Monocular 3D Position Estimation of a Moving Vehicle Based on a Kalman-Goldschmidt Adaptive Filter

Abstract

Determining the 3D position of a vehicle from a 2D image plays a key role in video surveillance, autonomous driving, and spatial localization. However, localization accuracy can significantly degrade in conditions of incomplete or synthetic measurement noise and keypoint jitter. In this paper, we propose a new iterative 3D position estimation algorithm (KGA). This algorithm includes geometric correction and calibration steps for converting from 2D to 3D coordinates; trajectory prediction and correction using a Kalman filter; and adaptive tuning of the filter parameters using the Goldschmidt algorithm. Experiments confirm that KGA outperforms the standard (FK) and modified (MFK) Kalman filters in accuracy and convergence speed, demonstrating robustness to various camera angles and noise levels. The novelty of this approach lies in the integration of the Goldschmidt algorithm into the Kalman filter to create an adaptation mechanism that dynamically adjusts the measurement noise covariance based on instantaneous innovation magnitude. Unlike end-to-end deep learning trackers or nonlinear filters (EKF/UKF), KGA is designed as a lightweight post-processing stage that can be seamlessly integrated into existing detection pipelines while maintaining the low computational footprint required for UAV-based edge deployment. The algorithm is of practical value for computer vision systems requiring accurate and robust tracking under varying observational conditions, with current implementation suitable for offline or buffered processing, and clear pathways to real-time deployment through code optimization. The algorithm is of practical value for computer vision systems requiring accurate and robust tracking under varying observational conditions.