Remote Estimation Research Articles

Resilient strategy design for cyber-physical system under active eavesdropping attack

We consider a remote state estimation process under an active eavesdropper for cyber-physical system. A smart sensor transmits its local state estimates to a remote estimator over an unreliable network, which is eavesdropped by an adversary. The intelligent adversary can work in passive eavesdropping mode and active jamming mode. An active jamming mode enables the adversary to interfere the data transmission from sensor to estimator, and meanwhile improve the data reception of itself. To protect the transmission data from being wiretapped, the sensor with two antennas injects noise to the eavesdropping link with different power levels. Aiming at minimizing the estimation error covariance and power cost of themselves while maximizing the estimation error covariance of their opponents, a two-player nonzero-sum game is constructed for sensor and active eavesdropper. For an open-loop case, the mixed Nash equilibrium is obtained by solving an one-stage nonzero-sum game. For a long term consideration, a Markov stochastic game is introduced and a Nash Q-learning method is given to find the Nash equilibrium strategies for two players. Numerical results are provided to show the effectiveness of our theoretical conclusions.

Remote estimation of grain yield based on UAV data in different rice cultivars under contrasting climatic zone

Timely and accurate estimation of grain yield is valuable for crop monitoring and breeding, and plays an important role in precision agriculture. In this study, we developed a method to predict grain yield based entirely on unmanned aerial vehicle (UAV) data in different rice cultivars under two contrasting climatic regions. Vegetation indices (VIs), which were derived from canopy reflectance collected by UAV, were used to correlate with rice phenotyping and estimate grain yield. It is found that the two-band enhanced vegetation index (EVI2) closely related to leaf area index (LAI) as well as canopy chlorophyll content (CCC), and the red edge chlorophyll index (CIrededge) related to above ground biomass (AGB). Thus, the phenotyping-related VIs – EVI2 and CIrededge were exploited to develop yield estimation model. Results showed that the single stage VIs weakly correlated with grain yield of different rice cultivars and was not able to estimate grain yield. By contrast, the multi-temporal VIs can be used to estimate grain yield in different rice cultivars with the estimation error below 7.1 %. In addition, the rice growth duration differed in different climatic zones, which may decrease the estimation accuracy of grain yield by using multi-temporal VIs. After adjusting the phenological stage of multi-temporal VIs used in estimation model, the estimation accuracy of grain yield in different climatic zones increased. In conclusion, this study demonstrated that the UAV-based multi-temporal VIs were reliable for grain yield estimation in different rice cultivars under contrasting climatic zones.

Improving the Evapotranspiration Estimation under Cloudy Condition by Extending the Ts-VI Triangle Model

Evapotranspiration (ET) of soil-vegetation system is the main process of the water and energy exchange between the atmosphere and the land surface. Spatio-temporal continuous ET is vitally important to agriculture and ecological applications. Surface temperature and vegetation index (Ts-VI) triangle ET model based on remote sensing land surface temperature (LST) is widely used to monitor the land surface ET. However, a large number of missing data caused by the presence of clouds always reduces the availability of the main parameter LST, thus making the remote sensing-based ET estimation unavailable. In this paper, a method to improve the availability of ET estimates from Ts-VI model is proposed. Firstly, continuous LST product of the time series is obtained using a reconstruction algorithm, and then, the reconstructed LST is applied to the estimate ET using the Ts-VI model. The validation in the Heihe River Basin from 2009 to 2011 showed that the availability of ET estimates is improved from 25 days per year (d/yr) to 141 d/yr. Compared with the in situ data, a very good performance of the estimated ET is found with RMSE 1.23 mm/day and R2 0.6257 at point scale and RMSE 0.32 mm/day and R2 0.8556 at regional scale. This will improve the understanding of the water and energy exchange between the atmosphere and the land surface, especially under cloudy conditions.

