This article addresses the problem of distributed state estimation (DSE) for discrete-time interconnected systems, where the observed system is composed of subsystems interconnected through state-to-state and state-to-output couplings. Inspired by the leader-follower consensus method, we propose a distributed observer that enables each subsystem to estimate the entire state of the interconnected system. Under certain structural assumptions, we derive necessary and sufficient conditions for the stability of the estimation error dynamics. We further present a decentralized design of the proposed observer, where the operation and construction of the observer can be completed by each subsystem using its locally available information, including the system's basic configuration, local measurements, and data exchanged with neighboring subsystems. In addition, we demonstrate that our distributed estimation framework can be applied to solve the distributed estimation problem for linear time-invariant (LTI) systems with fixed composition by employing an observability decomposition method. Finally, we illustrate the effectiveness of our scheme by applying it to vehicle platooning.

Cooperative localization and target tracking are essential for multi-robot systems to implement high-level tasks. To this end, we propose a distributed invariant Kalman filter (KF) based on covariance intersection (CI) for effective multi-robot pose estimation. The paper utilizes the object-level measurement models, which have condensed information further reducing the communication burden. Besides, by modeling states on special Lie groups, and representing uncertainty in corresponding Lie algebras, better linearity and consistency are obtained under the invariant KF framework. We also combine CI and invariant KF to avoid overly confident or conservative estimates in multi-robot systems with intricate and unknown correlations, and some level of robot degradation is acceptable through multi-robot collaboration. The simulation and real data experiment validate the practicability and superiority of the proposed algorithm. The source code is publicly available11https://github.com/LIAS-CUHKSZ/Distributed-object-based-SLAM.

We present SCORE, a visual relocalization system that achieves unprecedented map compactness through semantically labeled 3D line maps. SCORE requires only 0.01%-0.1% of the storage needed by structure-based or learning-based baselines, while maintaining practical accuracy and comparable runtime. The key innovation is a novel robust mechanism, Saturated Consensus Maximization (Sat-CM), which generalizes classical Consensus Maximization (CM) by assigning diminishing weights to inlier associations with probabilistic justification. Under extreme outlier ratios (up to 99.5%) arising from one-to-many ambiguity in semantic matching, Sat-CM enables accurate estimation when CM fails. To ensure computational efficiency, we propose an accelerating framework for globally solving Sat-CM formulations and specialize it for the Perspective-n-Lines problem at the core of SCORE.

Given 2D point correspondences between an image pair, inferring the camera motion is a fundamental issue in the computer vision community. The existing works generally set out from the epipolar constraint and estimate the essential matrix, which is not optimal in the maximum likelihood (ML) sense. In this paper, we dive into the original measurement model with respect to the rotation matrix and normalized translation vector and formulate the ML problem. We then propose an optimal two-step algorithm to solve it: In the first step, we estimate the variance of measurement noises and devise a consistent estimator based on bias elimination; In the second step, we execute a one-step Gauss-Newton iteration on manifold to refine the consistent estimator. We prove that the proposed estimator achieves the same asymptotic statistical properties as the ML estimator: The first is consistency, i.e., the estimator converges to the ground truth as the point number increases; The second is asymptotic efficiency, i.e., the mean squared error of the estimator converges to the theoretical lower bound - Cramer-Rao bound. In addition, we show that our algorithm has linear time complexity. These appealing characteristics endow our estimator with a great advantage in the case of dense point correspondences. Experiments on both synthetic data and real images demonstrate that when the point number reaches the order of hundreds, our estimator outperforms the state-of-the-art ones in terms of estimation accuracy and CPU time.

