magnetic field of the first stroke were measured and recorded. Direction finders of each system in Niigata were time-synchronized by communication lines, and return strokes were located by triangulation from simultaneous reports from two or more direction finders.

3. Site Errors

The systematic errors in the measured azimuth and the amplitude of the incoming electromagnetic wave have been a serious problem in the lightning location by the magnetic direction finding. It has also been studied over the past years in electromagnetic direction finding at a single frequency[5].

A principal cause of the errors is the existence of re-radiating conductors such as transmission lines, metal fences, underground pipes or buildings, in the vicinity of the magnetic loop antenna. The incoming electromagnetic wave induces currents in such conductors, which radiate scattering electromagnetic fields again. The scattering fields superpose the original electromagnetic wave, resulting in errors in the measurement of its bearing and amplitude.

The magnitude of the errors caused by such an scattering object depends on the position of the scattering body relative to the antenna. Naturally, the errors become functions of the azimuth, and those caused by nearby scattering objects become the well-known

Fig. 2 Diagram of incident and scattered

fields.

quadrantal errors[5]. Quadrantal errors are 2-cycle

sinusoidal curves and their harmonics, dependent on the

azimuth. When the distance between the antenna and a

scattering object cannot be disregarded compared with

the wavelength of an electromagnetic wave, the error

curves may include odd harmonics.

To analyze the influence of a nearby scattering object,

an analyzing model, consisting of a crossed-loop antenna

at the origin and a scattering object, is considered as

shown in Fig. 2. An incoming plane electromagnetic

wave has a bearing of 0 and magnetic field of Bo. The

apparent bearing 0' is influenced by the scattering object,

which is on the line of 90•‹ bearing. Generality of the

system is not lost, as the angle between the bearings of

the incoming wave and the scattering object is the only

parameter in the site error.

Let B I be the re-radiated magnetic field by the

scattering object; Vns and Vew, the induced voltages by

the incoming wave on the N-S and E-W open loops of

the antenna; Vns' and Vew', the induced voltages on the

loops in the presence of the scattering object. These are

dependent on 0 as seen in equations (1) to (5), where A

is a constant.

B1 =A Bo cos9 (1)Vns = Bo cos 0 (2)Vew = Bo sin 0 (3)Vns' = Bo cos 0 + B1 (4)Vew' = Bo sin 0 (5)

9' -0 is known to take the following expression[5].

Let S and S' be the signal strength at the antenna determined by equations (7) and (7').

From equations (1) to (5), S'/S is expressed by equation

(8).

When A << 1, which is usually the case ,

Comparing equation (6) with equation (9), it is known

that the phase of the amplitude error is delayed by 45•‹

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from the phase of the bearing error.Note that the above analysis is independent of the

frequency of the electromagnetic wave. Therefore, the

result is also applicable for wide band direction finding

like the case of lightning location. If the distance to the

source of scattering is comparable to the wavelength, the site error becomes dependent on the frequency of the

electromagnetic wave. In such cases, this means that at

wide band direction finding, site errors are also

dependent on the waveform of the electromagnetic field.

Fig. 3 Difference in bearings measured by

two direction finders at the same site.

Curves are most probable fits into 2-cycle

sinusoidal curves.

In the case of lightning location, taking account of the dominant frequency components of the observed electromagnetic field waveforms, the analysis here could be applied to scattering objects within a few hundreds of meters.

4. Result of Observation

The differences of measured bearings and amplitudes

Fig. 4 Ratio of the signal amplitudes measured by two direction finders at the

same site. Curves are most probable fits into

2-cycle sinusoidal curves.

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of observed lightning data by the two direction finders installed at the same site were compared. Pairs of data having time coincidence were selected for this analysis. The difference in the bearing of B-system from that of A-system, dependent on the measured bearing by A-system, is shown in Fig. 3. In Fig. 4 are shown the ratios of the observed signal amplitudes by the two direction finders at the same site, where the observed values by A-system are regarded as the standard.