Remote estimation of aquatic light environments using machine learning: A new management tool for submerged aquatic vegetation

Submerged aquatic vegetation (SAV; e.g. seagrasses, macroalgae), forms key habitats in shallow coastal systems that provide a plethora of ecosystem services, including coastal protection, climate mitigation and supporting fisheries production. Light limitation is a critical factor influencing the growth and survival of SAV, thus it is important to understand how much light SAV needs, and receives, to effectively assess the risk that light limitation poses. Light monitoring is commonly used to inform environmental decision making to minimise loss of SAV habitat, but the temporal and spatial extent of monitoring is often limited by cost and logistical difficulties. An ability to remotely estimate light across different locations can therefore improve the conservation and management of SAV habitats. Here we combine an extensive monitoring program with publicly available data and machine learning to develop a model that estimates the light reaching submerged seagrasses in a shallow subtropical embayment in southern Queensland, Australia. Our model accurately predicts the intensity of photosynthetically active radiation (PAR) reaching the canopy of SAV from entirely remotely available data. The best performing model predicted light intensity with >99% at the management relevant daily, and 14-day rolling average time resolutions. This model enables monitoring of light available to SAV without an ongoing need for in-water instruments, minimising cost and risk to personnel, and improving assessment speed. The technique can be applied to SAV management plans in shallow waters throughout the world, where suitable remote public data is available.

Optimal Stealthy Linear Attack on Remote State Estimation With Side Information

In this article, the innovation-based linear attack against state estimation in cyber-physical systems is studied. The scenario is considered where a sensor transmits its measurements to a remote estimator via a wireless channel. We propose an attack strategy to worsen the estimation performance of system when a passive detector is adopted. Different from the existing results, the side information is adopted synergistically besides the intercepted data. Meanwhile, the attacker needs to remain stealthy to the false-data detector. We analyze the performance degradation of system under the proposed attack strategy by deriving the remote estimation error covariance recursion. With the stealthiness constraint, the optimal stealthy attack can be obtained by solving a convex optimization problem accordingly. Besides, we provide a specific algorithm to calculate the falsified measurements. Finally, the effectiveness of explored attack strategy is demonstrated via simulation examples.

Optimal stealthy integrity attacks on remote state estimation: The maximum utilization of historical data

This paper considers the problem of optimal stealthy integrity attacks on remote state estimation. Smart sensors transmit innovations to a remote estimator through a wireless communication network, where transmitted data can be intercepted and manipulated by attackers. To bypass the false data detector, the attack sequence should satisfy the stealthiness constraint. Instead of utilizing only the current innovation, the historical data are also used for designing the attack policy at each sampling instant. With a finite horizon of historical data used, the evolution of the estimation error covariance at the remote estimator is obtained, and the optimal attack that yields the largest estimation error is derived analytically. To reduce the online computational burden, the optimal attack using sparse combinations of historical innovations is also designed. In addition, the optimal attacks on protected systems with encryption-based countermeasures are analyzed. If encryption resources are sufficient, there always exists such a countermeasure that can completely prevent the stealthy attacks based on historical data. Numerical comparisons illustrate the theoretical results.

Optimal stationary state estimation over multiple Markovian packet drop channels

In this paper, we investigate the state estimation problem over multiple Markovian packet drop channels. In this problem setup, a remote estimator receives measurement data transmitted from multiple sensors over individual channels. By the method of Markovian jump linear systems, an optimal stationary estimator that minimizes the error variance in the steady state is obtained, based on the mean-square (MS) stabilizing solution to the coupled algebraic Riccati equations (CAREs). An explicit necessary and sufficient condition is derived for the existence of the MS stabilizing solution, which coincides with that of the standard Kalman filter. More importantly, we provide a sufficient condition under which the MS detectability with multiple Markovian packet drop channels can be decoupled, and propose a locally optimal stationary estimator but computationally more tractable. Analytic sufficient and necessary MS detectability conditions are presented for the decoupled subsystems subsequently. Finally, numerical simulations are conducted to illustrate the results on the MS stabilizing solution, the MS detectability, and the performance of the optimal and locally optimal stationary estimators.

Remote estimates of CDOM using Sentinel-2 remote sensing data in reservoirs with different trophic states across China

Chromophoric dissolved organic matter (DOM) is called as CDOM which could affect the optical properties of surface waters, and is a useful parameter for monitoring complex inland aquatic systems. Large-scale monitoring of CDOM using remote-sensing has been a challenge due to the poor transferability of CDOM retrieval models across regions. To overcome these difficulties, a study is conducted using Sentinel-2 images, in situ reflectance spectral data, and water chemical parameters at 93 water reservoirs across China classified by trophic state. Empirical algorithms are established between CDOM absorption coefficient aCDOM(355) and reflectance band ratio (B5/B2,vegetation Red Edge/Blue) acquired in situ and via Sentinel-2 MSI sensors. Relationships are stronger (r2 > 0.7, p < 0.05) when analysis is conducted separately by trophic states. Validation models show that, by accounting for trophic state of reservoirs and using B5/B2 band ratios, it is possible to expand the geographical range of remote sensing-based models to determine CDOM. However, the accuracy of model validation decreased from oligotrophic (r2: 0.86) to eutrophic reservoirs (r2: 0.82), likely due to increased complexity of CDOM sources in nutrient-rich systems. This study provides a strategy for using local and remote-sensing data to monitor the spatial variations of CDOM in reservoirs based on different trophic states, and will contribute to water resources management.

