[SciPy-User] estimation problem

[Neal Becker]

josef.pktd at gmail.com wrote:

> On Fri, Jul 15, 2011 at 12:58 PM, Neal Becker <ndbecker2 at gmail.com> wrote:
>> I have a known signal (vector) 'x'.  I recieve a vector 'y'
>>
>> y = F(k x) + n
>>
>> where n is Gaussian noise, and k is an unknown gain parameter.
>>
>> I want to estimate k.
>>
>> F is a known function (nonlinear, memoryless).
>>
>> What might be a good approach to try?  I'd like this to be an 'online'
>> approach - that is, I provide batches of training vectors (x, n), and the
>> estimator will improve the estimate (hopefully) as more data is supplied.
> 
> scipy.optimize.curve_fit
> 
> I would reestimate with the entire sample after a batch arrives using
> the old estimate as a starting value.
> 
> There might be shortcuts reusing and updating the Jacobian and
> Hessian, but I don't know of anything that could be used directly. (I
> don't have much idea about non-linear kalman filters and whether they
> would help in this case.)
> 
> Josef
> 

Thanks.  One fix, that should have been
"I provide batches of training vectors (x, y)".  n is unknown noise.