Steady-state Kalman Predictors Research Articles

Robust Centralized and Weighted Measurement Fusion Kalman Predictors with Multiplicative Noises, Uncertain Noise Variances, and Missing Measurements

For multisensor uncertain systems with mixed uncertainties, including multiplicative noises in state and process noise transition matrices, uncertain-variance multiplicative and additive white noises, and missing measurements, this paper addresses the problem of designing robust centralized fusion (CF) and weighted measurement fusion (WMF) Kalman predictors. By introducing fictitious noises, the system under study is converted into a system with only uncertain noise variances. According to the minimax robust estimation principle, which is based on the worst-case system with conservative upper bounds of uncertain noise variances, the robust CF and WMF time-varying Kalman predictors are presented in a unified framework. Using the Lyapunov equation, the robustness of these predictors is proven in the sense that the actual prediction error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using an information filter, they are proven to have the same robust and actual accuracies. The complexity analysis shows that when the number of sensors is larger, the WMF algorithm more significantly reduces the computational burden than the CF algorithm. The corresponding robust fused steady-state Kalman predictors are also presented. The three modes of convergence in a realization among the time-varying and steady-state robust fused Kalman predictors are proposed and proven using the dynamic error system analysis method. Two simulation examples, autoregressive moving average signal processing and an uninterruptible power system, demonstrate the effectiveness of the proposed methods.

Robust weighted fusion steady-state kalman predictors with uncertain noise variances

In this paper, a direct approach of designing robust weighted fusion steady-state Kalman predictors with uncertain noise variances is presented. Based on the steady-state Kalman filtering theory, using the minimax robust estimation principle, the local and six weighted fusion robust steady-state Kalman predictors are proposed based on the worst case systems with the conservative upper bounds of noise variances. They include the three robust weighted state fusers, two robust weighted measurement fusers, and a modified robust covariance intersection (CI) fuser. Their actual prediction error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. A Lyapunov equation approach for robustness analysis and the concept of the robust accuracy are presented and their robust accuracy relations are proved. A simulation example verifies the accuracy relations and robustness.

Guaranteed cost robust weighted measurement fusion steady-state Kalman predictors with uncertain noise variances

Two classes of guaranteed cost robust weighted measurement fusion (WMF) one-step and multi-step Kalman predictors are presented by the Lyapunov equation approach for multisensor system with uncertain noise variances based on the minimax robust estimation principle. One class is to construct a maximal perturbation region of uncertain noise variances such that for all admissible perturbations in this region, the deviations of its actual accuracies with respect to the robust accuracy are guaranteed to remain within the prescribed range, and the maximal lower bound and minimal upper bound of accuracy deviations are given. The other class is to find minimal upper bound and maximal lower bound of accuracy deviations under given perturbation region of uncertain noise variances. The general and unified concept of guaranteed cost robustness is presented. The proof of the guaranteed cost robustness is presented by the Lyapunov equation approach. A simulation example shows the correctness and effectiveness of the proposed results.

A steady-state Kalman predictor-based filtering strategy for non-overlapping sub-band spectral estimation.

This paper focuses on suppressing spectral overlap for sub-band spectral estimation, with which we can greatly decrease the computational complexity of existing spectral estimation algorithms, such as nonlinear least squares spectral analysis and non-quadratic regularized sparse representation. Firstly, our study shows that the nominal ability of the high-order analysis filter to suppress spectral overlap is greatly weakened when filtering a finite-length sequence, because many meaningless zeros are used as samples in convolution operations. Next, an extrapolation-based filtering strategy is proposed to produce a series of estimates as the substitutions of the zeros and to recover the suppression ability. Meanwhile, a steady-state Kalman predictor is applied to perform a linearly-optimal extrapolation. Finally, several typical methods for spectral analysis are applied to demonstrate the effectiveness of the proposed strategy.

Robust Weighted Measurement Fusion Kalman Predictors with Uncertain Noise Variances

For the multisensor system with uncertain noise variances, using the minimax robust estimation principle, the local and weighted measurement fusion robust time-varying Kalman predictors are presented based on the worst-case conservative system with the conservative upper bound of noise variances. The actual prediction error variances are guaranteed to have a minimal upper bound for all admissible uncertainties of noise variances. A Lyapunov approach is proposed for the robustness analysis and their robust accuracy relations are proved. It is proved that the robust accuracy of weighted measurement robust fuser is higher than that of each local robust Kalman predictor. Specially, the corresponding steady-state robust local and weighted measurement fusion Kalman predictors are also proposed and the convergence in a realization between time-varying and steady-state Kalman predictors is proved by the dynamic error system analysis (DESA) method. A Monte-Carlo simulation example shows the effectiveness of the robustness and accuracy relations. DOI : http://dx.doi.org/10.11591/telkomnika.v12i6.5453 Full Text: PDF

Robust weighted fusion Kalman predictors with uncertain noise variances

In this paper, the problem of designing weighted fusion robust time-varying Kalman predictors is considered for multisensor time-varying systems with uncertainties of noise variances. Using the minimax robust estimation principle and the unbiased linear minimum variance (ULMV) rule, based on the worst-case conservative system with the conservative upper bounds of noise variances, the local and five weighted fused robust time-varying Kalman predictors are designed, which include a robust weighted measurement fuser, three robust weighted state fusers, and a robust covariance intersection (CI) fuser. Their actual prediction error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties of noise variances. Their robustness is proved based on the proposed Lyapunov equation approach. The concept of the robust accuracy is presented, and the robust accuracy relations are proved. The corresponding steady-state robust local and fused Kalman predictors are also presented, and the convergence in a realization between the time-varying and steady-state robust Kalman predictors is proved by the dynamic error system analysis (DESA) method and the dynamic variance error system analysis (DVESA) method. Simulation results show the effectiveness and correctness of the proposed results.

