⚡ electrical engineering

Resilient Consensus-Based Target Tracking under False Data Injection Attacks in Multi-Agent Networks

This paper proposes a resilient, consensus-based distributed target tracking algorithm that integrates saturation-based filtering and a dynamic false data injection detection mechanism to effectively suppress measurement faults and adversarial attacks while maintaining estimation accuracy and convergence speed in multi-agent networks.

Original authors: Amir Ahmad Ghods, Mohammadreza Doostmohammadian

Published 2026-08-04

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CC BY 4.0

Original authors: Amir Ahmad Ghods, Mohammadreza Doostmohammadian

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a swarm of drones, a fleet of self-driving cars, or a team of robots working together to find a lost hiker in a forest. They don't have a single "boss" drone telling them where to go; instead, they act like a school of fish, constantly chatting with their immediate neighbors to figure out where the target is. This is the world of multi-agent networks, a branch of robotics and engineering where many small, simple devices collaborate to solve big problems. To do this, they rely on distributed estimation, a fancy way of saying "let's all guess the answer together by sharing our local clues." But here's the catch: what if one of those neighbors is lying? What if a hacker sneaks into the network and feeds the group fake coordinates, causing the whole team to chase a ghost? This is the danger of false data injection attacks. The question isn't just about math; it's about trust. How do you build a team that can spot a liar in the crowd and keep moving forward without falling apart?

This paper tackles that exact problem by proposing a new way for these robot teams to track moving targets while ignoring bad actors. The authors, Amir Ahmad Ghods and Mohammadreza Doostmohammadian, suggest a two-part safety system. First, they use a "saturation filter," which acts like a shock absorber. If a neighbor suddenly shouts a wildly impossible number (like a drone claiming the target is moving at the speed of light), the filter dampens that shout so it doesn't knock the whole team off course. Second, and more importantly, they add a "lie detector." This mechanism constantly checks if a neighbor's new information matches what the team expects based on physics. If the data is too weird, the system flags that neighbor as compromised and temporarily ignores their input, keeping the rest of the group safe.

The researchers tested their idea using computer simulations, not real robots in the wild. They created virtual networks of agents and introduced different types of trouble: a few agents lying with huge numbers, half the team being hacked with varying lies, and even short bursts of fake data. The results were promising. In their simulations, the new system successfully identified and isolated the "liars," preventing their fake data from corrupting the group's shared map. When 50% of the agents were under coordinated attack, the new method reduced the tracking error by about 65% compared to the older, unprotected method. The study also found that having more connections between agents and letting them talk more often helped them agree faster and more accurately, though this required more communication power. However, the authors note that their system works best when the majority of the team is honest; if too many agents are compromised, the system might struggle. They also point out that their model assumes the target moves in a fairly predictable way (like a car on a straight road), so it might get confused if the target suddenly starts doing acrobatic flips. Ultimately, this work suggests that with the right mix of shock absorbers and lie detectors, decentralized robot teams can be much tougher against cyber-attacks than previously thought.

Technical Summary: Resilient Consensus-Based Target Tracking under False Data Injection Attacks

Problem Statement
Distributed target tracking in multi-agent networks is essential for applications such as autonomous surveillance and cooperative robotics. However, these systems face significant challenges in maintaining estimation accuracy and network resilience when subjected to faulty measurements, environmental disturbances, and cyber-physical threats. Specifically, False Data Injection Attacks (FDIA), where adversaries compromise agents or communication channels to feed erroneous data, can cause severe errors in position and velocity estimates. While existing decentralized frameworks, such as Distributed Kalman Filters (DKFs), offer scalability, they often lack robustness against such adversarial inputs and suffer from high communication overheads due to covariance exchanges. Furthermore, many adaptive or learning-based solutions introduce excessive computational burdens, limiting their practicality in resource-constrained networks.

