Multi-Hypotheses Navigation in Collaborative Localization subject to Cyber Attacks

TL;DR

The paper tackles resilient collaborative localization in multi-agent systems under RF spoofing by extending a multi-hypotheses framework to networks through tagged hypotheses and covariance-intersection fusion. It introduces geometric reductions (convex hull-based selection) and distance-based matching to limit hypothesis transmission, enabling distributed diagnosis of spoofed measurements. Numerical results show the approach can separate true and spoofed measurements and recover consistent estimates after identifying the correct hypothesis, though the inherent conservativeness of CI slows detection. The work lays groundwork for cyber-resilient multi-agent navigation and points to future directions in coordinated hypothesis management across the network.

Abstract

This paper addresses resilient collaborative localization in multi-agent systems exposed to spoofed radio frequency measurements. Each agent maintains multiple hypotheses of its own state and exchanges selected information with neighbors using covariance intersection. Geometric reductions based on distance tests and convex hull structure limit the number of hypotheses transmitted, controlling the spread of hypotheses through the network. The method enables agents to separate spoofed and truthful measurements and to recover consistent estimates once the correct hypothesis is identified. Numerical results demonstrate the ability of the approach to contain the effect of adversarial measurements, while also highlighting the impact of conservative fusion on detection speed. The framework provides a foundation for resilient multi-agent navigation and can be extended with coordinated hypothesis selection across the network.

Figures (6)

• Figure 1: The information exchanged by the agents are the imu measurements and the posteriors.
• Figure 2: The procedure of determining the set of hypotheses transmitted to the neighbours. The middle box shows that first through $\mathbf{B}_k^{(i,j)}$, similar hypotheses are found such as hypotheses numbered $1$ and $2$ are considered the same, where $1$ is retained due to its distance to the remaining hypotheses higher is higher than $2$. The convex hull has hypotheses $1$, $3$, $4$, $7$ and $8$ as vertices. The right box shows how the hypotheses not constituting a vertex in the convex hull are not considered. The rdp along with reductions on $\mathbf{B}_k^{(i,j)}$ remove vertices $4$ and $7$, falling inside the strip defined by $\varepsilon$.
• Figure 3: Multi-Agent system
• Figure 4: Specific time steps showing the operational hypotheses $h^{(i,t,\mathrm{op})}$ of agents $a^{(0)}$ and $a^{(7)}$ along with the neighbors estimate of their position The plots show the error ellipses with containment probability $99.73\%$. The relative positions of agents are shown in Fig. \ref{['fig:scenario']}. The attack occurs at time step $k=20$, affecting the measurements relative to anchors $\mathrm{RF}0$ and $\mathrm{RF}1$. At time step $k=55$ agent $a^{(7)}$ has received more than one hypothesis from one of its neighbour, adding a new tag such that new operational hypothesis is added. The same occurs at at agent $a^{(0)}$ at $k=57$. Time steps $k=165$ and $k=222$ shows how the true state fall within the error ellipses. The black dot represents the true coordinates of the agents. The gray curve shows the nominal trajectory, which the agent is supposed to track.
• Figure 5: