Question

Which of the following is tested using the Chi-square test in least squares adjustment?

• A. Adjusted and observed values of observations are statistically similar
• B. Presence of gross errors in observations
• C. Adjusted and assumed values of parameters are statistically similar
• D. High correlation between observations and residuals

Hint:

$\chi^2$ test is a {global} check (whole network); identifying which observation is bad needs {local} tests (e.g., Baarda data snooping or t-tests on normalized residuals).

Answer 1

The Correct Option is B

In least-squares adjustment, the $\chi^2$ (global model) test checks the stochastic model by comparing the observed variance factor $\hat{\sigma}_0^2$ (from residuals) with the a priori variance factor $\sigma_0^2$ via \[ \chi^2=\frac{v^\top P v}{\sigma_0^2} \text{with }\ \chi^2_{\nu,\alpha}\ \text{bounds, } \nu=\text{dof}. \] If the statistic lies outside the acceptance region, the model is rejected—typically indicating gross errors/blunders or an incorrect noise model. Hence, it is used to test for the presence of gross errors.