Continuing advances within unmanned aerial vehicles and scalar magnetic sensor technology are revolutionizing geophysical remote sensing. For perspective, examples of high resolution, low noise data presented in this study enabled detection and accurate positioning of human-made objects ferrous objects with a total mass of 0.5 kg, from altitudes around and above 2 m. However, with these new possibilities come a requirement of higher fidelity, where good sensor position estimates in particular are key to achieving a data quality sufficient for reliable data interpretation and geophysical inversion. Apart from inherent instrument properties, typical factors that hamper sensor position estimation are lag and parallax errors. Lag errors arise from time-stamping delays between the positioning system and sensor reading, while parallax errors stem from the imperfect recovery of sensor positions due to a decoupling and/or distancing of the positioning system and sensor head. The impact from each of these error sources is typically similar and partially or even completely inseparable. A number of correctional techniques exist, typically based on large-scale data correlations, or collection of specific additional data. We present a survey data adjustment method based on the simultaneous inversion of source parameters and a number of independent survey shifts or lags in pre-specified sections of a survey. The method is particularly suited for surveys where the sensor path through space can be assumed well known, but the sensor position itself may suffer lags or shifts relative to the position measurement. The approach is based on modelling an existing source signature within the data and requires no data transformations, such as continuation to a two-dimensional plane, or enforcing of smoothness. The approach is an amendment to independent source inversion and is ideal for scenarios where the source behaviour is thought to be well known, such as processing efforts in which the objective is source–parameter inversion. In this study, we validate the approach using a simple point-dipole model to adjust synthetic data and subsequently demonstrate it on an unmanned airborne scalar magnetic survey for small unexploded ordnance targets, where a hardware malfunction resulted in unknown time-shifts between magnetic sensor readings and positioning unit output. The adjustment procedure was carried out on line data, based on a single anomaly from a 155 mm shell, and enabled the recovery of signatures from several other ferrous unexploded ordnance targets as small as 0.5 kg. Subsequent inversion on the corrected signatures provided unexploded ordnance positions with an accuracy suitable for recovery purposes.