Estimation Error Research Articles

Sampled-data observer design for sensorless control of wind energy conversion system with PMSG

This paper presents a nonlinear observer for a variable-speed wind energy conversion system (WECS) utilizing a permanent magnet synchronous generator (PMSG). The study addresses the design of high-gain sampled-data observers based on the nonlinear WECS model, supported by formal convergence analysis. An essential aspect of this observer design is the incorporation of a time-varying gain, significantly enhancing system performance. Convergence of estimation errors is demonstrated using the input-to-state stability method. Simulation of the proposed observer is conducted using the MATLAB-Simulink tool. The obtained results are presented and analyzed to showcase the overall effectiveness of the proposed system.

Mapping geodetically inferred Antarctic ice surface height changes into thickness changes: a sensitivity study

Abstract. Determining recent Antarctic ice volume changes from satellite altimeter measurements of ice surface height requires a correction for contemporaneous vertical crustal deformation. This correction must consider two main sources of crustal deformation: (1) ongoing glacial isostatic adjustment (GIA), that is, the deformational, gravitational, and rotational response to Late Pleistocene and Holocene ice and ocean mass changes and (2) modern ice mass change. In this study, we seek to quantify the uncertainties associated with each of these corrections. Corrections of ice surface height changes for correction 1 have generally involved the adoption of global models of GIA defined by some preferred combination of ice history and mantle viscoelastic structure. We have computed the GIA correction generated from a coupled ice sheet–sea level model and a realistic Earth model incorporating three-dimensional viscoelastic structure. Integrating the difference between this correction and those from recent GIA analyses widely adopted in the literature yields an uncertainty in total present-day ice volume change equivalent to approximately 10 % of Antarctic ice mass loss inferred for the period 2010–2020. This reinforces earlier work indicating that ice histories characterized by relatively high excess ice volume at the Last Glacial Maximum may be introducing a significant error in estimates of modern melt rates. Regarding correction 2, a spatially invariant scaling has commonly been used to convert GIA-corrected ice surface height changes obtained from satellite altimetry to ice volume estimates. We adopt modeling results based on a projection of Antarctic ice mass change over the period 2015–2055 to demonstrate a spatial variability in the scaling of up to 10 % across the ice sheet. Furthermore, using these calculations, we find a systematic error of ∼ 3 % in the projected net ice volume change, with most of the difference arising in areas of West Antarctica above mantle zones of low viscosity.

An improved canopy interception scheme into biogeochemical model for precise simulation of carbon and water fluxes in subtropical coniferous forest

The process-based Biome-BGC (Biome Biogeochemical Cycles) model is widely used to simulate the fluxes of carbon and water of terrestrial ecosystems. While exhibiting excellent performance in simulating carbon cycle processes, this model provides a relatively simple simulation of the water cycle processes, particularly in canopy interception, which may result in significant errors in evapotranspiration (ET) and soil moisture estimations. This study initially refined the temporal scale of the original Biome-BGC model from a daily scale to an hourly scale, and then incorporated a theoretical interception module into the hourly-scale model for correcting canopy interception algorithm, to enhance the accuracy of hydrological processes simulations. The modified model was tested using the half-hourly observed meteorological and eddy covariance flux data at the Qianyanzhou subtropical coniferous forest site. In comparison with the original daily-scale model, simulations from the hourly-scale model showed better agreement with measurements at Qianyanzhou forest site, with 30.61 % and 40.92 % lower annual average gross primary productivity (GPP) and ET simulations. Although the accuracy of GPP and ET simulations did not show a significant improvement after canopy interception correction, it notably enhanced the accuracy of canopy interception and soil moisture simulations. The canopy interception rates were 55.8 % and 44.1 % for the original daily-scale and hourly-scale model, obviously overstimated compared with canopy correction simulation (31.1 %), leading to a significant underestimation of runoff. The canopy interception and runoff simulations after interception correction were proven relatively more reasonable. Additionally, the coefficient of determination (R2) for measured vs simulated soil water content (SWC) were 0.38, 0.51 and 0.60 for the original daily-scale, hourly-scale, and canopy interception correction simulations respectively, with a notable improvement in accuracy. This study suggested that improvements in temporal scale and canopy interception for process-based biogeochemical model can provide a better understanding of the carbon and water exchanges in response to instantaneous meteorological conditions and support improved water resource management.

