= Radio direction finding
\b[Radio direction finding] estimates the direction from which a <radio wave> arrives at a receiving station. It uses directional information in an <antenna> response, such as changes in amplitude or relative phase across several <antennas>. A direction is a bearing from one station; it is not, by itself, the distance to the transmitter. Combining bearings from separated stations can constrain position.
A two-element interferometer illustrates the measurement. For a plane <radio wave> arriving at angle $\theta$ from the perpendicular to an antenna baseline of length $d$, the path difference is $d\sin\theta$. Thus the relative phase is
$$
\Delta\phi=\frac{2\pi d}{\lambda}\sin\theta\pmod{2\pi},
$$
where $\lambda$ is the <wavelength>. With $d=\lambda/2$ and measured $\Delta\phi=\pi/2$, the ideal model gives $\sin\theta=1/2$, hence $\theta=30^\circ$ within a chosen arrival sector. One baseline does not resolve every directional ambiguity, and phase wrapping can introduce additional candidates. More <antennas> and other directional information can help distinguish them.
A useful field test places a transmitter at a known location, compares measured and geometric bearings, and repeats the comparison across directions and <frequencies>. The International Telecommunication Union's originating test recommendation includes controlled transmitters and known broadcast stations, emphasizing that a final installation can behave differently from an ideal test range. Reflections, obstructions and signal properties can bias the direction estimate; an error measured at one site cannot simply be transferred to another installation.<Recommendation ITU-R SM.2097-0: On-site accuracy measurements of a fixed DF system>[Considerations d–g; Annex 1 sections 1–2, controlled/known-location transmitters and installation-specific limitations.]{ref}
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