Robust Forecasting-Aided State Estimation in Power Distribution Systems With Event-Triggered Transmission and Reduced Mixed Measurements

This paper is concerned with the forecasting aided state estimation (FASE) problem for power distribution networks (PDNs) subject to nonlinear measurements and limited communication resources. For the sake of using bandwidth more effectively, a special closed-loop event triggering condition is first designed with the hope to reduce unnecessary data transmission from the measurement side to the remote estimator. And an event-based robust filtering algorithm is proposed to improve the estimation performance of estimator with the nonlinear intermittent observations. In this algorithm, the measurement output function with high-order nonlinearity is reasonably reduced to a quadratic alternative form, in order to avoid the computation burden caused by the use of the second-order extended Kalman filter (SOEKF), the quadratic nonlinear function is further linearized by Taylor series with quadratic norm bound. Furthermore, an upper bound of the filtering error covariance containing some uncertainties (includes quadratic term and non-triggering errors) is derived and subsequently minimized at each time step. The desired filter gain is obtained by recursively solving a set of Riccati-like matrix equations, which is easy to implement via online computation. Finally, the effectiveness of the proposed algorithm is demonstrated using the standard IEEE 13-bus and 123-bus distribution test feeders with both phasor measurement unit (PMU) and conventional measurements.

Multi-hop sensor network scheduling for optimal remote estimation

This paper studies a design problem of how a group of wireless sensors are selected and scheduled to transmit data efficiently over a multi-hop network subject to energy considerations, when the sensors are observing multiple independent discrete-time linear systems. Each time instant, a subset of sensors is selected to transmit their measurements to a remote estimator. We formulate an optimization problem, in which a network schedule is searched to minimize a linear combination of the averaged estimation error and the averaged transmission energy consumption. It is shown that the optimal network schedule forms a tree with root at the gateway node. From this observation, we manage to separate the optimization problem into two subproblems: tree planning and sensor selection. We solve the sensor selection subproblem by a Markov decision process, showing that the optimal solution admits a periodic structure when the transmission cost is sufficiently low. Efficient algorithms are proposed and they are shown to reduce the computational complexity of the original optimization problem. Numerical studies illustrate the effectiveness of the proposed algorithms, and show that they are scalable to large networks.

Jamming on Remote Estimation Over Wireless Links Under Faded Uncertainty: A Stackelberg Game Approach

This brief studies the transmission strategies of remote estimation over wireless channels subject to fading phenomenon within the framework of a leader-follower (Stackelberg) game. A smart sensor sends local estimates to a remote estimator via a stochastic time-varying faded channel, through which a jammer disrupts the signal transmission by injecting a high energy noise after observing the sensor's action. To balance energy consummation and estimation accuracy, a two-player general-sum noncooperative game is built on the infinite-time horizon, and is further transformed into a finite state Markov game according to data loss information. Then the existence of Stackelberg equilibrium of the Markov game is shown and a multiagent reinforcement learning algorithm is used to establish Stackelberg equilibrium strategies. Moreover, a numerical example is included to show the effectiveness of the current method.

Remote estimation of respiration rate by optical flow using convolutional neural networks

In this paper, we propose a novel system for remotely estimating the respiration rate of people. Periodic inhalation and exhalation during respiration cycles induce subtle upper body movements, which are reflected by the local image deformation over time when recorded by a digital camera. This local image deformation can be recovered by estimating the optical flow between consecutive frames. We propose the usage of convolutional neural networks designed for general image registration to estimate the induced optical flow, the periodicity of which is then leveraged to obtain the respiration rate by frequency analysis. The proposed system is robust to lighting condition, camera type (RGB, infrared), clothing, and posture (sitting in chair/lying in bed); and it could be used by individuals with a webcam, or by healthcare centers to monitor the patients at night.

Optimal Transmit Power Allocation for an Energy-Harvesting Sensor in Wireless Cyber-Physical Systems.

