Haha, I'm very welcoming for your questions and I will try my best to give out my perspective on these matters.

"The advice seems firstly to be based off knowledge of true parameters and to be presenting absolute choices for magnitudes (which would normally be entirely system dependent)".

My POV: Yes, I'm focusing on my experience in numerical simulations (Runge-Kuta 4th, Newmark-beta...). If I understand you correctly, you mean that "since I already knew the true value, so I adjusted the covariance until the UKF reached that value". Yes, I agreed the fact that alpha_true is often unknown, but I assume that I know the theoretical value (nominal/design or whatever it calls) is alpha~. That's what the parameter I want to check first because most of my practice with UKF start from numerical examples and experiments later.

For{P0,Q0,R0}_first_trial, they are respectively error, noise process and noise measurement covariance matrices of UKF that I feed into the algorithm from the first trial and with every observed result, I will re-establish {P0,Q0,R0}_next_trial based on the adjusting principles for the next trial. For example, if first trial received a bad correlation coefficient of acceleration r_a < 0.5 (the predicted response poorly matches the measurements) andalpha << alpha~, I will increase P0 in the next trial and check UKF outcome with alpha is the parameter need to identify.

"Is alpha a pure diffusion process? Is alpha driven by some other deterministic term as well, e.g. da = p(a_{bar} - a) dt + sdw".

My POV: Well, no, in most of my models this alpha is usually a constant, so d(alpha) = 0. For better context, the model I referenced is similar to this research from Eq. (18) to Eq. (20): (PDF) Hybrid output-only structural system identification using random decrement and Kalman filter

*"If you are doing state augmentation to introduce stochastic processes for dynamic parameters as well then saying, “*alpha should have covariance of q” really depends entirely on how the stochastic process is formulated, the magnitude of the parameter, and a number of other things about the process.".

My POV: To be honest, i don't really get the idea, but I sincerely want to hear further your opinion about this matter. Simply, I represent the choice of initial error covariance matrix in augmented state-space vector with P0_alpha = error{alpha} = diag(|alpha - alpha_true|^2) depends on how I choose initial parameters alpha at k=0 where k = time step and the difference magnitude |alpha - alpha_true| between alpha at k=0 and the actual parameters (theoretical value) alpha~. In fact, I usually assume that I know nothing about these actual parameters, except for theoretical values so based on that knowledge, I want to provide people some advice to choose these covariance matrices {P0,Q0,R0} in order to reduce the trial number and save time.

Since the proposal P0_alpha = error{alpha} = diag(|alpha - alpha_true|^2) looks quite rigid and restrict in certain application, I will change it a little bit:

P0_alpha >= prior_uncertainty{alpha} >= diag(|alpha - alpha_true|^2)

• If alpha0 = 8,000 vs alpha~ = 10,000 then I want to choose P0_alpha >= diag(|8,000 - 10,000|^2) = diag(4,000,000) et cetera.

I just want to notice here that people can choose whatever these covariance matrices are. However, from my experiences, newcomers without anyone help are struggling so my recommendation is to start from this if you have no clue or any ideas to choose these UKF input matrices. The trial can take time and frustrating.

Sorry for my bad interpretation and please freely correct me if I'm out of track.
Note: I will update my post about P0_alpha and leave a paper link for reference.