GPS/IMU-based Velocity & Path Estimation [MAT3008]

A public project archive for numerical analysis coursework on vehicle velocity estimation, sensor fusion, and trajectory reconstruction using real GPS and IMU measurements.

Overview

• Course: Numerical Analysis [MAT3008]
• Semester: Spring 2025 · Junior year, Semester 1
• Role: Team Leader
• Project period: May–June 2025
• Focus: numerical differentiation and integration, IMU drift correction, Kalman-filter sensor fusion, path reconstruction, RMSE-based comparison
• Main tool: MATLAB
• Recognition: Selected as an outstanding project team

Dataset and Preprocessing

The dataset contained longitudinal and lateral acceleration, yaw rate, GPS-derived Speed2D, wheel speed, latitude, and longitude measured from a real vehicle. Invalid samples were trimmed, the data was resampled at 100 Hz, and net acceleration was computed from the X- and Y-axis signals. A high-pass Butterworth filter reduced gravity bias and low-frequency drift. Yaw rate was integrated to obtain heading, and coordinates were converted between latitude/longitude and a local ENU frame for trajectory evaluation.

Numerical Methods

• GPS differentiation: 3-point forward, 3-point backward, 3-point central, and 5-point central difference
• IMU integration: trapezoidal rule, composite Simpson’s rule, Richardson extrapolation, third-order Runge–Kutta, and fourth-order Runge–Kutta
• Sensor fusion: Kalman Filter applied to RK4-based IMU velocity prediction using external reference measurements
• Path reconstruction: time-discretized kinematic integration using estimated velocity and heading, followed by conversion back to geographic coordinates

Key Results

• The 3-point central difference produced the lowest and most consistent error among the GPS differentiation methods.
• The theoretically higher-order 5-point central difference performed worst because boundary effects and noise sensitivity produced large error spikes.