Almost no positioning system measures position. Each one measures a distance, a difference of distances, or an angle, and the position is computed afterwards from several of those. Naming the quantity a system actually measures is the fastest way to understand what it can do and where it will fail.

• What does a positioning system actually measure ?
• How does a range become a position ?
• What are the main measurement types ?
• Why does one nanosecond matter ?
• What limits accuracy in practice ?
• Which technique does each system use ?
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What does a positioning system actually measure ?

Start with the question that separates the techniques, because it is not the one most descriptions open with. A receiver never observes where it is. It observes something about a signal that arrived, and position is what falls out of combining several such observations with known transmitter locations.

Three quantities cover nearly everything. A system measures how long a signal took to arrive, which is a distance. It measures how much longer one signal took than another, which is a difference of distances. Or it measures the direction the signal arrived from, which is an angle.

Each of the three needs something different from the network before it can be trusted. A flight time needs the transmitter and the receiver to agree on what time it is. A difference of flight times needs only the transmitters to agree with each other. An angle needs an antenna array and knowledge of which way that array is pointing.

There is a fourth observation that measures nothing geometric at all. Received power falls with distance, so a system can compare the power it sees against a survey recorded earlier and pick the closest match. That approach needs no clock and no array. It needs a map that somebody surveyed in advance.

• The measured quantity is the classification : time, time difference, angle or power. Every named technique further down this page is one of those four with a protocol wrapped around it.
• Each quantity carries its own precondition : a shared clock, synchronised transmitters, a calibrated array, or a survey. The precondition is usually what fails first in a deployment.
• Position is computed, never observed : the receiver solves for it. That is why the geometry of the transmitters matters as much as the quality of the measurements.

How does a range become a position ?

One distance measurement says very little on its own, and the way it says more is worth drawing. Each range places the receiver on a surface, and adding ranges intersects those surfaces until only one point survives. Figure 1 takes that from one range to three.

Figure 1. Ranges intersect rather than add. The third circle is not extra precision on the first two. It removes the second candidate, and that is why a two dimensional fix needs three anchors rather than two.

• One range is a circle, not a point : the receiver knows how far away it is and nothing about the direction. Every point at that distance is equally consistent.
• Two ranges leave an ambiguity rather than an answer : two circles cross at two points. Some systems resolve that with a rough prior, such as knowing the receiver is indoors or above ground.
• The third measurement does a different job from the first two : it selects between candidates rather than refining a position. A fourth and a fifth then start reducing the error.

The three dimensional case adds one twist that catches people, and it is the reason GNSS quotes four satellites rather than three. Each range becomes a sphere, and three spheres intersect at two points, which a rough altitude usually settles. The fourth satellite is there for a different reason.

The fourth satellite pays for the receiver clock. A GNSS receiver cannot carry an atomic clock, so it does not know the exact time. An unknown clock offset adds the same error to every range it measures. The solver therefore treats the offset as a fourth unknown alongside the three coordinates, and four measurements are needed to solve for four unknowns. A receiver that sees four satellites gets its position and the correct time. GNSS became the world's timing reference as well as its positioning one for that reason.

• Four satellites, four unknowns : three coordinates and the receiver clock offset. The fourth measurement pays for the clock rather than for the geometry.
• A common clock error is not the same as noise : it shifts every range by the same amount. That is exactly what makes it solvable rather than merely damaging.
• Timing comes free with the fix : the same solution gives position and time together, to within nanoseconds. A great deal of infrastructure now depends on that.

What are the main measurement types ?

The names in this table are the ones a specification will use. Each is one of the four quantities above with a procedure wrapped around it. Read the third column first, because what a technique demands of the network decides where it can be deployed.

Two rows in that table deserve a second look, because they solve the same problem in opposite ways. TOA needs the transmitter and receiver to share a clock, which is a demand nobody can meet cheaply. TDOA sidesteps it by subtracting : an unknown receiver clock offset appears in both flight times and cancels in the difference. That is why GNSS puts the atomic clocks in the satellites and leaves a quartz oscillator in the receiver.

Round trip time removes the same problem by another route. One clock starts the measurement and the same clock stops it, so no two devices ever have to agree on the time. The price is a turnaround delay at the far end that has to be known and stable. Calibrating that delay is most of the engineering in a Wi-Fi or UWB ranging product.

• Synchronisation is the real cost, not the measurement : every timing technique answers one question differently. Who has to agree with whom about the time ?
• TDOA cancels the receiver clock and needs the transmitters to agree : that trade is what makes a satellite constellation workable and a single beacon useless.
• Round trip time needs no shared clock at all : it needs a calibrated turnaround instead, which moves the difficulty from the network into the device.
• Angle and power need no timing : they need an array or a survey. Neither scales the way a timing method does, and both are useful where timing cannot reach.

Why does one nanosecond matter ?

One number explains more about positioning than any other, and it is worth committing to memory. Radio travels about 30 centimetres in a nanosecond. Every timing error a system makes is multiplied by the speed of light before it reaches the answer.

The bottom row is the one that reframes the problem. A free running receiver clock can be a millisecond away from truth without anybody noticing, and a millisecond is 300 kilometres. That is why no practical system asks a receiver to measure absolute flight time, and why the section above works so hard to avoid it.

