Augmented State Approach Research Articles

Robust Fusion Kalman Estimator of the Multi-Sensor Descriptor System with Multiple Types of Noises and Packet Loss.

Under the influence of multiple types of noises, missing measurement, one-step measurement delay and packet loss, the robust Kalman estimation problem is studied for the multi-sensor descriptor system (MSDS) in this paper. Moreover, the established MSDS model describes uncertain-variance noises, multiplicative noises, time delay and packet loss phenomena. Different types of noises and packet loss make it more difficult to build the estimators of MSDS. Firstly, MSDS is transformed to the new system model by applying the singular value decomposition (SVD) method, augmented state and fictitious noise approach. Furthermore, the robust Kalman estimator is constructed for the newly deduced augmented system based on the min-max robust estimation principle and Kalman filter theory. In addition, the given estimator consists of four parts, which are the usual Kalman filter, predictor, smoother and white noise deconvolution estimator. Then, the robust fusion Kalman estimator is obtained for MSDS according to the relation of augmented state and the original system state. Simultaneously, the robustness is demonstrated for the actual Kalman estimator of MSDS by using the mathematical induction method and Lyapunov's equation. Furthermore, the error variance of the obtained Kalman estimator is guaranteed to the upper bound for all admissible uncertain noise variance. Finally, the simulation example of a circuit system is examined to illustrate the performance and effectiveness of the robust estimators.

Robust fusion filter for multisensor descriptor system with uncertain‐variance noises and packet dropout

AbstractFor the multisensor linear stochastic descriptor system with uncertain‐variance noises and packet dropout, the standard state space model of the new reduced‐order augmented state is obtained based on the singular value decomposition (SVD) approach and augmented state approach. By applying the min‐max robust estimation principle and Kalman filtering theory, the local robust time‐varying Kalman filters of the reduced‐order augmented state and fictitious process noise are proposed. Then, the local robust time‐varying filters of the original descriptor system are presented according to the relation of the reduced‐order augmented state and the original state. And the distributed and covariance intersection (CI) fusion robust time‐varying filters are presented, and the actual and conservative filtering error variances are obtained. Further, the robustness of the local and fused robust filters are proved by applying Lyapunov equation approach, and the accuracy relation between them is analyzed. A simulation example applied to a circuit system shows its effectiveness and applicability.

Combining data assimilation and machine learning to estimate parameters of a convective‐scale model

AbstractErrors in the representation of clouds in convection‐permitting numerical weather prediction models can be introduced by different sources. These can be the forcing and boundary conditions, the representation of orography, the accuracy of the numerical schemes determining the evolution of humidity and temperature, but large contributions are due to the parametrization of microphysics and the parametrization of processes in the surface and boundary layers. These schemes typically contain several tunable parameters that are either not physical or only crudely known, leading to model errors. Traditionally, the numerical values of these model parameters are chosen by manual model tuning. More objectively, they can be estimated from observations by the augmented state approach during the data assimilation. Alternatively, in this work, we look at the problem of parameter estimation through an artificial intelligence lens by training two types of artificial neural network (ANN) to estimate several parameters of the one‐dimensional modified shallow‐water model as a function of the observations or analysis of the atmospheric state. Through perfect model experiments we show that Bayesian neural networks (BNNs) and Bayesian approximations of point estimate neural networks (NNs) are able to estimate model parameters and their relevant statistics. The estimation of parameters combined with data assimilation for the state decreases the initial state errors even when assimilating sparse and noisy observations. The sensitivity to the number of ensemble members, observation coverage and neural network size is shown. Additionally, we use the method of layer‐wise relevance propagation to gain insight into how the ANNs are learning and discover that they naturally select only a few grid points that are subject to strong winds and rain to make their predictions of chosen parameters.

