An Optimal Transmission Strategy for Kalman Filtering over Packet Dropping Links with Imperfect Acknowledgements

This paper presents a novel design methodology for optimal transmission policies at a smart sensor to remotely estimate the state of a stable linear stochastic dynamical system. The sensor makes measurements of the process and forms estimates of the state using a local Kalman filter. The sensor transmits quantized information over a packet dropping link to the remote receiver. The receiver sends packet receipt acknowledgments back to the sensor via an erroneous feedback communication channel which is itself packet dropping. The key novelty of this formulation is that the smart sensor decides, at each discrete time instant, whether to transmit a quantized version of either its local state estimate or its local innovation. The objective is to design optimal transmission policies in order to minimize a long term average cost function as a convex combination of the receiver's expected estimation error covariance and the energy needed to transmit the packets. The optimal transmission policy is obtained by the use of dynamic programming techniques. Using the concept of submodularity, the optimality of a threshold policy in the case of scalar systems with perfect packet receipt acknowledgments is proved. Suboptimal solutions and their structural results are also discussed. Numerical results are presented illustrating the performance of the optimal and suboptimal transmission policies.Comment: Conditionally accepted in IEEE Transactions on Control of Network System

Data-Driven Power Control for State Estimation: A Bayesian Inference Approach

We consider sensor transmission power control for state estimation, using a Bayesian inference approach. A sensor node sends its local state estimate to a remote estimator over an unreliable wireless communication channel with random data packet drops. As related to packet dropout rate, transmission power is chosen by the sensor based on the relative importance of the local state estimate. The proposed power controller is proved to preserve Gaussianity of local estimate innovation, which enables us to obtain a closed-form solution of the expected state estimation error covariance. Comparisons with alternative non data-driven controllers demonstrate performance improvement using our approach

Distributed Channel Access for Control Over Unknown Memoryless Communication Channels

We consider the distributed channel access problem for a system consisting of multiple control subsystems that close their loop over a shared wireless network. We propose a distributed method for providing deterministic channel access without requiring explicit information exchange between the subsystems. This is achieved by utilizing timers for prioritizing channel access with respect to a local cost which we derive by transforming the control objective cost to a form that allows its local computation. This property is then exploited for developing our distributed deterministic channel access scheme. A framework to verify the stability of the system under the resulting scheme is then proposed. Next, we consider a practical scenario in which the channel statistics are unknown. We propose learning algorithms for learning the parameters of imperfect communication links for estimating the channel quality and, hence, define the local cost as a function of this estimation and control performance. We establish that our learning approach results in collision-free channel access. The behavior of the overall system is exemplified via a proof-of-concept illustrative example, and the efficacy of this mechanism is evaluated for large-scale networks via simulations.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Linear Encoder-Decoder-Controller Design over Channels with Packet Loss and Quantization Noise

We consider a decentralized multisensor estimation problem where L sensor nodes observe noisy versions of a possibly correlated random source. The sensors amplify and forward their observations over a fading coherent multiple access channel (MAC) to a fusion center (FC). The FC is equipped with a large array of N antennas, and adopts a minimum mean square error (MMSE) approach for estimating the source. We optimize the amplification factor (or equivalently transmission power) at each sensor node in two different scenarios: 1) with the objective of total power minimization subject to mean square error (MSE) of source estimation constraint, and 2) with the objective of minimizing MSE subject to total power constraint. For this purpose, we apply an asymptotic approximation based on the massive multiple-input-multiple-output (MIMO) favorable propagation condition (when L ≪ N). We use convex optimization techniques to solve for the optimal sensor power allocation in 1) and 2). In 1), we show that the total power consumption at the sensors decays as 1/N, replicating the power savings obtained in Massive MIMO mobile communications literature. Through numerical studies, we also illustrate the superiority of the proposed optimal power allocation methods over uniform power allocation

Communication and sensing trade-offs in decentralized mobile sensor networks: a cross-layer design approach

In this paper we characterize the impact of imperfect communication on the performance of a decentralized mobile sensor network. We first examine and demonstrate the trade-offs between communication and sensing objectives, by determining the optimal sensor configurations when introducing imperfect communication. We further illustrate the performance degradation caused by non-ideal communication links in a decentralized mobile sensor network. To address this, we propose a decentralized motion-planning algorithm that considers communication effects. The algorithm is a cross-layer design based on the proper interface of physical and application layers. Simulation results will show the performance improvement attained by utilizing this algorithm

Markov Decision Processes with Applications in Wireless Sensor Networks: A Survey

Wireless sensor networks (WSNs) consist of autonomous and resource-limited devices. The devices cooperate to monitor one or more physical phenomena within an area of interest. WSNs operate as stochastic systems because of randomness in the monitored environments. For long service time and low maintenance cost, WSNs require adaptive and robust methods to address data exchange, topology formulation, resource and power optimization, sensing coverage and object detection, and security challenges. In these problems, sensor nodes are to make optimized decisions from a set of accessible strategies to achieve design goals. This survey reviews numerous applications of the Markov decision process (MDP) framework, a powerful decision-making tool to develop adaptive algorithms and protocols for WSNs. Furthermore, various solution methods are discussed and compared to serve as a guide for using MDPs in WSNs

Dynamic State Estimation of Microgrid With Imperfect Data Communication

Dynamic state estimation of power systems is essential for wide area control purposes. In this thesis, we present the results of dynamic state estimation for a grid-connected microgrid including two synchronous generators and three loads. The Unscented Kalman filter (UKF) and the Extended Kalman filter (EKF) are implemented using a classical generator model connected to a Thevenin equivalent of the remainder of the microgrid. The model is used to estimate the six states variables of the generator; namely, rotor angle, speed variant, d- and q- axis transient voltages, d-axis damper flux, and q-axis second damper flux. Both real power and reactive power are used as measurements in our state estimation algorithm. The estimation results are compared with the true values to demonstrate the accuracy of the state estimator. In addition to data loss or delay, sensor measurements may include outliers that distort state estimation. We utilized the Generalized Maximum Likelihood-extended Kalman filter (GM-EKF), as a robust estimator, which exhibits good tracking capabilities suppressing the effects of bad data (outliers). We also used two methods of state estimation on UKF to deal with bad data. Simulation results obtained from the UKFs are compared with those of GM-EKF. We present simulation results at a high frequency of 1 kHz of state estimation for different scenarios that include normal operation, fault at Point of Common Coupling (PCC), loss of generator, and loss of load. We also developed a scheme to use delayed data in Kalman filter estimation and used it to simulate the effect of data loss and/or delay in the communication system of the microgrid. For the same scenarios, we also present simulation results at 50 Hz, which is compatible with Phasor Measurement Units (PMU), including bad data as well as data loss or delay. Our results demonstrate that while both filters successfully detect bad data, the UKF methods provide better estimates than those of the GM-EKF

Achieving robust average consensus over lossy wireless networks

International audienceAverage consensus over unreliable wireless networks can be impaired by losses. In this paper we study a novel method to compensate for the lost information, when packet collisions cause transmitter-based random failures. This compensation makes the network converge to the average of the initial states of the network, by modifying the weights of the links to accommodate for the topology changes due to packet losses. Additionally, a gain is used to increase the convergence speed, and an analysis of the stability of the network is performed, leading to a criterion to choose such gain to guarantee network stability. For the implementation of the compensation method, we propose a new distributed algorithm, which uses both synchronous and asynchronous mechanisms to achieve consensus and to deal with uncertainty in packet delivery. The theoretical results are then confirmed by simulations