TDoA Multilateration and Accuracy

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David Robie
David Robie 2018-5-31
Github repository with files relevant to this question are located here.
Hello, I wrote Matlab code that accepts inputs of sensor locations and the TDoA of a signal with unknown source. The output is the 3D coordinates of the signal emitter. My problem is that this code only returns an accurate answer if the TDoA inputs have 8-9 decimal places of precision.
Is there a way that I could tweak my code, or perhaps another algorithm I could use, so that I can generate an accurate answer from TDoA inputs that have 4-6 decimal places of precision?
In testing, I've needed a way of generating TDoA conditions, so I made an Excel sheet that accepts the "unknown position" of the emitter, and creates the TDoA. These TDoA values are fed to my Matlab code, and if it's working, the output should be the same as what I input to Excel.
To use my algorithm for testing, open the Multilateration6.xlsx spreadsheet, and enter in x,y,z coordinates for "E". Then feed TDoA (in the spreadsheet these are called "t_PreciseN", where N is an integer representing how many decimal places that TDoA rounds to) values into t1-t6 of MultilatX.m. Make sure that MultilatX.m, SolverX.m, and combinator.m (shout out to Matt "Loginatorist", this combinator file is great (: ) are in the same folder when you run MultilatX. Feel free to experiment with feeding different levels of TDoA precision. Oh, and the .jpg files are hand written maths to explain what I've done and why.
Thanks guys!!!

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