ABSTRACT
A very general model that subsumes a whole class of special cases of interest in much the same way that linear regression does is the state-space model or the dynamic linear model (DLM), which was presented in Kalman (1960) and Kalman and Bucy (1961). The model arose in the space tracking setting, where the state equation defines the motion equations for the position or state of a spacecraft with location https://www.w3.org/1998/Math/MathML"> X t , t ∈ N https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429112638/a69a2ff5-a02c-4831-8fae-bdc86f3c20b4/content/eq1089.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and the data https://www.w3.org/1998/Math/MathML"> Y t , t ∈ N https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429112638/a69a2ff5-a02c-4831-8fae-bdc86f3c20b4/content/eq1090.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> reflect information that can be observed from a tracking device such as velocity and azimuth. According to various accounts (e.g., Cipra, 1993), although not interested at first, the researchers at NASA eventually latched onto the Kalman filter as a way of dealing with problems in satellite orbit determination and Kalman filtering became a mainstay of aerospace engineering. For example, it was used in the Ranger, Mariner, and Apollo missions of the https://www.w3.org/1998/Math/MathML"> 1960 s https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429112638/a69a2ff5-a02c-4831-8fae-bdc86f3c20b4/content/eq1091.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . In particular, the on-board computer that guided the descent of the Apollo 11 lunar module to the moon had a Kalman filter.