Multi-mode vehicle pose estimation under different GNSS conditions

The integrated navigation system combining the global navigation satellite system (GNSS) and inertial navigation system (INS) is a crucial method for pose estimation in the field of autonomous driving technologies. Nevertheless, the accuracy of pose estimation is severely compromised when GNSS signals are obstructed or disrupted. To address this issue, this study introduces a multi-mode pose estimation framework designed to ensure accurate pose estimation even under unstable GNSS conditions. By integrating vehicle kinematics model that considers steering characteristics (VKMSC) and the convolutional neural network-long short-term memory (CNN-LSTM) neural network (NN) model into various estimation modes, the framework enhances the robustness of the integrated navigation system against signal interference. The system dynamically selects the optimal estimation strategy based on the degree of GNSS signal disruption. The proposed method has been validated through real-vehicle experiments, which demonstrate its efficacy in providing precise pose estimation across a spectrum of interference scenarios. Under the multipath and non-line-of-sight (MP/NLOS) mode, compared to the integrated navigation system and the fusion of traditional vehicle kinematic models, the proposed method improved positional estimation accuracy by 61.8 % and 19.7 %, respectively. In GNSS outage mode, the proposed method increased the estimation accuracy by 36.5 % and 12.0 %, respectively, compared to the INS navigation system assisted by the VKMSC and CNN-LSTM network model. The proposed method effectively reduces pose estimation errors in the integrated navigation system during interference and suppresses data fluctuations, thereby enhancing the system's precision and robustness.

CRT-Based Clock Synchronization for Millimeter-Wave Communication with Asymmetric Propagation Delays

The rapid advancement of millimeter-wave communication technology has presented new challenges for time synchronization, driven by the need for high-speed and low-latency data transmission. Ethernet synchronization technologies, such as Precise Time Protocol (PTP), have emerged to overcome the limitations of point-to-point architecture and enable precise synchronization across multiple devices. A key drawback of conventional PTP is its reliance on symmetric packet exchange delays, which may not hold in real-world scenarios where there is relative mobility between master and slave nodes, leading to asymmetric propagation delays and clock offset errors. To address this issue, a novel clock synchronization protocol that integrates Chinese Remainder Theory (CRT) has been proposed. This protocol enhances conventional PTP by incorporating distance estimation based on CRT using multi-carrier phase measurement. By combining a coarse estimation of one-way propagation delay from conventional PTP with a fine estimation of remainder distance from CRT, the protocol accurately determines the distance between master and slave nodes, reducing motion errors and enhancing clock synchronization accuracy. Simulation results indicate that the Root Mean Square Error (RMSE) of distance estimation remains below 10−5 m, with a corresponding motion time error of approximately 0.01 picosecond.

Deep Learning Segmentation of Ascites on Abdominal CT Scans for Automatic Volume Quantification.

