Measurement Basics of Location Systems: Distance and Direction

A location system does not "see" where an object is. Instead, it measures properties of radio signals passing between devices at known and unknown positions. Software then uses those measurements to estimate location.

Most radio-frequency (RF) based location systems ultimately measure one of two things: distance or direction. Very few systems actually measure both, although these do exist and usually offer greater performance but at a greater price.

Understanding these basic measurement types makes industry terms such as ToF, TDoA, AoA, RSSI, trilateration, and triangulation much easier to evaluate.

The Basics: Transmitters & Receivers

A transmitter generates a radio signal and sends it through an antenna. A receiver detects a radio signal and extracts information from it. Some devices are transceivers, meaning that the same device can both transmit and receive a signal.

To determine where an object (transmitter) is located in a space, a system can calculate either how far away it is from several fixed points (receivers), or the direction from which its signal arrived.

By combining multiple distance measurements, the system can estimate the point where those measured distances intersect, a process called trilateration. By combining multiple angle measurements, a system can estimate the point where those directions intersect, known as triangulation. Related methods such as multilateration use differences in signal arrival times between several receivers to calculate position (more on this below).

In practice, measurements rarely intersect at one exact point, so location software calculates the position that best fits the available data. The more data received and the clearer that data, the more precise and accurate a location system's performance can be.

Measuring distance

There are multiple ways to measure the distance a signal has travelled between a mobile transmitter and a fixed receiver.

Measuring distance using signal strength

One way to estimate distance is to examine the strength of the signal arriving at the receiver.

This measurement is commonly called Received Signal Strength, or Received Signal Strength Indicator (RSSI).

In general, signal power decreases as distance from the transmitter increases (see our article on radio frequencies for more information). A system can therefore use a propagation model to convert received power into an estimated distance. If three or more known reference points provide distance estimates, their results can be combined to estimate position.

The problem is that buildings do not produce uniform signal loss. Walls, people, reflections, antenna orientation, machinery, interference, and other factors can change the signal strength (RSSI) without changing the actual distance.

RSSI can therefore provide useful proximity or location information, but signal strength is an indirect measurement of distance rather than a direct measurement of geometry. Academic reviews frequently identify environmental attenuation and interference as major factors affecting the relationship between RSS and distance. Whilst vendors have improved their algorithmic models to calculate distance based on signal strength, this measurement method limits the practical performance in busy or cluttered spaces.

Measuring distance using time

Radio waves travel through air at close to the speed of light. If a system can measure how long a signal took to travel between two points, it can calculate the distance:

distance = propagation time × speed of light

This principle is generally called Time of Flight (ToF). A related term, Time of Arrival (ToA), refers to measuring when a signal arrives at a receiver. If the transmission time is known accurately, the difference between transmission and arrival time gives the propagation time.

The difficulty with this measurement is scale. Radio travels roughly 30 cm in one nanosecond. A timing error of only a few nanoseconds can therefore translate into a substantial ranging error. Systems must be finely tuned and capable of synchronising time and measuring very small amounts of time reliably.

Two-way ranging

One way to avoid requiring perfectly synchronised clocks at the two devices is two-way ranging.

Device A sends a message to Device B. Device B responds. Device A measures the total round-trip time.

After allowing for the processing time at Device B, the system can estimate how long the RF signal spent travelling in each direction and calculate the range.

Two-way ranging makes clock synchronisation between devices less demanding, but it requires message exchanges between them. This consumes airtime and energy, which can become important when large numbers of mobile devices need frequent updates. If a mobile device (transceiver) needs to send a signal, receive back the signal, then make a calculation, it can have significant effects on power consumption and therefore battery lifetime.

Time Difference of Arrival

Time Difference of Arrival (TDoA) takes a different approach.

A transmitter sends a signal that is detected by several receivers at known locations. If those receivers share a precise time reference, the system can compare when the signal reached each one.

The system does not necessarily need to know exactly when the transmitter sent the signal. It needs to know the difference between arrival times at the different receivers.

If the signal reaches Receiver A before Receiver B, the transmitter must be closer to A by a distance corresponding to that time difference.

Combining several TDoA measurements produces a location solution based on intersecting geometric surfaces.

This technique is commonly referred to as multilateration.

Measuring direction

Instead of measuring how far away a transmitter is, a system can measure the direction from which its signal arrived.

Angle of Arrival (AoA)

One option is to measure the precise direction a signal arrives at a receiver. This is Angle of Arrival (AoA).

A receiver commonly uses several antenna elements arranged in an array. Because each antenna occupies a slightly different position, the RF wave reaches them with measurable phase differences.

The system uses those differences to estimate the direction of the incoming signal.

Angle of Departure (AoD)

A related technique is Angle of Departure (AoD).

Here, the direction information relates to the direction in which the radio wave leaves a transmitting antenna array. A receiving device can use known properties of the transmitted signals to estimate its direction relative to the transmitter.

Both methods convert characteristics of the electromagnetic wave into angular information.

Trilateration and triangulation

The terms trilateration and triangulation are often used interchangeably, but they describe different geometric methods.

Trilateration uses distances.

If the distance from an unknown object to several known points is available, the system calculates the position that best fits those distances.

Three distance measurements can provide a 2D solution under suitable conditions. Additional measurements can improve the solution and allow the system to manage measurement errors.

Triangulation uses angles.

If a system knows the direction of an object from multiple known points, the intersection of those directions can determine its position.

In real installations, measurements rarely intersect perfectly. Location software therefore uses mathematical estimation to determine the position that best fits the available data.

Different measurements answer different questions

RSSI asks: How strong was the signal?

ToF asks: How long did it travel?

TDoA asks: Which receiver received it first, and by how much?

AoA asks: From which direction did it arrive?

AoD asks: In which direction did it leave the transmitter?

No measurement method removes the laws of radio propagation. Each extracts different information from the same underlying electromagnetic signal.

The performance of an indoor location system therefore depends not only on which radio frequency it uses, but also on what it measures and how the system converts those measurements into a position.

Systems that use multiple measurement methods simultaneously can offer greater performance in terms of accuracy and reliability, but come with more sophisticated and potentially complex infrastructure and set-up. Simple measurement systems may give good performance at low cost in uncluttered spaces, but struggle to reliably locate objects in busier, denser, or architecturally complex environments.

There is therefore usually a trade-off in RTLS between performance, cost, and reliability, which can only be solved by understanding the requirements of the particular use case RTLS is being used for.