Underwater High Precision Wireless Acoustic Positioning Algorithm Based on L-p Norm

Abstract

Underwater wireless acoustic positioning technology uses the geometric relationship between a target and a receiving array to determine the target’s position by measuring distances between the target and the array elements, that the receiving array is usually symmetry in space. It is an indirect measurement approach, so ranging errors can significantly impact positioning accuracy due to error transmission effects. To improve precision, a similarity-matched localization algorithm based on the L-p norm (LPM) is introduced. This algorithm constructs a distance vector model with environmental parameters and performs similarity analysis by computing the L-p norm of the distance vector and a reference copy vector for three-dimensional localization in the observation area. Unlike conventional methods, this technology directly matches distance vectors without coupling error transmission, thereby enhancing positioning accuracy even though it remains contingent upon ranging precision. To validate the algorithm’s efficacy, Monte Carlo simulations are employed to analyze the distribution patterns of positioning errors in both horizontal and three-dimensional spaces. The results show an improvement from a mean positioning error of 0.0475 m to 0.0250 m and a decrease in error standard deviation from 0.0240 m to 0.0092 m. The results indicate that LPM offers improved accuracy and robustness by circumventing traditional error transmission issues.

Keywords

• acoustic positioning
• L-p norm
• similarity matched
• error transmission law
• least squares