Terminal Estimation Error Research Articles

Distributed Anti-Eavesdropping Fusion Estimation Under Energy Constraints

This paper studies the distributed fusion estimation problem with energy-constrained sensors in the presence of eavesdroppers, where smart sensors send their local estimates to a remote fusion center (FC). To enhance privacy level, a novel encryption strategy is proposed by establishing an optimization problem, where the optimization objective is constructed by maximizing a combination of the fusion terminal estimation error covariance and the cost of encryption process in finite time domain. Meanwhile, the established problem is decomposed into several independent sub-optimization problems under a relaxation condition, and a sufficient condition that depends on the system parameters is derived such that the sub-optimization problems have optimal solutions. In this case, an optimal encryption strategy is designed with an analytical solution. Finally, a simulation example is given to show the effectiveness of the proposed methods.

Optimal Jamming Attack System Against Remote State Estimation in Wireless Network Control Systems

Recently, public attention is thoroughly aroused as to the security threats of Wireless Network Control System (WNCS), which can seriously disrupt the system operation. In order to achieve the attack effect that each sensor is damaged and maximize the terminal estimation error covariance, it is necessary to study an attack system from the attacker’s perspective. In this paper, we establish an attack system, which includes: the multi-sensor importance evaluation model, the time allocation of jamming attack, and the attack rules. Specifically, we firstly establish the wireless network control system model and the jamming attack model. Then, according to the transmission data and channel parameter information which is intercepted by the attackers, we establish an evaluation model of sensor based on the Mean Impact Value (MIV) algorithm. Then, based on the evaluation results of each sensor, we establish a distribution model of the number of attacks on each sensor. Then, we perform two jamming attack rules(continuous attack rule and good-sensor-late-attack rule)to attack each sensor. Finally, we use the attack system to conduct digital simulation experiments in first-order and high-order system. There is no different between the MIV-based sensor evaluation method in the multi-sensor importance evaluation experiment and sensor performance evaluation based on estimation error. In the jamming attack time allocation experiment, effect that every sensor was attacked had been achieved. In the attack rule experiment, we compare the experimental results of “continuous attack” and “ discontinuous attack”, and the result shows that the effect of “continuous attack” is better than that of “intermittent attack”. Similarly, we have conducted comparative experiments on all attack strategies, and the results show that “ good-sensor-late-attack ” strategy has the best effect. The effectiveness of the attack system is proved by digital simulation experiment.

Optimal stealthy switching location attacks against remote estimation in cyber-physical systems

This paper studies the design of the optimal stealthy switching location attacks in cyber-physical systems with multi-channels. By introducing the Kullback–Leibler divergence to characterize the stealthiness, an attack strategy with the energy constraint is proposed, which is only able to modify a part of the channels at each time step. Under the proposed attacks, the terminal estimation error is analyzed by utilizing the statistical characteristics of the innovations. And then, different from the DoS attack scheduling problems in the related works, the optimal attack strategy is derived by solving a constrained optimization problem and a 0–1 programming problem, which maximizes the remote estimation error and keeps deceptive simultaneously. Finally, the results are illustrated via the simulation examples.

Optimal Denial-of-Service attack energy management against state estimation over an SINR-based network

We consider a scenario in which a DoS attacker with the limited power resource and the purpose of degrading the system performance, jams a wireless network through which the packet from a sensor is sent to a remote estimator. To degrade the estimation quality most effectively with a given energy budget, the attacker aims to solve the problem of how much power to obstruct the channel each time, which is the recently proposed optimal attack energy management problem. The existing works are built on an ideal network model in which the packet dropout never occurs when the attack is absent. To encompass wireless transmission losses, we introduce the signal-to-interference-plus-noise ratio-based network. First we focus on the case when the attacker employs the constant power level. To maximize the expected terminal estimation error at the remote estimator, we provide some more relaxed sufficient conditions compared with the existing work for the existence of an explicit solution to the optimal static attack energy management problem and the solution is constructed. For the other important index of system performance, the average expected estimation error, the associated sufficient conditions are also derived based on a different analysis approach with the existing work. And a feasible method is presented for both indexes to seek the optimal constant attack power level when the system fails to meet the proposed sufficient conditions. Then when the real-time ACK information can be acquired, a Markov decision process (MDP) based algorithm is designed to solve the optimal dynamic attack energy management problem. We further study the optimal tradeoff between attack energy and system degradation. Specifically, by moving the energy constraint into the objective function to maximize the system index and minimize the energy consumption simultaneously, the other MDP based algorithm is proposed to find the optimal dynamic attack power policy which is further shown to have a monotone structure. The theoretical results are illustrated by simulations.