"Just Accepted" papers have undergone full peer review and have been accepted for publication in Radiology: Artificial Intelligence. This article will undergo copyediting, layout, and proof review before it is published in its final version. Please note that during production of the final copyedited article, errors may be discovered which could affect the content. Purpose To evaluate the performance of an automated deep learning method in detecting ascites and subsequently quantifying its volume in patients with liver cirrhosis and ovarian cancer. Materials and Methods This retrospective study included contrast-enhanced and noncontrast abdominal-pelvic CT scans of patients with cirrhotic ascites and patients with ovarian cancer from two institutions, National Institutes of Health (NIH) and University of Wisconsin (UofW). The model, trained on The Cancer Genome Atlas Ovarian Cancer dataset (mean age, 60 years ± 11 [SD]; 143 female), was tested on two internal (NIH-LC and NIH-OV) and one external dataset (UofW-LC). Its performance was measured by the Dice coefficient, standard deviations, and 95% confidence intervals, focusing on ascites volume in the peritoneal cavity. Results On NIH-LC (25 patients; mean age, 59 years ± 14; 14 male) and NIH-OV (166 patients; mean age, 65 years ± 9; all female), the model achieved Dice scores of 85.5% ± 6.1% (CI: 83.1%-87.8%) and 82.6% ± 15.3% (CI: 76.4%-88.7%), with median volume estimation errors of 19.6% (IQR: 13.2%-29.0%) and 5.3% (IQR: 2.4%- 9.7%), respectively. On UofW-LC (124 patients; mean age, 46 years ± 12; 73 female), the model had a Dice score of 83.0% ± 10.7% (CI: 79.8%-86.3%) and median volume estimation error of 9.7% (IQR: 4.5%-15.1%). The model showed strong agreement with expert assessments, with r2 values of 0.79, 0.98, and 0.97 across the test sets. Conclusion The proposed deep learning method performed well in segmenting and quantifying the volume of ascites in concordance with expert radiologist assessments. ©RSNA, 2024.

Multivariate Hydrological Modeling Based on Long Short-Term Memory Networks for Water Level Forecasting

In the Department of Chocó, flooding poses a recurrent and significant challenge due to heavy rainfall and the dense network of rivers characterizing the region. However, the lack of adequate infrastructure to prevent and predict floods exacerbates this situation. The absence of early warning systems, the scarcity of meteorological and hydrological monitoring stations, and deficiencies in urban planning contribute to the vulnerability of communities to these phenomena. It is imperative to invest in flood prediction and prevention infrastructure, including advanced monitoring systems, the development of hydrological prediction models, and the construction of hydraulic infrastructure, to reduce risk and protect vulnerable communities in Chocó. Additionally, raising public awareness of the associated risks and encouraging the adoption of mitigation and preparedness measures throughout the population are essential. This study introduces a novel approach for the multivariate prediction of hydrological variables, specifically focusing on water level forecasts for two hydrological stations along the Atrato River in Colombia. The model, utilizing a specialized type of recurrent neural network (RNN) called the long short-term memory (LSTM) network, integrates data from hydrological variables, such as the flow, precipitation, and level. With a model architecture featuring four inputs and two outputs, where flow and precipitation serve as inputs and the level serves as the output for each station, the LSTM model is adept at capturing the complex dynamics and cross-correlations among these variables. Validation involves comparing the LSTM model’s performance with linear and nonlinear Autoregressive with Exogenous Input (NARX) models, considering factors such as the estimation error and computational time. Furthermore, this study explores different scenarios for water level prediction, aiming to utilize the proposed approach as an effective flood early warning system.

Using Geostationary Satellite Observations to Improve the Monitoring of Vegetation Phenology

Geostationary satellite data enable frequent observations of the Earth’s surface, facilitating the rapid monitoring of land covers and changes. However, optical signals over vegetation, represented by the vegetation index (VI), exhibit an anisotropic effect due to the diurnal variation in the solar angle during data acquisition by geostationary satellites. This effect, typically characterized by the bi-directional reflectance distribution function (BRDF), can introduce uncertainties in vegetation monitoring and the estimation of phenological transition dates (PTDs). To address this, we investigated the diurnal variation in the normalized difference vegetation index (NDVI) with solar angles obtained from geostationary satellites since the image had fixed observation angles. By establishing a temporal conversion relationship between instantaneous NDVI and daily NDVI at the local solar noon (LSNVI), we successfully converted NDVIs obtained at any time during the day to LSNVI, increasing cloud-free observations of NDVI by 34%. Using different statistics of the time series vegetation index, including LSNVI, daily averaged NDVI (DAVI), and angular corrected NDVI (ACVI), we extracted PTD at five typical sites in China. The results showed a difference of up to 41.5 days in PTD estimation, with the highest accuracy achieved using LSNVI. The use of the proposed conversion approach, utilizing time series LSNVI, reduced the root mean square error (RMSE) of PTD estimation by 9 days compared with the use of actual LSNVI. In conclusion, this study highlights the importance of eliminating BRDF effects in geostationary satellite observations and demonstrates that the proposed angular normalization method can enhance the accuracy of time series NDVI in vegetation monitoring.

