We consider sensor data scheduling for remote state estimation. Due to constrained communication energy and bandwidth, a sensor needs to decide whether it should send the measurement to a remote estimator for further processing. We propose an event-based sensor data scheduler for linear systems and derive the corresponding minimum squared error estimator. By selecting an appropriate event-triggering threshold, we illustrate how to achieve a desired balance between the sensor-to-estimator communication rate and the estimation quality. Simulation examples are provided to demonstrate the theory.

/pdf/event-based-sensor-data-scheduling-trade-off-between-1p4cfey1du.pdf

Event-Based Sensor Data Scheduling: Trade-Off Between Communication Rate and Estimation Quality

We propose an open-loop and a closed-loop stochastic event-triggered sensor schedule for remote state estimation. Both schedules overcome the essential difficulties of existing schedules in recent literature works where, through introducing a deterministic event-triggering mechanism, the Gaussian property of the innovation process is destroyed which produces a challenging nonlinear filtering problem that cannot be solved unless approximation techniques are adopted. The proposed stochastic event-triggered sensor schedules eliminate such approximations. Under these two schedules, the minimum mean squared error (MMSE) estimator and its estimation error covariance matrix at the remote estimator are given in a closed-form. The stability in terms of the expected error covariance and the sample path of the error covariance for both schedules is studied. We also formulate and solve an optimization problem to obtain the minimum communication rate under some estimation quality constraint using the open-loop sensor schedule. A numerical comparison between the closed-loop MMSE estimator and a typical approximate MMSE estimator with deterministic event-triggered sensor schedule, in a problem setting of target tracking, shows the superiority of the proposed sensor schedule.

Stochastic event-triggered sensor scheduling for remote state estimation

In this paper, we study the problem of optimal trajectory generation for a team of heterogeneous robots moving in a plane and tracking a moving target by processing relative observations, i.e., distance and/or bearing. Contrary to previous approaches, we explicitly consider limits on the robots' speed and impose constraints on the minimum distance at which the robots are allowed to approach the target. We first address the case of a single tracking sensor and seek the next sensing location in order to minimize the uncertainty about the target's position. We show that although the corresponding optimization problem involves a nonconvex objective function and a nonconvex constraint, its global optimal solution can be determined analytically. We then extend the approach to the case of multiple sensors and propose an iterative algorithm, i.e., the Gauss-Seidel relaxation (GSR), to determine the next best sensing location for each sensor. Extensive simulation results demonstrate that the GSR algorithm, whose computational complexity is linear in the number of sensors, achieves higher tracking accuracy than gradient descent methods and has performance that is indistinguishable from that of a grid-based exhaustive search, whose cost is exponential in the number of sensors. Finally, through experiments, we demonstrate that the proposed GSR algorithm is robust and applicable to real systems.

/pdf/multirobot-active-target-tracking-with-combinations-of-1br5a2fv94.pdf

Multirobot Active Target Tracking With Combinations of Relative Observations

In this paper, a security problem in cyberphysical systems (CPS) is studied. A remote state estimation process using multiple sensors is considered. The measurement innovation packets from each sensor, which may be modified by a malicious attacker, are sent to a remote fusion center through wireless communication channels. To avoid being detected by typical bad data detectors at the remote estimator's side, the attacker would maintain the statistical properties of the measurements. Based on the information extracted from the trusted sensors and the correlations between the trusted sensors and the suspicious sensors, we propose three sequential data verification and fusion procedures for different detection information scenarios. The corresponding impacts of possible attacking patterns on the estimation performance under different detectors are analyzed explicitly. Simulations are provided to illustrate the developed results.

Detection Against Linear Deception Attacks on Multi-Sensor Remote State Estimation

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this study, a bibliographical review on distributed Kalman filtering (DKF) is provided. The study contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-cta.2012.0732

Distributed Kalman filtering: a bibliographic review

Estimation and tracking of generally nonstationary Markov processes is of paramount importance for applications such as localization and navigation. In this context, ad hoc wireless sensor networks (WSNs) offer decentralized Kalman filtering (KF) based algorithms with documented merits over centralized alternatives. Adhering to the limited power and bandwidth resources WSNs must operate with, this paper introduces two novel decentralized KF estimators based on quantized measurement innovations. In the first quantization approach, the region of an observation is partitioned into N contiguous, nonoverlapping intervals where each partition is binary encoded using a block of m bits. Analysis and Monte Carlo simulations reveal that with minimal communication overhead, the mean-square error (MSE) of a novel decentralized KF tracker based on 2-3 bits comes stunningly close to that of the clairvoyant KF. In the second quantization approach, if intersensor communications can afford m bits at time n, then the ith bit is iteratively formed using the sign of the difference between the nth observation and its estimate based on past observations (up to time n-1) along with previous bits (up to i-1) of the current observation. Analysis and simulations show that KF-like tracking based on m bits of iteratively quantized innovations communicated among sensors exhibits MSE performance identical to a KF based on analog-amplitude observations applied to an observation model with noise variance increased by a factor of [1-(1-2/pi)m]-1.