Online advertising has been the mainstream monetization approach for internet-based companies, in which bid optimization plays a crucial role in enhancing advertising performance. Currently, the bid optimization problem has narrowed down to two specific forms: Budget-constrained bidding (BCB) and Multi-constraint bidding (MCB). Existing solutions try to solve BCB/MCB via linear programming solvers, learning methods, or feedback control. However, in large-scale complex e-commerce, they still suffer from inefficiency, poor convergence, or slow adaptation to the changing market. This research presents an online receding optimization method as a solution for practical bid optimization problems. We conduct a theoretical analysis of the optimal bidding strategy's structure. Further, an online receding optimization process is designed based on open-loop feedback control, which periodically updates a constructed optimal bid formulation that can be solved by linear programming. Then, considering large-scale linear programming problems, we propose an efficient down sampling scheme. Besides, a neural-network-based auction scale prediction is used to adapt to the changing market. Finally, a series of online A/B experiments onTaobao Sponsored Searchcompare our work to industrial methods and state-of-the-art from several aspects. The proposed method has been implemented onTaobao, a billion-scaled online advertising business, for over a year.

This paper studies the online reward poisoning problem, wherein an adversary deliberately manipulates the reward function during training to mislead the learning agent into adopting a mischievous policy. While the majority of existing reward poisoning research focuses on offline attacks, which assume prior knowledge of the transition probability, our work explores a more practical yet challenging dynamics-agnostic scenario. Specifically, we consider the scenario where the adversary has access to the agent’s replay buffer and can modify the reward data without the knowledge of transition probabilities. We formalize the poisoning task as an optimization problem and employ a reformulation method to circumvent the double-sampling issue. The proposed algorithm is provably convergent in the tabular setting and can be extended to the function approximation setting, where the poisoned reward network and the poisoned Q-value network are jointly learned to solve the problem. The algorithm’s effectiveness is validated through four distinct experimental evaluations.

Neural Radiance Fields (NeRF) have revolutionized 3D computer vision and graphics, facilitating novel view synthesis and influencing sectors like extended reality and e-commerce. However, NeRF's dependence on extensive data collection, including sensitive scene image data, introduces significant privacy risks when users upload this data for model training. To address this concern, we first propose SplitNeRF, a training framework that incorporates split learning (SL) techniques to enable privacy-preserving collaborative model training between clients and servers without sharing local data. Despite its benefits, we identify vulnerabilities in SplitNeRF by developing two attack methods, Surrogate Model Attack and Scene-aided Surrogate Model Attack, which exploit the shared gradient data and a few leaked scene images to reconstruct private scene information. To counter these threats, we introduce S^2NeRF, secure SplitNeRF that integrates effective defense mechanisms. By introducing decaying noise related to the gradient norm into the shared gradient information, S^2NeRF preserves privacy while maintaining a high utility of the NeRF model. Our extensive evaluations across multiple datasets demonstrate the effectiveness of S^2NeRF against privacy breaches, confirming its viability for secure NeRF training in sensitive applications.

This paper explores the stability problems of discrete-time linear time-invariant (LTI) systems subject to random time delays. We first develop a general mean-square small-gain stability condition for feedback systems containing structured stochastic multiplicative uncertainties. Subsequently, we apply this mean-square small-gain condition to certain LTI random delay systems, where delays exhibit random delay lengths. Necessary and sufficient mean-square stability criteria are derived. These criteria, applicable to systems with either single or multiple sources of random delays, typically involve computing the spectral radius of a constant matrix. This computation allows us to determine whether a system's state variance matrix converges asymptotically despite the presence of random delays.

The information regarding the driving states of all vehicles is crucial for achieving optimal group performance in a vehicle platoon. This article focuses on the fully distributed driving state estimation problem in open vehicle platoons, which frequently experience arrivals and departures of vehicles. To address this problem, we propose a distributed driving state observer inspired by the leader–follower consensus technique. This observer can reconstruct the global driving state of the platoon, including the positions, velocities, and accelerations of all vehicles. We also derive the necessary and sufficient conditions to ensure the stability of its estimation error dynamics. The proposed observer is highly flexible in platoons with a strongly connected communication network, as it can be constructed and operated using the local knowledge of each vehicle only, without relying on global information of a platoon such as the number of vehicles. We demonstrate the observer's plug-and-play operations in the face of platoon merging and splitting and analyze its estimation stability. Extensive simulation results demonstrate the effectiveness of our theoretical results and the potential of the proposed observer for platoon control.

