Unconstrained Estimation Research Articles

9D Rotation Representation-SVD Fusion with Deep Learning for Unconstrained Head Pose Estimation

Abstract Accurately estimating human head pose poses a significant challenge across various application domains. To address the inherent limitations of previous approaches, this research proposes an unconstrained head pose estimation strategy. The method combines deep learning with rotation matrices, utilizing nine-dimensional vectors output by the neural network, which are projected back to rotation matrices in SO (3) space through singular value decomposition. This ensures both the smoothness and uniqueness of the rotation representation. The approach demonstrates distinct advantages in handling the rotation estimation task, particularly when the rotated representation is used as the model output. It not only avoids the discontinuity and double-coverage issues associated with prior methods but also enhances the stability of the representation in high-dimensional space, thereby improving the learning process. Additionally, the geodesic loss function is incorporated to train the network. The proposed strategy surpasses previous state-of-the-art methods, as evidenced by experiments conducted on the AFLW2000 and BIWI datasets.

Estimating catch within integrated stock assessments: Distinguishing truth from error in sparse-spike data

Collecting accurate information on catch levels from marine recreational fishing can be challenging and often results in highly uncertain estimates of landings and discards. Sparse spikes are a common characteristic of these data, with isolated values much higher (e.g., 2–4 times) the surrounding values in a time series of annual estimates. In many cases, it is unclear whether these spikes represent observation error or true, even if anomalous, values. Utilizing multiple data sources simultaneously, integrated stock assessment models may be able to distinguish truth from error in sparse-spike catch estimates, however this supposition has not been well tested. Here, we developed a simulation study to elucidate conditions under which an integrated stock assessment model might perform well (or poorly) when confronted with sparse-spike catch estimates. We found that unconstrained estimation could distinguish truth from error in anomalous values, but only under specific conditions of supporting data. If the anomaly is known to be biased high, estimated catches can get closer to the true value. If the error mechanism is unknown, our results suggest that the true underlying value of a sparse spike is only recoverable when other input data are highly accurate, primarily a reliable index of abundance, but also age composition data in the same year.

Dual-Stream Fusion Network with ConvNeXtV2 for Pig Weight Estimation Using RGB-D Data in Aisles.

In the field of livestock management, noncontact pig weight estimation has advanced considerably with the integration of computer vision and sensor technologies. However, real-world agricultural settings present substantial challenges for these estimation techniques, including the impacts of variable lighting and the complexities of measuring pigs in constant motion. To address these issues, we have developed an innovative algorithm, the moving pig weight estimate algorithm based on deep vision (MPWEADV). This algorithm effectively utilizes RGB and depth images to accurately estimate the weight of pigs on the move. The MPWEADV employs the advanced ConvNeXtV2 network for robust feature extraction and integrates a cutting-edge feature fusion module. Supported by a confidence map estimator, this module effectively merges information from both RGB and depth modalities, enhancing the algorithm's accuracy in determining pig weight. To demonstrate its efficacy, the MPWEADV achieved a root-mean-square error (RMSE) of 4.082 kg and a mean absolute percentage error (MAPE) of 2.383% in our test set. Comparative analyses with models replicating the latest research show the potential of the MPWEADV in unconstrained pig weight estimation practices. Our approach enables real-time assessment of pig conditions, offering valuable data support for grading and adjusting breeding plans, and holds broad prospects for application.

Assessment of the double-parameter iterative Tikhonov regularization for single-epoch measurement model-based precise GNSS positioning

