# Noise reduction with known noise distribution

I have a time signal with a known noise distribution parameters (gaussian, sd is known). I would like to estimate the true value statistically and in the best case obtain a confidence interval.

As I understood Kalman filter requires a model of the signal itself, I wouldn't know how I get that. Could I still use a Kalman filter? What are approaches to estimate the signal statistically?

• Hi: The kalman filter is formulated with an observation equation and a system equation. If the observational variance is known and there's no system equation ( it sounds like you have an observation equation only. if not then, this is not true ), then the signal estimate is the mean of the response and you don't need the KF. – mlofton Feb 23 at 18:07
• At least I don't know how I can get the system equation, can it be extracted from the data itself? What are then alternatives to KF where I can use at least the known observational variance? – MikeHuber Feb 23 at 18:15
• Btw.: I saw sometimes is a system model used which just forwards the previous value, is that a valid approach? – MikeHuber Feb 23 at 19:20
• It's valid if the resulting model is a good description (model) of the process that produced the data. You're asking extremely general questions and omit any specifics we could work with; the answer in general is that using a model that's based only on the previous value may be a terrible approach; we currently have no basis on which to conclude that it might be something other than terrible for your case. e.g. If you had a random walk, it might work quite well but there's no good reason to think that this would be the case. You're the expert on your problem; we only know what you said. – Glen_b Feb 24 at 0:41
• Thank for the answer, but are there also approaches that can use only the noise parameters to to reduce noise without knowing the system model? – MikeHuber Feb 24 at 10:50