Robust time‐varying estimator for descriptor system with random one‐step measurement delay

AbstractFor the linear stochastic descriptor system with random one‐step measurement delay and uncertain‐variance correlated noises, the robust estimation problem is addressed. Applying the singular value decomposition method, augmented state approach and fictitious noise approach, the original descriptor system is transformed to new standard system only with uncertain‐variance fictitious noises. Based on Kalman filtering and the minimax robust estimation principle, the actual Kalman estimator for the proposed standard system with actual measurement and the upper bounds of the variances is presented, including the Kalman predictor, filter, smoother and white noise deconvolution estimator. According to the relation of the new standard system and the original system, the actual estimator of original state of descriptor system and actual estimation error variance are presented. Further, the robustness of the actual estimator is proved by the Lyapunov equation approach, that is, the actual estimation error variance is guaranteed to have minimal upper bound for all admissible uncertainties. A simulation example about circuits system verifies the correctness and effectiveness of the proposed results.

Needle Driver Control for a Robotic MIS Suturing System

Autonomous robotic suturing has attracted research attention for years. Few results have shown the performance of an integrated robotic arm with a needle driver. This research introduces a coupling mechanism to connect a Da Vinci® large needle driver to a six-axis robotic arm. The motion of the needle driver wrist is treated as two additional motion degrees-of-freedom for the robot to simultaneously maintain the remote center-of-motion (RCM) and the needle path. The experiment employed the augmented state approach for the RCM generation and formulated the desired needle trajectory into the task control framework. This framework enables the implementation of a common robot controller. A trajectory correction procedure is also introduced to correct for the error resulted from the wrong gripper dimensions. With the proposed system, the experimental results on a training phantom show a successful tracking of the predefined suturing path.

State Estimation for Multirate Measurements in the Presence of Integral Term and Variable Delay

Measurements in the process industry can arrive with fast or slow sampling rates. Fast measurements, such as flowrate and temperature, are sampled frequently and are obtained instantly after sampling. The slow measurements, which are usually related to chemical quality variables such as product composition, are sampled infrequently and have some delay due to laboratory analysis. Moreover, sample collection for laboratory analysis may extend over a significant time interval, and the slow measurements are actually functions of all the states during the sampling period. Our objective is to develop a multirate state estimation method for this situation. We propose two methods to solve the problem: the exact Bayesian approach and the augmented state approach. In the exact Bayesian approach, the algorithm is developed by implementing the Bayes rule. In the augmented state approach, the system is reformulated by augmenting the current state with past information required for fusing the slow measurements and then applying general state estimation procedures. The performance of the proposed methods for state estimation is demonstrated through simulation and experimental studies and by comparison with methods that only use the fast measurements.

Robust integrated covariance intersection fusion Kalman estimators for networked systems with random measurement delays, multiplicative noises, and uncertain noise variances

SummaryIn this article, the robust distributed fusion Kalman filtering problems are addressed for the networked mixed uncertain multisensor systems with random one‐step measurement delays, multiplicative noises, and uncertain noise variances. A new augmented state approach with fictitious measurement noises modeled by the first‐order moving average models is presented, by which the original system is transformed into a standard uncertain system only with uncertain‐variance fictitious white noises. Based on the minimax robust estimation principle and Kalman filtering theory, a universal integrated covariance intersection (ICI) fusion approach is presented in the sense that first of all the robust local estimators and their conservative error variances and crosscovariances are presented, and then integrating the local estimation information yields ICI fusers. An extended Lyapunov equation approach with two kinds of Lyapunov equations is presented in order to prove the robustness and to compute fictitious noise statistics. Applying these approaches, the minimax robust local, ICI, and fast ICI fused Kalman estimators (predictor, filter, and smoother) are presented, such that for all admissible uncertainties, their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds. Their robustness, accuracy relations, and convergence are also proved. The proposed ICI fusers improve the robust accuracies and overcome the drawbacks of the original covariance intersection fusers, such that the robust local estimators and their conservative variances are assumed to be known, and their conservative crosscovariances are ignored. Two simulation examples applied to the offshore platform system verify their correctness, effectiveness, and applicability.

