# Estimating state and state-covariance from noisy measurements

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

1. ### SrikanthGuest

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

Srikanth, Jul 11, 2010

2. ### Rune AllnorGuest

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

Rune Allnor, Jul 11, 2010

3. ### SrikanthGuest

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. ### SrikanthGuest

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