Estimation Problem For Systems Research Articles

Unknown Input Observer-Based Design for a Class of Nonlinear System with Time-Variable Delay

This paper addresses the problem of state estimation for nonlinear delay systems by proposing an unknown inputs observer. The observer design is based on using Taylor’s first-order development. The stability study has been proven using a modified Lyapunov–Krasovskii functional without reference to a linear matrix inequality. For the validation of the proposed approach, three examples are proposed. The first one is about comparative simulation, the second one treats the chaotic time-delay system and the final example considered the time-delay system with measurement noise.

Generalized Bussgang LMMSE Channel Estimation for One-Bit Massive MIMO Systems

In this paper, we consider the problem of channel estimation for uplink multiuser massive MIMO systems, where, in order to significantly reduce the hardware cost and power consumption, one-bit analog-to-digital converters (ADCs) are used at the base station (BS) to quantize the received signal. We first extend the conventional Bussgang linear minimum mean square error (BLMMSE) estimator to the general nonzero threshold case. We then study the problem of one-bit quantization design, aiming at minimizing the mean squared error of the generalized BLMMSE estimator. A set partition scheme is proposed to devise the quantization thresholds. The rationale behind the proposed scheme is to divide each antenna’s received samples into a number of disjoint subsets according to their pairwise correlation and assign diverse thresholds to those highly correlated data samples. In addition to the set partition scheme, a gradient descent scheme is developed to search for optimal quantization thresholds. The proposed schemes only require the statistical information of the received signals to devise the quantization thresholds, which can be calculated in advance before the training process begins. Simulation results show that the generalized BLMMSE estimator can achieve a significant performance improvement over the conventional Bussgang LMMSE estimator.

Supervisory Nonlinear State Observers for Adversarial Sparse Attacks.

This article investigates the problem of secure state estimation for continuous-time linear systems in the presence of sparse sensor attacks. Compared with the existing results, the attacked sensor set can be changed by adversaries against secure estimation. To address the more erratic attacks, a novel supervisory state observer is proposed, which employs a bank of candidate nonlinear subobservers and a switching logic administrated by a monitoring function to select the active subobserver at every instant of time. Based on the stability analysis of switched systems, it is proven that the supervisory observer asymptotically converges to a neighborhood of the true system state in the presence of the sensor attacks and bounded disturbances. A simulation example is given to substantiate the theoretical results.

Optimal Schedule of Secure Transmissions for Remote State Estimation Against Eavesdropping

In this article, we investigate the privacy issue of the remote state estimation problem in cyber-physical systems. Specifically, in the presence of an eavesdropper, a sensor observes a discrete linear time-invariant process and then sends the measurements to a remote state estimator with arbitrary finite kinds of transmission options through an unreliable wireless channel. The transmission options of the sensor are in silence state or transmitting aided by injection noise with different energy levels. The eavesdropper wiretaps the channel when the sensor transmits packets to the estimator. Aiming at minimizing the remote estimation error and the cost of the sensors transmission energy while maximizing the eavesdropper state estimation error, we theoretically prove that there exist some structural properties for the optimal transmission schedule for both the known and the unknown eavesdropper's estimation errors. Numerical simulation results are provided to validate the theoretical analysis.

Reachable Set Estimation for Neural Network Control Systems: A Simulation-Guided Approach

The vulnerability of artificial intelligence (AI) and machine learning (ML) against adversarial disturbances and attacks significantly restricts their applicability in safety-critical systems including cyber-physical systems (CPS) equipped with neural network components at various stages of sensing and control. This article addresses the reachable set estimation and safety verification problems for dynamical systems embedded with neural network components serving as feedback controllers. The closed-loop system can be abstracted in the form of a continuous-time sampled-data system under the control of a neural network controller. First, a novel reachable set computation method in adaptation to simulations generated out of neural networks is developed. The reachability analysis of a class of feedforward neural networks called multilayer perceptrons (MLPs) with general activation functions is performed in the framework of interval arithmetic. Then, in combination with reachability methods developed for various dynamical system classes modeled by ordinary differential equations, a recursive algorithm is developed for over-approximating the reachable set of the closed-loop system. The safety verification for neural network control systems can be performed by examining the emptiness of the intersection between the over-approximation of reachable sets and unsafe sets. The effectiveness of the proposed approach has been validated with evaluations on a robotic arm model and an adaptive cruise control system.

Low Complexity Beamspace Super Resolution for DOA Estimation of Linear Array.