Adaptive fixed-time fuzzy fault-tolerant control for robotic manipulator with unknown friction and composite actuator faults

This paper exploits the issue of fixed-time (FT) tracking control (TC) for uncertain robotic manipulator systems (RMS) with composite actuator faults (CAFs), unknown disturbances and joint friction. The fuzzy logic system (FLS) algorithm is introduced to fit the unknown uncertainties including unmodeled parameters, CAFs and joint friction of the RMS, after which a relevant updating algorithm is employed to generate the unidentified boundary of the plant disturbance and FLS approximation error. Then a novel adaptive fuzzy sliding mode (SM) fault-tolerant controller is synthesized, which not only guarantees the boundedness of estimation errors of the involved adaptive parameters, but also actualizes the reachability of the predevised sliding surface. Furthermore, the proof that the system trajectories can achieve the FT convergence to the expected position signals, is then provided on account of the FT stability theory. Ultimately, simulation experiments exhibit the rationality based upon the current control algorithm.

Sampling for Remote Estimation of the Wiener Process over an Unreliable Channel

In this paper, we study a sampling problem where a source takes samples from a Wiener process and transmits them through a wireless channel to a remote estimator. Due to channel fading, interference, and potential collisions, the packet transmissions are unreliable and could take random time durations. Our objective is to devise an optimal causal sampling policy that minimizes the long-term average mean square estimation error. This optimal sampling problem is a recursive optimal stopping problem, which is generally quite difficult to solve. However, we prove that the optimal sampling strategy is, in fact, a simple threshold policy where a new sample is taken whenever the instantaneous estimation error exceeds a threshold. This threshold remains a constant value that does not vary over time. By exploring the structure properties of the recursive optimal stopping problem, a low-complexity iterative algorithm is developed to compute the optimal threshold. This work generalizes previous research by incorporating both transmission errors and random transmission times into remote estimation. Numerical simulations are provided to compare our optimal policy with the zero-wait and age-optimal policies.

Adaptive synergetic control for electronic throttle valve system

AbstractThis study has developed adaptive synergetic control (ASC) algorithm to control the angular position of moving plate in the electronic throttle valve (ETV) system. This control approach is inspired by synergetic control theory. The adaptive controller has addressed the problem of variation in systems parameters. The control design includes two elements: the control law and adaptive law. The adaptive law is developed based on Lyupunov stability analysis of the controlled system, and it is responsible for estimating the potential uncertainties in the system. The effectiveness of the proposed adaptive synergetic control has been verified by numerical simulation using MATLAB/Simulink. The results showed that the ASC algorithm could give good tracking performance in the presence of uncertainty perturbations. In addition, a comparison study has been made to compare the tracking performance of ASC and that based on conventional synergetic control (CSC) for the ETV system. The simulated results showed that the performance of ASC outperforms that based on CSC. Moreover, the results showed that the estimation errors between the actual and estimated uncertainties are bounded and there is no drift in the developed adaptive law of ASC.

