Radio direction finding

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 iswhere $\lambda$ is the wavelength. With $d=\lambda /2$ and measured $\Delta \varphi =\pi /2$, 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.^[ref]

Radio triangulation estimates a radio transmitter's position by combining directions measured from different known locations. Each radio direction finding observation supplies a bearing line, with the forward direction selecting a ray. Their intersection gives an ideal position estimate. This is one method of radio tracking; detecting a signal at one station does not determine its distance.^[ref]

For two stations at $(0,0)$ and $(L,0)$ in a horizontal Cartesian coordinate system, let their bearings make angles $\alpha$ and $\beta$ from the positive horizontal axis. Away from vertical bearings, their lines satisfy $y=x\tan \alpha$ and $y=(x-L)\tan \beta$. Solving givesFor $L=4\mathrm{km}$, $\alpha =45^{\circ }$ and $\beta =135^{\circ }$, the result is $(2,2)\mathrm{km}$. The intersection must also lie in each observed forward direction; intersecting the infinite lines alone is insufficient.

The denominator exposes a limitation: nearly parallel bearings can make the position estimate highly sensitive to angular error. Observations taken at different times can also refer to different target positions. More stations allow consistency checks or a fitted estimate when noisy lines do not meet at a point. Smithsonian bird-tracking researchers use this combination of bearings to locate animals without needing continuous visual contact.^[ref]