Beamspace processing has become much attractive in recent radar and wireless communication applications, since the advantages of complexity reduction and of performance improvements in array signal processing. In this paper, we concentrate on the beamspace DOA estimation of linear array via atomic norm minimization (ANM). The existed generalized linear spectrum estimation based ANM approaches suffer from the high computational complexity for large scale array, since their complexity depends upon the number of sensors. To deal with this problem, we develop a low dimensional semidefinite programming (SDP) implementation of beamspace atomic norm minimization (BS-ANM) approach for DFT beamspace based on the super resolution theory on the semi-algebraic set. Then, a computational efficient iteration algorithm is proposed based on alternating direction method of multipliers (ADMM) approach. We develop the covariance based DOA estimation methods via BS-ANM and apply the BS-ANM based DOA estimation method to the channel estimation problem for massive MIMO systems. Simulation results demonstrate that the proposed methods exhibit the superior performance compared to the state-of-the-art counterparts.

Robust massive MIMO channel estimation for 5G networks using compressive sensing technique

The pilot overhead provides fundamental limits on the performance of massive multiple-input multiple-output (MIMO) systems. This is because the performance of such systems is based on the failure of the presentation of accurate channel state information (CSI). Based on the theory of compressive sensing, this paper presents a novel channel estimation technique as the mean of minimizing the problems associated with pilot overhead. The proposed technique is based on the combination of the compressive sampling matching and sparsity adaptive matching pursuit techniques. The sources of the signals in MIMO systems are sparsely distributed in terms of spatial correlations. This distribution pattern enables then use of compressive sampling techniques to solve the channel estimation problem in MIMO systems. Simulation results demonstrate that the proposed channel estimation outperforms the conventional compressive sensing (CS)-based channel estimation algorithms in terms of the normalized mean square error (NMSE) performance at high signal-to-noise ratios (SNRs). Furthermore, it reduces the computational complexity of the channel estimation compared to conventional methods. In addition to the achieved performance gain in terms of NMSE, the presented method significantly reduces pilot overhead compared to conventional channel estimation techniques.

An efficient approximation of the Kalman filter for multiple systems coupled via low-dimensional stochastic input

We formulate a recursive estimation problem for multiple dynamical systems coupled through a low dimensional stochastic input, and we propose an efficient sub-optimal solution. The suggested approach is an approximation of the Kalman filter that discards the off diagonal entries of the correlation matrix in its “update” step. The time complexity associated with propagating this approximate block-diagonal covariance is linear in the number of systems, compared to the cubic complexity of the full Kalman filter. The stability of the proposed block-diagonal filter and its behavior for a large number of systems are analyzed in some simple cases. It is then examined in the context of electric field estimation in a high-contrast space coronagraph, for which it was designed. The numerical simulations provide encouraging results for the cost-efficiency of the newly suggested filter.

Event-Triggered State Estimation of Linear Systems Using Moving Horizon Estimation

In this brief, a problem of event-triggered state estimation for networked linear systems is investigated. We consider that the stochastic system disturbances and noise are bounded and moving horizon estimation (MHE) is used to handle these constraints. We establish an event-based state estimation mechanism that aims to provide good state estimates while reducing the frequencies of both the evaluation of the state estimator and networked communication between the plant and the estimator. An event-triggering condition is used to govern the evaluation of the MHE-based estimator and the use of networked communication. An MHE-based estimator is designed to provide state estimates when there is an event. Stability analysis of the estimation error dynamics is carried out for the proposed event-triggered estimation mechanism. The effectiveness and the applicability of the proposed method are demonstrated through numerical simulations and an experiment.

State Estimation for Networked Systems With Markov Driven Transmission and Buffer Constraint

This article investigates the problem of state estimation for discrete-time systems with a Markov driven transmission strategy. A buffer with limited capacity is used to store the latest measurements, and they are transmitted simultaneously once the system accesses to the shared channel. A buffer-dependent smart estimator is then proposed to process the received measurements. A convex sufficient condition concerning the exponential mean-square stability and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{2}-l_{\infty }$ </tex-math></inline-formula> performance is established for the estimation error system to design the estimator gains. Finally, two examples are presented to illustrate the effectiveness of the derived result under different conditions.

