Conservativeness of estimates given by probability density functions: Formulation and aspects

In state estimation, the output of a filter can consist of a vector estimate with an associated quality matrix or it can be given by a probability density function. Although the first option prevails in tracking, in many problems, it is necessary to cope with multiple hypotheses, i.e. with multiple vector–matrix pairs. The pairs are called conservative, if the quality matrices do not undervalue a measure of uncertainty of the vector estimates. However, no conservativeness definition for multiple pairs or for densities has been coined yet. The paper proposes such a definition for densities, provides a sufficient condition, explores some aspects and gives several special cases and numerical examples.