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Microalgae reactors provide an efficient and clean alternative for the production of biofuels, nutritional and cosmetic bioproducts, wastewater treatment, and mitigation of industrial gases to reduce greenhouse gas emissions. The main control objective in these systems is productivity optimisation. For this reason, real-time monitoring of key biological performance indicators affecting microalgae production such as microalgae growth rate, biomass concentration, dissolved oxygen, pH level or total inorganic carbon is crucial. However, there are no sufficiently robust solutions on the market to estimate or measure all of these variables, especially for open reactors on an industrial scale. This paper presents a new online state estimator, based on a robust sliding mode observer combined with a nonlinear dynamic model endowed with a minimum number of states to capture dynamics of key biological performance indicators. This soft-sensor has been verified with a realistic reactor model that has been experimentally tested. Simulations showed promising results in terms of accuracy (with mean values of the state estimation errors in the order of 10−4 g m −3 for the biomass concentration, 10−5 to 10−13 mol m −3 for the other states and deviations in the order of 10−4 g m −3 for the biomass concentration, 10−5 to 10−10 mol m −3 for the other states) and robustness with respect to signal noise, state deviations, initial errors and parametric uncertainty. • Architecture and design of a soft-sensor for industrial raceway photobioreactor. • Sliding modes techniques for on-line robust monitoring main biological indicators. • Proposal and verification of a reduced model as mathematical reactor replica. • Soft-sensor tested by simulation with a experimentally verified reactor model. [ABSTRACT FROM AUTHOR]

In this paper a novel adaptive control algorithm is used to stabilize the line of sight (LOS) for a high contrast coronagraph instrument used for imaging of exoplanets. The algorithm successfully rejects broadband drift caused by simulated spacecraft motion, moving tonal disturbances caused by reaction wheel harmonics and fixed tones caused by the laboratory environment. Performance below 200 microarcseconds RMS per channel was validated in a ground based prototype of the flight instrument. At the heart of the control is a robust implementation of the filtered-X least mean squares (RLMS) algorithm that accounts for uncertainty in the frequency location of the harmonic disturbances. This uncertainty is caused by poor tachometer telemetry from the spacecraft. A wheel speed estimator is used to reduce this uncertainty before the wheel speed information is fed to the control. The LOS is sensed with a low order wavefront sensor (LOWFS) that translates Zernike phase distortions (Z2,Z3-Z11) across the pupil into pixel intensities. The feedback portion of the control optimally balances in-band jitter from the sensing noise with the attenuated broadband drift while the robust LMS filter targets the tonal disturbances. A fast steering mirror (FSM) is used to correct the first two Zernike components, Z2 and Z3, which correspond to LOS. A special low noise chopping amplifier is used to drive three FSM piezo stack actuators with local feedback from strain gauges. A model of the amplifier with piezo hysteresis is also described. [ABSTRACT FROM AUTHOR]

This paper develops an active sensing and estimation system for protecting the rider of an e-scooter from car-scooter collisions. The objective is to track the trajectories of cars behind the e-scooter and predict any real-time danger of car-scooter collision. If the danger of a collision is predicted, then a loud car-horn-like audio warning is sounded to alert the car driver to the presence of the scooter. A low-cost (∼$100) single-beam laser sensor is chosen for measuring the positions of cars behind the scooter. The sensor is mounted on a stepper motor and the region behind the scooter is scanned to detect vehicles. Once a vehicle is detected, its trajectory is tracked in real-time by using feedback control to focus the orientation of the laser sensor such as to make measurements of the right front corner of the vehicle. A nonlinear vehicle model and a nonlinear observer are used to estimate the trajectory variables of the tracked car. The estimated states are used in a receding horizon controller that controls the real-time position of the laser sensor to focus on the vehicle. The developed system is implemented on a Ninebot e-scooter platform. Extensive experiments conducted with multiple vehicle maneuvers show that the closed-loop system is able to accurately track vehicle trajectories and provide audio alerts to prevent collisions. This paper constitutes the first-ever development of active rider protection technology for the protection of e-scooters. [ABSTRACT FROM AUTHOR]

