Optimal interval estimation fusion based on sensor interval estimates and confidence degrees

The interval estimation fusion method based on sensor interval estimates and their confidence degrees is developed. When sensor estimates are independent of each other, a combination rule to merge sensor estimates and their confidence is proposed. Moreover, two popular optimization criteria: minimizing interval length with an allowable minimum confidence degree, or maximizing confidence degree with an allowable maximum interval length are suggested. In terms of the two criteria, an optimal interval estimation fusion can be obtained based on the combined intervals and their confidence degrees. Then we can extend the results on the combined interval outputs and their confidence degrees to obtain a conditional combination rule and the corresponding optimal fault-tolerant interval estimation fusion in terms of the two criteria. It is easy to see that Marzullo’s fault-tolerant interval estimation fusion is a special case of our method. We also point out that in some sense, our combination rule is similar to the combination rule in Dempster-Shafer evidence theory. However, the confidence degrees given in this paper is summable, but they (called mass function in Dempster-Shafer evidence theory) are not there; therefore, Dempster-Shafer’s combination rule is not applicable to the interval estimation fusion.