Estimating the Total and Regional Body Fat of Physically Active Men Is Not Appropriate for Sedentary Men

Objectives. The reliability of predictive body fat equations remains unclear due to their inappropriate use across different subject cohorts and conditions. The objective of this study was to validate and cross-validate equations to predict total and regional body fat in young physically active males. Material and methods. Three hundred and five young male participants were divided into the following groups: active validation (n=165), active cross-validation (n=70), or sedentary cross-validation ones (n=70). The study used a stratified random sampling based on weekly physical activity level. The total and regional body fat mass were measured using dual-energy X-ray absorptiometry (DEXA) after an overnight fast. Simultaneous measurements of height, body mass, skinfold thickness, body mass index, and body circumferences were taken. The total and regional body fat predictive equations were generated using multiple linear stepwise regression models. The coefficient of determination (R²) and standard error of estimation (SEE) were calculated to examine the accuracy of the predictive equations. Furthermore, cross-validation groups were analysed. Results. The percentage of total body fat, trunk fat, legs fat, arms fat, and body mass index of active cross-validation were found to be significantly lower than in the sedentary cross-validation groups. The total body fat percentage was highly associated with abdominal skinfold thickness (R=0.68-0.74, P<0.001), body mass index (R=0.55, P<0.001), and suprailiac skinfold thickness (R=0.67-0.71, P<0.001) in the active validation group. The predictive total and regional body fat equations of physically active men showed adjusted R² values ranging from 0.35 to 0.66, with standard error of estimation values between 2.74 to 4.35%. The standard error of estimation for the predictive percentage of total and regional body fat in the active cross-validation group was lower than in the sedentary cross-validation group. Conclusions. The findings demonstrate that new predictive total and regional body fat equations can be used to accurately estimate body fat in healthy young active males under fast conditions.

Nonlinear disturbance observer-based finite-time prescribed performance control for MSVs with input saturation

ABSTRACT A finite-time prescribed performance control scheme based on an improved nonlinear disturbance observer is proposed for tracking the trajectory of marine surface vessels (MSVs) under the disturbance of the marine environment. The objective of this paper is to design a nonlinear disturbance observer based on state estimation error feedback that accurately estimates and compensates for the unknown disturbance problem. An adaptive law is applied to estimate the upper bound of its error, removing the requirement of a priori knowledge of the unknown lumped disturbance upper bound. This paper also introduces a non-logarithmic performance function in order to efficiently solve the problem of considering both transient and steady state MSVs performance simultaneously. In addition, the adaptive dynamic system is introduced to overcome the adverse effects caused by nonlinear saturation factors for the input-constrained problem. With this control strategy, the system output error converges to a pre-defined region within a finite amount of time and meets the prescribed performance requirements. Finally, simulation and comparison verify the control scheme's effectiveness and superiority.

Layer Selection for Subtraction and Concatenation: A Method for Visual Velocity Estimation of a Mobile Robot

Kinematic information such as position, velocity, and acceleration is critical to determine the three-dimensional state of the robot in space. In this study, it is aimed to estimate as visual the linear and angular velocity of a mobile robot. Additionally, another aim of this study is to determine the suitability of the concatenation or subtraction layer in the Convolutional Neural Network (CNN) that will make this estimate. For these purposes, first, a simulation environment was created. 9000 pairs of images and necessary velocity information were collected from this simulation environment for training. Similarly, 1000 pairs of images and velocity information were gathered for validation. Four different CNN models were designed and these models were trained and tested using these datasets. As a result of the test, the lowest average error for linear velocity estimation was calculated as 0.93e-3m/s and angular velocity estimation was measured as 4.37e-3rad/s. It was observed that the results were sufficient for linear and angular velocity prediction according to statistical analysis of errors. In addition, it was observed that the subtraction layer can be used instead of the concatenation layer in the CNN architectures for hardware-limited systems. As a result, visual velocity estimation of mobile robots has been achieved with this study and the framework of CNN models has been drawn for this problem.

Mapping intracellular NAD content in entire human brain using phosphorus-31 MR spectroscopic imaging at 7 Tesla.

