Abstract
In the traditional measurement theory, precision is defined as the dispersion of measured value, and is used as the basis of weights calculation in the adjustment of measurement data with different qualities, which leads to the trouble that trueness is completely ignored in the weight allocation. In this paper, following the pure concepts of probability theory, the measured value (observed value) is regarded as a constant, the error as a random variable, and the variance is the dispersion of all possible values of an unknown error. Thus, a rigorous formula for weights calculation and variance propagation is derived, which solves the theoretical trouble of determining the weight values in the adjustment of multi-channel observation data with different qualities. The results show that the optimal weights are not only determined by the covariance array of observation errors, but also related to the model of adjustment.