Planar fiducial markers are commonly used to estimate a pose of a camera relative to the marker. This information can be combined with other sensor data to provide a global or local position estimate of the system in the environment using a state estimator such as the Kalman filter. To achieve accurate estimates, the observation noise covariance matrix must be properly configured to reflect the sensor output’s characteristics. However, the observation noise of the pose obtained from planar fiducial markers varies across the measurement range and this fact needs to be taken into account during the sensor fusion to provide a reliable estimate. In this work, we present experimental measurements of the fiducial markers in real and simulation scenarios for 2D pose estimation. Based on these measurements, we propose analytical functions that approximate the variances of pose estimates. We demonstrate the effectiveness of our approach in a 2D robot localisation experiment, where we present a method for estimating covariance model parameters based on user measurements and a technique for fusing pose estimates from multiple markers.