The paper System Identification using Symbolic Chaotic Sequence proposes EM-UKS estimator for system identification of a linear FIR channel when excited by non linear input.

In Fig 3 of the paper there is a comparative plot of system identification of FIR model

$$ y[n] = H^T x[n] + w[n] $$

Where $x[n]$ is a chaotic input and $w[n]$ is AWGN with unknown variance.

Performance is compared using CRLB vs MSE when the FIR system is driven by (a) chaotic deterministic numerical input, (b) chaotic quantized input (called as symbolic input), (c) filtered Gaussian input, and (d) PRBS input.

Q1: What is the estimation technique when the input is white Gaussian and PRBS ? Is it Ordinary Least Square as they mention that they are comparing with the CRLB of non-blind. So, OLS is a non-blind technique.

This is how I implemented when the input is white noise:

 h = [1    0.65   -0.2];  % MA channel coefficients
    x = randn(1000,2);  % white noise input
    u = filter(h,1,x);
    y = awgn(u,10,'measured'); % adding noise w of SNR =10dB
    X = [y,ones(n,1)];

Q2: I am not sure how to implement using PRBS. Can somebody please provide the code?

Q3: Is the system identification using EM-UKS when the input is chaotic and symbolic proposed by the Authors blind or semi-blind and why?


1 Answer 1


Interesting paper!

Q1: yes, seems like OLS, non-blind. Usually OLS is non-blind. Some sort of regulated least squares can be used in a bayesian ML-setting, blind. This paper looks interesting: http://www.cs.berkeley.edu/~jordan/papers/lindsten-etal-sysid12.pdf

Q2: PBRS: https://en.wikipedia.org/wiki/Pseudorandom_binary_sequence. There is a lot of literature on this, e.g. Coleman Brosilow, Babu Joseph, "Techniques of Model-Based Control"

Q3:they say it is semi-blind since the dynamics of the sequence generator is known.

  • $\begingroup$ Thank you for your answer. Could you please elaborate on the first point which is how OLS can be used as a blind estimator in a bayesian setting? I know that ML = OLS in Gaussian noise but is this meant for blind identification? $\endgroup$
    – Ria George
    Jun 27, 2015 at 19:33
  • 1
    $\begingroup$ You are right in ML = OLS with gaussian noise. Not that simple in bayesian/state-space settings so I edited my answer. $\endgroup$
    – Stig Uteng
    Jun 27, 2015 at 22:07

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