Linear estimation for discrete-time periodic systems with unknown measurement input and missing measurements

This paper considers the estimation problem for periodic systems with unknown measurement input and missing measurements. The missing measurements phenomenon is described by an independent and identically distributed Bernoulli process. The quality of the estimation achieved by an admissible filter is measured by a performance criterion described by the Cesaro limit of the mean square of the deviation between the remote signal and the estimated signal. By employing the minimum variance unbiased estimation technique, the periodic unbiased estimator is obtained, where the estimator gain is designed in terms of the unique periodic solution of a Lyapunov equation together with the periodic stabilizing solution of a Riccati equation. Finally, a numerical example is provided to show the effectiveness of the proposed estimation approach.     

Improvement on state estimation for discrete-time LTI systems with measurement loss

In this paper, we present a novel state estimation procedure for the LTI systems with loss of data at the output measurement channels. The proposed methodology aims at compensating such output measurement losses through an innovative design methodology which is based on the so-called linear prediction (LP) and Kalman filter theories. A compensated observation signal is first reconstructed using an LP subsystem and then supplied to a discrete-time Kalman filter in the closed-loop framework. We show that, under suitable assumptions, it is possible to reconstruct the lost data using an straightforward algorithm with the capability of associating an optimal filter order. A mass-spring-damper case study subject to measurement loss is provided to demonstrate some of the promising results of our proposed algorithm. Simulation results illustrate that the proposed estimation methodology is too far superior than those offered in the literature.     

Time-domain filtering for estimation of linear systems with colored noises using recent finite measurements

To date, finite impulse response (FIR) filters have been proposed to estimate linear systems with white Gaussian noises, but to the best of our knowledge, no solution exists for linear systems with colored noises. In this paper, we propose a new FIR filter to estimate linear state-space models with both process and measurement noises through state augmentation. In addition, we suggest a modified form of the colored-noise FIR filter to deal with the computational burden and singularity problem. Numerical examples are presented to describe the effectiveness of the colored-noise FIR filter.     

Partial state estimation for linear systems with output and input time delays

This paper deals with the problem of partial state observer design for linear systems that are subject to time delays in the measured output as well as the control input. By choosing a set of appropriate augmented Lyapunov–Krasovskii functionals with a triple-integral term and using the information of both the delayed output and input, a novel approach to design a minimal-order observer is proposed to guarantee that the observer error is ε-convergent with an exponential rate. Existence conditions of such an observer are derived in terms of matrix inequalities for the cases with time delays in both the output and input and with output delay only. Constructive design algorithms are introduced. Numerical examples are provided to illustrate the design procedure, practicality and effectiveness of the proposed observer.     

Resolver angle estimation using parameter and state estimation

In this paper, a new type of a resolver angle estimator that utilizes a combined parameter and state estimation scheme is proposed. A state-space model of a resolver is first developed with unknown parameters. Least square estimation is employed to obtain some unknown model parameters by using the measurements up to the current time. Based on the state-space model with estimated parameters, a constrained state estimator with finite memory is constructed to estimate the resolver angle. It is shown through simulation that the proposed scheme is very effective in suppressing noise and overcoming amplitude and phase imbalances compared with common angle tracking observers.     

Robust state estimation for a class of uncertain nonlinear systems: Comparison of two approaches

In this paper, two approaches for robust state estimation of a class of Lipschitz nonlinear systems are proposed. First, a novel Unknown Input Observer (UIO) is designed without observer matching condition satisfaction. Then, an $H_{\infty }$ observer for approximate disturbance decoupling is proposed. Sufficient conditions for the existence of both proposed observers are derived based on a Lyapunov function. The achieved conditions are formulated in terms of a set of linear matrix inequalities (LMIs) and optimal gain matrices are obtained. The minimum values of the disturbance attenuation levels for both methods are obtained through solving optimization problems. Finally, the proposed approaches are compared by simulation studies of an automated highway system.     

