Distribution Characteristics of Ranging Performance for Vertical Array Based on TDOA

This study primarily investigates the factors influencing the ranging performance of vertical arrays based on time difference of arrival (TDOA) and their underlying patterns of impact. We define and derive the detection accuracy (DA) and DA factor (DAF) based on the Cramér-Rao lower bound (CRLB). Through methods such as extremum analysis and mathematical induction, we identify the factors influencing detection performance and elucidate their impact patterns. Our findings indicate that DA is directly proportional to the variance of input parameter errors. The relative distribution of DA within a coordinate system defined by target distance, array depth, and array length is determined by the ratio of the variances of these input parameter errors. When the array length is significantly smaller than the array depth, the contours of DAF approximate a conical surface in the variable coordinate system. Case study analyses have been conducted to validate and refine these theoretical results, providing insights for system optimization. We conclude that when the array length is much smaller than the array depth, the effect of array depth measurement errors on DA can be considered negligible. Additionally, for fixed values of other parameters, either array depth or array length can yield an optimal solution, while DA increases monotonically with increasing array length. The experiments confirmed the results of the theoretical analysis.