Nicotinamide adenine dinucleotide (NAD) is a crucial molecule in cellular metabolism and signaling. Mapping intracellular NAD content of human brain has long been of interest. However, the sub-millimolar level of cerebral NAD concentration poses significant challenges for in vivo measurement and imaging. In this study, we demonstrated the feasibility of non-invasively mapping NAD contents in entire human brain by employing a phosphorus-31 magnetic resonance spectroscopic imaging (31P-MRSI)-based NAD assay at ultrahigh field (7 Tesla), in combination with a probabilistic subspace-based processing method. The processing method achieved about a 10-fold reduction in noise over raw measurements, resulting in remarkably reduced estimation errors of NAD. Quantified NAD levels, observed at approximately 0.4 mM, exhibited good reproducibility within repeated scans on the same subject and good consistency across subjects in group data (2.3 cc nominal resolution). One set of higher-resolution data (1.0 cc nominal resolution) unveiled potential for assessing tissue metabolic heterogeneity, showing similar NAD distributions in white and gray matter. Preliminary analysis of age dependence suggested that the NAD level decreases with age. These results illustrate favorable outcomes of our first attempt to use ultrahigh field 31P-MRSI and advanced processing techniques to generate a whole-brain map of low-concentration intracellular NAD content in the human brain.

Rapid Mass Conversion for Environmental Microplastics of Diverse Shapes.

Rivers have been recognized as the primary conveyors of microplastics to the oceans, and seaward transport flux of riverine microplastics is an issue of global attention. However, there is a significant discrepancy in how microplastic concentration is expressed in field occurrence investigations (number concentration) and in mass flux (mass concentration). Of urgent need is to establish efficient conversion models to correlate these two important paradigms. Here, we first established an abundant environmental microplastic dataset and then employed a deep neural residual network (ResNet50) to successfully separate microplastics into fiber, fragment, and pellet shapes with 92.67% accuracy. We also used the circularity (C) parameter to represent the surface shape alteration of pellet-shaped microplastics, which always have a more uneven surface than other shapes. Furthermore, we added thickness information to two-dimensional images, which has been ignored by most prior research because labor-intensive processes were required. Eventually, a set of accurate models for microplastic mass conversion was developed, with absolute estimation errors of 7.1, 3.1, 0.2, and 0.9% for pellet (0.50 ≤ C < 0.75), pellet (0.75 ≤ C ≤ 1.00), fiber, and fragment microplastics, respectively; environmental samples have validated that this set is significantly faster (saves ∼2 h/100 MPs) and less biased (7-fold lower estimation errors) compared to previous empirical models.

Distribution-informed and wavelength-flexible data-driven photoacoustic oximetry.

Photoacoustic imaging (PAI) promises to measure spatially resolved blood oxygen saturation but suffers from a lack of accurate and robust spectral unmixing methods to deliver on this promise. Accurate blood oxygenation estimation could have important clinical applications from cancer detection to quantifying inflammation. We address the inflexibility of existing data-driven methods for estimating blood oxygenation in PAI by introducing a recurrent neural network architecture. We created 25 simulated training dataset variations to assess neural network performance. We used a long short-term memory network to implement a wavelength-flexible network architecture and proposed the Jensen-Shannon divergence to predict the most suitable training dataset. The network architecture can flexibly handle the input wavelengths and outperforms linear unmixing and the previously proposed learned spectral decoloring method. Small changes in the training data significantly affect the accuracy of our method, but we find that the Jensen-Shannon divergence correlates with the estimation error and is thus suitable for predicting the most appropriate training datasets for any given application. A flexible data-driven network architecture combined with the Jensen-Shannon divergence to predict the best training data set provides a promising direction that might enable robust data-driven photoacoustic oximetry for clinical use cases.

