State-Space Kalman Smoothing of Airborne Gravity Data with Colored Noise

Abstract

Airborne gravimetry is a key technique for regional gravity field recovery where high quality surface gravity data is sparse, yet its accuracy is fundamentally limited by high-frequency measurement noise and temporally correlated instrumental errors along flight trajectories. Conventional processing often relies on low-pass filters, such as recursive Gaussian filters used in the well-known Gravity for the Redefinition of the American Vertical Datum (GRAV-D) project, to suppress the measurement noise, at the expense of signal attenuation and reduced spatial resolution. In this study, a state-space Kalman filtering and smoothing framework is designed for airborne gravity disturbance estimates that explicitly models colored measurement noise using an embedded autoregressive (AR) process. The proposed method is evaluated against a nominal triple-pass Gaussian filter commonly used to process scalar airborne gravity data in the GRAV-D project. Using scalar gravity data collected over the Colorado area that covers the Geoid Slope Validation Survey 2017 (GSVS-17) lines, this study demonstrates that gravity disturbances processed with the Kalman smoother yield a local gravity field model whose derived height anomalies achieve an accuracy of approximately 3.0 cm, improving upon the 3.8 cm accuracy obtained using Gaussian-filtered data alone. These results indicate that a mathematically rigorous, model-based state-space modeling with explicit representation of temporally correlated measurement noise provides a measurable improvement in local quasi-geoid models augmented solely by airborne gravity data (without the inclusion of local surface gravity data), while better preserving geophysical signal content across a broad range of wavelengths.