Adjustment of a large number of measurements in steps

The least-squares method is commonly utilized to address data processing problems. The "adjustment in steps" technique is used in this study to optimize the "adjustment of measurements only" method. We use an initial set of condition equations of a mathematical model, to compute the initial best estimates of a given set of measurements. Subsequently, we may add or remove conditions from either the same model or a new form of it. The final solution is produced by revising the initial estimations of the measurements without applying the adjustment procedure to the entire system of condition equations. This technique is generalized in several steps. Each stage involves revising measurement estimates. The splitting of the solution system into steps simplifies the adjustment procedure because each step includes the multiplication and inversion of smaller matrices than those used for the complete system. Furthermore, the efficiency of this technique as a function of the number of steps taken is examined. The smallest amount of computations required to handle a large number of measurements yields the best solution. Finally, nonlinear condition equations are investigated. Numerical experiments are used to validate the theoretical concepts.