Nonrandom Parameter Estimation Using Min-Max Theory

A decision-theoretic approach is proposed for bad-data elimination in parameter estimation. A linear measurement model with unknown additive noise having zero mean is considered and the noise distribution is assumed to be symmetrical and absolutely continuous. The partial covariance of the measurement random variable is considered to be constrained, and its minimum covariance and unbiasedness are chosen as criteria of goodness for the estimator. Using game-theory, a soft-limiter is shown to be optimal. It is also established that in the presence of bad data, performance of the proposed scheme is superior, and in its absence comparable, to that of linear estimators.