Camera Calibration Using Inaccurate and Asynchronous Discrete GPS Trajectory from Drones

This paper considers a stationary camera calibration problem, which estimates the camera orientation angles yaw, pitch and roll, using a drone trajectory recorded by a GPS. There are three challenges in using a GPS trajectory as ground truth for camera calibration. One, the altitude of GPS data is inaccurate with an unknown bias. Two, the GPS receiver and camera are not time synchronized, and there is an unknown time offset between the two systems. Three, the GPS trajectory is time-discrete and accurate interpolation is needed. This is actually an estimation problem since velocity is also needed. To address the first two challenges, we formulate the problem as a parameter estimation problem to estimate a vector consisting of the GPS altitude bias and time offset in addition to the camera yaw, pitch and roll biases. We then develop a special maximum likelihood estimator using the Iterated Least Squares algorithm which can work with a non-synchronized time-discrete GPS trajectory for the third challenge. Since the camera measurement errors are usually small, this requires a high calibration accuracy so that the residual bias error following the calibration should not be significant compared to the measurement error standard deviation. The calibration accuracy depends highly on the drone trajectory. This paper also recommends an appropriate drone trajectory which can yield a good calibration accuracy, namely, 14\% of the measurement error standard deviation. Simulation tests are conducted to demonstrate the algorithm performance. The estimation results meet the Cramer-Rao Lower Bound (CRLB) since the Normalized Estimation Error Squared w.r.t.\ the CRLB is statistically acceptable.

On the Brittleness of Maximum Likelihood Estimation for Gaussian Process Hyperparameter Optimization

Machine learning (ML) has become an indispensable part of modern engineering design workflows. A crucial step in training an ML model is the selection of the loss function which can be systematically formulated via various techniques such as maximum likelihood estimation (MLE) and cross-validation . While MLE is one of the most popular, effective, and intuitive mechanisms for training ML models, it is brittle: if the assumptions underpinning it are not met, the trained ML model may generalize poorly. This brittleness affects even Gaussian processes (GPs) which are widely used in engineering design and are often (incorrectly) presumed to be very robust to overfitting. In this paper, we fundamentally evaluate the brittleness of MLE in the context of training GPs for probabilistic regression or classification tasks. We compare theoretically grounded metrics against MLE and propose practical solutions. Our extensive studies demonstrate the effectiveness of our solutions in downstream design tasks such as Bayesian optimization and provide a blueprint for practitioners to build accurate and robust GPs that can even outperform tabular foundation models in terms of prediction accuracy, uncertainty quantification, and inference cost. Our contributions are publicly available via GitHub at https://github.com/Bostanabad-Research-Group/GP-vs-TabPFN-vs-GPyTorch.

Smooth Neural Point Processes via B-Splines

Temporal point processes (TPPs) provide a general and flexible framework for modeling sequences of events in continuous time. Neural networks have been successfully employed to model TPPs in a highly expressive and data-driven way. Neural TPPs are typically trained via Maximum Likelihood Estimation (MLE) by minimizing the negative log-likelihood (NLL), which depends on both the conditional intensity function (CIF) and its integral over time, the compensator. Recent neural TPP approaches enable exact evaluation of the NLL without numerical integration. However, these methods typically model the compensator rather than the CIF directly, impose constraints on the neural network architecture, and are computationally expensive during training, as event contributions to the NLL are evaluated sequentially rather than in parallel. In this work, we propose a novel neural TPP model that directly parametrizes the CIF as a non-negative combination of B-spline basis functions, whose coefficients are predicted by a neural network. This formulation enables exact evaluation of the NLL, preserves full flexibility in the neural architecture, allows efficient parallelization during training, and naturally supports CIF smoothness regularization through the integrated squared second derivative. Experiments on both synthetic and real-world datasets show improved computational efficiency and predictive accuracy compared to the reference neural TPP baseline.