Discrete-time Measurements Research Articles

Kinematic motion models based vessel state estimation to support advanced ship predictors

Advanced ship predictors can generally be considered as a vital part of the decision-making process of autonomous ships in the future, where the information on vessel maneuvering behavior can be used as the source of information to estimate current vessel motions and predict future behavior precisely. As a result, the navigation safety of autonomous vessels can be improved. In this paper, vessel maneuvering behavior consists of continuous-time system states of two kinematic motion models—the Curvilinear Motion Model (CMM) and Constant Turn Rate & Acceleration (CTRA) Model. Two state estimation algorithms—the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are implemented on these two models with certain modifications so that they can be compatible with discrete-time measurements. Four scenarios, created by combining different models and algorithms, are implemented using simulated ship maneuvering data from a bridge simulator. These scenarios are then verified through the proposed stability and consistency tests. The simulation results show that the EKF tends to be unstable combined with the CMM. The estimates from the other three scenarios can generally be considered more stable and consistent, unless sudden actions or variations in vessel heading occurred during the simulation. The CTRA is also proven to be more robust compared to the CMM. As a result, a suitable combination of mathematical models and estimation filters can be considered to support advanced ship predictors in future ship navigation.

Apparatus for Automated Continuous Hydrogen Deuterium Exchange Mass Spectrometry Measurements from Milliseconds to Hours.

Hydrogen deuterium exchange mass spectrometry (HDX-MS) is a rapidly growing technique for protein characterization in industry and academia, complementing the "static" picture provided by classical structural biology with information about the dynamic structural changes that accompany biological function. Conventional hydrogen deuterium exchange experiments, carried out on commercially available systems, typically collect 4-5 exchange timepoints on a timescale ranging from tens of seconds to hours using a workflow that can require 24 h or more of continuous data collection for triplicate measurements. A small number of groups have developed setups for millisecond timescale HDX, allowing for the characterization of dynamic shifts in weakly structured or disordered regions of proteins. This capability is particularly important given the central role that weakly ordered protein regions often play in protein function and pathogenesis. In this work, we introduce a new continuous flow injection setup for time-resolved HDX-MS (CFI-TRESI-HDX) that allows automated, continuous or discrete labeling time measurements from milliseconds to hours. The device is composed almost entirely of "off-the-shelf" LC components and can acquire an essentially unlimited number of timepoints with substantially reduced runtimes compared to conventional systems.

A two-state Markov chain model for slug flow in horizontal ducts

Intermittent flows are common flow patterns in gas–liquid horizontal flow and attract attention and great research effort due to its importance for industrial and engineering applications. The slug flow is typically modelled based on a unit cell varying from an elongated air bubble with a liquid film in segregated flow pattern and an aerated liquid plug, the slug region, with remarkable stochastic characteristics of its alternating regions. In this paper, a two-state Markov chain model is proposed to represent the stochastic dynamics of developed slug flow in horizontal pipes. Each state represents either the liquid slug or the elongated bubble regions and the transition probabilities dictate the change of the given discrete time measurement to stay at a given state or change. This simple but insightful description of the phenomenon allows an analytical treatment of the statistics of Markov chain stochastic process. Measurement stations with two double wire resistive sensors are used to obtain the void fraction time series and a corresponding two-state representation. Each state is classified by a threshold defined by an unsupervised and non-parametric pattern recognition approach. The state transition matrix is then estimated for each corresponding experimental point. Thus random samples can be synthetically regenerated with the same statistical features of the corresponding measurements. It is shown that the Markov chain model can successfully represent second-order statistics of the measurement, such as the autocorrelation and power spectral density, given an appropriate choice of the chain order. Moreover, a cross correlation-based time delay estimation is proposed for the two-sensor measurement station and additional information is obtained from the slug flow. Subsequently, statistics of some slug flow features are estimated using the proposed approach and their interpretation as random variables derived from the void fraction stochastic process is discussed.

Continuous–Discrete Time Neural Network Observer for Nonlinear Dynamic Systems Application to Vehicle Systems

This paper proposes a novel continuous-discrete (sampled data) time neural network (NSNN) observer for nonlinear systems. It can therefore be applied to systems with a high degree of non-linearity with no prior knowledge of the system dynamics. The proposed observer is a three-layer feedforward neural network that has been intensively trained using the error backpropagation learning algorithm, which includes an e-modification term to ensure robustness of the observer. A structure of the output predictor with a corrective term is added in the structure of the NN observer to overcome the problem of discrete time measurement. Simulations using MATLAB and CarSim are illustrated to demonstrate the performance of the proposed state observer strategy to reconstruct the state variables and parameters of a vehicle system.