Robust centralized and integrated covariance intersection fusion Kalman estimators for networked mixed‐uncertain systems

SummaryFor networked mixed uncertain time‐varying systems with uncertain noise variances, random one‐step measurement delay, state‐dependent and noise‐dependent multiplicative noises, and linearly dependent additive white noises, the robust local, centralized, and distributed fusion estimation problems are addressed. Three new approaches are presented, which include a new augmented state approach with fictitious white noises, an extended Lyapunov equation approach with two Lyapunov equations, and a universal integrated covariance intersection (ICI) fusion approach of integrating the minimax robust local Kalman estimators and their conservative cross‐covariances. They constitute a new important methodology of solving robust fusion estimation problems. Applying them, the local, centralized, and distributed ICI fusion time‐varying and steady‐state robust Kalman estimators (predictor, filter, and smoother) are presented in the sense that for all admissible uncertainties, their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds. Their robustness, convergence, and accuracy relations are proved. Specially, the proposed ICI fusers improve the robust accuracies of the original covariance intersection fusers, and overcome their drawbacks, such that the local estimators and their conservative variances are assumed to be known, and the conservative cross‐variances are ignored. A simulation example with application to a vehicle suspension system shows the effectiveness of the proposed approaches and results.

Robust fusion Kalman estimators for networked mixed uncertain systems with random one-step measurement delays, missing measurements, multiplicative noises and uncertain noise variances

For mixed uncertain multisensor networked systems simultaneously with four uncertainties including random one-step measurement delays, missing measurements, multiplicative noises and uncertain noise variances, three new approaches of solving robust fusion estimation problem are presented. They include augmented state approach with fictitious white noises, extended Lyapunov equation approach, and universal integrated covariance intersection (ICI) fusion approach. Applying them, the minimax robust local and five fused time-varying Kalman estimators (predictor, filter an smoother) are presented in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The five robust fusers include centralized fuser, fusers weighted respectively by matrices, diagonal matrices and scalars, and ICI fuser. Their robustness and accuracy relations are proved. The proposed approaches and results constitute an important methodology and a unified robust fusion Kalman filtering theory of solving the robust estimation problem. A simulation example applied to the vehicle suspension system shows their effectiveness and applicability.

Combined State-Parameter Estimation with the LETKF for Convective-Scale Weather Forecasting

AbstractWe investigate the feasibility of addressing model error by perturbing and estimating uncertain static model parameters using the localized ensemble transform Kalman filter. In particular we use the augmented state approach, where parameters are updated by observations via their correlation with observed state variables. This online approach offers a flexible, yet consistent way to better fit model variables affected by the chosen parameters to observations, while ensuring feasible model states. We show in a nearly operational convection-permitting configuration that the prediction of clouds and precipitation with the COSMO-DE model is improved if the two-dimensional roughness length parameter is estimated with the augmented state approach. Here, the targeted model error is the roughness length itself and the surface fluxes, which influence the initiation of convection. At analysis time, Gaussian noise with a specified correlation matrix is added to the roughness length to regulate the parameter spread. In the northern part of the COSMO-DE domain, where the terrain is mostly flat and assimilated surface wind measurements are dense, estimating the roughness length led to improved forecasts of up to 6 h of clouds and precipitation. In the southern part of the domain, the parameter estimation was detrimental unless the correlation length scale of the Gaussian noise that is added to the roughness length is increased. The impact of the parameter estimation was found to be larger when synoptic forcing is weak and the model output is more sensitive to the roughness length.

Robust Weighted Fusion Kalman Estimators for Networked Multisensor Mixed Uncertain Systems With Random One-Step Sensor Delays, Uncertain-Variance Multiplicative, and Additive White Noises

For networked multisensor systems with mixed uncertainties, including random one-step sensor delays, multiplicative noises and uncertain noise variances, a new augmented state approach with the fictitious noises is presented, by which the original system model is transformed into one without sensor delays and only with white noises. An extended Lyapunov equation approach with two Lyapunov equations is presented, which is applied to prove the robustness of the estimators. According to the minimax robust estimation principle, based on the worst-case system with conservative upper bounds of uncertain noise variances, the four weighted fusion robust time-varying and steady-state Kalman estimators (predictor, filter and smoother) are presented in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Their robustness and accuracy relations are proved, and their convergence in a realization is proved by the dynamic error system analysis (DESA) method. Specially, the presented modified robust covariance intersection (CI) fuser has higher robust accuracy than the original one. A simulation example applied to the uninterruptible power system (UPS) shows the effectiveness of the proposed approaches and results.

