A Pattern Recognition Technique for System Error Analysis

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 ¿v = A¿r, where ¿v is a vector of the measurements and ¿r is a vector of error parameters, and in part by specification of the relations between the parameters ¿ri 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 ¿r and its interpretation as physical errors, we introduce a criterion function ¿ = ¿0 + ¿1; ¿0 is a measure of ¿¿v - A¿r¿ and ¿1 is a measure of the likelihood of the composite physical error associated with ¿r. With this criterion, the common least-squares (pseudoinverse) solution of the model equations is shown to be inadequate (it minimizes ¿0 but not ¿). A pattern recognition technique is presented and shown to yield solutions that are both numerically and physically reasonable, i.e., both ¿0 and ¿1 are small. The technique is illustrated by application to miscalibration analysis using an inertial guidance system model.