We consider signal source localization from range-difference measurements. First, we give some readily-checked conditions on measurement noises and sensor deployment to guarantee the asymptotic identifiability of the model and show the consistency and asymptotic normality of the maximum likelihood (ML) estimator. Then, we devise an estimator that owns the same asymptotic property as the ML one. Specifically, we prove that the negative log-likelihood function converges to a function, which has a unique minimum and positive definite Hessian at the true source’s position. Hence, it is promising to execute local iterations, e.g., the Gauss-Newton (GN) algorithm, following a consistent estimate. The main issue involved is obtaining a preliminary consistent estimate. To this aim, we construct a linear least-squares problem via algebraic operation and constraint relaxation and obtain a closed-form solution. We then focus on deriving and eliminating the bias of the linear least-squares estimator, which yields an asymptotically unbiased and further consistent estimate. Noting that the bias is a function of the noise variance, we further devise a consistent noise variance estimator that involves a 3-order polynomial rooting. Based on the preliminary consistent location estimate, a one-step GN iteration suffices to achieve the same asymptotic property as the ML estimator. Simulation results demonstrate the superiority of our proposed algorithm in the large sample case.

Robot audition systems with multiple microphone arrays have many applications in practice. However, the accurate calibration of multiple microphone arrays remains challenging because there are many unknown parameters to be identified, including the relative transforms (i.e., orientation and translation) and asynchronous factors (i.e., initial time offset and sampling clock difference) between microphone arrays. To tackle these challenges, in this article, we adopt batch simultaneous localization and mapping (SLAM) for joint calibration of multiple asynchronous microphone arrays and sound source localization. Using the Fisher information matrix (FIM) approach, we first conduct the observability analysis (i.e., parameter identifiability) of the abovementioned calibration problem and establish necessary/sufficient conditions under which the FIM and the Jacobian matrix have full column rank, which implies the identifiability of the unknown parameters. We also discover several scenarios where the unknown parameters are not uniquely identifiable. Subsequently, we propose an effective framework to initialize the unknown parameters, which is used as the initial guess in batch SLAM for multiple microphone array calibration, aiming to further enhance optimization accuracy and convergence. Extensive numerical simulations and real experiments have been conducted to verify the performance of the proposed method. The experimental results show that the proposed pipeline achieves higher accuracy with fast convergence in comparison to methods that use the noise-corrupted ground truth of the unknown parameters as the initial guess in the optimization and other existing frameworks.

State estimation is an essential part of autonomous systems. Integrating the Ultra-Wideband (UWB) technique has been shown to correct the long-term estimation drift and bypass the complexity of loop closure detection. However, few works on robotics treat UWB as a stand-alone state estimation solution. The primary purpose of this work is to investigate planar pose estimation using only UWB range measurements. We prove the excellent property of a two-step scheme, which says we can refine a consistent estimator to be asymptotically efficient by one step of Gauss-Newton iteration. Grounded on this result, we design the GN-ULS estimator, which reduces the computation time significantly compared to previous methods and presents the possibility of using only UWB for real-time state estimation.

The Perspective-n-Point (PnP) problem has been widely studied in both computer vision and photogrammetry societies. With the development of feature extraction techniques, a large number of feature points might be available in a single shot. It is promising to devise a consistent estimator, i.e., the estimate can converge to the true camera pose as the number of points increases. To this end, we propose a consistent PnP solver, named CPnP, with bias elimination. Specifically, linear equations are constructed from the original projection model via measurement model modification and variable elimination, based on which a closed-form least-squares solution is obtained. We then analyze and subtract the asymptotic bias of this solution, resulting in a consistent estimate. Additionally, Gauss-Newton (GN) iterations are executed to refine the consistent solution. Our proposed estimator is efficient in terms of computations—it has$O(n)$time complexity. Simulations and real dataset tests show that our proposed estimator is superior to some well-known ones for images with dense visual features, in terms of estimation precision and computing time.