This article introduces the special issue on 'Estimated Truths' which investigates the role of estimation in knowledge-making about water and, through it, contributes to thinking place as environment in the historical geography and history of knowledge. It argues that while historical geographers and historians of science have paid much attention to precision and quantification, approximation and estimation have also played an important role in knowledge-making and deserve more attention. It discusses the roles played by uncertainty and estimation in the water sciences and makes the case for more sustained engagement with the influence of the environment – understood as a dynamic set of human and non-human actors and forces – on knowledge-making. Finally, the article presents the five papers and discusses their individual and collective contributions to the themes of the special issue and to further investigation into the making and operation of estimated truths. • Introduces the five articles of the 'Estimated Truths' special issue. • Highlights the role of approximation and estimation in knowledge-making. • Emphasizes the persistence of uncertainty and estimation in the water sciences. • Shows the value of taking into account the role of place as environment in shaping science. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we study the statistical estimation of the Gerber–Shiu function in the compound Poisson risk model perturbed by diffusion. This problem has been solved in [32] by the Fourier–Sinc series expansion method. Different from [32] , we use the Laguerre series to expand the Gerber–Shiu function and propose a relevant estimator. The estimator is easily computed and has fast convergence rate. Various simulation studies are presented to confirm that the estimator performs well when the sample size is finite. [ABSTRACT FROM AUTHOR]

[Display omitted] • Diffusion editing CPMG measurements have important industrial applications. • The conventional processing technique wastes much of the available signal. • New techniques are presented that use all of the available signal. • The new techniques improve the accuracy of diffusion-relaxation map estimation. Two dimensional diffusion and transverse ( T 2 ) NMR relaxation measurements are effective for a variety of research and industrial processes. Conversion of the measurements into a D - T 2 map is performed using an inverse integral transformation. A difficulty with D - T 2 estimation from data acquired without pulsed field gradients (using, for example, the inherent static field gradient of a single-sided magnet) is that the diffusion and relaxation kernels are coupled. One commonly used solution is to introduce a time offset to enable the kernels to be decoupled, but this has the undesirable results of causing some of the data, and a large proportion of the signal energy, to become unusable. This paper presents two methods of processing the data that do not require this wastage. Both methods are based on insights that arise from considering the linear operator that describes the forwards integral transformation. One method involves data compression, while the other method is an application (that we call FLINT) of the fast iterative soft thresholding algorithm. Both methods are able to use all of the available data. The paper demonstrates the improved accuracy that results from these methods on simulated data, as well as the improved discovery of important features on measured data. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to monitoring rotor blade flap, lead-lag and pitch using an embedded gyroscope and symmetrically mounted MEMS accelerometers. The central hypothesis is that differential accelerometer measurements are proportional only to blade motion; fuselage acceleration and blade bending are inherently compensated for. The inverse kinematic relationships (from blade position to acceleration and angular rate) are derived and simulated to validate this hypothesis. An algorithm to solve the forward kinematic relationships (from sensor measurement to blade position) is developed using these simulation results. This algorithm is experimentally validated using a prototype device. The experimental results justify continued development of this kinematic estimation approach. [ABSTRACT FROM AUTHOR]

In this paper we address the problem of estimating θ1 when Yi∼indN(θi,σi2), i=1,2, are observed and |θ1−θ2|⩽c for a known constant c. Clearly Y2 contains information about θ1. We show how the so-called weighted likelihood function may be used to generate a class of estimators that exploit that information. We discuss how the weights in the weighted likelihood may be selected to successfully trade bias for precision and thus use the information effectively. In particular, we consider adaptively weighted likelihood estimators where the weights are selected using the data. One approach selects such weights in accord with Akaike''s entropy maximization criterion. We describe several estimators obtained in this way. However, the maximum likelihood estimator is investigated as a competitor to these estimators along with a Bayes estimator, a class of robust Bayes estimators and (when c is sufficiently small), a minimax estimator. Moreover we will assess their properties both numerically and theoretically. Finally, we will see how all of these estimators may be viewed as adaptively weighted likelihood estimators. In fact, an over-riding theme of the paper is that the adaptively weighted likelihood method provides a powerful extension of its classical counterpart. [Copyright &y& Elsevier]

Most existing ESC (Electronic Stability Control) systems rely on the measurement of both yaw rate and sideslip angle. However, one of the main issues is that the sideslip angle cannot be measured directly because the sensors are too expensive. For this reason, sideslip angle estimation has been widely discussed in the relevant literature. The modeling of sideslip angle is complex due to the non-linear dynamics of the vehicle. In this paper, we propose a novel observer based on ANFIS, combined with Kalman Filters in order to estimate the sideslip angle, which in turn is used to control the vehicle dynamics and improve its behavior. For this reason, low-cost sensor measurements which are integrated into the actual vehicle and executed in real time have to be used. The ANFIS system estimates a “pseudo-sideslip angle” through parameters which are easily measured, using sensors equipped in actual vehicles (inertial sensors and steering wheel sensors); this value is introduced in UKF in order to filter noise and to minimize the variance of the estimation mean square error. The estimator has been validated by comparing the observed proposal with the values provided by the CARSIM model, which is a piece of experimentally validated software. The advantage of this estimation is the modeling of the non-linear dynamics of the vehicle, by means of signals which are directly measured from vehicle sensors. The results show the effectiveness of the proposed ANFIS+UKF-based sideslip angle estimator. [ABSTRACT FROM AUTHOR]

Let S 1 , S 2 , … , S k be survival functions of life distributions. They are said to be uniformly stochastically ordered, S 1 ≤ u s o S 2 ≤ u s o ⋯ ≤ u s o S k , if S i / S i + 1 is a survival function for 1 ≤ i ≤ k − 1 . The nonparametric maximum likelihood estimators of the survival functions subject to this ordering constraint are known to be inconsistent in general. Consistent estimators were developed only for the case of k = 2 . In this paper we provide consistent estimators in the k -sample case, with and without censoring. In proving consistency, we needed to develop a new algorithm for isotonic regression that may be of independent interest. [ABSTRACT FROM AUTHOR]

• A new technique for estimating the basic reproduction number from large counts data. • Qualitative properties of the SEIR deterministic system are exploited in estimation. • The model consists of paired non homogeneous Poisson processes. • The statistical analysis is based on a generalized linear model methodology. • The method is promising as a comparative tool in data analysis. In this paper, we propose an easy to implement generalized linear models (GLM) methodology for estimating the basic reproduction number, R 0 , a major epidemic parameter for assessing the transmissibility of an infection. Our approach rests on well known qualitative properties of the classical SIR and SEIR systems for large populations. Moreover, we assume that information at the individual network level is not available. In inference we consider non homogeneous Poisson observation processes and mainly concentrate on epidemics that spread through a completely susceptible population. Further, we examine the performance of the estimator under various scenarios of relevance in practice, like partially observed data. We perform a detailed simulation study and illustrate our approach on Covid-19 Canadian data sets. Finally, we present extensions of our methodology and discuss its merits and practical limitations, in particular the challenges in estimating R 0 when mitigation measures are applied. [ABSTRACT FROM AUTHOR]

Abstract: The cylinder pressure is arguably the most important variable characterizing the combustion process in internal combustion engines. In light of the recent advances in combustion technologies and in engine control, the use of cylinder pressure is now frequently considered as a feedback signal for closed-loop combustion control algorithms. In order to generate an accurate pressure trace for real-time combustion control and diagnostics, the output of the in-cylinder pressure transducer must be conditioned with signal processing methods to mitigate the well-known issues of offset and noise. While several techniques have been proposed for processing the cylinder pressure signal with limited computational burden, most of the available methods still require one to apply low-pass filters or moving average windows in order to mitigate the noise. This ultimately limits the opportunity of exploiting the in-cylinder pressure feedback for a cycle-by-cycle control of the combustion process. To this extent, this paper presents an estimation algorithm that extracts the pressure signal from the in-cylinder sensor in real-time, allowing for estimating the 50% burn rate location and IMEP on a cycle-by-cycle basis. The proposed approach relies on a model-based estimation algorithm whose starting point is a crank-angle based engine combustion model that predicts the in-cylinder pressure from the definition of a burn rate function. Linear parameter varying (LPV) techniques are then used to expand the region of estimation to cover the engine operating map, as well as allowing for real-time cylinder estimation during transients. The estimator is tested on the experimental data collected on an engine dynamometer as well as on a high-fidelity engine simulator. The results obtained show the effectiveness of the estimator in reconstructing the cylinder pressure on a crank-angle basis and in rejecting measurement noise and modeling errors, with considerably low computation effort. [Copyright &y& Elsevier]

