Application Note

Time Difference of Arrival (TDOA)

Introduction

Time Difference of Arrival (TDOA) is a technique for geo-locating RF sources. It requires three or more remote

receivers (probes) capable of detecting the signal of interest. Each probe is synchronized in time to capture

corresponding I/Q data blocks. Software shifts the time signature of each I/Q data set to nd the difference in the

arrival time at each probe. This gives the difference in the distance of the source from each set of probes. Using

several probes provides a set of curved lines that indicate solutions to the distance equations. The actual RF source

sits at the intersection of these lines.

1. A modulated signal is transmitted from an

unknown source.

2. The signal is captured at three or more probes at

various locations around the source.

3. The signal captured at each probe is shifted in

time to nd a position of maximum alignment.

4. The time shift necessary to align each signal is

multiplied by the speed of light to get a distance

difference between each probe.

5. The distance difference is plotted as a set of

the RF source.

Application Note

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Considerations

Modulated Signals. In order to time-align the received signal at each probe, the signal must contain non-random,

non-repeating structure. Many interference sources emit white noise, which lacks the structure necessary to align

the signal. Simple sources, such as a sine wave generator, produce a repeating pattern that has structure, but the

repeating pattern does not allow for a unique time-alignment. Repeating patterns can be aligned at multiple

positions with no means of distinguishing a correct time-shift.

Modulated signals contain internal structure that can be aligned in time. Good examples of modulated signals

strength will not necessarily produce a better answer.

Multi-path signals will tend to broaden the I/Q pattern and make it more dicult to nd the proper time-

alignment. If the strongest component of the signal is a reection off of some nearby surface, then the distance

calculation will be the reected signal path, rather than the direct straight-line path between the probe and source.

The software cannot know this, so the result is a systematic offset to the distance calculation, equal in magnitude

to the reected distance of the signal.

Probe Synchronization. In order to do the TDOA calculation wherein each data stream is shifted in time to nd

the optimal signal alignment, it is necessary to capture the same signal at each probe location. Not just capturing

the RF signal from the same source, but the same signal in time must be captured. If the source is a radio

transmission, for instance, then each probe needs to capture the same utterance, or musical note. Special

A good TDOA system will produce location estimates within 100 meters of the source location. An RF signal travels

100 meters in about 300 nanoseconds. Therefore the timing of the signal must be known with very high precision.

Every I/Q sample point is not time stamped. In practice, an internal clock is synchronized once each second

with GPS satellites. The internal clock tracks time between the GPS synchronization pulses. This clock needs to

be very stable as it inserts a timestamp to the data stream at regular intervals. If one of the clocks drift, then it is

impossible to get a good time-alignment since features lined up in one section will not align further on. Various

spectrum monitors are capable of capturing I/Q data streams. Unless the spectrum monitor is designed with high

precision timing, it will not work adequately for TDOA measurements.

Hyperbolic Lines. The result of a TDOA measurement is a time difference in the arrival of the signal of interest at

two or more probes. The time difference is multiplied by the speed of light to give a difference in distance between

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Triangulation. Using three probes gives three

sets of two probes, so a TDOA measurement of

three probes will produce three hyperbola, the

intersections of which yield possible locations for

the RF emitter (See gure 1.) If the source is inside

the triangle formed by the three probes, then you

may get a single intersection point. However, it is

not unusual to have a couple of intersection points

for the three curved lines, especially if the source

is very far outside the probe triangle. It is usually

This is by denition the temporal resolution: the

spacing in time of the sample data points. The

time separation is multiplied by the speed of light

to get the distance separation, so the spatial

resolution is directly proportional to the

temporal resolution.

As a specic example, consider a sampling rate of 250 kHz. . A 4 μs

time resolution gives 4 μs * 3 x108 m/sec = 1.2 km per data point. A spatial resolution of 1.2 km is not very good.

If the sample rate is 2.5 MHz, then we have increased the resolution of the measurement by a factor of 10, or 120

meters. That is a useful result when hunting for an interference source or rogue transmission. We will discuss

signal typically has a maximum modulation frequency of 20 kHz.

