Estimating state and state-covariance from noisy measurements

Hi

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

 

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

 

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

 

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.