The Kalman filter can be derived as the conditional mean/variance of a multivariate normal. You assume a linear state-space model and walk the equations forwar

The Kalman filter can be derived as the conditional mean/variance of a multivariate normal. You assume a linear state-space model and walk the equations forward. Those are the key limitations: linear state space; Gaussian innovations. You can derive it other ways, but that's the way I grok it. You are correct about hidden states. A linear state-space model with omitted variables will suffer the same kinds of bias present in an OLS model with omitted variables [4]. Deriving the equations is a nice way to distract yourself from the apocalypse. [1],[2] should be enough of a toe hold if you are familiar with OLS. Ignore the control term u[n] in the Matlab documentation. Kalman's original paper [3] is also a really nice, although I didn't really get it until I had already approached it as a conditional moment problem. [1] https://stats.stackexchange.com/questions/30588/deriving-the-conditional-distributions-of-a-multivariate-normal-distribution https://stats.stackexchange.com/questions/30588/deriving-the... [2] https://www.mathworks.com/help/control/ug/kalman-filtering.html https://www.mathworks.com/help/control/ug/kalman-filtering.h... [3] https://pdfs.semanticscholar.org/bb55/c1c619c30f939fc792b049172926a4a0c0f7.pdf https://pdfs.semanticscholar.org/bb55/c1c619c30f939fc792b049... [4] https://en.wikipedia.org/wiki/Omitted-variable_bias https://en.wikipedia.org/wiki/Omitted-variable_bias