In this article, we investigate optimal transmission power allocation at a sensor equipped with the energy-harvesting technology for remote state estimation in wireless cyber-physical systems. The sensor has access to an energy harvester, which can collect energy from the external environment and is an everlasting but unreliable energy source compared with conventional batteries. For the wireless dropping communication channel, the packet dropout rates depend on both the signal-to-noise ratio and the transmission power used by the sensor. We formulate the problem of the optimal transmission power allocation to minimize the remote estimation error covariances as a Markov decision processes (MDPs) subject to energy constraint of the sensor. By analyzing the MDP algorithm, we show that an optimal deterministic and stationary transmission power policy exists. Moreover, we show that the optimal policy has a threshold-type structure. A numerical simulation is provided to illustrate the performance of the transmission power allocation algorithm.

An Analysis on Optimal Attack Schedule Based on Channel Hopping Scheme in Cyber-Physical Systems.

In this paper, we investigate the issue of security on the remote state estimation in cyber-physical systems (CPSs), where a wireless sensor utilizes the channel hopping scheme to transmit the data to the remote estimator over multiple channels in the presence of periodic denial-of-service attacks. Assume that the jammer can interfere with a subset of channels at each attack time in active period. For an energy-constraint jammer, the problem of how to select the number of channels at each attack time to maximally deteriorate the CPS performance is investigated. Based on the index of average estimation error, we introduce two different attack strategies, which include selecting identical number of channels and unequal number of channels at each attack time, and further show theoretically that the attack effect by selecting unequal number of channels is better than that of selecting identical number of channels. By formulating the problem of selecting the number of channels as integer programming problems, we present the corresponding algorithm to approximate the optimal attack schedule for both cases. The numerical results are presented to validate the theoretical results and the effectiveness of the proposed algorithms.

Data-Driven Sensor Scheduling for Remote Estimation in Wireless Networks

Sensor scheduling is a well-studied problem in signal processing and control with numerous applications. Despite its successful history, most of the related literature assumes the knowledge of the underlying probabilistic model of the sensor measurements such as the correlation structure or the entire joint probability density function. Herein, a framework for sensor scheduling for remote estimation is introduced in which the system design and the scheduling decisions are based solely on observed data. Unicast and broadcast networks and corresponding receivers are considered. In both cases, the empirical risk minimization can be posed as a difference-of-convex optimization problem, and locally optimal solutions are obtained efficiently by applying the convex-concave procedure. Our results are independent of the data's probability density function, correlation structure, and the number of sensors.

Model of on-line control for the smart object by communication technologies

Based on analysis of opportunities of usage existing models, methods and techniques for on-line monitoring and control of unmanned dynamic objects, a mathematical model of remote estimation of distance to wire-controlled unmanned mobile object is proposed. The presence of model and techniques of remote estimation of distance to wire-controlled unmanned object increases the reliability of control for exclusion of critical situations in the strict radio counteraction conditions and powerful electromagnetic jamming setting during control.

Building characterization through smart meter data analytics: Determination of the most influential temporal and importance-in-prediction based features

The present paper aims at determining the most influential features to be extracted from smart meter data to facilitate machine learning-based classification of non-residential buildings. Smart meter-driven remote estimation of the chosen characteristics (the buildings’ performance class, use type, and operation group) is significantly helpful in buildings’ commissioning, benchmarking, and diagnostics applications. As the first step, state-of-the-art feature selection methods and a proposed customized approach are utilized for determining the most influential parameters in the pool of temporal features, proposed in a previous study. Next, importance-in-prediction based features, generated from an hour-ahead load prediction pipeline, that can improve the classification accuracy are proposed and added as additional input parameters. Finally, interpretations about some of the most influential features for different classification targets are provided. The obtained results demonstrate that, while aiming at estimating the buildings’ use type, through performing feature selection and adding importance-in-prediction based features, the number of utilized features is reduced from 290 (initial pool of features proposed in a previous study) to 29, while also increasing the accuracy from 71% to 74%. Similarly, number of employed features for estimating the performance class is decreased from 224 to 17 and the achieved accuracy is improved from 56% to 62%. Finally, using only 6 selected features, compared to 287 features in the initial set, the obtained accuracy for the classification of operation group is increased from 98% to 100%. It is thus demonstrated that the proposed methodology, through selecting and utilizing notably fewer features, results in a notable simplification of the feature extraction procedures, improves the achieved accuracy, and facilitates providing interpretations about the reason behind the influence of some of the most important features.

