A Pattern Recognition Technique for System Error Analysis

Abstract

The error analysis problem is the resolving of a limited set of measurements in terms of a large set of possible but improbable physical errors. The relation between the measurements and the errors is modeled in part as a set of linear undetermined equations δv = Aδr, where δv is a vector of the measurements and δr is a vector of error parameters, and in part by specification of the relations between the parameters δr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</sub> and the physical errors. An approximate solution to the model equations is deemed physically reasonable if it reflects one or only a few of the physical errors. To evaluate a candidate solution consisting of δr and its interpretation as physical errors, we introduce a criterion function γ = γ0 + γ1; γ0 is a measure of ||δv - Aδr|| and 㬱 is a measure of the likelihood of the composite physical error associated with δr. With this criterion, the common least-squares (pseudoinverse) solution of the model equations is shown to be inadequate (it minimizes γ0 but not γ). A pattern recognition technique is presented and shown to yield solutions that are both numerically and physically reasonable, i.e., both γ0 and γ1 are small. The technique is illustrated by application to miscalibration analysis using an inertial guidance system model.