Practical Measures and Test for Credibility of an Estimator

Most estimators and filters provide assessments of their own estimation errors. Are these self-assessments trustable? What is the degree to which they are trustable? This paper provides practical answers to such questions, referred to as the (level of) credibility of the estimators/filters. It formulates the concept of credibility, proposes several practical measures of credibility, and discusses a credibility test. A special effort is made to explain the underlying rationales as clearly as possible. Numerical examples are provided to illustrate the pros and cons of the measures and test.