In the field of target precision localization, how to accurately locate static targets using a distributed multi-sensor system is an important scientific problem. This research focuses on this problem, investigating how to distribute multiple time-of-arrival (TOA) sensor locations to achieve high-precision localization of a single static target. The TOA sensors can be mounted on multiple mobile platforms such as UAVs and unmanned surface vessels, while the static target can be a hostile radar station, trapped personnel, underwater beacons, etc. Therefore, the proposed method has applications covering military strikes, underwater exploration, and civilian search and rescue.
This study first uses MATLAB software combined with a gradient descent-based program to arbitrarily distribute multiple sensors in a three-dimensional space, setting the target position at the origin. Then, the true geometrical relative relationships between each sensor and the target are calculated. Next, using the trace (tr(CRLB)) of the Cramero lower bound as the cost function in the gradient method, the program automatically calculates how the multiple sensors can be moved to reduce the cost function and converge to the global minimum position. Finally, the obtained optimal sensor distribution is compared with the theoretical value to verify the superiority of the proposed method. Furthermore, this study employs a practical estimation strategy for verification. Multiple sensors are arranged in different geometric distributions at various specific locations to determine the specific measurement noise variance in the simulation. The maximum likelihood estimation algorithm is used, and Monte Carlo randomization is employed for repeated calculations to verify the effectiveness of the proposed theory.
Experimental results show that the mean square error obtained by maximum likelihood estimation under the optimal distribution in practical estimation problems is basically consistent with the theoretical derivation. In the experimental example, by arranging N TOA sensors with measurement variance noise of σ² according to the proposed method, the minimum mean square error of target estimation can reach 9σ²/(4N), which is consistent with the relevant conclusions of the optimal accuracy theory first proposed in this paper.
The proposed method can quickly evaluate the best achievable accuracy of a TOA (Time of Arrival) 3D target localization strategy and provides sensor distribution strategies to improve estimation accuracy. This method can be applied to military reconnaissance, including the precise location of targets such as enemy radar stations, ships, and submarines, and can also be used in civilian fields such as UAV search and rescue, maritime beacon search, and underground mineral exploration.