Uncertainty estimation in equality-constrained MAP and maximum likelihood estimation with applications to system identification and state estimation

In unconstrained maximum a posteriori (MAP) and maximum likelihood estimation, the inverse of minus the merit-function Hessian matrix is an approximation of the estimate covariance matrix. In the Bayesian context of MAP estimation, it is the covariance of a normal approximation of the posterior around the mode; while in maximum likelihood estimation, it is an approximation of the inverse Fisher information matrix, to which the covariance of efficient estimators converges. These measures are routinely used in system identification to evaluate the estimate uncertainties and diagnose problems such as overparameterization, improper excitation and unidentifiability. A wide variety of estimation problems in systems and control, however, can be formulated as equality-constrained optimizations with additional decision variables to exploit parallelism in computer hardware, simplify implementation and increase the convergence basin and efficiency of the nonlinear program solver. The introduction of the extra variables, however, dissociates the inverse Hessian from the covariance matrix. Instead, submatrices of the inverse Hessian of the constrained-problem’s Lagrangian must be used. In this paper, we derive these relationships, showing how the estimates’ covariance can be estimated directly from the augmented problem. Application examples are shown in system identification with the output-error method and joint state-path and parameter estimation.

Intermediate Observer-Based Robust Distributed Fault Estimation for Nonlinear Multiagent Systems With Directed Graphs

This article focuses on the problem of robust distributed fault estimation for nonlinear multiagent systems with actuator faults and sensor faults. The communication topology of the multiagent systems is assumed to be directed. A novel intermediate observer design method is proposed to estimate the system states, actuator faults, and sensor faults. For the observer constructed in one agent, the output estimation errors of itself and its neighbors are considered, simultaneously. The observer matching condition is not needed in the observer design process. Based on Schur decomposition, the observer parameter calculation method is presented in terms of solution to one linear matrix inequality, which is with the same order as it is for the single agent system. Thus, the calculated amount remains unchanged even when the number of agents increases, since the inequality dimension is independent of the agent number. At last, simulation results are provided to illustrate the effectiveness of the proposed technique.

Pilot Sequence Design for Mitigating Pilot Contamination With Reduced RF Chains

Massive multiple-input multiple-output (MIMO) communication is a promising technology for increasing spectral efficiency in wireless networks. Two of the main challenges massive MIMO systems face are degraded channel estimation accuracy due to pilot contamination and increase in computational load and hardware complexity due to the massive number of antennas. In this paper, we focus on the problem of channel estimation in massive MIMO systems, while addressing these two challenges: We jointly design the pilot sequences to mitigate the effect of pilot contamination and propose an analog combiner which maps the high number of sensors to a low number of RF chains, thus reducing the computational and hardware cost. We consider a statistical model in which the channel covariance obeys a Kronecker structure, and treat two special cases, corresponding to fully- and partially-separable correlations. We prove that under these models, the analog combiner design can be performed independently of the pilot sequences. Given the resulting combiner, we derive a closed-form expression for the optimal pilot sequences in the fully-separable case and suggest a greedy sum of ratio traces maximization (GSRTM) method for designing sub-optimal pilots in the partially-separable scenario. We demonstrate via simulations that our pilot design framework achieves lower mean squared error than the common pilot allocation framework previously considered for pilot contamination mitigation.

Mode separability-based state estimation for uncertain constrained dynamic systems

This paper addresses the state estimation problem for dynamic systems subject to uncertain constraints, i.e., all possible constraints are described by a finite set, and only one constraint is satisfied at each moment. For this typical hybrid system estimation problem with coupled discrete constraint modes and continuous states, we design a mode separability-based state estimation (MSSE) framework. Based on the measurement model over a window, the hypothesis testing is performed to detect whether the mode changes firstly. Then the maximum-likelihood criterion is used to estimate the mode change sequence once detecting the change. Next, to consider the possible impact of the decided modes on the state estimation, a metric of mode separability is proposed to evaluate the separability of the recognized modes, and two different state estimation methods are introduced. Specifically, if the recognized modes are separable from the others, the state estimates are obtained by a recursive mode-based constraint Kalman filter (MCKF) which is proved that the estimation error is bounded in mean square. Otherwise, the estimation results output the fused state estimates (FSE) of the inseparable modes. Finally, simulation results of road-constrained vehicle tracking are provided to demonstrate the effectiveness of the proposed framework.

State estimation for linear hybrid systems with periodic jumps and unknown inputs

SummaryIn order to solve the state estimation problem for linear hybrid systems with periodic jumps and unknown inputs, some hybrid observers are proposed. The proposed observers admit a Luenberger‐like structure and the synthesis is given in terms of linear matrix inequalities (LMIs). Therefore, the proposed observer designs are completely constructive and provide some input‐to‐state stability properties with respect to unknown inputs. It is worth mentioning that the structure of the hybrid observers, as well as the structure of the LMIs, depends on some observability properties of the flow and jump dynamics, respectively. Then, in order to compensate the effect of the unknown inputs, a hybrid sliding‐mode observer is added to the Luenberger‐like observer structure, providing exponential convergence to zero of the state estimation error despite certain class of unknown inputs. The existence of the hybrid observers and the unknown input hybrid observer is guaranteed if and only if the hybrid system is observable and strongly observable, respectively. Some numerical examples illustrate the feasibility of the proposed estimation approach.

