Nonlinear state estimation for fermentation process using cubature Kalman filter to incorporate delayed measurements☆

State estimation of biological process variables directly influences the performance of on-line monitoring and op-timal control for fermentation process. A novel nonlinear state estimation method for fermentation process is proposed using cubature Kalman filter (CKF) to incorporate delayed measurements. The square-root version of CKF (SCKF) algorithm is given and the system with delayed measurements is described. On this basis, the sample-state augmentation method for the SCKF algorithm is provided and the implementation of the proposed algorithm is constructed. Then a nonlinear state space model for fermentation process is established and the SCKF algorithm incorporating delayed measurements based on fermentation process model is presented to implement the nonlinear state estimation. Finally, the proposed nonlinear state estimation methodology is applied to the state estimation for penicillin and industrial yeast fermentation processes. The simulation results show that the on-line state estimation for fermentation process can be achieved by the proposed method with higher esti-mation accuracy and better stability.     

Attitude estimation using high-grade gyroscopes

This paper addresses the problem of attitude estimation using the angular velocity of Earth as a reference vector. A nonlinear observer is proposed that evolves on the special orthogonal group and is aided by angular velocity readings containing implicit measurements of the Earth’s spin. Additionally, the observer resorts to body-fixed measurements of one constant inertial reference vector. The observer’s sole tuning parameter, shaped as a matrix gain, is computed from a time-varying Kalman filter strategically applied to a uniformly observable linear time-invariant system, which is obtained from the linearized rotation matrix error dynamics. The nonlinear observer is proved to be locally exponentially stable but, most noticeably, in spite of this local-based inception, a Monte Carlo simulation analysis demonstrates the good properties of the observer in terms of convergence rate, tuning capability, and large basin of attraction. Furthermore, extensive experimental results confirm the properties of the proposed technique and validate its usage in real world applications.     

Individual-based multi-objective optimal structured treatment interruption for HIV infection

In this paper, based on the measurable quantities from an individual patient that has infection to human immunodeficiency virus (HIV) and his/her condition is near to acquired immune deficiency syndrome (AIDS), individual-based multi-objective optimal treatments have been proposed. Firstly, the most effective parameters of the patient in computing Long-term non-progressor (LTNP) equilibrium are derived using global sensitivity analysis (GSA). To accomplish GSA effectively, Latin hypercube sampling (LHS) and partial rank correlation coefficients (PRCC) are utilized to rank each of the parameters based on each state of the 5-dimensional model. Then, these results are used by Dempster–Shafer (D–S) evidence theory (DSET) to rank the most effective parameters comprehensively. Now, these effective identified parameters are estimated using extended Kalman filter (EKF), which its covariance matrices are optimized based on particle swarm optimization (PSO) algorithm. Thus, the proposed methodology gives a calibrated model corresponding to the individual patient. Based on this calibrated model, the LTNP equilibrium related to the individual patient is derived. Using the derived individual-based LTNP equilibrium optimal structured treatment interruption (STI) strategies are extracted by defining suitable multi-objective optimization problem and solving it through using non-dominated sorting genetic algorithm-II (NSGA-II). The results demonstrate that the proposed optimal treatments are able to effectively reach LTNP equilibrium with using the minimum and maximum drug usage of 3.6% and 35.1% of full drug usage treatment. Meanwhile, the different optimal treatments give the decision-makers enough flexibility to choose the suitable treatment based on existing facilities and necessities.     

New version of continuous–discrete cubature Kalman filtering for nonlinear continuous–discrete systems

For nonlinear continuous–discrete systems, this paper elaborates a new accurate implementation of continuous–discrete cubature Kalman filter (CD-CKF). As the main contribution of this work, the new Kalman prediction stage begins by integrating the nonlinear continuous model for all the cubature sample vectors; the prior estimate state and covariance prediction are based on the weighted statistics of these integrated cubature sample vectors and the Gauss–Legendre approximation scheme. The new square root form CD-CKF is also derived and accurately implemented by combining with the modified variable stepsize NIRK. As the advantages of proposed approach, the complicated and error-prone processes of solving covariance differential equation or calculating derivatives are avoided, while the positive semi-definiteness of prior error covariance are numerically guaranteed. Simulations of traffic control scenarios further confirm the new approach’s superior filtering performance in both reliability and accuracy.     

Maximum likelihood estimation of noise covariance matrices for state estimation of autonomous hybrid systems

A critical aspect of developing Bayesian state estimators for hybrid systems, that involve a combination of continuous and discrete state variables, is to have a reasonably accurate characterization of the stochastic disturbances affecting their dynamics. Recently, Bavdekar et al. (2011) have proposed a maximum likelihood (ML) based framework for estimation of the noise covariance matrices from operating input–output data when an EKF is used for state estimation. In this work, the ML framework is extended to estimation of the noise covariance matrices associated with autonomous hybrid systems, and, to a wider class of recursive Bayesian filters. Under the assumption that the innovations generated by an estimator form a white noise sequence, the proposed ML framework computes the noise covariance matrices such that they maximize the log-likelihood function of the estimator innovations. The efficacy of the proposed scheme is demonstrated through the simulation and experimental studies on the benchmark three-tank system.     

