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  • $\begingroup$ Thank you for your response. What you mention is the statistical approach, which I have worked with. I have worked with ML estimation, CRLB, fisher information matrices and so on... so, I suggested the same to my colleague: try to characterize the noise and go for ML estimation, or reconsider if the model does not fit your data. I was asking for another approaches... if they exist.. $\endgroup$ Commented Dec 11, 2018 at 16:42
  • $\begingroup$ OK, I think I get the idea now. Check out my second proposition in the edit. If I have more time I'll try to explain the idea further, later today or tomorrow. $\endgroup$ Commented Dec 11, 2018 at 17:08
  • $\begingroup$ OK, I'll take my time to read your second approach. I think I can also give more details about the model and the data. Thank you so much! $\endgroup$ Commented Dec 11, 2018 at 17:12
  • $\begingroup$ I have added the mathematical formulation of the problem. I think that trying to get a ML estimator analytically will be quite difficult since all the observed values $\theta$ are not independent, they come from a sensing unit which is a black-box for us.... so trying to make assumptions about its pdf will be very challenging. For your "data-driven" approach, Iam sorry but i don't understand the idea of sorting the samples... $\endgroup$ Commented Dec 12, 2018 at 9:24
  • $\begingroup$ It's because I thought theta was just a scalar value! With a multi-dimensional output it is much more complicated. I'll think about it. $\endgroup$ Commented Dec 12, 2018 at 12:03