The Pseudoinverse Gradient Descent Method with Eight Branch Directions (8B-PGDM): An Improved Dead Reckoning Algorithm Based on the Local Invariance of Navigation

This paper establishes a fundamental connection between the local time invariance of motion parameters and dead reckoning (DR) accuracy. This insight enables the reformulation of navigation parameter estimation as a convex optimization problem solvable through our novel Eight-Branch Pseudoinverse Gradient Descent Method (8B-PGDM). This method addresses non-cooperative positioning challenges in sparse-sensor regimes, particularly enabling real-time trajectory prediction when facing intermittent measurements (e.g., <5 Hz sampling rates) or persistent signal blockages. This method achieves an excellent estimation accuracy with only three samplings and an prediction MSE of 0.7906, significantly better than traditional dead reckoning (DR) methods. This approach effectively mitigates the impact of data scarcity, enabling robust and accurate trajectory predictions in challenging environments.