Crossbearing

Crossbearing is a method used in navigation and surveying to locate an unknown point by measuring its bearing from two or more known observation points. The procedure involves taking a direction to the target from each station—typically with a compass, theodolite, or similar instrument—then plotting those directions as lines on a map. Where the bearing lines intersect (or come closest to each other) is taken as the position of the target object.

In practice, observers at two or more fixed locations determine the bearing to the same object. Each bearing is translated into a line on a map that starts at the corresponding observation point and follows the measured direction. The intersection of these lines identifies the object's location. When more than two observations are available, the data can be combined using a least-squares approach to reduce measurement errors and improve accuracy.

Crossbearing is used in various contexts, including search and rescue, land surveying, and military reconnaissance, as well as some forms of orienteering and navigation in featureless terrain. It is particularly useful when direct distance measurements are difficult or impractical.

Key limitations include sensitivity to bearing errors, misidentification of the target, and the potential for lines to intersect at a distant or ambiguous point if observations are imprecise. Accurate results rely on well-calibrated instruments, correct declination adjustments, clear identification of the target, and careful plotting. Related methods include triangulation and resection, which also use angular measurements to determine positions.