# tdoa | Time Difference of Arrival ) is estimated using GCC

## kandi X-RAY | tdoa Summary

## kandi X-RAY | tdoa Summary

TDOA (Time Difference of Arrival) is estimated using GCC-PHAT. A realtime DOA (Direction Of Arrival) is also elstimated using 2 microphones.

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QUESTION

I have 3 receivers (A, B and C), and some signal producing source (let's say sound or light) with an unknown location. Given the locations of A,B and C, and the time at which each receiver "heard" the signal, I'd like to determine the direction of the source.

I understand there are ways to do so with TDoA multilateration/trilateration, however I'm having trouble implementing the calculation. There isn't a lot of clear, detailed information on this out there for those entirely new to the subject. What is out there is vague, more theoretical, or a bit too esoteric for me.

Some similar posts on SO (but not quite what I'm after): TDOA multilateration to locate a sound source Trilateration of a signal using Time Difference(TDOA)

This is also interesting, but assumes we have some boundaries: Multiliteration implementation with inaccurate distance data

@Dave also commented an excellent and fairly accessible resource https://sites.tufts.edu/eeseniordesignhandbook/files/2017/05/FireBrick_OKeefe_F1.pdf, but it falls short of going into enough depth that one might be able to actually implement this in code (at least, for someone without deep knowledge of regression, finding the intersection of the resulting hyperbolas, etc).

[EDIT]: I should add that I can assume the 3 sensors *and* the source are on the surface of the Earth, and the effects of the curvature of the Earth are negligible (i.e. we can work in 2-dimensions).

ANSWER

Answered 2020-Sep-09 at 15:25The simplest (but not fastest) approach would be to solve the equations with gradient descent.

I'm assuming that we know

- the positions of the receivers, A, B, and C, which do not lie on the same line;
- the pseudorange of the unknown source X to each of A, B, and C.

Intuitively, we simulate a physical system with three ideal springs configured like so, where the equilibrium length of each spring is the corresponding pseudorange.

QUESTION

I am trying to use TDOA to find the sound source location in a coordinate system.

We have a costfunction looks like this:

...ANSWER

Answered 2020-Oct-08 at 18:26BFGS will not guarantee anything but a local minimum. If you know that your sensors will always be between -50 and 50 and -2 and 2, then I would suggest:

- As a first step, try a bounded local minimization - using L-BFGS-B, SLSQP, etc... and give your variables those bounds
- If the above is not satisfactory enough, bring out the big artillery and try global optimization algorithms, such as SHGO, DifferentialEvolution, DualAnnealing. They are all available in SciPy, might be slower but you’ll be much more confident in your results.

QUESTION

I've written the following algorithm designed to solve the Time Delay of Arrival problem through a "brute force" method. The problem is as follows: given the *known* locations of three receivers in a plane, and the propagating speed of some signal, determine the location of the signal source knowing only the times at which each receiver "saw" the signal.

The algorithm works by assuming the source to be within a 1000 x 1000 kilometre square area, and then iterating (with 1 km "resolution") over every possible location, calculating the time to travel to each receiver and determining which location matches most closely with the known delay of arrival between each receiver (so, for each location [x,y], I calculate the time to arrive to receivers 1, 2, and 3, then determine how close time to arrive at 1 - time to arrive at 2 is to the live data, and similarly for the combinations 1 - 3 and 2 - 3 (ignoring other possible combinations, for simplicity).

Here's the problem: it's *highly* unlikely each signal event is coming from the same direction. However, my code seems to suggest every event is at [0,0]. While it is technically *possible* that this is the case, it is far more likely that there is something wrong with my code, so for the purposes of this question let's assume that to be the case. Perhaps I've made some obvious mistake here?

ANSWER

Answered 2020-Sep-11 at 21:14alphaEst, betaEst and gammaEst are assigned the same values.

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## Install tdoa

You can use tdoa like any standard Python library. You will need to make sure that you have a development environment consisting of a Python distribution including header files, a compiler, pip, and git installed. Make sure that your pip, setuptools, and wheel are up to date. When using pip it is generally recommended to install packages in a virtual environment to avoid changes to the system.

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