Quantification of Time-Domain Truncation Errors for the Reinitialization of Fractional Integrators

In recent years, fractional differential equations have received a significant increase in their use for modeling a wide range of engineering applications. In such cases, they are mostly employed to represent non-standard dynamics that involve long-term memory effects or to represent the dynamics of system models that are identified from measured frequency response data in which magnitude and phase variations are observed that could be captured either by low-order fractional models or high-order rational ones. Fractional models arise also when synthesizing CRONE (Commande Robuste d'Ordre Non Entier) and/or fractional PID controllers for rational or fractional systems. In all these applications, it is frequently required to transform the frequency domain representation into time domain. When doing so, it is necessary to carefully address the issue of the initialization of the pseudo state variables of the time domain system model. This issue is discussed in this article for the reinitialization of fractional integrators which arises among others when solving state estimation tasks for continuous-time systems with discrete-time measurements. To quantify the arising time-domain truncation errors due to integrator resets, a novel interval observer-based approach is presented and, finally, visualized for a simplified battery model.

Event-triggered interval-based state estimator for continuous-time linear systems

In this paper we propose an interval-based state estimator for continuous-time linear systems with discrete-time measurements using an event-triggered mechanism and an explicit reachability method. An output injection method combined with a state variables permutation procedure are applied to design the robust estimator. In addition, the convergence of the proposed set-membership state estimator and the existence of a lower bound on the inter-event times are shown. Throughout a numerical example, the performance of this estimator are illustrated and compared to related works.

Estimation of dynamic systems using a method of characteristics filter

This paper deals with the technical formulation and implementation details of an algorithm that provides an estimate of the probability density function of the state of a nonlinear dynamical system from discrete time measurements. In contrast to other state estimation methods that propagate the conditional moments, the proposed filter is shown to propagate and update the full probability density function of the state. Characteristic solutions to the Liouville equation are used to propagate the exact probability density values along the flow of the dynamical system. The reconstruction of the state probability density function is then posed as a convex programming problem. An adaptive regression-tree based region-decomposition approach is used to efficiently compute expectation integrals involved in implementing the Bayes rule associated with posterior density function. Numerical examples capturing the non-Gaussian nature of the uncertainty in the duffing oscillator problem and the two body problem are used to demonstrate the efficacy of the proposed methods.

Comparison of Several Filtering Approaches on Water Treatment Processes

This paper addresses the state estimation problem of a bioreactor in wastewater treatment processes. The state variables of this process are the concentrations of the organic pollutants and of the bacteria inside the bioreactor. A specific growth rate function is used to describe the variation of the bacteria concentration when the amount of pollutants increases. This rate can also represent the speed of the biological degradation of the pollutants. Most research work in this field uses only deterministic models that do not conveniently account for uncertainties. These models are often obtained using several simplifications during the modeling procedure such as neglecting the measurement noises. In this paper, we consider stochastic models and study the state estimation problem using three approaches: the Extended Kalman filter, the Unscented Kalman filter and the Particle filter. These methods are adapted to the models in study and compared to understand which is the most adequate for this type of processes considering their slow evolution, discrete time measurements and high-intensity noises. Further, we also apply a Multiple Model Adaptive method which adapts the filters to the correct growth rate type. This method is also used to automatically choose the most efficient estimation method for this type of biological processes.

Cover Feature: Parameter and state estimation of backers yeast cultivation with a gas sensor array and unscented Kalman filter.

DOI: 10.1002/elsc.202000058 Successful operation, control and optimization of biotechnological process depend on reliable real-time available measurements of the process variables. Although some hardware sensors are readily available, they often have several drawbacks: cost, sample destruction, discrete-time measurements, processing delay, sterilization, disturbances in the hydrodynamic conditions inside the bioreactor, etc. It is therefore of interest to use software sensors [29, 30]. The central idea behind a soft sensor is to use easily accessible on-line data for the estimation of other process variables that are either difficult to measure or only measured at low frequency [30]. The figure illustrates a software sensor for on-line monitoring of substrate and biomass production in backers yeast cultivation. For details see article DOI 10.1002/elsc.202000058 on page 169.

