Evaluation and Optimization of Positional Accuracy for Maritime Positioning Systems

TL;DR

This work addresses GNSS vulnerability in maritime navigation by proposing a radar-based backup that relies on timestamped radar detections and multilateration to localize vessels in 2D. The method combines circumambient circle generation (α from timestamps via $α = 2π τ_{ij} / P$ and $r(α,d_{ij})$) with confidence ellipse construction, producing a $95\%$ uncertainty region through covariance fusion across sensor tuples. An optimization framework minimizes total expenditure Exp_total while enforcing a positioning error cap $Ω$, incorporating installation, energy, and data costs, and allowing sensor standby to reduce operating cost. Validation in Rhine and Forggensee campaigns shows accurate positioning with reduced sensor counts in many regions, while larger areas require more sensors to maintain target accuracy, highlighting practical trade-offs for GNSS-resilient maritime sensing.

Abstract

Navigation and trajectorial estimation of maritime vessels are contingent upon the context of positional accuracy. Even the smallest deviations in the estimation of a given vessel may result in detrimental consequences in terms of economic and ecologic quotients. To ensure an agile and precise environment for maritime vessel positional estimation, preexisting marine radar technologies can be utilized in a way that ensures a higher level of precision compared to GNSS-based identification and positioning. In this paper, we present a positional optimization for radarbased vessel navigation systems that utilize the installment of vessel detection sensors. The main objective of this research is to employ as fewer sensors as possible while preserving the attainable error threshold for positioning that is defined by International Maritime Organization (IMO). Our approach leads most of the time to a positioning error of up to 5 m along shorelines and rivers and up to 50 m along open coastal regions.

Figures (7)

• Figure 1: (left) Upper- and lower-bounding circumambient circles, (middle) uncertainty area generation pertaining to distinct circumambient circle, (right) Final confidence region covering approximately 95% of all potential vessel positions.
• Figure 2: An example 4-sensor setup consisting of a singular vessel. Orange dots represent vessel route over time. The confidence region for each time step is illustrated with red ellipses.
• Figure 3: The error in the radius based on two receivers and the distance to the ship. The two MRD receivers are marked as red dots. Solid contour lines depict the best case scenario to corresponding radius error propagation; dashed lines depict the worst case.
• Figure 4: Three sensors placed with equidistant horizontal alignment. Sections between the sensors elongate on the same horizontal axis yield higher accuracy error compared to sections with elevated angle to the sensors.
• Figure 5: UTM heatmap depictions of the Rhine and Forggensee campaign. MRD locations are marked with red dots. The pattern of granularity is illustrated with respect to positioning error below $1$ m and $5$ m for Rhine, $25$ m. and $50$ m for Forggensee respectively.