Abstract: In a low-cost attitude heading reference system (AHRS), the measurements made by MEMS inertial and magnetic sensors are affected by large parameter uncertainties, stochastic noises and unknown disturbances. In this paper, considering the robustness of the sliding mode observers (SMO) against both structured and unstructured uncertainties as well as exogenous inputs, the process of design and implementation of a nonlinear SMO is proposed for a low-cost AHRS. For simultaneous estimation of orientation variables and calibration biases of gyroscopes, a nonlinear and non-affine model of the AHRS is considered. Therefore, based on the Lie-algebraic method, the estimation algorithm is designed for a general class of non-affine nonlinear MIMO systems. In the proposed observer, owing to decreasing the required assumptions for coordinate transformation in recent literatures, the design process of the SMO is simplified. The gain matrices of the proposed SMO are obtained through ensuring the stability and the convergence of estimation errors based on Lyapunov''s direct method. The expected tracking performance of the robust state and parameter estimation algorithm compared to that of the extended Kalman filter (EKF) is evaluated through simulations and real experiments of a strapped AHRS on a ground vehicle. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a framework of outer product least squares for covariance (COPLS) to directly estimate covariance in the growth curve model based on an analogy, between the outer product of a data vector and covariance of a random vector, and the ordinary least squares technique. The COPLS estimator of covariance has an explicit expression and is shown to have the following properties: (1) following a linear transformation of two independent Wishart distribution for a normal error matrix; (2) having asymptotic normality for a nonnormal error matrix; and (3) having unbiasedness and invariance under a linear transformation group. And, a corresponding two-stage generalized least squares (GLS) estimator for the regression coefficient matrix in the model is obtained and its asymptotic normality is investigated. Simulation studies confirm that the COPLS estimator and the two-stage GLS estimator of the regression coefficient matrix are satisfying competitors with some evident merits to the existing maximum likelihood estimator in finite samples. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: There are many ways to measure the dispersion of a random variable. One such method uses the concept of peakedness. If the random variable is symmetric about a point , then Birnbaum [Z.W. Birnbaum, On random variables with comparable peakedness, The Annals of Mathematical Statistics 19 (1948) 76–81] defined the function , as the peakedness of . If two random variables, and , are symmetric about the points and , respectively, then is said to be less peaked than , denoted by , if for all , i.e.,  is stochastically larger than . For normal distributions this is equivalent to variance ordering. Peakedness ordering can be generalized to the case where and are arbitrary points. However, in this paper we study the comparison of dispersions in two continuous random variables, symmetric about their respective medians, using the peakedness concept where normality, and even moment assumptions are not necessary. We provide estimators of the distribution functions under the restriction of symmetry and peakedness ordering, show that they are consistent, derive the weak convergence of the estimators, compare them with the empirical estimators, and provide formulas for statistical inferences. An example is given to illustrate the theoretical results. [Copyright &y& Elsevier]

Abstract: This paper obtains conditions for minimaxity of hierarchical Bayes estimators in the estimation of a mean vector of a multivariate normal distribution. Hierarchical prior distributions with three types of second stage priors are treated. Conditions for admissibility and inadmissibility of the hierarchical Bayes estimators are also derived using the arguments in Berger and Strawderman [Choice of hierarchical priors: admissibility in estimation of normal means, Ann. Statist. 24 (1996) 931–951]. Combining these results yields admissible and minimax hierarchical Bayes estimators. [Copyright &y& Elsevier]

