Accuracy of the relative orientation by Poivillier's method

Summary When the method of Poivilliers is used, the mean (square) errors in the elements of relative orientation, caused by those in the measurements of the want of correspondence, can be computed by applying the law of propagation of errors. The mean errors of the quantities p, q and the tilt ω determined from the measurement of the want of correspondence in three points of the spatial model in a plane perpendicular to the base, and on the same height, are computed for various positions of the points chosen. See Table 1. When measuring the want of correspondence in a flat spatial model in the six points of Figure 1 the elements of relative orientation can be determined by the formulae for the numerical method, or by the method of Poivilliers. The result, and so the accuracy, is the same for the fore and aft tilt φ, the tilt ω and the base-component b z . For the swing x and the base-component b y the result is the same only when the measurements of the six wants of correspondence satisfy the equation existing between them. When eliminating the want of correspondence in the vertical plane through the base with κ, the mean error is κ is only about twice as great. When applying the method of Poivilliers in aerial triangulation, when for reasons of economy the wants of correspondence are only measured in these six points, the swing must be determined in the latter way. The base-component b y then has to be computed as the arithmetical mean of the residual wants of correspondence after applying the other corrections. The exceptional cases the method may beused to obtain the highest possible accuracy in the relative orientation by measuring the wants of correspondence in more than three points in a plane, and in more than two planes. When using more than three points in a plane, assuming the same values of p, q and d ω can be determined as in an adjustment by the method of least squares, the mean errors in three quantities can, again in a flat spatial model, hardly be brought down to less than 0.8 times their smallest values in the case of three points. When using, e.g., six planes, and with the same assumption for the determination of the p and q lines, the mean errors in the elements of relative orientation can be reduced from 0.8 to 0.6 times their amount in the case of two planes, depending on the choice of the planes used. (See Table 4 and the computations below it). So, by applying the method of Poivilliers in a flat spatial model, but at a considerable expense of time, mean errors in fore and aft tilt, tilt and base-component b z may be achieved, with half the magnitude they have when the numerical method is used. Swing, however, can always be determined more accurately by the numerical method or by eliminating the wants of correspondence in the vertical plane through the base with swing.