We present the subspace-constrained Tyler's estimator (STE) designed for recovering a low-dimensional subspace within a dataset that may be highly corrupted with outliers. STE is a fusion of the Tyler's M-estimator (TME) and a variant of the fast median subspace. Our theoretical analysis suggests that, under a common inlier-outlier model, STE can effectively recover the underlying subspace, even when it contains a smaller fraction of inliers relative to other methods in the field of robust subspace recovery. We apply STE in the context of Structure from Motion (SfM) in two ways: for robust estimation of the fundamental matrix and for the removal of outlying cameras, enhancing the robustness of the SfM pipeline. Numerical experiments confirm the state-of-the-art performance of our method in these applications. This research makes significant contributions to the field of robust subspace recovery, particularly in the context of computer vision and 3D reconstruction.

The paper considers a Mixture Multilayer Stochastic Block Model (MMLSBM), where layers can be partitioned into groups of similar networks, and networks in each group are equipped with a distinct Stochastic Block Model. The goal is to partition the multilayer network into clusters of similar layers, and to identify communities in those layers. Jing et al. (2020) introduced the MMLSBM and developed a clustering methodology, TWIST, based on regularized tensor decomposition. The present paper proposes a different technique, an alternating minimization algorithm (ALMA), that aims at simultaneous recovery of the layer partition, together with estimation of the matrices of connection probabilities of the distinct layers. Compared to TWIST, ALMA achieves higher accuracy, both theoretically and numerically.

Platooning of connected vehicles is a solution geared toward improving traffic throughput, highway safety, driving comfort, and fuel efficiency. These vehicles are equipped with Cooperative Adaptive Cruise Controller (CACC) that integrates information from dedicated short-range communication (DSRC) radio and sensors for safe navigation. The possibility of malicious attacks such as Denial of Service (DoS) or False Data Injection (FDI) on sensor data or control inputs tends to affect reliability, and jeopardize the safety of connected vehicles. Thus, securing sensor data of these vehicles from DoS or FDI attacks is essential to avoid unwanted consequences. To withstand sensor attacks, resilient state estimators have been developed for networked cyber-physical systems (CPS). However, such estimators do not perform well as the number of compromised sensors of the system increases. As such, we propose a novel convex optimization based Resilient Distributed State Estimator (RDSE) that bounds the state estimation error, irrespective of the magnitude of the attack and the number of compromised sensors. We theoretically prove that the proposed estimator has similar performance compared to the state-of-the-art Distributed Kalman Filter (DKF) under attack free and noise free scenarios. While under attack, our RDSE outperforms the DKF and we provide a theoretical bound on state estimation error generated by RDSE during an attack. We also demonstrate the effectiveness of RDSE against FDI attacks in a platoon with five vehicles and compare its performance during attack against the DKF and the Resilient Distributed Kalman Filter (RDKF).

In this paper, we study the collaboratively estimating problem of a discrete-time LTI system with a time-varying undirected communication graph among sensors. The performance of resilient state estimators developed for cyber-physical systems (CPS) degenerates if the sensor measurements are compromised. To obtain robustness for the estimation, we propose Resilient Distributed Estimator with Information Consensus (RDEIC). RDEIC is a consensus-based resilient distributed algorithm that produces bounded state estimation errors with faulty sensors. Our algorithm converges to the true state in an attack-free scenario and it produces bounded estimation errors during an attack. The performance of the proposed algorithm is demonstrated with Matlab simulations.

The performance of resilient state estimators developed for cyber-physical systems (CPSs) decreases as the number of compromised sensors of the system increases. Furthermore, some of these algorithms leverage computationally expensive optimization techniques to incorporate resiliency. As such, we propose a fast resilient distributed state estimator (FRDSE), which is a novel resilient distributed algorithm that produces bounded state estimation errors regardless of the magnitude of the attack and the number of compromised sensors. Our algorithm converges to the true state in an attack-free and noise-free scenario and it produces bounded estimation errors during an attack. Compared to existing algorithms, FRDSE is more computationally efficient. We provide theoretical guarantees on the convergence of FRDSE in attack-free scenario and prove its resiliency during an attack. We demonstrate the performance of our algorithm against false data injection (FDI) attack in a platoon of vehicles and compare its runtime against existing algorithms. We observe that on a platoon of eight vehicles, runtime of our algorithm is 0.102 s, much lower than the state-of-the-art solutions.

Automotive systems have always been designed with safety in mind. In this regard, the functional safety standard, ISO 26262, was drafted with the intention of minimizing risk due to random hardware faults or systematic failure in design of electrical and electronic components of an automobile. However, growing complexity of a modern car has added another potential point of failure in the form of cyber or sensor attacks. Recently, researchers have demonstrated that vulnerability in vehicle's software or sensing units could enable them to remotely alter the intended operation of the vehicle. As such, in addition to safety, security should be considered as an important design goal. However, designing security solutions without the consideration of safety objectives could result in potential hazards. Consequently, in this paper we propose the notion of security for safety and show that by integrating safety conditions with our system-level security solution, which comprises of a modified Kalman filter and a Chi-squared detector, we can prevent potential hazards that could occur due to violation of safety objectives during an attack. Furthermore, with the help of a car-following case study, where the follower car is equipped with an adaptive-cruise control unit, we show that our proposed system-level security solution preserves the safety constraints and prevent collision between vehicle while under sensor attack.