The double-parameter iterative Tikhonov regularization is assessed for strengthening the single-epoch model-based precise GNSS positioning within the framework of cognitive meanings. The simultaneous iterative Tikhonov regularization of the least-squares (LS) estimators of the parameters of interest in the single-epoch GNSS model is analyzed to enhance their accuracy properties. Regularization parameters (RP) are collected in the regularization operator, which can play a standardizing role in the regularization principle. Thus, the double-parameter approach can consider the heteroscedasticity of the LS estimators of interest in the regularization principle. This approach employs the quality-based mean squared error (mse) matrix trace minimization criterion to select optimal double-RP values simultaneously. Then, the unconstrained LS estimation is iteratively regularized, obtaining regularized float solutions. The numerical tests indicate that the double-parameter approach successfully strengthens the single-epoch GNSS measurement models due to considering the heteroscedasticity of the LS estimators of interest in the regularization principle. The regularized variance–covariance (vc) matrix describes float solutions of improved precision properties at the cost of losing the LS estimator’s unbiasedness. The accuracy is thus superior in the sense of mse. Therefore, the regularized LS estimator is well-scaled but with a biased localization. It also provides a more peaked probability density function (PDF) of real-valued ambiguities, obtaining a lower failure rate (FR) of integer least-squares (ILS) ambiguity resolution (AR). In this way, the regularized ILS estimator performs well in the ambiguity domain with the presence of regularized bias.

Improved lumped electrical characteristic modeling and adaptive forgetting factor recursive least squares-linearized particle swarm optimization full-parameter identification strategy for lithium-ion batteries considering the hysteresis component effect

Electric vehicles, as a new green mode of transportation, have put forward higher demand indicators for accurate modeling and efficient parameter identification strategies for lithium-ion batteries. In this paper, a lumped electrical characteristic model is constructed for lithium-ion batteries considering the hysteresis component effect based on a proposed adaptive forgetting factor recursive least squares-linearized particle swarm optimization (AFFRLS-LPSO) algorithm with strong working condition characterization capability for full parameter identification. First, to characterize the relationship accurately and intuitively between the external characteristics and the internal state quantities of the battery, the charging and discharging measurement information is captured, and the difference in the open circuit voltage (OCV) caused by the hysteresis phenomenon is resolved. Then, the complex working condition experiments is conducted, and through online inspection of experimental data, the fusion strategy concept is introduced to prevent the phenomenon of “filter saturation” and improve the ability of the algorithm to track the variable characteristic parameters of the battery. The full parameter identification results and terminal voltage tracking effects under different identification strategies are compared. Also, the consistency verification results of the adaptive parameter identification strategy under different working conditions are further analyzed. The experimental results show that the voltage tracking error of the model with an added hysteresis component is significantly smaller than the error without hysteresis. Furthermore, at an ambient temperature of 15 °C, the root mean squared error and mean absolute percentage error of the AFFRLS-LPSO algorithm are reduced by 0.0037 V and 0.300 %, respectively, under the dynamic stress test and Beijing bus dynamic stress test working conditions, and the consistency accuracy of the unconstrained parameter estimation is improved by 9.9 %. The fusion strategy provides a theoretical basis for real-time parameter identification models for lithium-ion batteries with high precision and adaptability for electric vehicles.

Distributed state estimation with state equality constraints in the presence of packet dropping

In this paper, we investigate distributed Kalman consensus filter with state equality constraints in the presence of packet dropping. Firstly, the unconstrained distributed Kalman filter is designed by utilizing the local measurement information of each sensor node, and then the consensus term is added to it to derive the unconstrained distributed Kalman consensus filter. Secondly, we research the equality constrained distributed Kalman consensus filter based on the projection operator to achieve better filter performance, where the unconstrained estimation gain is calculated by solving a modified algebraic Riccati equation and a Lyapunov equation. Additionally, we design the second type of equality constrained distributed Kalman consensus filter by using time-stamping technology and projection operator to eliminate the effect of the Lyapunov equation in the infinite time domain on the convergence analysis, and its unconstrained estimation gain only requires solving a modified algebraic Riccati equation. Finally, the simulation experiments demonstrate that the equality constrained distributed Kalman consensus filter outperforms the unconstrained filter and that the second type of estimator exhibits superior performance compared to the first.

Monotone response surface of multi-factor condition: estimation and Bayes classifiers.

We formulate the estimation of monotone response surface of multiple factors as the inverse of an iteration of partially ordered classifier ensembles. Each ensemble (called PIPE-classifiers) is a projection of Bayes classifiers on the constrained space. We prove the inverse of PIPE-classifiers (iPIPE) exists, and propose algorithms to efficiently compute iPIPE by reducing the space over which optimisation is conducted. The methods are applied in analysis and simulation settings where the surface dimension is higher than what the isotonic regression literature typically considers. Simulation shows iPIPE-based credible intervals achieve nominal coverage probability and are more precise compared to unconstrained estimation.

