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

[Spencer Graves]

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