Estimation of parameter bounds from bounded-error data: a survey

Set-membership techniques for estimating parameters from uncertain data are reviewed. Contrary to the prevailing usage, the error in the data is not considered as a random variable with known or parameterized probability density function. Instead, the error is assumed to lie between some known upper and lower bounds. One is then looking for a suitable characterization of the set of all parameter vectors consistent with the model structure, data, and bounds on the errors.