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Classification, Parameter Estimation and State Estimation, 2nd Edition by David M. J. Tax, Dick de Ridder, Ferdinand van der Heijden, Yaobin Zou, Ming Feng, Guangzhu Xu, Bangjun Lei

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5State Estimation

The theme of the previous two chapters will now be extended to the case in which the variables of interest change over time. These variables can be either real-valued vectors (as in Chapter 4) or discrete class variables that only cover a finite number of symbols (as in Chapter 3). In both cases, the variables of interest are called state variables.

The state of a system is a description of the aspects of the system that allow us to predict its behaviour over time. For example, a system describing elevator controller can have basic enumeration of states such as ‘closed’, ‘closing’, ‘open’ and ‘opening’, which can be the elements of a finite state space. A state space that is described using more than one variable, such as a counter for seconds and a counter for minutes in a clock system, can be described as having more than one state variables (in the example it can be ‘seconds’ and ‘minutes’).

The design of a state estimator is based on a state space model, which describes the underlying physical process of the application. For instance, in a tracking application, the variables of interest are the position and velocity of a moving object. The state space model gives the connection between the velocity and the position (which, in this case, is a kinematical relation). Variables, like position and velocity, are real numbers. Such variables are called continuous states.

Although a system is supposed to move through some sequence of states over time, instead ...

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