Modeling approaches for cross-sectional integrative data analysis: Evaluations and recommendations.

Integrative data analysis (IDA) jointly models participant-level data from multiple studies. In psychology, IDA has been conducted using different fixed-effects and multilevel modeling (MLM) approaches. However, evaluations regarding the performance of these models in an IDA context are limited. The goal of this article is to evaluate three fixed-effects models (aggregated vs. disaggregated vs. study-specific coefficients regressions) and two MLMs (fixed-slope vs. random-slopes MLM) for cross-sectional IDA. Using a simulation study with study sample sizes and numbers of studies consistent with applied IDA (e.g., two to 35 studies), we evaluated estimation bias and type I error rates for participant-level and study-level effects and variance components for these models; for the MLMs, we evaluated different estimation methods (i.e., constrained vs. unconstrained variance estimation and five degrees of freedom methods). Disaggregated and study-specific coefficients regressions and both MLMs yielded fixed effects estimates with ignorable bias, but only the random-slopes MLM fully modeled between-study heterogeneity and, consequently, provided well-controlled type I error rates for testing both fixed effects. Overall, we found that MLMs could be feasible under IDA conditions with three to six studies and well-chosen estimation methods. A real-data IDA example is used to illustrate and compare the application of the five models. We hope our results will help researchers choose appropriate modeling methods when conducting IDA. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Maximum Likelihood Estimation of Destination Choice Models with Constrained Attractions

Attraction constraints are common and often appropriate for destination choice models, including, but not limited to, doubly constrained gravity distribution models. Estimation of their parameters by discrete-choice methods, however, seldom accounts for the constraints, despite bias known from their omission. For multinomial logit destination choice, this paper first formulates the parameter estimation for maximum likelihood of a set of observations, subject to exogenous attraction constraints on the model’s application to a population. Second, this formulation is extended for attraction constraints being linear combinations of size variables with coefficients to be estimated. Both the utility and size parameter estimations are distinct from the well-known formulation for unconstrained estimation, because of the contribution of the constraining shadow-price utilities to the likelihood gradients. Gradients and the Hessian are identified, along with adaptations of them for Newton-Raphson parameter updates and Cramér-Rao bounds. Experiments demonstrate its computational tractability and performance, and compare its estimations with those of unconstrained and other methods.

Episode-based personalization network for gaze estimation without calibration

Appearance-based methods employing deep convolutional architectures have achieved impressive performance for unconstrained gaze estimation. However, due to inter-personal anatomical differences, existing methods always get biased results for person-independent tasks. Generally, improvements can be achieved by adapting the models to a specified person with few calibration samples. Nevertheless, the calibration-based strategies are likely to collapse to high errors as over-parameterized neural networks easily fall into over-fitting. In this paper, we propose an Episode-based Personalization Network (EbPN) for person-independent gaze estimation, which does not rely on any calibration samples. Firstly, inspired by multi-task learning, we propose a two-branch gaze estimation network, including appearance-aware network and personalization-aware network. Secondly, during training, our model is optimized with a collection of episodes, each of which is designed to imitate a few-shot gaze estimation task. Through multiple episodes, our EbPN model progressively accumulates the experience on capturing appearance and personalized information of each image, which would help our model get lower errors and generalize well on any new persons. Experiments on GazeCapture, MPIIGaze and ETH-XGaze datasets demonstrate the effectiveness of our method.