Bandwidth sets a second limit, and it is independent of the clock. A receiver can place an arrival in time only to about one over the bandwidth. The distance resolution is therefore roughly the speed of light divided by the bandwidth. Twenty megahertz gives about 15 metres, a hundred megahertz gives about 3 metres, and the 500 megahertz of an ultra wideband radio gives about 60 centimetres. Averaging improves on those figures and the ranking between them never changes.

GNSS shows both limits in one system. The GPS C/A ranging code runs at 1.023 megachips per second, so one chip lasts about 978 nanoseconds and covers 293 metres of flight. Tracking that code to a hundredth of a chip is what produces a few metres of accuracy. The carrier underneath it has a wavelength of about 19 centimetres at L1. Tracking that carrier instead is what makes the centimetre results in the video list below possible.

That ranging code is worth a footnote of its own. The C/A code is a Gold code of length 1023, built from two ten stage shift registers. At the chip rate above it repeats once every millisecond. The Gold code and m sequence pages cover why such a family is chosen. Every satellite needs a code that correlates sharply with itself and weakly with all the others.

• 30 centimetres per nanosecond : the single conversion worth memorising. It turns every clock specification into a distance without further work.
• Bandwidth and clock accuracy are separate limits : a perfect clock on a narrow signal still cannot resolve a short delay. UWB therefore wins on bandwidth rather than on timing hardware.
• Carrier phase is a finer ruler than the code : 19 centimetres against 293 metres. The catch is that the carrier repeats, so the whole number of cycles has to be established separately.

What limits accuracy in practice ?

Everything above assumes the signal travelled in a straight line from the transmitter to the receiver. Outdoors with a clear sky that is close enough to true. Anywhere else it is the assumption that breaks first, and it breaks in a way that averaging cannot repair.

A radio signal reaches a receiver by several paths at once, and each reflection arrives later than the direct one because its route is longer. The impulse response of the channel is the list of those arrivals. Figure 2 draws two of them.

Figure 2. The distinction a ranging receiver lives or dies by. The correct arrival is the earliest one and not the largest one. When the direct path is blocked entirely, the earliest arrival is itself a reflection, and no processing can identify it as one.

• First and strongest are different arrivals : a reflection can easily be the taller peak. A correlator that takes the maximum then reports a range that is too long.
• Multipath error is always positive : every alternative route is longer than the direct one, so the bias adds distance and never subtracts it.
• A blocked direct path is the harder case : nothing in the measurement marks the first arrival as a reflection. The receiver reports a confident and wrong answer.

Geometry limits the result independently of any of that. Transmitters clustered close together give ranges that intersect at a shallow angle. A small ranging error then moves the intersection a long way. Engineers quote it as dilution of precision, and it multiplies the ranging error rather than adding to it. A receiver seeing four satellites spread across the sky does far better than one seeing six in a line.

Put the three together and the practical ranking follows. Open sky gives good geometry and a clean direct path. An urban street gives poor geometry, because buildings hide half the sky. The buildings that remain add long reflections. Indoors removes the direct path altogether, which is why indoor positioning uses short range anchors rather than trying harder with the same satellites.

• Three failures, and only one of them is noise : bandwidth limits resolution, geometry multiplies error, and multipath adds a bias. Averaging helps with the first and not with the third.
• Dilution of precision is a multiplier : the same ranging accuracy produces very different position accuracy depending only on where the transmitters are.
• Indoors is a different problem, not a harder one : the direct path is gone, so the answer is new anchors rather than a better receiver.

Which technique does each system use ?

The table below places the common systems against the measurements above. The last column is the useful one. It names the quantity a designer would have to change, rather than quoting an accuracy figure that depends on the deployment.

The site covers several of these in their own right. 5G Positioning goes through the cellular reference signals and procedures, and WLAN indoor positioning covers the Wi-Fi side. AI and ML for positioning covers the recent work on learning a map rather than solving geometry.

One pattern runs through the whole table. Every system that reaches centimetres measures something with a short wavelength or a wide bandwidth. Every system that settles for metres measures something coarse and cheap. No technique escapes the nanosecond. The differences between them are about who pays for the clock, and how much spectrum the measurement may use.

• Accuracy tracks wavelength and bandwidth : carrier phase and ultra wideband reach centimetres for the same underlying reason, and neither does it with a better clock.
• The technique follows the environment : satellites outdoors, short range anchors indoors, and an angle measurement where neither timing route is available.
• Ask what would have to change : more bandwidth, tighter synchronisation, better geometry or a shorter wavelength. Every improvement in this field is one of those four.

YouTube

• Centimeter Positioning with a Smartphone-Quality GNSS Antenna (Oct 2014)
• RTK on Your Smartphone or Tablet (Jun 2015)
• New Generation GNSS Solutions: Precise Positioning, Navigation & Applications (Aug 2016)
• Centimeter-Accurate Mobile Positioning (Sep 2016)
• Centimetre Surveying With Your Smartphone (Jul 2017)
• Adventures in Science: How GPS Works (Jul 2017)
• What is Real-Time Kinematic (RTK) and how does it work? (Jan 2018)
• Neo-M8P RTK setup and demo (courtesy u-blox) (Mar 2018)
• GPS, How does it work? | ICT #12 (Sep 2019)

Reference