This work studies distributed (probability) density estimation of large-scale systems. Such problems are motivated by many density-based distributed control tasks in which the real-time density of the swarm is used as feedback information, such as sensor deployment and city traffic scheduling. This work is built upon our previous work [1] which presented a (centralized) density filter to estimate the dynamic density of large-scale systems through a novel integration of mean-field models, kernel density estimation (KDE), and infinite-dimensional Kalman filters. In this work, we further study how to decentralize the density filter such that each agent can estimate the global density only based on its local observation and communication with neighbors. This is achieved by noting that the global observation constructed by KDE is an average of the local kernels. Hence, dynamic average consensus algorithms are used for each agent to track the global observation in a distributed way. We present a distributed density filter which requires very little information exchange, and study its stability and optimality using the notion of input-to-state stability. Simulation results suggest that the distributed filter is able to converge to the centralized filter and remain close to it.
This paper investigates the distributed Kalman filtering (DKF) from distributed optimization viewpoint. Motivated by the fact that Kalman filtering is a maximum a posteriori estimation (MAP) problem, which is a quadratic optimization problem, we reformulate DKF problem as a consensus optimization problem, resulting in that it can be solved by many existing distributed optimization algorithms. A new DKF algorithm employing the dual ascent method is proposed, and its stability is proved under mild assumptions. The performance of the proposed algorithm is evaluated through numerical experiments.
Stochastic Average Consensus Filtering and Distributed State Estimation for Boolean Control Networks
School of Mathematics, Southwestern University of Finance and Economics（西南财经大学数学学院）；School of Computing and Artificial Intelligence, Southwestern University of Finance and Economics（西南财经大学计算机与人工智能学院）
For consensus on measurement-based distributed filtering (CMDF), through infinite consensus fusion operations during each sampling interval, each node in the sensor network can achieve optimal filtering performance with centralized filtering. However, due to the limited communication resources in physical systems, the number of fusion steps cannot be infinite. To deal with this issue, the present paper analyzes the performance of CMDF with finite consensus fusion operations. First, by introducing a modified discrete-time algebraic Riccati equation and several novel techniques, the convergence …
Distributed Kalman filtering with minimum-time consensus algorithm
Huazhong University of Science and Technology（华中科技大学）；The Hong Kong University of Science and Technology（香港科技大学）；University of Waterloo（滑铁卢大学）；The University of Newcastle（纽卡斯尔大学）；University of Cambridge（剑桥大学）；University of Luxembourg, Faculté des Sciences, de la Technologie et de la Communication（卢森堡大学科学与技术通讯学院）
Recent years have bore witness to the proliferation of distributed filtering techniques, where a collection of agents communicating over an ad-hoc network aim to collaboratively estimate and track the state of a system. These techniques form the enabling technology of modern multi-agent systems and have gained great importance in the engineering community. Although most distributed filtering techniques come with a set of stability and convergence criteria, the conditions imposed are found to be unnecessarily restrictive. The paradigm of stability and convergence in distributed filtering is rev…
Distributed data collection is a fundamental task in open systems. In such networks, data is aggregated across a network to produce a single aggregated result at a source device. Though self-stabilizing, algorithms performing data collection can produce large overestimates in the transient phase. For example, in [1] we demonstrated that in a line graph, a switch of sources after initial stabilization may produce overestimates that are quadratic in the network diameter. We also proposed monotonic filtering as a strategy for removing such large overestimates. Monotonic filtering prevents the tra…
This paper proposed a distributed filter for spatially interconnected systems (SISs), which considers missing measurements in the sensors of sub-systems. An SIS is established by many similar sub-systems that directly interact or communicate with connective neighbors. Despite that the interactions are simple and tractable, the overall SIS can perform rich and complex behaviors. In actual projects, sensors of sub-systems in a sensor network may break down sometimes, which causes parts of the measurements unavailable unexpectedly. In this work, distributed characteristics of SISs are described b…
This paper considers the distributed filtering problem for a class of stochastic uncertain systems under quantized data flowing over switching sensor networks. Employing the biased noisy observations of the local sensor and interval-quantized messages from neighboring sensors successively, an extended state based distributed Kalman filter (DKF) is proposed for simultaneously estimating both system state and uncertain dynamics. To alleviate the effect of observation biases, an event-triggered update based DKF is presented with a tighter mean square error bound than that of the time-driven one b…
MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；IBM Research（IBM研究院）
This paper presents a new approach to distributed linear filtering and prediction. The problem under consideration consists of a random dynamical system observed by a multi-agent network of sensors where the network is sparse. Inspired by the consensus+innovations type of distributed estimation approaches, this paper proposes a novel algorithm that fuses the concepts of consensus and innovations. The paper introduces a definition of distributed observability, required by the proposed algorithm, which is a weaker assumption than that of global observability and connected network assumptions com…
This paper addresses distributed multi-target tracking (DMTT) over a network of sensors having different fields-of-view (FoVs). Specifically, a cardinality probability hypothesis density (CPHD) filter is run at each sensor node. Due to the fact that each sensor node has a limited FoV, the commonly adopted fusion methods become unreliable. In fact, the monitored area of multiple sensor nodes consists of several parts that are either exclusive of a single node, i.e. exclusive FoVs (eFoVs) or common to multiple (at least two) nodes, i.e. common FoVs (cFoVs). In this setting, the crucial issue is …
