I have a 7 sensors uniform linear array that have some errors to be estimated (i.e. to do array calibration). The errors are: gain, phase, and position (in y and z axes). So, the total is 28 variables. I used fmincon MATLAB function in two ways: 1) stack all the 28 variables in one long vector, and 2) stack the gain and phase errors in one vector and the position errors in another vector and solve iteratively. Both ways gave bad estimation for the actual errors.
I would really appreciate it if some one can give me an advice on which optimization method is best to solve this problem with good-enough accuracy.
Note: the cost function to be minimized is the Frobenius norm of the error between the nominal steering matrix (A1) and the actual (i.e. measured) steering matrix (A2).
Thanks,
What type of sensors are you talking about? Acoustic (aka microphones)?
If so, I'd expect any position error to translate into some phase error. (If the inter-sensor distance is large, a noticeable gain error might occur as well.) Anyway, this would reduce the problem down to 14 variables.
Thank you Dreher for your answer. The sensors here are antenna dipoles. We need to account for these errors to get a better estimate of the direction of the received signals by an air-born radar.
Have you considered a method like annealed optimization or a genetic search? I think these methods are usually more robust in cases with lots of degrees of freedom. They are computationally costly (but then again - 28 variables), but easy to parallelize and run on a multi-core CPU.
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