Mapping bull kelp canopy in northern California using Landsat to enable long-term monitoring

Extending from central California to Alaska, bull kelp (Nereocystis luetkeana) forms seasonal kelp forests that are iconic coastal ecosystems in much of the eastern Pacific. Historical and ongoing field surveys and aerial imagery are used to provide biological data on kelp canopy cover and health, but satellite remote sensing provides the opportunity to generate consistent, long-term datasets over a large spatial scale. Robust satellite-based timeseries measurements of giant kelp (Macrocystis pyrifera) are available for much of the California coastline (e.g., Santa Barbara to Santa Cruz), but there have been no equivalent publications for bull kelp. Recent loss of bull kelp in northern California emphasized the need for more expansive long-term monitoring of canopy trends. We tested various kelp classification approaches using Multiple Endmember Spectral Mixture Analysis (MESMA) applied to Landsat imagery, which allowed sufficient temporal and spatial data collection during bull kelp's narrow seasonal maximum, and compare with the California Department of Fish and Wildlife (CDFW) aerial survey canopy area product. We addressed five main topics that have relevance to enabling Landsat in long-term monitoring of bull kelp canopy coverage in northern California: (1) the effect of MESMA configurations applied to Landsat imagery, including software dependencies and endmember configurations, (2) comparison of Landsat to traditional surveys, (3) differences across Landsat sensors, (4) tidal influence on canopy area, and (5) trends in the decadal timeseries. We found that there was no statistical difference (p = 0.53) between MESMA platforms (IDL-based and a Python-scripted method; RMSE 1.5 km2 or 17.6% when normalized by the range in CDFW), and that a 7-endmember MESMA model provided the lowest RMSE (1.4 km2 or 16.9%). Furthermore, while tidal phases can submerge or emerge kelp canopy and thus potentially affect kelp detection, we found a weak and statistically insignificant correlation between tides and performance of our remote estimate of kelp canopy area. Canopy estimations from Landsat-8 images yielded a higher NRMSE than Landsat-4 and -5 images, but the lack of matchup limits comparison. Imagery from early fall yielded the largest coverage estimates. Overall, our results show that Landsat enables broad remote measurement of bull kelp canopy coverage to supplement existing survey methods and increase continuity of timeseries for monitoring long-term trends.

H∞ Proportional-Integral State Estimation for T-S Fuzzy Systems Over Randomly Delayed Redundant Channels With Partly Known Probabilities.

In this article, we consider the H∞ proportional-integral (PI) state estimation (SE) problem for discrete-time T-S fuzzy systems subject to transmission delays, external disturbances, and redundant channels. Multiple redundant communication channels are utilized between the sensors and the remote estimator to enhance the reliability of data transmissions. In order to characterize the transmission delays in network-based communication, a family of random variables with partly known probabilities, which are independent and identically distributed, is adopted to describe the random behavior of the transmission delays with the redundant channels. The objective of this work is to put forward a PI state estimator such that the dynamics of the estimation error is exponentially mean-square stable and satisfies the prescribed H∞ performance index of the disturbance attenuation/rejection. By employing the stochastic analysis approach, the error dynamics of the SE under the proposed state estimator is analyzed and sufficient conditions are obtained to ensure the existence of the required PI state estimator. Furthermore, the desired estimator parameters are derived by solving a nonlinear optimization problem. Finally, two simulation examples are exploited to demonstrate the validity of the proposed SE scheme.

Error Analysis for Status Update From Sensors With Temporally and Spatially Correlated Observations

This paper studies the status update performance in wireless sensor networks when status, describing the physical reality that is being sensed, is temporally and spatially correlated. The status is modeled as a time-varying Gauss-Markov Random Field (GMRF), whereby the estimation error of status update at the fusion center is analyzed. The transmission latency introduced by wireless networks is modeled as exponentially distributed random variables. We extend the existing queuing analysis results for Age of Information (AoI) with uncorrelated sources to GMRF in the considered scenario. Closed-form expressions of average remote estimation error are obtained for both one- and two-dimensional GMRFs assuming the exponential time-correlation function, both First-Come First-Served (FCFS) and Last-Come First-Served (LCFS) service disciplines, and a single wireless link. The analytical results are then extended to scenarios wherein multi-packet reception, i.e., multiple concurrent wireless links, is enabled; the difficulty of analyzing obsolete updates in this case is addressed leveraging a reasonable approximation validated by theoretical analysis in the regime where the number of sensors is far more than that of wireless links. Monte-Carlo simulation results are also presented which agree with our theoretical analysis. Based on the results, optimal time and spatial domain sampling rates (e.g., sensor density) can be obtained, providing helpful guidance to wireless sensor deployment.