Detecting small low-contrast targets in the airspace is an essential and challenging task. This article proposes a simple and effective data-driven support vector machine (SVM)-based spatiotemporal feature fusion detection method for small low-contrast targets. We design a novel pixel-level feature, called a spatiotemporal profile, to depict the discontinuity of each pixel in the spatial and temporal domains The spatiotemporal profile is a local patch of the spatiotemporal feature maps concatenated by the spatial feature maps and temporal feature maps in channelwise, which are generated by the morphological black-hat filter and a ghost-free dark-focusing frame difference methods, respectively. Instead of the handcrafted feature fusion mechanisms in previous works, we use the labeled spatiotemporal profiles to train an SVM classifier to learn the spatiotemporal feature fusion mechanism automatically. To speed up detection for high-resolution videos, the serial SVM classification process on central processing units (CPUs) is reformed as parallel convolution operations on graphics processing unit (GPUs), which exhibits over 1000+ times speedup in our real experiments. Finally, blob analysis is applied to generate final detection results. Elaborate experiments are conducted, and experimental results demonstrate that the proposed method performs better than 12 baseline methods for the small low-contrast target detection. The field tests manifest that the parallel implementation of the proposed method can realize real-time detection at 15.3 FPS for videos at a resolution of 2048×1536 and the maximum detection distance can reach 1 km for drones in sunny weather.

This paper studies the localization problem using noisy range-difference measurements, or equivalently time difference of arrival (TDOA) measurements. There is a reference sensor, and for each other sensor, the TDOA measurement is obtained with respect to the reference one. By minimizing the sum of squared errors, a nonconvex constrained least squares (CLS) problem is formulated. In this work, we focus on devising an algorithm to seek the global minimizer of the CLS problem, hoping that the numerical solution meets some precision requirement in terms of relative error. Based on the Lagrange multiplier method, we first branch the feasible Lagrange multiplier set into several subsets and develop a workflow in terms of if-then-else control structure to seek the global minimizer by searching for the optimal Lagrange multiplier. The execution order is carefully organized so that it is in line with the general principle of putting the flow that one normally understands to be executed first. We then dive into detailed searching methods in different cases and conduct computational error analysis, giving the error bound on the Lagrange multiplier, when we search for it, to meet the precision requirement on an approximate solution. Based on the above achievements, a programmable global minimizer seeking algorithm is proposed for the CLS problem. Simulations and experimental tests on a public dataset demonstrate the effectiveness of the proposed algorithm.

In this paper we focus on the dynamic state estimation which harnesses a vast amount of sensing data harvested by multiple parties and recognize that in many applications, to improve collaborations between parties, the estimation procedure must be designed with the awareness of protecting participants' data and model privacy, where the latter refers to the privacy of key parameters of observation models. We develop a state estimation paradigm for the scenario where multiple parties with data and model privacy concerns are involved. Multiple parties monitor a physical dynamic process by deploying their own sensor networks and update the state estimate according to the average state estimate of all the parties calculated by a cloud server and security module. The paradigm taps additively homomorphic encryption which enables the cloud server and security module to jointly fuse parties' data while preserving the data privacy. Meanwhile, all the parties collaboratively develop a stable (or optimal) fusion rule without divulging sensitive model information. For the proposed filtering paradigm, we analyze the stabilization and the optimality. First, to stabilize the multi-party state estimator while preserving observation model privacy, two stabilization design methods are proposed. For special scenarios, the parties directly design their estimator gains by the matrix norm relaxation. For general scenarios, after transforming the original design problem into a convex semi-definite programming problem, the parties collaboratively derive suitable estimator gains based on the alternating direction method of multipliers (ADMM). Second, an optimal collaborative gain design method with model privacy guarantees is provided, which results in the asymptotic minimum mean square error (MMSE) state estimation. Finally, numerical examples are presented to illustrate our design and theoretical findings.