Methodology
The paper proposes a resilient, decentralized target tracking algorithm that integrates a consensus-based estimation framework with a dynamic fault detection mechanism. The approach is built upon three core components:

System Modeling: The target's motion is modeled using a Nearly-Constant-Velocity (NCV) kinematic model with process noise to account for acceleration uncertainties. Agents utilize Time-of-Arrival (TOA) multilateration to generate local observation matrices, allowing them to estimate distances to the target based on signal arrival times. The network topology is represented as an Erdős–Rényi random graph.
Consensus-Based Estimation with Saturation Filtering: Building on the authors' previous work, the algorithm employs a two-step process: a local observation update followed by an iterative consensus step.
- Observation Update: Agents apply a saturation-based filter to their local measurements. A saturation gain ( $g_i(k)$ ) limits the influence of large innovations (differences between measured and predicted values), effectively suppressing impulsive measurement variations caused by noise or attacks.
- Consensus Step: Agents iteratively exchange state estimates with immediate neighbors to reach a global agreement. This step is repeated $L$ times per time step to improve convergence and accuracy without requiring global covariance information.
Dynamic FDIA Detection and Isolation: The primary contribution of this study is the addition of a detection and isolation layer.
- Innovation Monitoring: At each time step, agents compute an innovation value ( $\gamma_i(k)$ ) representing the deviation between the current measurement and the predicted state.
- Dynamic Thresholding: A dynamic detection threshold ( $\varphi_i(k)$ ) is calculated based on the state transition matrix norm, the previous estimation error bound, the global consensus mismatch, and predefined noise bounds.
- Isolation Logic: If the innovation magnitude exceeds the threshold, the agent is flagged as compromised. Instead of updating its state with the suspicious measurement, the agent relies solely on the dynamic model prediction ($x(k) = Ax(k-1)$), effectively isolating the faulty data from the consensus process.

Key Contributions

Integration of Detection and Consensus: The paper extends a baseline consensus-based tracker by embedding a real-time FDIA detection mechanism that operates without requiring centralized oversight or complex learning models.
Dynamic Thresholding: Unlike static thresholds, the proposed detection threshold adapts to the network's current state (consensus mismatch) and noise characteristics, allowing for more accurate identification of anomalies.
Fault Isolation Strategy: The method prevents compromised data from corrupting the global estimate by switching to a model-based prediction for detected faulty agents, rather than attempting to correct the data.
Comprehensive Evaluation: The study provides a rigorous evaluation across six distinct case studies, covering benign conditions (varying connectivity, consensus iterations, and filter parameters) and three adversarial scenarios (localized, widespread coordinated, and transient attacks).

Results
Simulation results in a MATLAB environment demonstrate the following:

Baseline Performance: Under benign conditions, higher network connectivity ( $p=0.7$ vs. $p=0.3$ ) and increased consensus iterations ( $L=100$ vs. $L=10$ ) significantly improved estimation accuracy and convergence speed, albeit with higher communication costs. A conservative saturation filter ( $\xi=2$ ) offered better robustness against noise but reduced sensitivity to legitimate state changes.
Adversarial Resilience:
- Localized Attacks: The algorithm successfully identified and isolated two compromised agents, preventing the propagation of false data and maintaining low Mean Squared Estimation Error (MSEE).
- Widespread Coordinated Attacks: In scenarios where 50% of agents were compromised with varying attack magnitudes, the proposed algorithm (Algorithm 2) reduced the average MSEE by approximately 65% compared to the baseline algorithm (Algorithm 1) without detection. While low-magnitude attacks near the threshold were occasionally missed, the system maintained significantly better accuracy than the baseline.
- Transient Attacks: The detection mechanism quickly identified short-duration attacks, allowing the system to recover with minimal delay.
Trade-offs: The study confirms that while the detection mechanism adds a layer of security, it operates with modest computational and communication overheads, making it suitable for decentralized networks.

Significance and Claims
The authors claim that this study provides a simplified, fault-tolerant solution that significantly enhances the accuracy and resilience of distributed target tracking without imposing excessive communication or computational burdens. The paper asserts that the proposed algorithm effectively balances the trade-off between fault suppression and accurate estimation. By successfully identifying and isolating compromised agents under localized, coordinated, and transient attack scenarios, the method ensures that the distributed global estimate remains uncorrupted. The work positions itself as a practical alternative to complex learning-based or centralized approaches, offering a scalable framework for secure multi-agent systems in dynamic and adversarial environments. The authors acknowledge limitations, including the assumption that a majority of agents are benign, the reliance on the NCV model for non-linear dynamics, and the potential for missed detections when attack magnitudes are very close to the dynamic threshold.

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