Time-Resolved Focused Ion Beam Microscopy: Modeling, Estimation Methods, and Analyses

In a focused ion beam (FIB) microscope, source particles interact with a small volume of a sample to generate secondary electrons that are detected, pixel by pixel, to produce a micrograph. Randomness of the number of incident particles causes excess variation in the micrograph, beyond the variation in the underlying particle-sample interaction. We recently demonstrated that joint processing of multiple time-resolved measurements from a single pixel can mitigate this effect of source shot noise in helium ion microscopy. This paper is focused on establishing a rigorous framework for understanding the potential for this approach. It introduces idealized continuous- and discrete-time abstractions of FIB microscopy with direct electron detection and estimation-theoretic limits of imaging performance under these measurement models. Novel estimators for use with continuous-time measurements are introduced and analyzed, and estimators for use with discrete-time measurements are analyzed and shown to approach their continuous-time counterparts as time resolution is increased. Simulated FIB microscopy results are consistent with theoretical analyses and demonstrate that substantial improvements over conventional FIB microscopy image formation are made possible by time-resolved measurement.

Robust nonlinear observer design based on impulsive dissipativity

The paper considers the design of a nonlinear dissipative impulsive observer based on non-periodic discrete-time measurements. Sufficient conditions are derived for (i) exponential convergence of the observer in absence of measurement uncertainty, and (ii) input-to-state stability (ISS) with respect to measurement uncertainty, by combining notions from impulsive and dissipative systems theory. The conditions mainly include constraints on the minimum and maximum time between measurements depending on system characteristics, the correction gain and the desired ISS gain. The results are illustrated with a numerical case example.

Simulating a Ground Truth for Transit Time Analysis of Indicator Dilution Curves

Abstract Transit times of a bolus through an organ can provide valuable information for researchers, technicians and clinicians. Therefore, an indicator is injected and the temporal propagation is monitored at two distinct locations. The transit time extracted from two indicator dilution curves can be used to calculate for example blood flow and thus provide the surgeon with important diagnostic information. However, the performance of methods to determine the transit time Δt cannot be assessed quantitatively due to the lack of a sufficient and trustworthy ground truth derived from in vivo measurements. Therefore, we propose a method to obtain an in silico generated dataset of differently subsampled indicator dilution curves with a ground truth of the transit time. This method allows variations on shape, sampling rate and noise while being accurate and easily configurable. COMSOL Multiphysics is used to simulate a laminar flow through a pipe containing blood analogue. The indicator is modelled as a rectangular function of concentration in a segment of the pipe. Afterwards, a flow is applied and the rectangular function will be diluted. Shape varying dilution curves are obtained by discrete-time measurement of the average dye concentration over different cross-sectional areas of the pipe. One dataset is obtained by duplicating one curve followed by subsampling, delaying and applying noise. Multiple indicator dilution curves were simulated, which are qualitatively matching in vivo measurements. The curves temporal resolution, delay and noise level can be chosen according to the requirements of the field of research. Various datasets, each containing two corresponding dilution curves with an existing ground truth transit time, are now available. With additional knowledge or assumptions regarding the detection-specific transfer function, realistic signal characteristics can be simulated. The accuracy of methods for the assessment of Δt can now be quantitatively compared and their sensitivity to noise evaluated.

Consensus of Continuous-Time Linear Multiagent Systems With Discrete Measurements.

This article concerns the robust consensus problem of continuous-time linear multiagent systems (MASs) with uncertainty and discrete-time measurement information, where the output measurement information is in the data-sampled form. Distributed output-feedback protocol with or without controller interaction is proposed for each agent. Specifically, the output-feedback protocol runs in continuous time with an output error correction term mixed with the discrete-time measurement information. The concrete algorithm is given for the construction of the feedback matrices. Then, by using the delay-input approach, sufficient conditions are provided for the robust consensus of this kind of MASs interacting over networks described by the directed graphs. Finally, numerical simulations are given to illustrate the theoretical results.

Observer-Based Decentralized Predictor Control for Large-Scale Interconnected Systems With Large Delays

This article proposes a decentralized predictor-based output feedback to compensate for large delays in large-scale interconnected systems under the premise that the interconnections between subsystems are not strong. The full state of each subsystem is assumed to be unmeasurable and the observer-based output feedback is employed. Two methods are used to tackle the large delays: the backstepping-based partial differential equation (PDE) approach and the reduction-based ordinary differential equation (ODE) approach. The PDE method is used for continuous-time control and manages with larger delays, whereas the ODE method is applicable to sampled-data implementation under discrete-time measurement.

