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In this paper, we revisit the Kalman filter theory. After giving theintuition on a simplified financial markets example, we revisit the mathsunderlying it. We then show that Kalman filter can be presented in a verydifferent fashion using graphical models. This enables us to establish theconnection between Kalman filter and Hidden Markov Models. We then look attheir application in financial markets and provide various intuitions in termsof their applicability for complex systems such as financial markets. Althoughthis paper has been written more like a self contained work connecting Kalmanfilter to Hidden Markov Models and hence revisiting well known and establishresults, it contains new results and brings additional contributions to thefield. First, leveraging on the link between Kalman filter and HMM, it givesnew algorithms for inference for extended Kalman filters. Second, it presentsan alternative to the traditional estimation of parameters using EM algorithmthanks to the usage of CMA-ES optimization. Third, it examines the applicationof Kalman filter and its Hidden Markov models version to financial markets,providing various dynamics assumptions and tests. We conclude by connectingKalman filter approach to trend following technical analysis system and showingtheir superior performances for trend following detection.

Kalman filter demystified: from intuition to probabilistic graphical model to real case in financial markets