Are alpha-beta (or alpha) filters a subset of Kalman Filters?

I ask because I don't know enough about the Kalman Filter. But it seems that the parent post could also be accurate.

I imagine many implementations of the Kalman Filter take advantage of the local use case, and don't necessarily have to carry a fully generalised Kalman filter.

One of the defining characteristics of the Kalman filter is that it computes a gain (called the Kalman gain) that is a function of the state covariance and the measurement covariance. Alpha-beta filters use constants, so I'd say no, they are not a subset.

You can define alpha/beta in terms of the covariance of the Kalman filter. See my book (linked above) for the derivation (I call it a g-h filter, some literature uses alpha-beta, some g-h, they are the same thing). Eli Brookner in "Tracking and Kalman Filters Made Easy" uses a different but mathematically equivalent derivation to show the relationship.

There are at least a couple dozen of commonly used filters that can be understood as form of the alpha-beta filter. Some use constants for g/h, some vary them over time. The Kalman filter varies them on each epoch based on the covariance of the state and measurements. There are other schemes. The KF is optimal in the least squares sense when the noise is Gaussian and and the system obeys the Markov property.

Another way to look at these is to derive them from Bayes' theorem. You can derive both the alpha-beta filter and Kalman filter from Bayes' theorem. It's all the same family, just with different assumptions/knowledge about your process and measurement noise.

I'd agree that the alpha-beta filter is a special case of the Kalman filter (which isn't what I'd call a subset, but maybe we're just arguing semantics). All the filters you mention are certainly related, but claiming that the alpha-beta filter is a Kalman filter is either naive or obstinate.