Self-tuning measurement fusion Kalman predictors and their convergence analysis

For multisensor systems with unknown parameters and noise variances, three self-tuning measurement fusion Kalman predictors based on the information matrix equation are presented by substituting the online estimators of unknown parameters and noise variances into the optimal measurement fusion steady-state Kalman predictors. By the dynamic variance error system analysis method, the convergence of the self-tuning information matrix equation is proved. Further, it is proved by the dynamic error system analysis method that the proposed self-tuning measurement fusion Kalman predictors converge to the optimal measurement fusion steady-state Kalman predictors in a realisation, so they have asymptotical global optimality. Compared with the centralised measurement fusion Kalman predictors based on the Riccati equation, they can significantly reduce the computational burden. A simulation example applied to signal processing shows their effectiveness.

Robustness and coordination in voltage control of large-scale power systems

In this paper it is shown how the robustness and the coordination of the voltage regulation actions for the transmission grid can be improved. Simpler approaches which ensure higher robustness and performances can be used if the control objectives are pursued at two hierarchical levels of different nature. Also, this is a way to coordinate means of control of different nature with a sufficient time and methodological separation in order to avoid negative mutual influence. At the first level, called the static level, optimal reachable set-points are computed for the second control level, called the dynamic level. The static level can be combined with the shunt reactive power compensation. The system non-linearities are taken into account at the static level while the dynamic level is a linear robust predictive control which takes into account the presence of asynchronous transmission delays. The predictive control strategy is based on the separation property; the output delays are handled using an original steady-state Kalman predictor of order equal to the length of the state of the system without delays. The robustness is improved at the dynamic level against uncertain delays, parametric uncertainties (like, e.g., moderate topological errors and load variations not taken into account in the control model) and unmodelled dynamics. The two-level organisation of the control allows, on one hand, to take into account the important evolutions of the system (like, e.g., large and known topological and load changes) and, on the other hand, a coherent hybrid reactive power control: the switched control of the grid shunt compensation for the reactive power is done at the static level while the reactive power injection provided by the generators is continuously handled at the dynamic level. This is a theoretical analysis of how concepts of automatic control and voltage regulation of power systems can be combined. To be applied as a control scheme, the results presented here should be adapted to a specific context (particularities of the power system and of the organisation of the power industry). They can be used, eventually in conjunction with other improvements, to existing horizontally-organised interconnections (in which all generators of a controlled region can be easily managed since owned by the same utility) or to face specific requirements of moving to the open access in the electric power industry like, e.g., tolerating simplified models in order to cover larger regions, taking into account the interaction between regions, recalibrating set-points, assisting human operator when necessary or facilitating implementation of mechanisms for the management of the reactive power based on price signals.

Distributed optimal fusion steady-state Kalman filter for systems with coloured measurement noises

Based on the optimal fusion criterion weighted by matrices in the linear minimum variance sense, an optimal information fusion steady-state Kalman filter is given for the discrete time-invariant linear stochastic control system measured by multiple sensors with coloured measurement noises, which is equivalent to an optimal information fusion steady-state Kalman predictor with a two-layer fusion structure for system with correlated noises. Furthermore, the steady-state optimal fusion predictor can be obtained only by fusing once after all local subsystems enter the steady-state predictions. The solution of steady-state prediction error cross-covariance matrix between any two subsystems can be obtained by iteration with an arbitratry initial value, whose convergence is proved. Applying it to a tracking system with three sensors shows its effectiveness.

Robust state-predictive control with separation property: A reduced-state design for control systems with non-equal time delays

A robust state-predictive control strategy is proposed for discrete-time multi-input/output systems with non-equal delays on signal buses. It is based on a separation property between control and prediction. The input delays are taken into account in the control law synthesis and the output delays are handled using an original steady-state Kalman predictor of order equal to the length of the state of the system without delays. Robustness, especially against uncertain delays, is improved using a state extension in the predictive gain synthesis. The classic optimal separation theorem (in the case of an one step predictor) is extended to the general case of a d+1 step prediction for a delayed discrete-time system.

A Generalized Predictive Control for CARIMA Systems Using the State-Space Approach

A generalized predictive control (GPC) which can be designed in a state-space framework is proposed for single-input/single-output CARIMA systems. It is first shown that, in designing the steady-state 1-step Kalman predictor by applying the innovation model, there are two ways depending on whether the output value of the plant is directly used or not ; one is called here “direct output method” and another is called “output deviation method”. When solving the 1-step predicted estimate of the original output, the latter method can be further classified into two approaches which differ in respect of the interpretation of the predicted estimate for the output deviation. Thus, three different j-step ahead state-space output predictors can be designed for the GPC strategy. Finally, the performances of three GPCs are compared through some numerical simulations.