Vision-Based Gaze Estimation: A Review

Eye gaze is an important natural behavior in social interaction as it delivers complex exchanges between observer and observed, by building up the geometric constraints and relation of the exchanges. These interperson exchanges can be modeled based on gaze direction estimated using computer vision. Despite significant progresses in vision-based gaze estimation in last 10 years, it is still nontrivial since the accuracy of gaze estimation is significantly affected by such intrinsic factors as head pose variance, individual bias between optical axis and visual axis, eye blink, occlusion and image blur, degrade gaze features, lead to inaccurate gaze-involved human social interaction analysis. This article aims to review and discuss existing methods addressing above-mentioned problems, gaze involved applications and data sets against the state of the arts in vision-based gaze estimation. It also points out future research directions and challenges of gaze estimation in terms of metalearning, causal inference, disentangled representation, and social gaze behavior for unconstrained gaze estimation.

Hybrid Inversion of Reservoir Parameters Based on Cosimulation and the Gradual Deformation Method

A new hybrid inversion methodology for petrophysical properties (porosity, water saturation, and volume of clay) based on partially stacked seismic angle gathers was presented. The innovation of this method is that it combines the advantages of high efficiency of analytical and semianalytical multistep petrophysical estimation with the advantages of spatial continuity and high resolution of geostatistical direct inversion of reservoir parameters. A trace-by-trace linearized amplitude versus offset (AVO) inversion and semianalytical petrophysical estimation approach could efficiently achieve a preliminary estimation of reservoir parameters under some assumptions and approximations. These laterally unconstrained preliminary estimation results are able to provide effective information for finer-resolution geostatistical simulation and improve the computational efficiency of stochastic optimization. The 3-D fast Fourier transform moving average (FFT-MA) geostatistical cosimulation and the stochastic optimization by gradual deformation method (GDM) improve the resolution and spatial continuity of the preliminary estimation results. At the same time, stochastic inversion overcomes the assumptions in the analytical inversion algorithm that the parameters need to conform to the logarithmic Gaussian distribution and the linear approximation of the Zoeppritz equation. The method was tested on a synthetic case and a real case. The results show that compared with the analytical and semianalytical methods, this hybrid inversion can obtain results with finer resolution and better spatial continuity, and the computational efficiency is significantly improved compared with the geostatistical direct inversion of reservoir parameters. Uncertainty evaluation can be obtained by performing statistical analysis on the multiple realizations of stochastic inversions.

Ensemble sparse estimation of covariance structure for exploring genetic disease data

High-dimensional data often occur nowadays in various areas, such as genetic and microarray data. The covariance matrix is of fundamental importance in analyzing the relationship between multivariate variables. A powerful tool for estimating a covariance matrix is the modified Cholesky decomposition, which allows for unconstrained estimation and guarantees the positive definiteness of the estimate. However, it requires a pre-specified ordering of variables before analysis, which is often not available in the real data. Hence, an ensemble Cholesky-based sparse estimation is proposed for a high-dimensional covariance matrix by adopting the model averaging idea. The asymptotically theoretical convergence rate is established under some regularity conditions. The merits of the proposed model are illustrated by the numerical study and two genetic disease data.

An end-to-end framework for unconstrained monocular 3D hand pose estimation

This work addresses the challenging problem of unconstrained 3D hand pose estimation using monocular RGB images. Most of the existing approaches assume some prior knowledge of hand (such as hand locations and side information) is available for 3D hand pose estimation. This restricts their use in unconstrained environments. Therefore, we present an end-to-end framework that robustly predicts hand prior information and accurately infers 3D hand pose by learning ConvNet models while only using keypoint annotations. To enhance the hand detector’s robustness, we propose a novel keypoint-based method to simultaneously predict hand regions and side labels, unlike existing methods that suffer from background color confusion caused by using segmentation or detection-based technology. Moreover, inspired by the human hand’s biological structure, we introduce two geometric constraints directly into the 3D coordinates prediction that further improves its performance. Experimental results show that our proposed framework outperforms the state-of-art methods on standard benchmark datasets while providing robust predictions.

