Estimating state and state-covariance from noisy measurements

Discussion in 'MATLAB' started by Srikanth, Jul 11, 2010.

  1. Srikanth

    Srikanth Guest


    I have two noisy (iid) sensors for a system y=x, where x is supposed
    to be stationary. So basically, I get several measurements for each
    state. I would like to estimate the 'actual' mean and state-covariance
    for x.

    I have around 300 readings for each state in y1 and y2. Most of the
    work I read talks about finding the covariance of the error, which is
    not what I am trying to estimate. Is there a way in matlab to estimate
    the state-covariances and means?

    Thank you
    Srikanth Sridharan
    Srikanth, Jul 11, 2010
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  2. Srikanth

    Rune Allnor Guest

    Then you need to find out *why* what you read does not
    treat the question you want to ask:

    1) Do you read the wrong literature?
    2) Or do you read the right literature but have missed some
    essential insights?

    Rune Allnor, Jul 11, 2010
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  3. Srikanth

    Srikanth Guest

    I looked in the estimation and detection literature - maximum
    likelihood estimators, Kalman filters etc. I suspect that this is a
    common problem, so I must be missing something trivial. The simplest
    problem I can come up with is given two means and covariance matrices,
    finding a mean and covariance matrix that would explain both
    'satisfactorily'. My initial idea was to find the smallest 'sphere'
    that might enclose these equally-trusted observations (I might be
    trying to visualize something that isn't really correct, so that could
    be part of the problem). Any ideas/tips would be appreciated.

    Thank you
    Srikanth, Jul 12, 2010
  4. Srikanth

    Srikanth Guest

    Looks like I found the solution for my own question.

    For anyone else who might have a similar problem, there is a Mixed
    Models Theory (and certain simplifications of it for known
    covariances) that can be used to solve this type of problem. The
    corresponding Matlab function is lscov.
    Srikanth, Jul 12, 2010
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