# CHAPTER 10WEIGHTS OF OBSERVATIONS

## 10.1 INTRODUCTION

When surveying data are collected, they usually must conform to a given set of geometric conditions, and when they do not, the observations are adjusted to force that geometric closure. For a set of uncorrelated observations, a measurement with a high precision, as indicated by a small variance, implies a good observation, and in the adjustment it should receive a relatively small portion of the overall correction. Conversely, a measurement with a lower precision as indicated by a larger variance implies an observation with a larger error, and thus it should receive a larger portion of the correction.

The weight of an observation is a measure of an observation's relative worth compared to other observations. *Weights* are used to control the sizes of corrections applied to observations in an adjustment. The more precise an observation is, the higher its weight should be; in other words, the smaller the variance, the higher the weight. From this analysis, it can be stated intuitively that *weights are inversely proportional to variances*. Thus, it also follows that *correction sizes should be inversely proportional to weights*.

In situations where observations are correlated, weights are related to the inverse of the covariance matrix, ∑. As discussed in Chapter 6, the elements of this matrix are variances and covariances. Since weights ...

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