Searching an avalanche victim using a transmitter with a rotat-ing magnetic dipole

Abstract

Avalanche beacons are transmitters and receivers of 457 kHz magnetic field which are widely used for rescue of avalanche victims. Conventionally, a dipolar magnetic field is created by using one of three, orthogonal coils in a victim's transmitter, and then a searcher measures its magnetic flux density by using all three coils of a receiver to find a victim. A problem, however, is that a searcher should make a detour along the magnetic line of force to reach the victim. In this paper, we propose to use all the three coils of a transmitter in order to navigate searchers linearly to a victim. Detecting the posture of a transmitter by using accelerometers, we create a magnetic dipole equivalently rotating in the xy-plane. Then, the searcher can determine the direction to linearly proceed toward the victim by quadrature detection of the x- and y-components of the magnetic flux density. Although the use of a rotating magnetic dipole was proposed by Paperno [1]for magnetic tracking, their method needs to know the phase of a signal input to the transmitter, which is not applicable to avalanche rescue. Our method can navigate the searcher irrespective of the phase of the transmitter's signal. 2. Method As shown in Fig.1, the xyz-axes are set along the receiver's orthogonal coils, where the xy-plane is a searching plane. The aim is to find a direction of a transmitter viewing from the receiver, $\varphi $. By putting three orthogonal accelerometers, a rotating matrix $R$from the xyz-frame to the transmitter's XYZ-frame can be obtained. Then, in order to create a magnetic dipole rotating in the xy-plane with frequency of $f \quad = \omega / ( 2 \pi )$, the current proportional to $Ri$is input to three orthogonal coils of the transmitter, where $i = \cos \Omega t * (\cos({\omega{t} + \theta_0}), sin(\omega{t} + \theta_0), 0)^T$, where $F \quad = \quad \Omega / ( 2 \pi )=457$kHz and $\theta_0$is an initial phase. As shown in Fig.1, denote the envelopes of the x- and y-components of the magnetic flux density measured by a receiver by $Bx$and $By$, respectively. Let $I_{k} \quad = \int B_{k} \cos \omega t$dt and $Q_{k} \quad = \int B_{k} \sin \omega t$dt for $k \quad = \quad x$and $y$. Then, we can show that $\tan 2 \varphi \quad =\{ ( \mathrm {Q}_{x}+ \mathrm {I}_{y})( \mathrm {I}_{x}+ \mathrm {Q}_{y})+( \mathrm {I}_{x}- \mathrm {Q}_{y})( \mathrm {I}_{y}- \mathrm {Q}_{x})\} /${$- ( \mathrm {Q}_{x}+ \mathrm {I}_{y})( \mathrm {I}_{y}- \mathrm {Q}_{x})+( \mathrm {I}_{x}- \mathrm {Q}_{y})( \mathrm {I}_{x}+ \mathrm {Q}_{y})\}$. Note that this equation holds irrespective of $\theta_0$, showing that the direction of a line along which the searcher should proceed to reach the victim can be determined from the quadrature detection of the magnetic flux density without knowing the initial phase of the transmitter signal. Although $\varphi $itself is determined up to $\pi $, the direction to proceed can be decided by measuring $\vert B\vert $. The goal of search, that is, the place just above the victim, can be also judged by detecting the maximum of $\vert B\vert $. 3. Experimental results The orthogonal bar coils (BA-200) and variable capacitors (CBM-223) tuned with $F \quad =457$kHz were used as a transmitter. Modulation frequency $f \quad = \omega / ( 2 \pi )$was 5 Hz. The other, same-type coils were used as a receiver to measure the magnetic flux density. After obtaining its envelope by a quadrature detection with frequency $F$, the quadrature detection with frequency $f$was conducted to obtain $I_{k}$and $Q_{k}$, from which $\tan 2 \varphi $was estimated. The transmitter was moved on circles of radius $r \quad =300$mm centered at the receiver, where $\varphi \quad =0$, 45, 90, 135, and 180 degrees. Fig. 2shows the angle errors between the estimated line and the line connecting the transmitter and receiver. The mean and maximum error was 10.7 degrees and 24.3 degrees, respectively, which shows the validity of our method. Experimental results for wider search range has been preliminarily conducted and will be shown in the paper.