Use for TDOA in our system?

[jakapoor]

Many SDR approaches to RDF. Can they be combined?

The new direction for our RDF system (i.e. using coherent RTL SDRs) has revealed several open-source examples of RDF systems that have used similar hardware to what we are currently considering for the AMRUPT project. The use of SDRs, which are by their nature made flexible through the offloading of much functionality to software rather than hardware, makes it possible (in theory) for us to combine the advances in the approaches of several of these existing RDF systems.

"Thrifty" system by Krüger

One such system which may offer a particularly promising way to refine our own approach is the "Thrifty" system created by Schalk-Willem Krüger. In his system, described in detail in his dissertation (see Literature section of the repository), Krüger uses TDOA with non-coherent RTL-SDRs to achieve ~3.5 m localization resolution. This is achieved through the use of known-location beacon signals which, with cross correlation, are used to calibrate the clock offsets of the various receivers.

Combining TDOA and phase-based DOA?

Such an approach could potentially make it possible to combine his TDOA approach with our own DOA approach. In cases where the phase-based approach leads to higher quality estimates we could use those, and in cases where TDOA is superior those estimates could be used. In addition, a combined approach could help reduce the parameter space over which the phase-integer disambiguation algorithm would need to search (e.g. TDOA might produce a 10 meter area of high confidence for the location of a transmission, and the phase-based DOA ranging algorithm could then search within this area to further refine position estimates).

Hardware modifications necessary

Hardware modification that would need to occur to add in TDOA to our existing design include:

1. Addition of known-location beacons (which may also enhance DOA estimate accuracy)
2. Addition of transmitter hardware that would allow for UWB signals to be produced. The CC1310 (our intended transmitter transceiver IC) does not support OOK at the required MHz baud rate for creating an UWB signal, but Krüger's work indicates a potential solution: modulation of the transceiver's power amplifier (PA) through toggling the PA's RF power supply pin with a FET controlled by one of the transceiver's own GPIO pins. Whether such an approach is possible with the CC1310 is not known, but there is a separate RF power supply for the CC1310, which is a first step towards accomplishing this goal. The use of OOK (as opposed to BPSK or FSK) was also identified by Krüger as a necessary modulation scheme to bolster SNR / transmission detection probability. This scheme, which contains half of its power in the UWB parts of the spectrum and half of its power near the carrier frequency seems optimal for combining phase and TDOA approaches, since the former is essential for accurate timestamps, and the latter is important for accurate phase comparisons.

[russellmsilva]

My suggestion is no, TDOA in the "Thrifty" system would not improve resolution in our system.

Kruger's system uses Direct Sequence Spread Spectrum (DSSS) techniques to allow for greater resistance to interference by spreading the transmitted signal over a bandwidth that is significantly greater than the minimum bandwidth required to communicate the message signal. One of the purposes of these techniques (whether On-Off Keying, etc.) is to cross-correlate an incoming signal (with a certain gold-code modulated using OOK) with a local template signal. This would vastly improve a receiver's ability to determine the exact arrival time of a signal in TDOA, making the "Thrifty" system much more resilient to external noise and system-inherent noise. However, I propose that the use of OOK actually increases a TDOA sytem's susceptibility to multipath interference.

In Kruger's dissertation the arrival time estimation problem is stated as follow: "Suppose a time-limited, bandlimited radio signal s(t) of duration d is transmitted at time tx. Estimate the arrival time tx + τ from the observed signal r(t) at the receiver, where τ is the propagation time of the signal along the direct line-of-sight path between the transmitter and the receiver. For a simple model of the propagation medium it can be assumed that r(t) is a scaled and time-delayed replica of s(t) with additive noise n(t): r(t)= As(t−τ)+n(t).

In the presence of multipath propagation, the received signal will consist of the superposition of multiple copies of s(t) with different amplitudes and different propagation times greater or equal to τ."

Under this model, multiple refracted signals with certain gold codes would be transmitted to a receiver at different arrival times. Even if the refracted signals were separated from the original source signal on the microsecond level, a cross correlation with a refracted signal's gold code would yield highly inaccurate arrival time estimates.

In a standard TDOA system, the arrival time is determined by the precise instant at which the received signal's amplitude exceeds a set threshold. For a short-lived signal pulse, the line of sight (LOS) signal amplitude would cross this threshold before any refracted signal. Thus, if the transmitter sent short pulses separated in time, the standard TDOA system as described would not take into account the multiple copies of a signal that would be received after a LOS signal.

It is also important to note that the use of beacons does not help with the multipath problem, as the purpose of beacons only assist with "estimating the difference in arrival time without accurate estimates of the sample time, with unsynchronized real-time clocks, and with differences in the receivers' sample rates."