Distributed robust filtering with hybrid consensus strategy for sensor networks

The problem of distributed state estimation for time-varying uncertain systems over a sensor network within the robust Kalman filtering framework is studied. It is assumed that the parameters of the underlying model are subjected to stochastic uncertainties. At the first step, the authors present a particular form of the Kalman filter named information form of a robust Kalman filter. Then, using a consensus scheme that guarantees an agreement in estimation among nodes, they propose a new consensus-based robust filtering approach. The consensus methodology is a hybrid method that is a combination of consensus on information (CI) and consensus on measurement (CM). To this end, before proposing the hybrid consensus filtering algorithm, distributed robust filtering based on CI and CM have been presented. Next, they show that the estimation error in the proposed consensus algorithm is exponentially mean square bounded using a Lyapunov function. Finally, they provide two illustrative examples to show the robust performance and effectiveness of the proposed consensus filtering algorithms.

Parameter estimation for dual-rate sampled Hammerstein systems with dead-zone nonlinearity

The identification of nonlinear systems with multiple sampled rates is a difficult task. The motivation of our paper is to study the parameter estimation problem of Hammerstein systems with dead-zone characteristics by using the dual-rate sampled data. Firstly, the auxiliary model identification principle is used to estimate the unmeasurable variables, and the recursive estimation algorithm is proposed to identify the parameters of the static nonlinear model with the dead-zone function and the parameters of the dynamic linear system model. Then, the convergence of the proposed identification algorithm is analyzed by using the martingale convergence theorem. It is proved theoretically that the estimated parameters can converge to the real values under the condition of continuous excitation. Finally, the validity of the proposed algorithm is proved by the identification of the dual-rate sampled nonlinear systems.

Moving Horizon Estimation With Unknown Inputs Under Dynamic Quantization Effects

This article is concerned with the moving horizon estimation (MHE) problem for networked linear systems (NLSs) with unknown inputs under dynamic quantization effects. For the NLSs with unknown input signals, the conventional MHE strategy is incapable of guaranteeing the satisfactory performance as the estimation error is dependent on the external disturbances. In this work, a novel MHE strategy is developed to cope with the underlying NLS with unknown inputs by dedicatedly introducing certain temporary estimates of unknown inputs, where the desired estimator parameters are designed to decouple the estimation error dynamics from the unknown inputs. A two-step design strategy (namely, decoupling step and convergence step) is proposed to obtain the estimator parameters. In the decoupling step, the decoupling parameter of the moving horizon estimator is designed based on certain assumptions on system parameters and quantization parameters. In the convergence step, by employing a special observability decomposition scheme, the convergence parameters of the moving horizon estimator are achieved such that the estimation error dynamics is ultimately bounded. Moreover, the developed MHE strategy is extended to the scenario with direct feedthrough of unknown inputs. Two simulation examples are given to demonstrate the correctness and effectiveness of the proposed MHE strategies.

Fault estimation for fractional-order linear systems with polytopic uncertainties in the finite frequency domain

This paper investigates the problem of fault estimation for fractional-order systems with polytopic uncertainties. The faults and disturbances are considered to belong to finite frequency domains, and a fractional-order robust fault estimation filter is proposed for fault estimation with the known frequency ranges. As applications of the generalized Kalman–Yakubovich–Popov lemma, the fault estimation filter design problem is transformed into a multi-objective optimisation problem. By using the projection lemma and a linearising change of variables, sufficient conditions for the existence of the robust fault estimator are derived on the basis of a set of linear matrix inequalities. Numerical examples are used to demonstrate the validity of the presented method.

Distributed Fusion Estimation for Unstable Systems With Quantized Innovations

This article is concerned with the distributed networked fusion estimation problems for unstable systems with limited communication capacity, where the system and measurement noises are unknown but bounded. To overcome the unboundedness of measurement information for unstable systems, it is proposed to quantize the innovations that are sent to the fusion center over bandwidth constrained channels. By using the bounded recursive optimization idea, the design problems of local stable estimators and distributed fusion criterion under the quantized innovations are converted into two different convex optimization problems that can be easily solved by the standard software. The target tracking system is employed to demonstrate the effectiveness of the proposed methods.