[R-sig-dyn-mod] differential equations with unknown inputs?

[Thomas Petzoldt]

Hello Spencer,

your question is a little bit vague, because I don't know what kind of 
inputs you have and how is your model constructed. Nevertheless, I would 
probably start with deSolve and then explore other methods if required.

I'm not sure if the developers of dlm and sde are already on this list, 
so let's send them an invitation.

Thomas

On 3/24/2011 10:40 PM, Spencer Graves wrote:
> Hello:
>
>
> How would you approach solving a linear differential equation system
> with constant coefficients and unknown inputs sampled at irregular time
> intervals? I'm trying to model the motion of a bridge driven by traffic
> and heating with a 6-dimensional linear state space model with constant
> coefficients but with no knowledge of the traffic and large gaps in my
> records on the temperature.
>
>
> I perceive 3 primary options: dlm, deSolve, and sde.
>
>
> deSolve: I'm concerned that the difference between observation and
> transition noise could be large in my current application.
>
>
> dlm: This seems like the best option, because unknown inputs can be
> handled as transition noise. The primary difficulty I see is in
> translating the differential equation into a difference equation,
> including estimating the noise variance as proportional to
> integral(exp(A(t-tau))d.tau).
>
>
> sde: It might make most sense to model this as a stochastic differential
> equation. However, I have the impression that sde will not handle a
> multivariate state vector.
>
>
> Thanks in advance for any thoughts you may have on this.
>
>
> Best Wishes,
> Spencer Graves
>
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-- 
---------------------------------------------
Dr. Thomas Petzoldt
Member of academic staff
(Limnology and Ecological Modelling)


Technische Universitaet Dresden
Faculty of Forest, Geo and Hydro Sciences
Institute of Hydrobiology
01062 Dresden, Germany

Tel.: +49 (351) 463-34954
Fax:  +49 (351) 463-37108
E-Mail: thomas.petzoldt at tu-dresden.de
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