# Feasibility of Initial Bias Estimation in Real Maritime IMU Data Including X- and Y-Axis Accelerometers

## TL;DR

This paper tests methods to estimate sensor biases in real maritime IMUs and finds the Butterworth filter performs best.

## Contribution

Demonstrates the effectiveness of a bias estimation framework in real-world maritime IMU data for the first time.

## Key findings

- The Butterworth filter achieved the smallest residuals in accelerometer and gyroscope data.
- Estimated X-axis and Y-axis accelerometer biases were 0.0405 m/s2 and 0.1615 m/s2, respectively.
- The optimization converged successfully with an objective function value of 9.314.

## Abstract

This study aimed to validate a bias estimation framework for low-cost maritime IMUs by applying it to real-world shipborne data. Six estimation methods—including statistical (mean, median), model-based (least squares, cross-correlation), and signal-processing approaches (FFT, Butterworth filter)—were compared. The results demonstrated that the low-frequency Butterworth filter achieved the smallest residuals, with RMS residuals below 0.038 m/s2 for accelerometers and 0.0035 deg/s for gyroscopes. In particular, AccX and AccZ residuals converged to 3.04 × 10−2 m/s2 and 2.30 × 10−2 m/s2, respectively, while GyroZ achieved 5.58 × 10−4 deg/s. Estimated accelerometer biases were 0.0405 m/s2 (X-axis) and 0.1615 m/s2 (Y-axis), and the optimization successfully converged with an objective function value of 9.314. The findings confirm that the previously proposed bias estimation method, originally validated in simulation, is effective under real-world maritime conditions. However, as ground truth bias values cannot be obtained in shipborne experiments, verification relied on residual statistics and cross-correlation analysis. This limitation has been explicitly stated in the conclusion, and future studies should incorporate sensitivity analyses and controlled experiments to further quantify error sources.