Individuals, or organizations, cooperate with or compete against one another in a wide range of practical situations. Such strategic interactions are often modeled as games played on networks, where an individual’s payoff depends not only on her action but also on that of her neighbors. The current literature has largely focused on analyzing the characteristics of network games in the scenario where the structure of the network, which is represented by a graph, is known beforehand. It is often the case, however, that the actions of the players are readily observable while the underlying interaction network remains hidden. In this paper, we propose two novel frameworks for learning, from the observations on individual actions, network games with linear-quadratic payoffs, and in particular, the structure of the interaction network. Our frameworks are based on the Nash equilibrium of such games and involve solving a joint optimization problem for the graph structure and the individual marginal benefits. Both synthetic and real-world experiments demonstrate the effectiveness of the proposed frameworks, which have theoretical as well as practical implications for understanding strategic interactions in a network environment.

To invade a cyber-physical system (CPS) successfully, hackers are prone to simultaneously launching multiple cyber attacks on different sensors in a CPS. However, little attention has been paid to the problem of detecting multiple cyber attacks up to now. Therefore, in this paper, we deal with the problem on how to efficiently detect multiple cyber attacks aiming at different sensors in CPSs. To achieve the goal of simultaneously detecting both the number of attacks and the attacked sensors, we formulate this problem via a random finite set (RFS) theory, and then apply an iterative RFS-based Bayesian filter and its approximation to solve the problem. Four numerical experiments with different attacks are provided, and the results have demonstrated the effectiveness of the RFS-based approach for the problem of multiple attacks detection in CPSs.

In this paper, we investigate probabilistic stability of Kalman filtering over fading channels modeled by *-mixing random processes, where channel fading is allowed to generate non-stationary packet dropouts with temporal and/or spatial correlations. Upper/lower almost sure (a.s.) stabilities and absolutely upper/lower a.s. stabilities are defined for characterizing the sample-path behaviors of the Kalman filtering. We prove that both upper and lower a.s. stabilities follow a zero-one law, i.e., these stabilities must happen with a probability either zero or one, and when the filtering system is one-step observable, the absolutely upper and lower a.s. stabilities can also be interpreted using a zero-one law. We establish general stability conditions for (absolute) upper and lower a.s. stabilities. In particular, with one-step observability, we show the equivalence between absolutely a.s. stabilities and a.s. ones, and necessary and sufficient conditions in terms of packet arrival rate are derived; for the so-called non-degenerate systems, we also manage to give a necessary and sufficient condition for upper a.s. stability.

This paper proposes and investigates a Boolean gossip model as a simplified but non-trivial probabilistic Boolean network. With positive node interactions, in view of standard theories from Markov chains, we prove that the node states asymptotically converge to an agreement at a binary random variable, whose distribution is characterized for large-scale networks by mean-field approximation. Using combinatorial analysis, we also successfully count the number of communication classes of the positive Boolean network explicitly in terms of the topology of the underlying interaction graph, where remarkably minor variation in local structures can drastically change the number of network communication classes. With general Boolean interaction rules, emergence of absorbing network Boolean dynamics is shown to be determined by the network structure with necessary and sufficient conditions established regarding when the Boolean gossip process defines absorbing Markov chains. Particularly, it is shown that for the majority of the Boolean interaction rules, except for nine out of the total 216- 1 possible nonempty sets of binary Boolean functions, whether the induced chain is absorbing has nothing to do with the topology of the underlying interaction graph, as long as connectivity is assumed. These results illustrate the possibilities of relating dynamical properties of Boolean networks to graphical properties of the underlying interactions.

This paper considers decentralized state estimation subject to communication constraints. A group of agents measure the state of a process and obtain their state estimates by exchanging data with one another. Due to the communication constraint, only a few communication channels are available. The main objective of this paper is to allocate these channels among the agents so as to minimize their average estimation errors. Assuming the agents have the same sensing capability, we provide the optimal allocation strategy for both directed and un-directed communication channels.