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Classification, Parameter Estimation and State Estimation: An Engineering Approach Using MATLAB by David M. J. Tax, Dick de Ridder, Ferdinand van der Heijden, Robert Duin

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4

State 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 3), or discrete class variables that only cover a finite number of symbols (as in Chapter 2). In both cases, the variables of interest are called state variables.

The design of a state estimator is based on a state space model that 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.

The design of a state estimator is also based on a measurement model that describes how the data of a sensory system depend on the state variables. For instance, in a radar tracking system, the measurements are the azimuth and range of the object. Here, the measurements are directly related to the two-dimensional position of the object if represented in polar coordinates.

The estimation of a dynamic class variable, i.e. a discrete state variable is sometimes called mode estimation or labelling. An example is in speech recognition where – for the recognition of a word – a sequence of phonetic classes must be estimated from a sequence of acoustic ...

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