Over the past couple of days I have been battling with solving the multilateration equations. Today I got them working in the guise of a numerical solution using matlabs fminsolve function. It took a while to figure out how it worked, but when it did, it worked straight away. The next thing was to throw some real data at it, and this is what has taken much of the day up. There must be still something wrong in the main routine, because I am sure that the numerical solutions are ok.
Either way, it takes for ever. The idea was to take an abitrary set of 3 pulses to test the fourth and iterate over all combinations. Then we keep the iteration that provides the smallest (acceptable) error. The problem with this is that when the rain rate gets up, then it is inevitable that 10+ pulses appear in the same time window. Now, for 10, there are somewhere around 200 combinations of 1-10 in sets of 4. The fminsearch takes somewhere around 10ms to compute, so 200*0.01 = 2s. This is only for one set of 4, and thats even if it works out in the end. So when we have maybe 100 pulses, simulation times get loooong.
There are two ways around this, firstly just dont use the estimation. Secondly find another way. What we could also do with the final device is when the rain rate does get too high, then just raise the threshold and ignore all the smaller drops.
I’ll email kevin tommorow and see what he thinks.
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