Input Bias Correction in Gaussian Process Regression

In traditional Gaussian process (GP) regression, the inputs are typically assumed to be known, and uncertainty enters only through the measurements. When scalar fields are mapped using GP regression with measurements obtained from a mobile sensor, the inputs correspond to the estimated pose of the mobile sensor. The goal in this letter is to understand how a recorded GP, trained on erroneous inputs (e.g., pose estimates from dead-reckoning), can be corrected in a numerically efficient way when better estimates of the inputs become available. In the developed bias-aware GP (Ba-GP) framework, the recorded GP posterior-mean gradient is used to propagate estimated input bias and noise into mean and covariance corrections. The resulting additive covariance structure is then exploited to develop numerically efficient first-order correction algorithms. A simulation study and an indoor light-intensity mapping experiment show that Ba-GP improves predictive accuracy and uncertainty calibration relative to noisy-input GP baselines, with an order-of-magnitude reduction in computational cost relative to full GP retraining.