MATLAB Simulation of Ultra-Wideband TOA Positioning with Kalman Filter Algorithm

Ultra-Wideband (UWB) technology, with its high-precision time resolution, commonly employs Time of Arrival (TOA) methods for distance measurement in positioning systems. Integrating Kalman filtering with TOA positioning effectively suppresses measurement noise and improves dynamic positioning accuracy.

Core Implementation Workflow: TOA Ranging Model Calculate inter-node distances using UWB signal time-of-flight measurements. Due to multipath effects and clock synchronization errors, raw measurements contain Gaussian noise. In MATLAB implementation, this typically involves generating simulated TOA data with `randn()` function to add Gaussian noise components.

State Space Modeling Define target state vectors (e.g., position, velocity) and establish linear motion models (constant velocity or acceleration models). Convert TOA observations into measurement equations related to state vectors. Key MATLAB functions include defining state transition matrices and measurement matrices for the Kalman filter structure.

Kalman Filter Iteration Prediction Phase: Estimate next-time-step state and error covariance using motion models. This involves matrix multiplication operations for state prediction and covariance propagation. Update Phase: Correct predictions using TOA measurements, balancing prediction and measurement weights through Kalman gain calculation. The implementation requires solving the Kalman gain equation and updating state estimates using measurement residuals.

MATLAB Simulation Key Points: Simulate movement trajectories (e.g., linear or curved motion) using trajectory generation functions Add Gaussian noise to simulate TOA measurement errors with appropriate variance settings Visualize and compare pre-filtering and post-filtering positioning trajectories using `plot()` functions Analyze Root Mean Square Error (RMSE) metrics to quantify performance improvement

Optimization Directions: Extend to Extended Kalman Filter (EKF) for handling nonlinear scenarios through Jacobian matrix calculations Introduce multi-base station data fusion to enhance robustness in complex environments using sensor fusion techniques