Yes, the Doppler effect applies to any electromagnetic wave. No matter whether that is an actual Radar pulse, or a microwave oven falling from an office tower, or a passenger aircraft's transponder, or an LPWAN device.
But, this possibility is especially limited for LPWAN devices, as I'll explain below.
Low Doppler shift due to low carrier frequency
Starting at the top and working my way down.
Good questions, by the way!
So basically state and output is modelled as gaussian distributions
that have slowly changing means (to be estimated), with additive
zero-mean gaussian noise on top (to be cancelled)?
Yes, that's correct. The KF formulation can work with other distributions, but the standard ...
Have you considered trying a constant jerk model as opposed to a constant acceleration model? Perhaps a higher order model would capture the acceleration better. See, for instance:
K. Mehrotra and P. R. Mahapatra, "A jerk model for tracking highly maneuvering targets," in IEEE Transactions on Aerospace and Electronic Systems, vol. 33, no. 4, pp. 1094-1105, ...
I suggest this reference regarding the comparison between least-squares and Kalman filters :
Fundamentals of Kalman Filtering: A Practical Approach by P. Zarchan & H. Mussof
Especially Chapter 3 (Recursive Least-Squares Filtering) and Chapter 4 (Polynomial Kalman Filters).
In Chapter 4, the authors show that the discrete (time) n-th order polynomial ...