It would be unlikely for the Thrifty system to perform well in multipath environments. The ~3.5 resolution was achieved in a road test conducted "on a relatively straight road" in a rural environment, which presumably contains a sparse number of scattering objects compared to a forest or urban area. Furthermore, it is stated in the design premises that "it is is assumed that the system will be used in an LOS environment and that the effects of multipath propagation can be ignored."

A TDOA system's accuracy is capped by the following tradeoff: Increase noise resiliency and multipath susceptibility with DSSP techniques or decrease noise resiliency and multipath susceptibility using the arrival times of LOS signals. However, I would not completely rule out the utilization of standard TDOA in our system to reduce the parameter space for a combined AoA or PDOA approach under strong multipath conditions.

[jakapoor]

Thanks for this detailed response Russell! My thoughts on this are included below:

Detailed response:

... However, I propose that the use of OOK actually increases a TDOA sytem's susceptibility to multipath interference.... Even if the refracted signals were separated from the original source signal on the microsecond level, a cross correlation with a refracted signal's gold code would yield highly inaccurate arrival time estimates.

I disagree. My understanding is that this is precisely the advantage (not disadvantage) of the PRN [Gold] codes. TDOA is less susceptible to multipath interference than other forms of localization, and all TDOA systems that I am aware of use UWB signals; i.e. the type of signal you suggest would make it difficult to achieve an accurate time of arrival. The reason I believe that you are incorrect about the assertion that multi-path signals will yield inaccurate arrival time estimates is that PRN codes have low auto-correlation. If you compare the template to a received signal (i.e. one produced to match the template) the correlation between the template and signal will be very low until the template and signal are perfectly aligned, at which point the correlation will reach a peak. That's how extremely accurate time of arrival estimates are achieved. With sub-sample interpolation, that time of arrival estimate can be even further refined. Now, in the presence of multipath interference, you will receive several "images" of the correct signal (the LOS signal, and one or more delayed signals). All of these signals will have some (different) frame shift (or lag time) that results in its own cross correlation peak, but, in the cases where the LOS signal arrives at all it will always be the first correlation peak. TOA and TDOA applications use this fact to reject the other delayed signals that produce peaks, and thereby reduce multipath effects.

Another strong advantage of the PRN codes is that they strongly resemble white noise when they are not perfectly aligned to the template, and therefore those multipath reflections (Incidentally, I believe it's reflections, not refractions that we're talking about) don't end up significantly reducing the signal-to-noise ratio. This is primarily because the energy of the signal is spread broadly across the spectrum.

In a standard TDOA system, the arrival time is determined by the precise instant at which the received signal's amplitude exceeds a set threshold. For a short-lived signal pulse, the line of sight (LOS) signal amplitude would cross this threshold before any refracted signal. Thus, if the transmitter sent short pulses separated in time, the standard TDOA system as described would not take into account the multiple copies of a signal that would be received after a LOS signal.

This is incorrect. If you look at all TDOA systems, they use UWB signals (please correct me if you find a system that uses a narrowband signal). The reason for this relates to the Heisenberg-Gabor principle (i.e. one cannot simultaneously sharply localize a signal in both the time domain and frequency domain). In your hypothetical example in which a signal is extremely well defined in the time domain (i.e. an [ideally] infinitely short pulse), the frequency content of that signal, in compensation, would have to be extremely [in the ideal case, infinitely] wide-band. Conversely, that means that a hypothetical sinusoidal (i.e. narrowband) signal cannot be produced that will be ideally pulse-like in the time domain; we can define the frequency exactly (e.g. 1500 kHz) but cannot identify the exact start or end of the signal. Recall that a pure sinusoid, by definition is infinite in the time domain. To create a non-infinite sinusoid you have to introduce more and more frequency content to cut the beginning and end of the signal, so that a short sinusoid can no longer be thought to actually be a pure tone. So, bringing this perspective back to the ideal pulse-like signal we want for our TDOA localization technique, we need the frequency content of that signal to be as close to infinite as possible. The way this is accomplished is by rapidly modulating (pseudo) randomly to create something similar to white noise, but without the disadvantage of white noise not having low autocorrelation at nonzero lag times. Modulation can happen with phase-, frequency-, or amplitude-shift keying (also known as on-off-keying). Kruger discusses the advantages and disadvantages of these different modulation schemes, but I can explain if they aren't clear.

So, bringing it back to your suggestion that a TDOA system with pulsed (narrowband) signals would not be as susceptible to multipath interference, a pulsed narrowband signal would be far less definable in time than a pulsed UWB signal. You are absolutely correct that we could create a shorter pulse with a narrowband signal, but the increased temporal resolution of a longer ultrawideband signal would vastly outweigh the cost of having to produce a longer signal. The PRN's specific advantages (low autocorrelation, and noise-like spectrum) serve as further benefits over narrowband signals.

It is also important to note that the use of beacons does not help with the multipath problem, as the purpose of beacons only assist with "estimating the difference in arrival time without accurate estimates of the sample time, with unsynchronized real-time clocks, and with differences in the receivers' sample rates."

