I have 2 datasets with sensor values, say for example temperature readings from a thermometer, which I want to combine and predict the temperature at a period (t+1).
I've modelled my Kalman Filter and it works exactly as I want it regarding the estimation of the "actual" value (or the fused value of the datasets), but the prediction (t+1) is basically equal to (t). This is a result of the fact that the State Predicion (see image below) in my case has no control variables (Un), hence I've set it to 0, meaning that the equation can be simplified to just the State Transition Matrix - A (for a time period 1) multiplied the previous state (+ Noise), and it gives the exact same prediction as the previous state. Which just makes the predictions lag behind the observations making it rather unuseful for what I'm trying to achieve.
Instead, I've decided to use Exponential Smoothing for the prediction step in the Kalman Filter, which is giving me far-better prediction results, but disregards noise (which I don't think is a great issue for my dataset, but I'm not sure if it does affect the Kalman Filter itself).
My question is, if it's mathematically plausible to combine the methods and does this substitution of the prediction state affect the reliability of the Kalman Filter.
Thank you for your time!