Event triggered state estimation techniques for power systems with integrated variable energy resources

For many decades, state estimation (SE) has been a critical technology for energy management systems utilized by power system operators. Over time, it has become a mature technology that provides an accurate representation of system state under fairly stable and well understood system operation. The integration of variable energy resources (VERs) such as wind and solar generation, however, introduces new fast frequency dynamics and uncertainties into the system. Furthermore, such renewable energy is often integrated into the distribution system thus requiring real-time monitoring all the way to the periphery of the power grid topology and not just the (central) transmission system. The conventional solution is two fold: solve the SE problem (1) at a faster rate in accordance with the newly added VER dynamics and (2) for the entire power grid topology including the transmission and distribution systems. Such an approach results in exponentially growing problem sets which need to be solver at faster rates. This work seeks to address these two simultaneous requirements and builds upon two recent SE methods which incorporate event-triggering such that the state estimator is only called in the case of considerable novelty in the evolution of the system state. The first method incorporates only event-triggering while the second adds the concept of tracking. Both SE methods are demonstrated on the standard IEEE 14-bus system and the results are observed for a specific bus for two difference scenarios: (1) a spike in the wind power injection and (2) ramp events with higher variability. Relative to traditional state estimation, the numerical case studies showed that the proposed methods can result in computational time reductions of 90%. These results were supported by a theoretical discussion of the computational complexity of three SE techniques. The work concludes that the proposed SE techniques demonstrate practical improvements to the computational complexity of classical state estimation. In such a way, state estimation can continue to support the necessary control actions to mitigate the imbalances resulting from the uncertainties in renewables.     

Decentralized state estimation for a large-scale spatially interconnected system

A decentralized state estimator is derived for the spatially interconnected systems composed of many subsystems with arbitrary connection relations. An optimization problem on the basis of linear matrix inequality (LMI) is constructed for the computations of improved subsystem parameter matrices. Several computationally effective approaches are derived which efficiently utilize the block-diagonal characteristic of system parameter matrices and the sparseness of subsystem connection matrix. Moreover, this decentralized state estimator is proved to converge to a stable system and obtain a bounded covariance matrix of estimation errors under certain conditions. Numerical simulations show that the obtained decentralized state estimator is attractive in the synthesis of a large-scale networked system.     

Robust particle filter for state estimation using measurements with different types of gross errors

For industrial processes, the state estimation plays a key role in various applications, such as process monitoring and model based control. Although the particle filter (PF) is able to deal with nonlinear and non-Gaussian processes, it rarely considers the influence of measurements with gross errors, such as outliers, biases and drifts. Nevertheless, measurements of dynamical systems are often influenced by different types of gross errors. This paper proposes a robust PF approach, in which gross error identification is used to estimate magnitudes of gross error. The gross errors can be removed or compensated so that a feasible set of particle sampling can contain the true states of the system. The proposed robust PF approach is implemented on a complex nonlinear dynamic system, the free radical polymerization of styrene. The application results show that the proposed approach is an appealing alternative to solving PF estimation problems with measurements containing gross errors.     

Analysis of the optimal sampling rate for state estimation in sensor networks with delays

When addressing the problem of state estimation in sensor networks, the effects of communications on estimator performance are often neglected. High accuracy requires a high sampling rate, but this leads to higher channel load and longer delays, which in turn worsens estimation performance. This paper studies the problem of determining the optimal sampling rate for state estimation in sensor networks from a theoretical perspective that takes into account traffic generation, a model of network behaviour and the effect of delays. Some theoretical results about Riccati and Lyapunov equations applied to sampled systems are derived, and a solution was obtained for the ideal case of perfect sensor information. This result is also interesting for non-ideal sensors, as in some cases it works as an upper bound of the optimisation solution.     

Reachable set estimation for Takagi-Sugeno fuzzy systems against unknown output delays with application to tracking control of AUVs

In this paper, we address the problem of reachable set estimation for continuous-time Takagi-Sugeno (T-S) fuzzy systems subject to unknown output delays. Based on the reachable set concept, a new controller design method is also discussed for such systems. An effective method is developed to attenuate the negative impact from the unknown output delays, which likely degrade the performance/stability of systems. First, an augmented fuzzy observer is proposed to capacitate a synchronous estimation for the system state and the disturbance term owing to the unknown output delays, which ensures that the reachable set of the estimation error is limited via the intersection operation of ellipsoids. Then, a compensation technique is employed to eliminate the influence on the system performance stemmed from the unknown output delays. Finally, the effectiveness and correctness of the obtained theories are verified by the tracking control of autonomous underwater vehicles.     

Recursive parameter estimation for Hammerstein-Wiener systems using modified EKF algorithm

This paper focuses on the recursive parameter estimation for the single input single output Hammerstein-Wiener system model, and the study is then extended to a rarely mentioned multiple input single output Hammerstein-Wiener system. Inspired by the extended Kalman filter algorithm, two basic recursive algorithms are derived from the first and the second order Taylor approximation. Based on the form of the first order approximation algorithm, a modified algorithm with larger parameter convergence domain is proposed to cope with the problem of small parameter convergence domain of the first order one and the application limit of the second order one. The validity of the modification on the expansion of convergence domain is shown from the convergence analysis and is demonstrated with two simulation cases.     