This is exactly my question: can beacons additionally help us to synchronize non-coherent receivers in phase in addition to time? Whiting has shown that it is possible to synchronize non-coherent receivers in time, and alludes to being able to synchronize them in frequency and phase. So it is possible, and that therefore would help with the multipath problem because the beacons would then serve the purpose of standardizing initial phase offsets. The question now is how.

It would be unlikely for the Thrifty system to perform well in multipath environments. The ~3.5 resolution was achieved in a road test conducted "on a relatively straight road" in a rural environment, which presumably contains a sparse number of scattering objects compared to a forest or urban area. Furthermore, it is stated in the design premises that "it is is assumed that the system will be used in an LOS environment and that the effects of multipath propagation can be ignored."

Agreed, the "Thrifty" system may well be somewhat susceptible to multipath effects, but this is not an indication that any other technique would necessarily be better. Multipath effects are always a problem, no matter what you do, but TDOA tends to offer a far better solution (despite still not being perfect) than other techniques.

A TDOA system's accuracy is capped by the following tradeoff: Increase[d?] noise resiliency and multipath susceptibility with DSSP techniques or decrease[d?] noise resiliency and multipath susceptibility using the arrival times of LOS signals. However, I would not completely rule out the utilization of standard TDOA in our system to reduce the parameter space for a combined AoA or PDOA approach under strong multipath conditions.

I believe that this conclusion is faulty because of what I've mentioned above. The UWB signals can assist in both signal detectability and multipath resilience. The modulation scheme used (PSK, FSK, OOK/ASK) can significantly alter the spectral profile of the signal, and therefore its detectability, however. I'd recommend re-reading Kruger's work about the pros/cons of modulation schemes.

Reframing the question:

All this said, the question I was hoping to address with this issue was whether TDOA can help us to further refine our phase-based system.

The PDOA ranging algorithms become increasingly computationally costly as the parameter space over which the phase cycle integer is being searched. For instance, if a signal could be located between 0.5 m and 290.5 m from a pair of receivers spaced 300 m apart (from the perspective of one of those receivers, and in a 1D situation), the ranging algorithm would have to search for all possible solutions of phase cycle integers between 0.5 and 290.5 m. However, with TDOA, we could first identify that the signal very likely emanated somewhere between 23.4 and 27.8 m from receiver one, and then pass this information to the ranging algorithm. This might not only decrease computation time, but might allow us to get away with fewer frequencies in the HMFCW stage.

In a way, I've already answered my own question about whether this would help us, the main questions now are 1) Is it worth the effort? and 2) If so, how do we achieve this?

Please let me know if this makes sense, or if you disagree with anything I've said here.

-Julian

[russellmsilva]

Now, in the presence of multipath interference, you will receive several "images" of the correct signal (the LOS signal, and one or more delayed signals). All of these signals will have some (different) frame shift (or lag time) that results in its own cross correlation peak, but, in the cases where the LOS signal arrives at all it will always be the first correlation peak. TOA and TDOA applications use this fact to reject the other delayed signals that produce peaks, and thereby reduce multipath effects.

From Kruger's Dissertation: "The cross-correlation function will exhibit maximum magnitude where the template aligns best with the incoming signal. A precise line-up yields the position, i.e. the arrival time, of the code that is embedded in the incoming signal. The ability to estimate the code phase of the incoming signal forms the basis of the use of DSSS for arrival time estimation and ultimately position estimation."

The main point of my argument is: What is the shortest duration of a gold-code necessary for cross correlating an incoming signal with a local template? If a reflected signal is received 1 microsecond after a line of sight signal, and the gold-code is 20 microseconds long, then the receiver cannot determine an accurate arrival time based on the cross-correlation function.

This is incorrect. If you look at all TDOA systems, they use UWB signals (please correct me if you find a system that uses a narrowband signal).

I did not state this explicitly in my response, but the response was written with the understanding that TDOA systems use UWB signals. The wording "short-lived signal pulse" refers to a UWB pulse with a short time duration. In a standard TDOA (not "Thrifty") system, I assume that these pulses are spread out sufficiently in time, so that a LOS signal will not be received at the same time as a reflection of a previous pulse.

Multipath effects are always a problem, no matter what you do, but TDOA tends to offer a far better solution (despite still not being perfect) than other techniques.

I agree that multipath effects are always a problem; however, it is unclear whether TDOA is more accurate than triangulating a source signal with subspace angle of arrival techniques. The multiple signal classification (MUSIC) algorithm can be specifically tailored to a multipath environment with subspace smoothing methods. Furthermore, the Ettus MUSIC code integrates forward and forward-backwards subspace smoothing. It is important to note that the two systems are incompatible (unless AoA and TDOA measurements are done sequentially, adding a layer of complexity to our system), because MUSIC utilizes narrowband signals and TDOA utilizes ultra-wideband signals.