Impulsive observer design for a class of nonlinear Lipschitz systems with time-varying uncertainties

In this paper, a nonlinear impulsive observer for a class of Lipschitz nonlinear systems with time-varying uncertainties is investigated. The observer uses discrete time measurements of the system output. A time-varying Lyapunov function is used to show that, under sufficient conditions based on linear matrix inequalities, the estimation error is globally practically stable at the origin. The dynamic observer is tested on an example to demonstrate the effectiveness of the proposed approach.

Long baseline navigation filter with clock offset estimation

In underwater navigation, the global positioning system is unavailable; hence, other solutions must be pursued in the development of navigation systems. In this paper, filters for the position, linear velocity, and acceleration of underwater vehicles are derived by combining a long baseline acoustic positioning system with an inertial navigation system. A dynamic model is devised via state augmentation, including the bias of the pseudo-ranges, which accounts for the effect of the unknown offset between the emitters’ and receivers’ clocks. With this technique, the resulting dynamics are linear, in spite of the original nonlinear nature of the problem. The proposed solution, which includes the explicit dynamic estimation of the bias of the pseudo-ranges, is a linear Kalman filter. The observability of the system is assessed, which allows to establish globally exponentially stable error dynamics. The performance of the solution is evaluated with realistic simulation results, considering sensor noise and discrete-time measurements. Finally, the comparison with the extended Kalman filter (EKF), the unscented Kalman filter (UKF), and the Bayesian Cramer–Rao bound is presented, including Monte Carlo simulations. This comparison shows the goodness of the proposed solution, which converges for all initial conditions and exhibits performance comparable to the EKF and the UKF, whereas the EKF and UKF are shown to lack global convergence.

Predictor methods for decentralized control of large-scale systems with input delays

This paper develops a decentralized predictor-based control for large-scale systems with large input delays under the premise that the interconnections between subsystems are not strong. The local controller operates independently. Given any large delays, the predictor which exponentially stabilizes each uncoupled system, will stabilize the coupled one provided that the coupling is not solid. We propose two methods for the delay compensation: the backstepping-based partial differential equation (PDE) approach and the reduction-based ordinary differential equation (ODE) approach. We present decentralized Lyapunov-based analysis under the two predictor methods. It appears that the first predictor method leads to simpler conditions and manages with larger delays, whereas the second is easily applied to decentralized asynchronous sampled-data implementation, both under continuous and under discrete-time measurements. Through a benchmark example of two coupled cart–pendulum systems, the proposed methods are demonstrated to be effective when the input delays are too large for the system to be stabilized without a predictor.

On Maximum Likelihood Estimation of Continuous-Time Oscillators Modelled as Continuous-Time Autoregressive System

In this paper, we address the problem of identifying a continuous-time oscillator. We use a continuous-time autoregressive model to represent the oscillators. We asume that only discrete-time measurements are available, from which we obtain the oscillator equivalent discrete-time model in terms of the continuous-time model parameters. We identify the model using the Maximum Likelihood method.

Dissolved oxygen level output feedback control based on discrete-time measurements during a Pseudomonas putida mt-2 fermentation

In this paper, the problem of controlling the dissolved oxygen level (DO) during an aerobic fermentation is considered. The proposed approach deals with three major difficulties in respect to the nonlinear dynamics of the DO, the poor accuracy of the empirical models for the oxygen consumption rate and the fact that only sampled measurements are available on-line. A nonlinear integral high-gain control law including a continuous-discrete time observer is designed to keep the DO in the neighborhood of a set point value without any knowledge on the dissolved oxygen consumption rate. The local stability of the control algorithm is proved using Lyapunov tools. The performance of the control scheme is first analyzed in simulation and then experimentally evaluated during a successfull fermentation of the bacteria over a period of three days. Pseudomonas putida mt-2.

A New Continuous Discrete Unscented Kalman Filter

The time and measurement update for the discrete time Kalman filter can be formulated in terms of conditional means and covariances. The unscented Kalman filter can be interpreted as calculating these conditional means and covariances by using the unscented transform. This approach can also be directly applied to nonlinear models as an alternative to the discrete time extended Kalman filter. In this paper, a novel method for computing the unscented Kalman filter for a nonlinear model with continuous time dynamics and discrete time measurements is presented. Compared to the existing approaches, this method is far simpler and less computationally demanding, and it performs at least as well.