Optimal Denial-of-Service Attack Scheduling With Energy Constraint Over Packet-Dropping Networks

The recent years have seen a surge of security issues of cyber-physical systems (CPS). In this paper, denial-of-service (DoS) attack scheduling is investigated in depth. Specifically, we consider a system where a remote estimator receives the data packet sent by a sensor over a wireless network at each time instant, and an energy-constrained attacker that cannot launch DoS attacks all the time designs the optimal DoS attack scheduling to maximize the attacking effect on the remote estimation performance. Most of the existing works concerning DoS attacks focus on the ideal scenario in which data packets can be received successfully if there is no DoS attack. To capture the unreliability nature of practical networks, we study the packet-dropping network in which packet dropouts may occur even in the absence of attack. We derive the optimal attack scheduling scheme that maximizes the average expected estimation error, and the one which maximizes the expected terminal estimation error over packet-dropping networks. We also present some countermeasures against DoS attacks, and discuss the optimal defense strategy, and how the optimal attack schedule can serve for more effective and resource-saving countermeasures. We further investigate the optimal attack schedule with multiple sensors. The optimality of the theoretical results is demonstrated by numerical simulations.

Optimal multiple-sensor scheduling for general scalar Gauss–Markov systems with the terminal error

In this work, we study finite-horizon multiple-sensor scheduling for general scalar Gauss–Markov systems, extending previous results where only a class of systems are considered. The scheduling objective is to minimize the terminal estimation error covariance. At each time instant, only one sensor can transmit its measurement and each sensor has limited energy. Through building a comparison function and solving its monotone intervals, an efficient algorithm is designed to construct the optimal schedule. In addition, we also provide the result for selecting multiple sensors per time instant under an assumption. Examples are provided to illustrate the proposed results.

Optimal Sensor Power Scheduling for State Estimation of Gauss–Markov Systems Over a Packet-Dropping Network

We consider sensor power scheduling for estimating the state of a general high-order Gauss-Markov system. A sensor decides whether to use a high or low transmission power to communicate its local state estimate or raw measurement data with a remote estimator over a packet-dropping network. We construct the optimal sensor power schedule which minimizes the expected terminal estimation error covariance at the remote estimator under the constraint that the high transmission power can only be used m <; T + 1 times, given the time-horizon from k = 0 to k = T. We also discuss how to extend the result to cases involving multiple power levels scheduling. Simulation examples are the provided to demonstrate the results.

On Optimal Partial Broadcasting of Wireless Sensor Networks for Kalman Filtering

State estimation using wireless sensor networks (WSNs) is an important technique in many commercial and military applications, in which a group of (nonidentical) sensors take noisy observations of system state and send back to a fusion center through wireless broadcasting for state estimation. In order to minimize the terminal estimation error covariance at the fusion center, a partial broadcasting policy should tell which sensors to broadcast at each stage. The limited battery allows each sensor to broadcast only a few times. The limited wireless communication bandwidth allows only a few sensors to broadcast at the same time. Due to these couplings, the optimal partial broadcasting policy is not clear in general. Despite the abundant applications of partial broadcasting policies, theoretical analysis is rare. In this technical note, we provide a first study on the properties of optimal partial broadcasting policies. When there is no packet drop, a good-sensor-late-broadcast (GSLB) rule is shown to perform optimally for both the scalar system and the vector system. When packet drops with positive probability, situations in which the GSLB rule may or may not perform optimally are analyzed. Under different dropping rates, the GSLB rule is compared with several other policies through simulations.

Deterministic Sensor Data Scheduling Under Limited Communication Resource

We consider finite time-horizon sensor data scheduling under limited communication resource. A sensor can only send <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> of its measurement data to a remote estimator within a time-horizon <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> >;>; <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> . When use the terminal estimation error covariance of the estimator as a performance metric, we provide an explicit form of the optimal data schedule; when use the average estimation error covariance as a performance metric, we provide a necessary condition for a schedule to be optimal for a general <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> . When <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> has a special form, the necessary condition allows us to construct an explicit optimal data schedule.

Sensor scheduling over a packet-delaying network

We consider sensor scheduling for state estimation of a scalar system over a packet-delaying network. The current measurement data can be sent over a delay-free channel if the sensor uses larger communication energy; the data will be delayed for one time step if the sensor uses less communication energy. We consider a cost function consisting of a weighted average estimation error and a weighted terminal estimation error and explicitly construct optimal power schedules to minimize this cost function subject to communication energy constraint. Simulations are provided to demonstrate the key ideas of the paper.

Dual-Control Guidance Strategy for Homing Interceptors Taking Angle-Only Measurements

A discrete dual-control homing guidance law is proposed to improve intercept capabilities when angle-only measurements are available. A two-maneuver intercept is considered where the first maneuver inserts a measurable line-of-sight (LOS) rate to enhance the estimate of a key guidance parameter prior to the terminal maneuver used to null intercept miss. A numerical technique is proposed to evaluate the gradient of the variance of the chosen parameter with respect to a velocity correction. A first-order search is used to find a velocity correction that minimizes or substantially reduces the terminal variance. The algorithm is extended to multipleburn scenarios and is evaluated using the terminal estimation error in miss, velocity correction, and time-to-go, respectively, as the control criterion. The results yield interesting insights into the information content in the angle measurements. More importantly, they indicate that the dual-control guidance law suggested here could reduce rms angle-measurement accuracy requirements by a factor of 10 or more, compared to that needed by a more traditional guidance approach, while still maintining terminal intercept performance.