The TOA-LS Positioning Computation Based on Bancroft Algorithm and Time Synchronization Method for Wide-Area Multilateration

Wide Area Multilateration (WAM) is an advanced aircraft positioning and measurement technology that is widely used for precise surveillance of aircraft in complex airspace, playing a significant role in ensuring operational safety. The measurement accuracy is typically influenced by factors such as time synchronization and positioning algorithms. To address the challenges of difficult time synchronization and low positioning accuracy, this paper proposes a mathematical model for time synchronization and message extraction based on Time of Arrival (TOA), as well as a weighted least squares algorithm for TOA positioning equations based on the Bancroft algorithm. The time synchronization model uses TOA count values as the reference time to calculate the synchronized start time of the sensors, addressing synchronization interference caused by the non-simultaneous startup of distributed sensors and uneven signal reception, and extracts the TOA of synchronized messages for positioning measurements. In terms of positioning algorithms, the Bancroft TOA-LS algorithm formulates the positioning problem as a range error optimization problem, with weighting coefficients related to the target position and the target signal transmission time. The Bancroft algorithm is used to provide initial values and solve the TOA-LS equations, completing the iterative update of the weighting coefficients. Through Taylor expansion, the bias in the solution is derived and corrected to improve positioning accuracy and accelerate convergence. Additionally, the proposed Bancroft TOA-LS algorithm can solve for the synchronized start time using the time component in the solution vector, thereby updating the synchronization time. Experimental results show that the Bancroft TOA-LS algorithm can better approximate the Cramer-Rao Lower Bound (CRLB), outperforming other algorithms. Practical engineering tests have proven that the time synchronization model and positioning algorithm proposed in this paper can be practically applied, with positioning accuracy errors within the standard requirements, demonstrating their feasibility and practicality.