Road geometry estimation is essential for self-driving vehicles and modern advanced driver-assistance systems (ADAS). State-of-the-art techniques utilize a Kalman filter to perform road geometry estimation. A common assumption in these Kalman filters is that the process- and measurement noise covariances are constant over time. However both sensor performance and process dynamics may change over time in real-world applications. Sensor performance may be affected by environmental factors such as rain and lighting conditions and process dynamics may depend on the road type. Noise processes like these with a feature dependent covariance are known as heteroscedastic noise. By estimating the heteroscedastic process- and measurement noise covariances more accurately both the filter performance and state uncertainty estimation may improve.