A tutorial – game theory-based extended H infinity filtering approach to nonlinear problems in signal processing

In this paper, we provide a tutorial for the applications of “game-theory-based extended H infinity filtering (EHIF)” approach to various problems in disciplines of signal processing. The algorithm of this filtering approach is similar to that of the extended Kalman filtering (EKF). Since its invention, the Kalman filtering approach has been successfully and widely employed for many problems in scientific and engineering fields, e.g. target tracking, satellite systems, control, communications, etc. Therefore, the H infinity filtering approach also can be applied to all these problems. One big difference of EHIF from the EKF approach is that we apply it with unknown noise statistics of the state and measurement. In this tutorial, we introduce this non-well-known approach in spite of its practical usefulness, by providing the step by step algorithm with example problems of a number of signal processing disciplines. We also show that EHIF can outperform other approaches including the EKF that need to know the noise statistics in their applications, in some scenarios. By the contribution of this tutorial, we look forward to easy, and disseminative applications of EHIF to problems where, particularly, the EKF or particle filter could have been applied if noise statistics were known.     

Fusion of multifocus images by lattice structures

Image fusion methods based on multiscale transform (MST) suffer from high computational load due to the use of fast Fourier transforms (ffts) in the lowpass and highpass filtering steps. Lifting wavelet scheme which is based on second generation wavelets has been proposed as a solution to this issue. Lifting Wavelet Transform (LWT) is composed of split, prediction and update operations all implemented in the spatial domain using multiplications and additions, thus computation time is highly reduced. Since image fusion performance benefits from undecimated transform, it has later been extended to Stationary Lifting Wavelet Transform (SLWT). In this paper, we propose to use the lattice filter for the MST analysis step. Lattice filter is composed of analysis and synthesis parts where simultaneous lowpass and highpass operations are performed in spatial domain with the help of additions/multiplications and delay operations, in a recursive structure which increases robustness to noise. Since the original filter is designed for the undecimated case, we have developed undecimated lattice structures, and applied them to the fusion of multifocus images. Fusion results and evaluation metrics show that the proposed method has better performance especially with noisy images while having similar computational load with LSWT based fusion method.     

Distributed Kalman filter for linear system with complex multi-channel stochastic uncertain parameter and decoupled local filters

This article considers a distributed Kalman filtering problem for linear system contaminated by complex multi-channel random uncertain parameter in which a number of nodes cooperative without central coordination to estimate a common state based on local measurements and data received from neighbors. We propose an approach to eliminate this error propagation. The proposed local filters are guaranteed to be stable under some mild conditions on certain global structural data, and their fusion yields the centralized Kalman estimate. Then, we extend this method to smoothing and deconvolution algorithm. Finally, simulation experiments demonstrate the validity of the proposed approach.     

Limit behaviors of extended Kalman filter as a parameter estimator for a sinusoidal signal

In this note, the basic limit behaviors of the solution to Riccati equation in the extended Kalman filter as a parameter estimator for a sinusoidal signal are analytically investigated by using lim sup and lim inf in advanced calculus. We show that if the covariance matrix has a limit, then it must be a zero matrix.     

Decentralized damage detection of seismically-excited buildings using multiple banks of Kalman estimators

Natural hazards result in ill-conditioned structures with unfavorable damage. To early recognize damage existence, structures can be screened by damage detection methods after a critical hazard event. These damage detection methods are often developed based on a centralized acquiring and computing system that challenges the feasibility of deployment in a large-scale structure. Decentralized damage detection methods alter a single system to multiple subsystems that allow spatially distributing in a structure and yield comparable performance with the centralized approach. In this study, a decentralized damage detection method based on modal prediction errors via multiple banks of Kalman estimators is proposed. First, a sensor network is comprised of multiple subsystems over a structure of which the subsystems have overlapped sensing nodes. These subsystems are individually identified by an input–output frequency-domain system identification method under ambient vibrations. The identified models are then converted into several banks of Kalman estimators, and the estimators generate the estimation of structural modal responses. The prediction errors are calculated from the differentiation between measured and estimated modal responses, and the accumulated standard deviations of modal prediction errors serve as the damage indices for recognizing the damage occurrence, locations, and levels. A numerical example is introduced to demonstrate the proposed method as well as to evaluate the detection effectiveness. Moreover, the proposed method is also experimentally verified by a scaled twin-tower building using shake table testing. The experimental results indicate that the proposed method is quite effective to inform damage of structures in terms of damage occurrence, locations, and levels.