At sites 1 and 3, the differences fit into 2-cycle sinusoidal curves. It is obvious that the scattering objects which are the source of the difference exist in the

proximity of the two antennas at the same site, as the two antennas are apart for only few tens of meters. According to the theory described in the previous chapter, this means that the site error caused by the source of the difference produces quadrantal errors. The observational results at site 1 in Figs. 3 and 4 agree quite well with the theory. The results at site 3 also show the

Fig. 5 Arrangement of antennas for the two

systems at site 1.

Fig. 6 Fourier spectrum of the difference in

measured bearings at site 2.

same characteristics, though they are not so clear as seen at site 1. Note the difference in phase for curves of Figs. 3 and 4. Both for the cases of sites 1 and 3, they are about 450 as is predicted by equation (9). Figure 5 shows the plan view of site 1. There are two buildings in the vicinity of the two antennas, and one of the buildings is the base of an antenna for A-system. These two buildings and the steel fence are likely the cause of the difference in the measurement by the two direction finders. At site 3, the two antennas are more apart, but

Fig. 7 Estimated site error of A-system in the bearing calculated through optimization by equation (10). Lines are drawn based on the harmonic analysis of errors,

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there is a grounding of an overhead telephone line nearby. This might be the cause of the difference in the measured results at site 3 in Figs. 3 and 4.

At site 2, the differences in the measured bearings and the amplitudes are much smaller, and the 2-cycle sinusoidal curves are not obvious. Fourier analysis is applied to the measured difference in the bearing, and the result is shown in Fig. 6. The presence of other orders of harmonics than the 2nd is conspicuous, which means that the influence of nearby scattering objects on the measured bearings at this site is not dominant.

Fig. 8 Estimated site errors of B-system

calculated through optimization in each

location. Lines are drawn based on the

harmonic analysis of errors.

5. Estimation of Site Error

Several techniques have been reported to estimate site errors, and they are basically either parametric[2][4] or non-parametric[3] methods. A parametric method assumes a particular function, mostly 2-cycle sinusoidal curves, for the site error in the bearing dependent on the azimuth. So, in the parametric method, few parameters which characterize the particular function are estimated, A non-parametric method does not assume a functional form for the site error curve.

We employed a combination of the both techniques. This method determines an optimum estimate of each location of a lightning stroke by minimizing x12 in

Fig. 9 Fourier spectra of error curves of A-

system in Fig. 7.

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equation (10),

where N is the number of direction finders, e i is the

measured bearings, a of is the direction to the optimum

Fig. 10 Estimated difference in the bearing

between two direction finders at the same

site. These figures are derived from the

estimation shown in Figs. 7 and Fig. 8.

location from the i-th direction finder station, and a i is

the standard deviation of the random angle error

distribution.

Actually, a i acts as a weight to express accuracy of

each direction finder, and if each a i is the same, the

value of a i does not affect the computed result. Site

error in the bearing at each data point is estimated as

0 i - Į oi , and this procedure is non-parametric. Then, a

regression curve is derived from harmonic analysis,

which takes account of odd harmonics also.

The estimated site errors of the two systems in the

bearing, computed from the data simultaneously

observed by three direction finders of each system, are

shown in Figs. 7 and 8. All a i in equation (10) were

assumed to be the same. Fourier analysis was applied to

the estimated discrete error points in these figures, and

regression curves were derived from the sum from 1st to

4th harmonics.

The result of the harmonic analysis for the bearing

error of A-system is shown in Fig. 9. At sites 1 and 3,

the quadrantal component is dominating, whereas at site

2, other frequency components are more prominent. This

result suggests that the site errors at sites 1 and 3 are

caused mainly by nearby scattering objects. At site 2, the

application of the method postulating quadrantal error in

estimating site error is not adequate. This is the same

conclusion as is derived from the observed difference in

the measurement of the bearing and the amplitude of

simultaneously observed signals.