Variance-Reduced Accelerated First-Order Methods: Central Limit Theorems and Confidence Statements

In this paper, we consider a strongly convex stochastic optimization problem and propose three classes of variable sample-size stochastic first-order methods: (i) the standard stochastic gradient descent method, (ii) its accelerated variant, and (iii) the stochastic heavy-ball method. In each scheme, the exact gradients are approximated by averaging across an increasing batch size of sampled gradients. We prove that when the sample size increases at a geometric rate, the generated estimates converge in mean to the optimal solution at an analogous geometric rate for schemes (i)–(iii). Based on this result, we provide central limit statements, whereby it is shown that the rescaled estimation errors converge in distribution to a normal distribution with the associated covariance matrix dependent on the Hessian matrix, the covariance of the gradient noise, and the step length. If the sample size increases at a polynomial rate, we show that the estimation errors decay at a corresponding polynomial rate and establish the associated central limit theorems (CLTs). Under certain conditions, we discuss how both the algorithms and the associated limit theorems may be extended to constrained and nonsmooth regimes. Finally, we provide an avenue to construct confidence regions for the optimal solution based on the established CLTs and test the theoretical findings on a stochastic parameter estimation problem. Funding: This work was supported by the Office of Naval Research [Grant N00014-22-1-2589] and Basic Energy Sciences [Grant DE-SC0023303]. The work of J. Lei was partially supported by the National Natural Science Foundation of China [Grants 72271187 and 62088101]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/moor.2021.0068 .

An Interactive Transient Model Correction Active Sonar Target Tracking Method

Active sonar can usually only directly measure the distance and bearing information of underwater targets, and cannot directly obtain target velocity, acceleration and other information. Therefore, the amount of information is relatively small, making it difficult to support the construction of complex motion models. At the same time, the motion state of underwater maneuvering targets is changeable. In response to the problem of detecting and tracking underwater moving targets by active sonar, this paper proposes a target transient model correction (TMC) filtering tracking method. Based on the conventional Kalman filter (KF) estimation, residual covariance is used as a signal quantity. When there is a large change in it, a transient filter with constant gain is adopted to filter the measurement value. The filtered output is used to correct the KF gain matrix and the target motion state model, to avoid the problem of increasing or even diverging KF estimation errors caused by changes in process noise. Using this method can solve the problem of maintaining stability and filtering estimation accuracy of active sonar tracking of underwater maneuvering targets with less computational and engineering costs.

Ensemble forecasting: A foray of dynamics into the realm of statistics

AbstractUncertain quantities are often described through statistical samples. Can samples for numerical weather forecasts be generated dynamically? At a great expense, they can. With statistically constrained perturbations, a cloud of initial states is created and then integrated forward in time. By now, this technique has become ubiquitous in weather and climate research and operations. Ensembles are widely used, with demonstrated value. The atmosphere evolves in a multidimensional phase space. Does a cloud of ensemble solutions encompass the evolution of the real atmosphere? Theoretically, random perturbations in high‐dimensional spaces have negligible projection in any direction, including the error in the best estimate, therefore consistently degrading that. As the bulk of the perturbation variance lies in the null space of error, samples in multidimensional space do not contain reality. An evaluation suggests that initial and short‐range forecast error and ensemble perturbations are random draws from a high‐dimensional domain we call the subspace of possible error. Error in any initial condition is partly a result of stochastic observational and assimilation noise, while perturbations explore other, mostly independent directions from the subspace of possible error that may have resulted from other configurations of stochastic noise. What benefits may arise from the deterministic projection of such noise? Consistent with theoretical expectations, ensemble members consistently degrade the skill of the unperturbed forecast until medium range. The mean and all other products derived from ensembles suffer an 18‐hour loss in forecast Information. Since Information is a sufficient statistic, any rational user can benefit more from the unperturbed, than from an ensemble of weather forecasts. Furthermore, case‐dependent variations in the distribution or spread of ensembles have no impact on commonly used metrics. Can alternative, statistical applications provide comparable, or even higher‐quality probabilistic and other products, at the fraction of the cost of running an ensemble?