Mehra, Raman K. Scientific Systems, Inc., Cambridge, Massachusetts.
Manitius, Andre Z. Department of Electrical and Computer Engineering, George Mason University, Fairfax, Virginia.
- Approaches to estimation
- Least-squares estimation
- Maximum-likelihood estimation
- Bayesian estimation
- Gauss-Markov processes
- Kalman filter
- Discrete-time case
- Continuous-time case
- Other state estimation methods
- Nonlinear filters
- System identification
- Batch versus recursive identification
- Least-squares identification
- Choice of input signal
- Applications of system identification
- Related Primary Literature
- Additional Reading
A branch of probability and statistics concerned with deriving information about properties of random variables, stochastic processes, and systems based on observed samples. Some of the important applications of estimation theory are found in control and communication systems, where it is used to estimate the unknown states and parameters of the system. For example, the position and velocity of a satellite is estimated from ground radar observations of its range, elevation, and azimuth. These observations are contaminated with random noise due to atmospheric propagation and radar circuitry. The statistical properties of random noise are assumed known except for some parameters which can be estimated from the data. Generally, the random noise is assumed to have a gaussian distribution, and its mean and covariance may be known or unknown. It is also assumed to be “white,” that is, uncorrelated from one time instant to the next. The integral of white noise is a Wiener process or brownian motion process which plays a fundamental role in the theory of stochastic processes. See also: Distribution (probability); Electrical noise; Stochastic process
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