Fig. 10 shows the estimated difference in bearings

derived from Figs. 7 and 8. The estimated differences

for sites 1 and 3 in the phase, shown in Fig. 10, coincide

with the measured results of Fig . 3, though the

amplitudes are a little smaller, especially for site 1 . It is

also noticed that harmonics of higher order are more

pronounced in Fig. 10 than actual data of Fig. 3. The

smaller number of data available to produce Fig . 8 is

believed to be partly responsible to these differences .

The characteristic of the non-parametric method of

estimating site error[6], that estimated error in the

bearing tends to be smaller than the actual magnitude, is

also considered to be related; because if the evaluated

site error is small, the difference has to be small, too,

though the inverse is not true, of course .

6. Conclusions

The site errors in magnetic direction finding have

been known and analyzed from the earliest days, but few

examples of direct evidence of the existence of site errors

in wide band magnetic direction finding have been

reported. The authors operated two magnetic direction

finding systems for location of lightning having three

direction finders each. By placing two direction finders

of the different systems at a same site , the authors

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obtained direct evidence related to the influence of nearby objects that scatter electromagnetic waves. At two of the three sites, observed results are clearly explained by the theory.

Site errors in the bearing were estimated by the combination of non-parametric and parametric methods from numerous data actually observed by wide band direction finders. The estimated results are compared with the directly measured difference in the bearing site errors of two direction finders set in a same site. The estimated and directly measured characteristics of the difference in the observed bearings agree quite well.

(Manuscript received August 1, 1994,revised February 10, 1995)

References

[1] R. Binford et al.: "Wideband magnetic direction finder networks for locating cloud-to-ground lightning", 1983 Int. Aerospace and Ground Conf on Lightning and Static Electricity, Ft. Worth, 50 (1983)

[2] W. L. Hiscox et al.: "A systematic method for identifying and correcting 'Site Errors' in a network of magnetic direction finders", Int. Aerospace and Ground Conf. on Lightning and Static Electricity, Orlando, 7-1 (1984)

[3] D. M. Mach et al.: "Site errors and detection efficiency in a magnetic direction-finder network for locating lightning strikes to ground", J. Atmospheric and Oceanic Technology, 3, 67 (1986)

[4] R. M. Passi and R.E.Lopez: "A parametric estimation of systematic errors in networks of magnetic direction finders", J. Geophys. Res., 94, 13,319 (1989)

[5] Y. Ito and M. Goto: "Radio Direction Finder", Corona-Sha, Tokyo (1957) (in Japanese)

[6] S. Hidayat and M. Ishii: "Direction error correction in lightning location using time-difference and direction

(TDD) technique", Meeting of IEEJ on High Voltage Engineering, Hamamatsu, HV-94-183 (1994)

Yukihiro Miyake (Member) He was born in Japan on January 22, 1955. He received B.S. degree from Rikkyou University in 1980. He

joined Sankosha Corporation in 1980 and joined Franklin Japan Corporation in 1991. Currently he is a director of Lightning Research Division.

Masaru Ishii (Member) He was born in Tokyo on March 11, 1949. He received B.S., M.S. and Dr. Eng. degrees in electrical engineering all from the University of Tokyo in 1971, 1973 and 1976, respectively. He joined Institute of Industrial Science, the University of Tokyo in 1976, and has been a Professor since 1992. His specialty is high voltage engineering. He is a Senior Member of IEEE.

Tatsuo Kawamura (Member) He was born in Tokyo on August 16, 1930. He received B.S., M.S.

and Dr. Eng. degrees in electrical engineering all from the University of Tokyo in 1954, 1956 and 1959, respectively. He joined Institute Industrial Science, the University of Tokyo in 1959, and had been a professor since 1969. In 1991 he became a Professor of the Dept. of

Electrical Engineering, Shibaura Institute of Technology. His specialty is electric power engineering and high voltage engineering. He is a Professor Emeritus of the University of Tokyo. He is a Fellow of IEEE.

Noriyasu Honma (Member) He was bom in Japan on May 1, 1957. He received B.S. and M.S. degrees both from Tohoku University in 1981 and 1983, respectively. He joined Tohoku Electric Power Co. in 1983. Currently he is a research staff of Electricity Technology R&D Center, and principally engaged in research of lightning.

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