Measurement systems are widely used in engineering applications such as structural health monitoring and nondestructive evaluation to enhance periodic inspections with continuous data acquisition. These systems are often assumed to exhibit linear time-invariant behavior, although over time, their performance is affected by environmental factors and internal degradation, resulting in time-variant behavior. In this study, we investigated the effects of aging on measurement systems, using laser triangulation sensors as a case study, and propose a novel approach to compensate for these time-dependent effects. Through a series of more than 140 subtests, we identified both random and systematic measurement errors, such as those caused by cable length, sensor placement, and temperature variations. We introduced a compensation method based on Bayesian model updating (BMU) that effectively accounts for the time-dependent drift in measurement accuracy, especially in the early stages of sensor aging. The BMU model was validated through experiments, demonstrating its ability to mitigate aging-induced measurement errors with high accuracy. In this work, we highlight the importance of compensating for time-variant behavior and provide a reliable approach to ensuring measurement accuracy in long-term measurement systems. The results are applicable to various engineering applications and contribute to improving the longevity and reliability of monitoring systems.