We present a novel Kalman filter for spatiotemporal systems called the numerical Gaussian process Kalman filter (GPKF). Numerical Gaussian processes have recently been introduced as a physics informed machine learning method for simulating time-dependent partial differential equations without the need for spatial discretization. We bring numerical GPs into probabilistic state space form. This model is linear and its states are Gaussian distributed. These properties enable us to embed the numerical GP state space model into the recursive Kalman filter algorithm. We showcase the method using two…
Distributed Algorithms for Filtering, Estimation, and Fault Detection over Cyber-Physical-Systems: A Tutorial and Survey
Semnan University（塞姆南大学）；Sharif University of Technology（谢里夫理工大学）；Qom University of Technology（库姆理工大学）；Qatar University（卡塔尔大学）；Instituto Superior Tecnico, University of Lisbon（里斯本大学高等理工学院）；Boston College（波士顿学院）
Non-Linear Estimation using the Weighted Average Consensus-Based Unscented Filtering for Various Vehicles Dynamics towards Autonomous Sensorless Design
This paper studies the distributed average tracking problem pertaining to a discrete-time linear time-invariant multi-agent network, which is subject to, concurrently, input delays, random packet-drops, and reference noise. The problem amounts to an integrated design of delay and packet-drop tolerant algorithm and determining the ultimate upper bound of the tracking error between agents' states and the average of the reference signals. The investigation is driven by the goal of devising a practically more attainable average tracking algorithm, thereby extending the existing work in the literat…
Distributed graph filters have found applications in wireless sensor networks (WSNs) to solve distributed tasks such as consensus, signal denoising, and reconstruction. However, when employed over WSN, the graph filters should deal with the network limited energy, processing, and communication capabilities. Quantization plays a fundamental role to improve the latter but its effects on distributed graph filtering are little understood. WSNs are also prone to random link losses due to noise and interference. The filter output is affected by both the quantization error and the topological randomn…
We study distributed filtering for a class of uncertain systems over corrupted communication channels. We propose a distributed robust Kalman filter with stochastic gains, through which upper bounds of the conditional mean square estimation errors are calculated online. We present a robust collective observability condition, under which the mean square error of the distributed filter is proved to be uniformly upper bounded if the network is strongly connected. For better performance, we modify the filer by introducing a switching fusion scheme based on a sliding window. It provides a smaller u…
Conditions for detectability in distributed consensus-based observer networks
School of Engineering and IT, University of NSW at the Australian Defence Force Academy（新南威尔士大学澳大利亚国防军学院工程与信息技术学院）；Australian National University（澳大利亚国立大学）
A decentralized approach for joint frequency and phase synchronization in distributed antenna arrays is presented. The nodes in the array share their frequencies and phases with their neighboring nodes to align these parameters across the array. Our signal model includes the frequency drifts and phase jitters of the local oscillators as well as the frequency and phase estimation errors at the nodes and models them using practical statistics. A decentralized frequency and phase consensus (DFPC) algorithm is proposed which uses an average consensus method in which each node in the array iterativ…
Australian National University（澳大利亚国立大学）；Defence Science and Technology Group（国防科学技术集团）
We present a new approach to the cooperative localisation problem by applying the theory of minimum energy filtering. We consider the problem of estimating the pose of a group of mobile robots in an environment where robots can perceive fixed landmarks and neighbouring robots as well as share information with others over a communication channel. Whereas the vast majority of the existing literature applies some variant of a Kalman Filter, we derive a set of filter equations for the global state estimate based on the principle of minimum energy filtering. We show how the filter equations can be …
This work studies how to estimate the mean-field density of large-scale systems in a distributed manner. Such problems are motivated by the recent swarm control technique that uses mean-field approximations to represent the collective effect of the swarm, wherein the mean-field density (especially its gradient) is usually used in feedback control design. In the first part, we formulate the density estimation problem as a filtering problem of the associated mean-field partial differential equation (PDE), for which we employ kernel density estimation (KDE) to construct noisy observations and use…
Distributed Filter Design for Cooperative H-Infinity-Type Estimation
University of Stuttgart（斯图加特大学）；University of Technology, Sydney（悉尼科技大学）；University of New South Wales at the Australian Defence Force Academy（澳大利亚国防军学院新南威尔士大学）
This paper investigates the H2 and H-infinity suboptimal distributed filtering problems for continuous time linear systems. Consider a linear system monitored by a number of filters, where each of the filters receives only part of the measured output of the system. Each filter can communicate with the other filters according to an a priori given strongly connected weighted directed graph. The aim is to design filter gains that guarantee the H2 or H-infinity norm of the transfer matrix from the disturbance input to the output estimation error to be smaller than an a priori given upper bound, wh…
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Imperial College London（帝国理工学院）；University of Salerno（萨勒诺大学）
This work studies networked agents cooperating to track a dynamical state of nature under partial information. The proposed algorithm is a distributed Bayesian filtering algorithm for finite-state hidden Markov models (HMMs). It can be used for sequential state estimation tasks, as well as for modeling opinion formation over social networks under dynamic environments. We show that the disagreement with the optimal centralized solution is asymptotically bounded for the class of geometrically ergodic state transition models, which includes rapidly changing models. We also derive recursions for c…