Abstract: In this paper we consider different least-squares-based approaches for estimating the complex Young''s modulus and the complex Poisson''s ratio of a viscoelastic material using a longitudinal wave propagation experiment. We present a statistical analysis of different estimation approaches and compare their performances. The analytical covariance expressions are validated using experimental data. [Copyright &y& Elsevier]

Abstract: The estimation of the covariance matrix or the multivariate components of variance is considered in the multivariate linear regression models with effects being fixed or random. In this paper, we propose a new method to show that usual unbiased estimators are improved on by the truncated estimators. The method is based on the Stein–Haff identity, namely the integration by parts in the Wishart distribution, and it allows us to handle the general types of scale-equivariant estimators as well as the general fixed or mixed effects linear models. [Copyright &y& Elsevier]

With the advent of event-related paradigms in functional MRI, there has been interest in finding the optimal stimulus timing, especially when the interstimulus interval is varied during the imaging run. Previous works have proposed stimulus timings to optimize either the estimation of the impulse response function (IRF) or the detection of signal changes. The purpose of this paper is to clarify that estimation and detection are fundamentally different goals and to determine the optimal stimulus timing and distribution with respect to both the accuracy of estimating the IRF and the power of detection assuming a particular hemodynamic model. Simulated stimulus distributions are varied systematically, from traditional blocked designs to rapidly varying event related designs. These simulations indicate that estimation of the hemodynamic impulse response function is optimized when stimuli are frequently alternated between task and control states, with shorter interstimulus intervals and stimulus durations, whereas the detection of activated areas is optimized by blocked designs. The stimulus timing for a given experiment should therefore be generated with the required detectability and estimation accuracy. [Copyright &y& Elsevier]

• We compare continuous and discrete numerical representations in numerosity judgements. • Occam's razor makes different predictions for these two forms of representation. • These predictions are tested using both experiments and model fitting. • Both empirical and computational results suggest the use of continuous formats. • Learners appear to rely on innate over acquired numerical representations. Previous research has established that numeric estimates are based not just on perceptual data but also past experience, and so may be influenced by the form of this stored information. It remains unclear, however, how such experience is represented: numerical data can be processed by either a continuous analogue number system or a discrete symbolic number system, with each predicting different generalisation effects. The present paper therefore contrasts discrete and continuous prior formats within the domain of numerical estimation using both direct comparisons of computational models of this process using these representations, as well as empirical contrasts exploiting different predicted reactions of these formats to uncertainty via Occam's razor. Both computational and empirical results indicate that numeric estimates commonly rely on a continuous prior format, mirroring the analogue approximate number system, or 'number sense'. This implies a general preference for the use of continuous numerical representations even where both stimuli and responses are discrete, with learners seemingly relying on innate number systems rather than the symbolic forms acquired in later life. There is however remaining uncertainty in these results regarding individual differences in the use of these systems, which we address in recommendations for future work. [ABSTRACT FROM AUTHOR]

• Simultaneous estimation of torque, speed and axial translation in rotating shafts. • Novel hardware and algorithm allows decoupled estimation of axial translation and torque. • Simulations confirm accuracy of estimates based on timing measurements. • Experiments reveal that estimation accuracy improves with axial translation compensation. This paper focuses on the development and experimental demonstration of a unique non-contacting Variable Reluctance (VR) sensor system that enables simultaneous estimation of torque, speed, and axial translation in high-speed rotating shafts. A novel tooth geometry is introduced featuring alternating slants on every third tooth of an otherwise standard toothed wheel. A novel torque and axial processing (TAP) algorithm allows axial translation to be extracted from the VR sensor measurements. Simulations confirm shaft speed, torque, and axial translation can be accurately estimated based on timing measurements. Experiments conducted on a high-speed driveshaft further validate the TAP approach and reveal that the accuracy of shaft torque estimation improves significantly with axial translation compensation. [ABSTRACT FROM AUTHOR]