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Most introductory books on control theory usually start their state observation part by introducing the Luenberger observer, and after that they might continue by introducing the Kalman filter. When reading papers from academic journals I have also come across all kinds of fancy nonlinear estimation methods (sliding-mode observers, passive observers, etc...).

However, from my short experience, it seems like there is only one type of state-estimation method used outside academia: the Kalman filter.

Is my observation correct or are other types also being used? If so, why is the Kalman filter so predominantly used over other state observers? Is it because it's fairly easy to implement?

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I can only speak for the industry I have worked in (heavy machinery). I have only seen Kalman filters used in practice as observers.

Most of the data sources in heavy machinery tend to be quite noisy (pressure or accelerometer sensors). Kalman filters (as compared to simpler Luenberger observers) provide better resilience when faced with high noise levels. I have seen them overall behave more robustly than Luenberger observers. I have seen extended Kalman filters used for sensor fusion in nonlinear systems as well.

The various fancier methods may often have increased computing requirements which make implementation harder in embedded microprocessors. Additionally, the general popularity of Kalman filters means that there is a higher chance managers and engineers outside of controls areas have at least heard of them before. This sort of "brand recognition" can help when selling a solution internally in a large company that isn't focused on controls. Along with this, the support in various libraries or in packages such as Simulink/Matlab is quite old and has been stress tested considerably already.

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I know that Luenberger and sliding-mode observers are used in field oriented control algorithms to estimate rotor position and speed of permanent magnet synchronous machines (PMSM). Here is a white paper by TI where they mention the sliding-mode observer. And here is a white paper by Freescale that mentions the Luenberger observer. Here is another from Freescale talking about the sliding-mode observer.

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