Secure Distributed Dynamic State Estimation in Wide-Area Smart Grids

Smart grid is a large complex network with a myriad of vulnerabilities, usually operated in adversarial settings and regulated based on estimated system states. In this study, we propose a novel highly secure distributed dynamic state estimation mechanism for wide-area (multi-area) smart grids, composed of geographically separated subregions, each supervised by a local control center. We firstly propose a distributed state estimator assuming regular system operation, that achieves near-optimal performance based on the local Kalman filters and with the exchange of necessary information between local centers. To enhance the security, we further propose to (i) protect the network database and the network communication channels against attacks and data manipulations via a blockchain (BC)-based system design, where the BC operates on the peer-to-peer network of local centers, (ii) locally detect the measurement anomalies in real-time to eliminate their effects on the state estimation process, and (iii) detect misbehaving (hacked/faulty) local centers in real-time via a distributed trust management scheme over the network. We provide theoretical guarantees regarding the false alarm rates of the proposed detection schemes, where the false alarms can be easily controlled. Numerical studies illustrate that the proposed mechanism offers reliable state estimation under regular system operation, timely and accurate detection of anomalies, and good state recovery performance in case of anomalies

Optimal Sensor Collaboration for Parameter Tracking Using Energy Harvesting Sensors

In this paper, we design an optimal sensor collaboration strategy among neighboring nodes while tracking a time-varying parameter using wireless sensor networks in the presence of imperfect communication channels. The sensor network is assumed to be self-powered, where sensors are equipped with energy harvesters that replenish energy from the environment. In order to minimize the mean square estimation error of parameter tracking, we propose an online sensor collaboration policy subject to real-time energy harvesting constraints. The proposed energy allocation strategy is computationally light and only relies on the second-order statistics of the system parameters. For this, we first consider an offline non-convex optimization problem, which is solved exactly using semidefinite programming. Based on the offline solution, we design an online power allocation policy that requires minimal online computation and satisfies the dynamics of energy flow at each sensor. We prove that the proposed online policy is asymptotically equivalent to the optimal offline solution and show its convergence rate and robustness. We empirically show that the estimation performance of the proposed online scheme is better than that of the online scheme when channel state information about the dynamical system is available in the low SNR regime. Numerical results are conducted to demonstrate the effectiveness of our approach

Outlier-Detection Based Robust Information Fusion for Networked Systems

We consider state estimation for networked systems where measurements from sensor nodes are contaminated by outliers. A new hierarchical measurement model is formulated for outlier detection by integrating the outlier-free measurement model with a binary indicator variable. The binary indicator variable, which is assigned a beta-Bernoulli prior, is utilized to characterize if the sensor's measurement is nominal or an outlier. Based on the proposed outlier-detection measurement model, both centralized and decentralized information fusion filters are developed. Specifically, in the centralized approach, all measurements are sent to a fusion center where the state and outlier indicators are jointly estimated by employing the mean-field variational Bayesian inference in an iterative manner. In the decentralized approach, however, every node shares its information, including the prior and likelihood, only with its neighbors based on a hybrid consensus strategy. Then each node independently performs the estimation task based on its own and shared information. In addition, an approximation distributed solution is proposed to reduce the local computational complexity and communication overhead. Simulation results reveal that the proposed algorithms are effective in dealing with outliers compared with several recent robust solutions

Nonlinear consensus+innovations under correlated heavy-tailed noises: Mean square convergence rate and asymptotics

We consider distributed recursive estimation of consensus+innovations type in the presence of heavy-tailed sensing and communication noises. We allow that the sensing and communication noises are mutually correlated while independent identically distributed (i.i.d.) in time, and that they may both have infinite moments of order higher than one (hence having infinite variances). Such heavy-tailed, infinite-variance noises are highly relevant in practice and are shown to occur, e.g., in dense internet of things (IoT) deployments. We develop a consensus+innovations distributed estimator that employs a general nonlinearity in both consensus and innovations steps to combat the noise. We establish the estimator's almost sure convergence, asymptotic normality, and mean squared error (MSE) convergence. Moreover, we establish and explicitly quantify for the estimator a sublinear MSE convergence rate. We then quantify through analytical examples the effects of the nonlinearity choices and the noises correlation on the system performance. Finally, numerical examples corroborate our findings and verify that the proposed method works in the simultaneous heavy-tail communication-sensing noise setting, while existing methods fail under the same noise conditions

A Survey of Recent Advances in Particle Filters and Remaining Challenges for Multitarget Tracking

[EN]We review some advances of the particle filtering (PF) algorithm that have been achieved in the last decade in the context of target tracking, with regard to either a single target or multiple targets in the presence of false or missing data. The first part of our review is on remarkable achievements that have been made for the single-target PF from several aspects including importance proposal, computing efficiency, particle degeneracy/impoverishment and constrained/multi-modal systems. The second part of our review is on analyzing the intractable challenges raised within the general multitarget (multi-sensor) tracking due to random target birth and termination, false alarm, misdetection, measurement-to-track (M2T) uncertainty and track uncertainty. The mainstream multitarget PF approaches consist of two main classes, one based on M2T association approaches and the other not such as the finite set statistics-based PF. In either case, significant challenges remain due to unknown tracking scenarios and integrated tracking management

Robust state estimation methods for robotics applications

State estimation is an integral component of any autonomous robotic system. Finding the correct position, velocity, and orientation of an agent in its environment enables it to do other tasks like mapping and interacting with the environment, and collaborating with other agents. State estimation is achieved by using data obtained from multiple sensors and fusing them in a probabilistic framework. These include inertial data from Inertial Measurement Unit (IMU), images from camera, range data from lidars, and positioning data from Global Navigation Satellite Systems (GNSS) receivers. The main challenge faced in sensor-based state estimation is the presence of noisy, erroneous, and even lack of informative data. Some common examples of such situations include wrong feature matching between images or point clouds, false loop-closures due to perceptual aliasing (different places that look similar can confuse the robot), presence of dynamic objects in the environment (odometry algorithms assume a static environment), multipath errors for GNSS (signals for satellites jumping off tall structures like buildings before reaching receivers) and more. This work studies existing and new ways of how standard estimation algorithms like the Kalman filter and factor graphs can be made robust to such adverse conditions without losing performance in ideal outlier-free conditions. The first part of this work demonstrates the importance of robust Kalman filters on wheel-inertial odometry for high-slip terrain. Next, inertial data is integrated into GNSS factor graphs to improve the accuracy and robustness of GNSS factor graphs. Lastly, a combined framework for improving the robustness of non-linear least squares and estimating the inlier noise threshold is proposed and tested with point cloud registration and lidar-inertial odometry algorithms followed by an algorithmic analysis of optimizing generalized robust cost functions with factor graphs for GNSS positioning problem

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity