Enhanced error spectrum for estimation performance evaluation

The error spectrum is a comprehensive metric for estimation performance evaluation in that it is an aggregation of many incomprehensive measures. However, the error spectrum is a two-dimensional curve for any estimand (i.e., the quantity to be estimated) of interest. Therefore, unless one error spectrum dominates the others, it is in general not straightforward to say which one is better. Although the dynamic error spectrum (i.e., the average height of the error spectrum) was proposed to tackle this problem, it suffers from the problem of information loss due to the mapping of the whole error spectrum at a time instant into a single point. Particularly, if the average heights of two error spectrums are the same, they are still indistinguishable. To alleviate this, two new metrics called range error spectrum induced area and dynamic error spectrum induced area are proposed in this paper. Then how to combine these two new metrics, called as enhanced error spectrum, are further studied. An additive and a multiplicative form of the enhanced error spectrum are presented respectively for different scenarios. A numerical example is provided to illustrate the effectiveness of the metrics. It is shown that due to the consideration of more information, the new metrics have greater applicability than the dynamic error spectrum.