Efficient Error Model Construction

Abstract

This paper describes a new method for error model construction. Instead of the standard local slope analysis of the Allan variance, two major modifications are proposed: (1) the Direct Bound principle, i.e. finding an entire error model that generates analyzing tool values that tightly bound the analyzing tool values generated by the real data; (2) instead of using Allan variance as a unique analyzing tool, a variety of analyzing tools termed Direct Predictor (DP) types 0, 1, 2, and 3 are introduced. In the paper, a uniform structure of DPs is developed and their parameterization is extended. For a nominal model that consists of a Markov process with additive white noise, the analytical functions for DPs are presented (for infinite data length). The errors due to the final data length are analyzed. Using these results, a reliable optimization problem is presented to implement the Direct Bound approach. The flexibility of working with hard and soft bounds is introduced. The presented simulation results show that the proposed method is indeed efficient and provides satisfactory results for model parameter estimations. The paper concludes with a description of an entire engineering process to cover test design and its analysis.