I have some time series data of measurements taken at random intervals with dimensions >> measurements, with intervals anywhere between 15 seconds and a few minutes. Ideally I would like to have a continuous time estimate to give me the state of the system at any time between the beginning and end of measurements with some sort of confidence interval or statistical guarantee.
I've looked into Kalman-type smoothers, but I dont have a model of state transitions, noise, or control-input. Furthermore I know my data are not of a linear system and they are quite noisy. It seems like setting all the matrices to the identity matrix would be okay to get a smoothed data, and would jive well with the random interval-ness of my data but I can't seem to find anywhere where other people have done the same (so it seems like it's probably not a good idea)
I'm a bit agnostic and I'll accept approximations, such that my variables are independent of each other and the pretending the system is linear, although techniques like polynomial fitting and linear interpolation are not very satisfactory, as they don't deal with the noise at all.
Useful facts about my data: Data is acquired at varying-intervals, dimensions >> data points, data is of a non-linear system and data is noisy
What I would like: An estimate of system-state anywhere between the beginning and end of acquisition time