I am searching for a recursive or online non linear least squares algorithm. I want to spread the computation out as new data is sampled like in the linear Recursive Least Squares or the LMS.

Ideally a recursive Levenberg–Marquardt algorithim would exist as Levenberg–Marquardt works great on my non linear problem but need to reuse all the samples to calculate a new estimate.

The online recursive non linear estimators I have found so far are:

  • The Extended Kalman Filter

  • Unscented Kalman Filter

  • Particle filter

Some articles I have found interesting:

  • Two step estimator as described in the paper "Optimal recursive iterative algorithm for discrete nonlinear least-squares estimation (1996)" by Gordon T. Haupt, N. J. Kasdin, George M. Keiser, and Bradford W. Parkinson

  • The Modified Extend Kalman Filter as described in the paper "A recursive algorithm for nonlinear least-squares problems (2007)" by A. Alessandri, M. Cuneo, S. Pagnan, M. Sanguineti

Do other online non linear estimators exist? What are the popular online non linear estimators? I have minimal experience with non linear estimation.

  • $\begingroup$ it is not a good idea to place particle filter in the same category as the "modified" kalman ones, since they are based on linearization $\endgroup$ Apr 8, 2019 at 8:16
  • $\begingroup$ @Fat32, The Unscented Kalman Filter (UKF) doesn't linearize the problem. $\endgroup$
    – Royi
    Jun 26, 2019 at 6:54


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