Estimating distance sampling detection functions when distances are measured with errors

Distance sampling methods assume that distances are known but in practice there are often errors in measuring them. These can have substantial impact on the bias and precision of distance sampling estimators. In this paper we develop methods that accommodate both systematic and stochastic measurement errors. We use the methods to estimate detection probability in two surveys with substantial measurement error. The first is a shipboard line transect survey in the North Sea in which information on measurement error comes from photographically measured distances to a subset of detections. The second is an aerial cue-counting survey off Iceland in which information on measurement error comes from pairs of independently estimated distances to a subset of detections. Different methods are required for measurement error estimation in the two cases. We investigate by simulation the properties of the new estimators and compare them to conventional estimators. They are found to perform better than conventional estimators in the presence of measurement error, more so in the case of cue-counting and point transect estimators than line transect estimators. An appendix on the asymptotic distributions of conditional and full likelihood estimators is available online.