Imagine a modulated sine wave that you want to sample in order to reproduce the signal. Sampling once per

period is not enough. One would probably end up with something very much like a at line. Sampling 20 times per

period would give a fair representation of the sine wave’s shape. Sampling 50 times per period might be a little

bit better, but sampling 1000 times per period isn’t really going to give you more information. A real signal always

carries some noise anyway, so there is a practical limit to the usefulness of sampling at higher and higher rates. A

good rule of thumb is that sampling at 20 points per period is pretty good. Doubling that might gain something,

but beyond that is pointless. So for an FM signal, a practical limit is around 500 kHz, and 250 kHz is pretty good.

250 kHz =

three probes.

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Figure 3 below shows the data from two probes, one slightly ahead of the other. The dots represent sample

points. There are not enough data points to accurately reproduce the shape of the curve, so the green and blue

lines represent the best guess at the peak position for each set. Because the sample rate is too low, a large error i

s introduced. In Figure 4, the sample rate has increased and the peak positions are accurately found. Increasing

the sampling rate further is not necessarily going to increase the accuracy.

Cable Length. An important consideration when doing detailed timing measurements is cable length and

internal timing delays. In an ideal TDOA system, the I/Q data stream is timestamped at each I/Q pair with the

precisely synchronized time-of-arrival of the signal at the antenna of each probe. In practice, this is very hard to

do. Errors in timing typically produce a systematic error that shifts the geo-location estimate consistently in one

direction. Systematic errors cannot be eliminated with averaging. Instead, the average will consistently converge

to a stable wrong answer. The error in the estimated direction and distance depends on the particular timing

differences between the probes in use.

The typical speed of transmission in a coaxial cable is about 2/3 the speed of light. So for every 20 meters

lengths, then this should be accounted for. Remember, it is not the total cable length that is important, but the

difference in cable length. Most TDOA systems will allow for entry of the cable lengths for each probe in the

system, and the software calculates the differences.

Timing Delays. Of similar concern are internal delays in the probe hardware and the analog and digital paths

used to capture, process, and store the I/Q data stream. This internal delay adds a systematic error that cannot

be removed with signal averaging. The internal delay will vary from probe to probe and is often frequency

dependent, as the center frequency and range will affect hardware and software  lters in place to correctly

capture the signal of interest.

The I/Q data pairs must be time stamped in the data stream in order to do the time-alignment. Any uncertainty

in the clocks used to generate the timestamps will introduce uncertainty in the location estimate. Most remote

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In Figure 5 notice that the signals are aligned at the green vertical

line. In this case, the clocks run at slightly different rates, so the green

data points are spread out more in time. When this happens, it is not

possible to get a meaningful result as there is not a single time shift at

which the data are all aligned in time.

Location of Emitter. The location of the RF source is also a factor in

determining the accuracy of the location estimation. If the source is

inside the triangle formed by the three probes, then the accuracy is

expected to be high. When the emitter is behind one of the probes,

as long as it is high enough above the background to be able to get a reasonable I/Q capture.

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Referring back to  gure 2, and looking at the more distant intersection of the three lines, it is seen that the blue

and green lines especially, and the red line somewhat, approach each other at narrow angles. If the uncertainty

in the measurement is 100 meters, then the true location of the RF source lies whenever the three lines are within

100 meters of each other. In  gure 2 this is true of the blue and green lines for about 15 km. The red line crosses

at a small enough angle that the actual area of possibility is more than a kilometer long. This is another case where

a different probe set would be very useful so the source position is closer within the probe triangle.

Signal Averaging. Averaging is a good way to reduce random uncertainties in

measurements. With TDOA this is accomplished by repeating the measurement

several times and averaging the distance differences found for each probe pair.

The probes all have to begin capturing at the same time, and they have to each

capture a long enough data set that the overlap of the signal will be signi cant.

To accomplish this, Anritsu implements proprietary algorithms to capture and

time align each bursted signal.

Anritsu provides TDOA measurements with MS2710xA Remote Spectrum Monitors (RSM) and the Vision software

suite. The RSM probes have the necessary I/Q capture and precision timing features necessary to collect and

transmit the timestamped I/Q data used in TDOA measurements. RSM probes can monitor and measure

frequencies up to 6 GHz, with a maximum capture bandwidth of 20 MHz. RSM probes also come in a number of

form factors and packages to suite a wide variety of situations. Options include multi-port enclosures that use a

single receiver board to access up to 24 different antenna inputs. This provides a convenient means of deploying a

single probe to cover multiple frequency ranges and tuned to speci c band widths. RSM probes are also available

in IP67 quali ed enclosures to be mounted and operated outdoors for extended periods of time. See  gures 11, 12,