Which one among the following is the correct method employed by GPS to find the location of a target ?

Correct — A, (a) Trilateration method, which measures lengths of sides of triangle with target location as one of the heads of the triangle. TRILATERATION is the name of the method GPS uses, and it is the only one of the four options that names a method at all rather than a single measurement.

How the receiver actually fixes a position. Every satellite continuously broadcasts a coded signal along with the exact time of transmission and its own orbital data. The receiver reads the time of arrival, and the difference between transmission and arrival, multiplied by the speed of light, gives the distance to that satellite. One distance places the receiver somewhere on a SPHERE around that satellite. A second distance intersects the first sphere in a circle; a third narrows it to two points, of which one is absurd — far out in space or moving impossibly — leaving a single position. A fourth satellite is needed in practice because an ordinary receiver has a cheap quartz clock that cannot keep atomic time: the fourth range lets the receiver solve for its own clock error along with latitude, longitude and altitude. That is why four satellites in view is the working minimum.

The word matters. TRILATERATION fixes a point from measured DISTANCES; TRIANGULATION fixes it from measured ANGLES, as a surveyor does with a theodolite. A GPS receiver measures no angles at all — it has no way to tell the direction a signal came from — so it can only be doing trilateration. The option's own gloss about the lengths of the sides of a triangle is a loose way of putting it, and 'heads' is not the word a geometer would use for a vertex, but the method it names is the right one and the emphasis on measuring LENGTHS is exactly the distinguishing feature.

Why the others are wrong

• (b)Dilation method, which measures distance of target location from two already known landmarks — Two faults. 'Dilation' is not a positioning method — in this field the word appears in 'dilution of precision', a measure of how much satellite geometry degrades a fix, and the resemblance is probably what suggested it. And two distances are not enough: two spheres intersect in a whole circle of possible positions, which is why three ranges are needed for a position and four to solve the clock error as well.
• (c)Measurement of the distance of target from the designated geostationary satellite — Wrong on both counts. A distance from ONE satellite locates the receiver only on a sphere, not at a point. And GPS satellites are not geostationary: they orbit at about 20,200 km with a period of roughly twelve hours, arranged so that several are above the horizon anywhere on earth at any time. Geostationary satellites sit far higher, over the equator, and are used in navigation only by augmentation systems that broadcast corrections, such as India's GAGAN.
• (d)Measurement of the distance of target from the designated polar satellite — Identical in form to (c) with one word changed, and it fails for the same first reason — one distance gives a sphere, not a fix. Polar orbits are used for earth observation and weather satellites, which need to sweep the whole globe as it rotates beneath them; the GPS constellation uses medium earth orbits inclined at about 55 degrees, not polar ones. Where two options differ by a single word, the fault usually lies in the part they share.

The Global Positioning System has three segments. The SPACE segment is a constellation of satellites in medium earth orbit, each carrying atomic clocks. The CONTROL segment is the ground stations that track the satellites, correct their clocks and upload fresh orbital data. The USER segment is every receiver, which listens passively — it transmits nothing, which is why any number of users can be served at once and why a receiver cannot be detected by using it. Position comes from timing: distance equals the speed of light times the signal's travel time, and three such distances intersect at a point, with a fourth solving the receiver's clock error. Errors come from the ionosphere and troposphere slowing the signal, from signals bouncing off buildings, and from poor satellite geometry. India's own regional system, NavIC, provides an independent service over India and its neighbourhood.

Key facts

• GPS positions are computed by trilateration — from measured distances, not from angles.
• Distance to a satellite is the signal travel time multiplied by the speed of light.
• Three ranges fix a position; a fourth is used to solve the receiver's clock error, so four satellites in view is the practical minimum.
• GPS satellites orbit at about 20,200 km in roughly twelve-hour, medium earth orbits inclined near 55 degrees — not geostationary and not polar.
• Receivers are passive: they only listen, so the system serves unlimited users simultaneously.
• Triangulation, by contrast, determines a position from measured angles and is the surveyor's method.
• Ionospheric and tropospheric delay, multipath reflection and satellite geometry are the main sources of positioning error.
• NavIC is India's regional navigation satellite system; GAGAN is the satellite-based augmentation system that broadcasts corrections for civil aviation.

Common traps

• Answering 'triangulation' from habit; GPS measures distances, never angles.
• Assuming navigation satellites are geostationary because communication satellites are.
• Thinking two or three satellites suffice in practice; the fourth is what removes the receiver's clock error.
• Believing a GPS receiver transmits its position to the satellites — it does not; it only receives.

• practice — not a real PYQ

  What is the minimum number of satellites whose signals a GPS receiver must acquire in order to compute latitude, longitude and altitude while also correcting its own clock error ?

  • (a)Two
  • (b)Three
  • (c)Four
  • (d)Six

  Answer(c) Four

• practice — not a real PYQ

  Which one among the following distinguishes trilateration from triangulation ?

  • (a)Trilateration measures distances, triangulation measures angles
  • (b)Trilateration measures angles, triangulation measures distances
  • (c)Trilateration works only at sea
  • (d)Trilateration requires geostationary satellites

  Answer(a) Trilateration measures distances, triangulation measures angles