/pdf/decentralized-quantized-kalman-filtering-with-scalable-2d31q2913y.pdf

Decentralized Quantized Kalman Filtering With Scalable Communication Cost

Consider a wireless sensor network (WSN) with a fusion center (FC) deployed to estimate signal parameters from noisy sensor measurements. If the WSN has a large number of low-cost, battery-operated sensor nodes with limited transmission bandwidth, then conservation of transmission resources (power and bandwidth) is paramount. To this end, the present paper develops a novel data reduction method which requires no inter-sensor collaboration and results in only a subset of the sensor measurements transmitted to the FC. Using interval censoring as a data-reduction method, each sensor decides separately whether to censor its acquired measurements based on a rule that promotes censoring of measurements with least impact on the estimator mean-square error (MSE). Leveraging the statistical distribution of sensor data, the censoring mechanism and the received uncensored data, FC-based estimators are derived for both deterministic (via maximum likelihood estimation) and random parameters (via maximum a posteriori probability estimation) for a linear-Gaussian model. Quantization of the uncensored measurements at the sensor nodes offers an additional degree of freedom in the resource conservation versus estimator MSE reduction tradeoff. Cramer-Rao bound analysis for the different censor-estimators and censor-quantizer estimators is also provided to benchmark and facilitate MSE-based performance comparisons. Numerical simulations corroborate the analytical findings and demonstrate that the proposed censoring-estimation approach performs competitively with alternative methods, under different sensing conditions, while having lower computational complexity.

Sensor-Centric Data Reduction for Estimation With WSNs via Censoring and Quantization

Motivated by the savings in communication bandwidth and sensor transmission energy, data selection for estimation with wireless sensor networks is investigated in this paper. Existing approaches to data selection inherently treat sensing and transmission to a central fusion unit as of equal cost. However, energy expenditure in sensing is generally a fraction of that needed for communication. To alleviate the latter, measurement censoring at sensor nodes is proposed here for data reduction, along with a novel maximum likelihood estimator that optimally incorporates knowledge of the censored data model. Furthermore, a closed-form expression for the Cramer-Rao lower bound on the estimator variance is presented. Numerical studies show that the estimator using censored measurements achieves error values that are competitive with alternative methods, under various sensing conditions, while retaining lower computational complexity.

Distributed measurement censoring for estimation with wireless sensor networks

Methods and apparatus for provision of equalization effort-balancing of transmit (TX) Finite Impulse Response (FIR) and receive (RX) Linear Equalizer (LE) or RX Decision Feedback Equalizer (DFE) structures in high-speed serial interconnects are described. In some embodiments, data corresponding to a plurality of transmit equalization values and a plurality of receive equalization values for each lane of a link having a plurality of lanes is detected. At least one of the plurality of the transmit equalization values and at least one of the plurality of the receive equalization values are selected for each lane of the plurality of lanes of the link based on detection of saturation in a Decision Feedback Equalizer (DFE) tap of a corresponding lane of the link. Other embodiments are also claimed and/or disclosed.

Equalization effort-balancing of transmit finite impulse response and receive linear equalizer or receive decision feedback equalizer structures in high-speed serial interconnects

We consider state estimation of a Markov stochastic process using an ad hoc wireless sensor network (WSN) based on noisy linear observations. Due to power and bandwidth constraints present in resource- limited WSNs, the observations are quantized before transmission. We derive a distributed recursive mean-square error (MSE) optimal quantizer-estimator based on the quantized observations. The resultant Kalman-like algorithm based on quantized observations exhibits MSE performance and computational complexity comparable to the Kalman filter based on un-quantized observations even for 2-3 bits of quantization per observation.

/pdf/distributed-kalman-filtering-based-on-quantized-innovations-27da1lphpo.pdf

Eric J. Msechu

Papers

Decentralized Quantized Kalman Filtering With Scalable Communication Cost

Sensor-Centric Data Reduction for Estimation With WSNs via Censoring and Quantization

Distributed measurement censoring for estimation with wireless sensor networks

Equalization effort-balancing of transmit finite impulse response and receive linear equalizer or receive decision feedback equalizer structures in high-speed serial interconnects

Distributed Kalman filtering based on quantized innovations