A natural observer for optimal state estimation in second order linear structural systems

A state observer for mechanical and structural systems is derived in the context of the second order differential equation of motion of linear structural systems. The proposed observer possesses similar characteristics to the Kalman filter in the sense that it minimizes the trace of the state error covariance matrix within the predefined structure of the feedback gain. The main contribution of the paper consists of the fact that the proposed observer can be implemented directly as a modified linear finite element model of the system, subject to collocated corrective forces proportional to the measured response. The proposed algorithm is effectively illustrated in two different types of second order systems; a close-coupled spring–mass–damper multi-degree of freedom system and a plate subject to transverse vibrations.     

Robust fault diagnosis algorithm for a class of Lipschitz system with unknown exogenous disturbances

A robust fault diagnosis scheme for nonlinear system is designed and a novel algorithm for a robust fault diagnosis observer is proposed in this paper. The robustness performance index is defined to ensure the robustness of the observer designed. The norm of most unknown input disturbances are assumed bounded at present. However, some systems are proved unstable under traditional assumptions. In the proposed algorithm, the external disturbances constraint condition that satisfies the system stability is derived based on Gronwall Lemma. The design procedure of the observer proposed is implemented by pole assignment. Adaptive threshold is generated using the designed observer. Simulations are performed on continuous stirred tank reactor (CSTR) and the results show the effectiveness and superiority of the proposed algorithm.     

Distributed and decentralized state estimation in gas networks as distributed parameter systems

In this paper, a framework for distributed and decentralized state estimation in high-pressure and long-distance gas transmission networks (GTNs) is proposed. The non-isothermal model of the plant including mass, momentum and energy balance equations are used to simulate the dynamic behavior. Due to several disadvantages of implementing a centralized Kalman filter for large-scale systems, the continuous/discrete form of extended Kalman filter for distributed and decentralized estimation (DDE) has been extended for these systems. Accordingly, the global model is decomposed into several subsystems, called local models. Some heuristic rules are suggested for system decomposition in gas pipeline networks. In the construction of local models, due to the existence of common states and interconnections among the subsystems, the assimilation and prediction steps of the Kalman filter are modified to take the overlapping and external states into account. However, dynamic Riccati equation for each subsystem is constructed based on the local model, which introduces a maximum error of 5% in the estimated standard deviation of the states in the benchmarks studied in this paper. The performance of the proposed methodology has been shown based on the comparison of its accuracy and computational demands against their counterparts in centralized Kalman filter for two viable benchmarks. In a real life network, it is shown that while the accuracy is not significantly decreased, the real-time factor of the state estimation is increased by a factor of 10.     

Enhanced extended state observer-based control for systems with mismatched uncertainties and disturbances

This paper presents an enhanced Extended State Observer (ESO)-based control strategy to deal with the disturbance attenuation problem for a class of non integral-chain systems subject to non-linear mismatched uncertainties and external disturbances. The proposed control strategy does not assume the integral-chain form and it is formed by a state-feedback plus a dynamic disturbance compensation term, which is designed to reject the disturbance effect in the system output. From a theoretical point of view, the proposed strategy is reduced to the conventional ESO when the integral chain form and the matched condition hold. In this sense, this paper is presented as an extension of the ESO principles to cover a wider class of systems. The theoretical results show that the internal zero-dynamics plays an important role in ESO-based control design. Also, the closed-loop stability is analyzed and some numerical simulations show the effectiveness of the proposal in comparison with previous ESO-based techniques.     

A thinning algorithm for GPS-based unbiased FIR estimation of a clock TIE model

A thinning algorithm is proposed for real-time unbiased finite impulse response (FIR) estimation of the local clock time interval error (TIE) model (time error, fractional frequency offset, linear frequency drift rate, etc.) employing GPS-based sawtooth measurements. We show that the approach allows obtaining practically optimal estimates of the clock states, by large horizons (number of the points in the average). The algorithm is applied to the TIE measurements allowing for different time steps and averaging horizons for each of the clock states and compared to the three state Kalman filter. It is demonstrated that, in the presence of the sawtooth noise induced by the GPS receiver, the unbiased FIR estimates with thinning out fit the clock states better than the Kalman filter, in terms of the Allan deviation and precision time protocol deviation.