A bearing gives only direction, not range — the emitter could be near or far along the same line. Drawn honestly it is a line of position (LOP), a ray running off toward the horizon, not an arrow ending on the emitter.
Crossing two LOPs from two known receiver locations to get a single fix. The baseline is the segment joining the two receivers; the two measured bearings and the baseline form a triangle whose third corner is the emitter.
The crossing angle at which the two bearings meet. It — not receiver quality — sets the fix error, because each bearing is a noise wedge and the fix lives where the wedges overlap. The shape of that overlap depends entirely on the cut.
A small, roughly circular overlap — a tight, near-circular fix. Bearing errors push the intersection only slightly and in different directions, so the result is tight in every direction. This is the geometry you want.
The wedges slide along each other and the overlap stretches into a long, thin sliver — the error smears along range (toward/away from the receivers) while staying decent across range. A tiny bearing error now slews the fix far down the line of sight.
A collinear geometry: emitter and both receivers on one line. There is no cut at all — both LOPs coincide — so range along the baseline is unobservable and the fix runs to infinity along that direction.
Three or more noisy bearings give more equations than the two unknowns (the emitter's north/east coordinates), so they almost never meet at one point. The near-miss triangle is information, not failure.
The single position that best fits all the bearings at once — the point that minimizes the total mismatch between each receiver's bearing and the candidate location. It replaces a clean two-line intersection when bearings overdetermine the fix.
Redundancy (extra bearings average down noise, and a well-placed receiver opens the cut) and outlier detection (a bad bearing shows up as a large residual — its LOP misses the consensus fix — so you can spot and down-weight it).
Registration (common time and common grid), then association (decide which measurements are the same emitter across receivers), then fusion (cross or least-squares the associated bearings into a position).
Receivers meters apart collapse to a shallow cut almost immediately with range; platforms 100 km apart hold a strong near-\(90^\circ\) cut against an emitter hundreds of km away. This is the B-21 standoff case — geolocating a threat from outside its lethal range.
Intercept → PDW → deinterleave → AoA → associate → fuse/geolocate → track → cue. The first four are single-receiver (L12); the last four are across-receiver (L13–L14), turning many bearings into a tracked, located threat.
Crossing assumes both receivers heard the same emitter; in a dense scene that must be verified by matching on frequency, PRI, and PW first. Cross two different emitters and the lines still intersect — at a ghost, a confident, precise-looking fix on nothing. Geolocation is only as good as its association.