Consensus-Based Filter for Distributed Sensor Networks with Colored Measurement Noise.

Consensus filtering is an effective method for distributed state estimation of distributed sensor networks and the assumption of white measurement noise is widely used. However, when the measurement noise is colored, the traditional consensus filter cannot work well. In this paper, we first propose a consensus-based distributed filter for colored measurement noise by augmenting the state to include the colored measurement noise. To improve the efficiency of the filter, only local colored measurement noise is integrated into the augmented state for each local filter. Furthermore, another consensus-based distributed filter based on measurement differencing scheme is developed to eliminate the ill-conditioned computations of the augmented state approach. In addition, this method does not need to augment the state and thus has lower dimension than the augmented state filter. Simulation results demonstrate the superiority of the proposed methods.

Robust weighted fusion time-varying Kalman smoothers for multisensor system with uncertain noise variances

This paper addresses the design of robust weighted fusion time-varying Kalman smoothers for multisensor time-varying system with uncertain noise variances by the augmented state approach. According to the minimax robust estimation principle and the unbiased linear minimum variance (ULMV) optimal estimation rule, the six robust weighted fusion time-varying Kalman smoothers are presented based on the worst-case conservative system with the conservative upper bounds of noise variances. The actual smoothing error variances of each fuser are guaranteed to have a minimal upper bound for all admissible uncertainties. Their robustness is proved by the Lyapunov equation approach. Their robust accuracy relations are analyzed and proved. Specially, the corresponding steady-state robust Kalman smoothers are also presented for multisensor time-invariant system, and the convergence in a realization between the time-varying and steady-state robust Kalman smoothers is proved by the dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A simulation example is given to verify the robustness and robust accuracy relations.

Data Assimilation for a Coupled Ocean–Atmosphere Model. Part II: Parameter Estimation

Abstract The parameter estimation problem for the coupled ocean–atmosphere system in the tropical Pacific Ocean is investigated using an advanced sequential estimator [i.e., the extended Kalman filter (EKF)]. The intermediate coupled model (ICM) used in this paper consists of a prognostic upper-ocean model and a diagnostic atmospheric model. Model errors arise from the uncertainty in atmospheric wind stress. First, the state and parameters are estimated in an identical-twin framework, based on incomplete and inaccurate observations of the model state. Two parameters are estimated by including them into an augmented state vector. Model-generated oceanic datasets are assimilated to produce a time-continuous, dynamically consistent description of the model’s El Niño–Southern Oscillation (ENSO). State estimation without correcting erroneous parameter values still permits recovering the true state to a certain extent, depending on the quality and accuracy of the observations and the size of the discrepancy in the parameters. Estimating both state and parameter values simultaneously, though, produces much better results. Next, real sea surface temperatures observations from the tropical Pacific are assimilated for a 30-yr period (1975–2004). Estimating both the state and parameters by the EKF method helps to track the observations better, even when the ICM is not capable of simulating all the details of the observed state. Furthermore, unobserved ocean variables, such as zonal currents, are improved when model parameters are estimated. A key advantage of using this augmented-state approach is that the incremental cost of applying the EKF to joint state and parameter estimation is small relative to the cost of state estimation alone. A similar approach generalizes various reduced-state approximations of the EKF and could improve simulations and forecasts using large, realistic models.

Kalman estimation with brownian disturbances

In this paper we consider a dynamical system with a state and an output disturbances which are Brownian motions. Two solutions to the problem of state estimation from output observations are proposed. The first one is based on the augmented state approach and the second is based on the prefiltering approach. The performance obtained is illustrated by some theoretical and simulation results.