Distributed Kalman filtering for uncertain dynamic systems with state constraints

SummaryThis article addresses the distributed state estimation problem for uncertain time‐varying dynamic systems with state constraints over a sensor network. By using a null space method, the distributed state estimation problem for uncertain dynamic systems with state constraints can be cast into a new unconstrained distributed state estimation problem for reduced uncertain dynamic systems. A constrained distributed Kalman filter is proposed, and it is shown that the full state estimates can be recovered at any time and satisfy the constraints. An optimized upper bound of the estimation error covariance of each sensor is obtained, and the corresponding gains are designed. The application conditions of the proposed algorithm are mild, and they can be off‐line checked. Furthermore, the computational requirements in this article are also reduced compared with the existing results. Finally, the performance of the proposed filter algorithm is demonstrated through numerical simulations.

Iterative Truncated Unscented Particle Filter

The particle filter method is a basic tool for inference on nonlinear partially observed Markov process models. Recently, it has been applied to solve constrained nonlinear filtering problems. Incorporating constraints could improve the state estimation performance compared to unconstrained state estimation. This paper introduces an iterative truncated unscented particle filter, which provides a state estimation method with inequality constraints. In this method, the proposal distribution is generated by an iterative unscented Kalman filter that is supplemented with a designed truncation method to satisfy the constraints. The detailed iterative unscented Kalman filter and truncation method is provided and incorporated into the particle filter framework. Experimental results show that the proposed algorithm is superior to other similar algorithms.

Tracking the maneuvering spacecraft propelled by swing propulsion of constant magnitude

This paper proposes partially norm-preserving filtering for a class of spacecraft in the presence of time-varying, but constant-magnitude maneuver. The augmented state Kalman filter (ASKF) is commonly used to track the maneuvering spacecraft with unknown constant propulsion; however, if the maneuver varies via time, the estimation performance will be degraded. To promote the tracking performance of the ASKF in case of time-invariant, constant-magnitude disturbance, the partially norm-preserving ASKF is developed by applying the norm constraint on the unknown maneuver. The proposed estimator, which is decomposed into two partial estimators and iteratively propagated in turns, projects the unconstrained maneuver estimation onto the Euclidian surface spanned by the norm constraint. The illustrative numerical example is provided to show the efficiency of the proposed method.

Non-negative variance component estimation for the partial EIV model by the expectation maximization algorithm

A difficulty in variance component estimation (VCE) is that the estimates may become negative, which is not acceptable in practice. This article presents two new methods for non-negative VCE that utilize the expectation maximization algorithm for the partial errors-in-variables model. The former searches for the desired solutions with unconstrained estimation criterion and concludes statistically that the variance components have indeed moved to the edge of the parameter space when negative estimates appear implemented by the other existing VCE methods. We concentrate on the formulation and provide non-negative analysis of this estimator. In particularly, the latter approach, which has greater computational efficiency, would be a practical alternative to the existing VCE-type algorithms. Additionally, this approach is easy to implement, the non-negative variance components are automatically supported by introducing non-negativity constraints. Both algorithms are free from a complex matrix inversion and reduce computational complexity. The results show that our algorithms retrieve well to achieve identical estimates over the other VCE methods, the latter approach can quickly estimate parameters and has practical aspects for the large volume and multisource data processing.

Constraints in estimating the proton density fat fraction

The study evaluates four physically motivated constraints in the estimation of the proton density fat fraction (PDFF). Least squares approaches were developed for constraining the parameters in PDFF quantification based on the physics of magnetic resonance imaging. These were smooth fieldmap, smooth initial phase, nonnegative proton density and moderate R2∗ values. The constraints were evaluated in terms of their influence on the bias and standard deviation of the estimated parameters using numerical simulations and in vivo data acquired at 0.35 T. Results show that unconstrained least squares estimation is noisy and biased and that constraints can be effective at reducing both the standard deviation and bias.

Projection‐based state estimation using noisy destination

The problem of state estimation with a destination constraint using the noisy prior information of the destination is investigated. With the utilisation of constraint information in estimation system, the estimation accuracy can be significantly enhanced. A projection-based constrained state estimation method is proposed to address this problem. In this method, the unscented Kalman filter is employed to obtain the unconstrained estimation. The Taylor series expansion is adopted to deal with the non-linearity of the destination constraint and the projection method is used to project the unconstraint estimate onto the constraint surface. Monte Carlo simulation results are presented to illustrate the effectiveness of the new approach.