Applications of estimation theory were limited primarily to astronomy, geodesy, and regression analysis up to the first four decades of the twentieth century. However, during World War II and in the following decades, there was an explosive growth in the number and types of estimation applications. At least four reasons were responsible for this growth. First, development of the new radar, sonar, and communication technology greatly expanded the interest in signal processing theory. Second, development of digital computers provided a means to implement complex math-based algorithms. Third, the start of space exploration and associated expansion in military technology provided a critical need for estimation and control, and also increased interest in state-space approaches. Finally, papers by Kalman (1960, 1961), Kalman and Bucy (1961), and others provided practical algorithms that were sufficiently general to handle a wide variety of problems, and that could be easily implemented on digital computers.
Today applications of least-squares estimation and Kalman filtering techniques can be found everywhere. Nearly every branch of science or engineering uses estimation theory for some purpose. Space and military applications are numerous, and implementations are even found in common consumer products such as Global Positioning System (GPS) receivers and automotive electronics. In fact, the GPS system could not function properly without the Kalman filter. ...