Parameter Estimation Error Research Articles

Semantically-Aware Pedestrian Intent Prediction With Barrier Functions and Mixed-Integer Quadratic Programming

We develop algorithms for inferring long-term intentions and parameters of local collision-avoidance behavior of agents in a multiagent system from their trajectories. This problem is challenging because an agent's observed trajectory only partially manifests its long-term task; it also contains adjustments made by the agent to ensure collision avoidance with other agents and obstacles in the environment. Since an observer would have no means to determine the magnitude of these adjustments, it is difficult to isolate the task-oriented component from the observed motion. To circumvent this problem, we model the agent's dynamics using a reactive optimization whose objective function captures the long-term task while its constraints capture collision-avoidance behavior. We develop two robust mixed-integer programming algorithms that infer the task and safety related parameters of this optimization problem from the positions and velocities of the agents. These algorithms are validated on synthetic datasets using parameter estimation errors, displacement errors and computation time as metrics. We further test these algorithms on a dataset of real human trajectories. We show that the learned parameters capture the true underlying pedestrian dynamics by rolling out the learned model and showing similarity between the ground truth trajectories and the reconstructed trajectories.

Data-Based and Opportunistic Integral Concurrent Learning for Adaptive Trajectory Tracking During Switched FES-Induced Biceps Curls.

Hybrid exoskeletons, which combine functional electrical stimulation (FES) with a motorized testbed, can potentially improve the rehabilitation of people with movement disorders. However, hybrid exoskeletons have inherently nonlinear and uncertain dynamics, including combinations of discrete modes that switch between different continuous dynamic subsystems, which complicate closed-loop control. A particular complication is the uncertain muscle control effectiveness associated with FES. In this work, adaptive integral concurrent learning (ICL) motor and FES controllers are developed for a hybrid biceps curl exoskeleton, which are designed to achieve opportunistic and data-based learning of the uncertain human and electromechanical testbed parameters. Global exponential trajectory tracking and parameter estimation errors are proven through a Lyapunov-based stability analysis. The motor effectiveness is assumed to be unknown, and, to help with fatigue reduction, FES is enabled to switch between multiple electrodes on the biceps brachii, further complicating the analysis. A consequence of switching between the different uncertain subsystems is that the parameters must be opportunistically learned for each subsystem (i.e. each electrode and the motor), while that subsystem is active. Experiments were performed to validate the developed ICL controllers on twelve healthy participants. The average (± standard deviation) position tracking errors across each participant were 1.44 ± 5.32 deg, -0.25 ± 2.85 deg, and -0.17 ± 2.66 deg across biceps Curls 1-3, 4-7, and 8-10, respectively, where the average across the entire experiment was 0.28 ± 3.53 deg.

A Modification of Generalized Parameter-Based Adaptive Observer for Linear Systems with Relaxed Excitation Conditions*

This paper proposes the adaptive state observer for linear time-invariant systems. The problem statement is classical except that there is no assumption about the sufficiently rich input signal. The solution is based on the generalized parameter estimation based observer (GPEBO). Firstly, the linear regression for the unknown parameters and initial conditions are constructed. With the proposed novel parameterization, a sufficient number of independent linear regressions are generated in contrast to the original GPEBO. Then the mixing stage of the dynamic regressor extension and mixing method is applied to obtain independent scalar regression models. Next, the parameters and initial conditions are estimated by the gradient descent method with finite-time modification. Finally, with obtained estimates, the value of the state vector is reconstructed. Under weak assumptions about interval excitation, the proposed observer provides convergence of the parameter and state estimation errors to zero at the predefined finite time in the noise-free case. The numerical simulations demonstrate the efficiency of the proposed observer in comparison with the original GPEBO.

Parameter Convergence in Adaptive Control in Presence of Unmatched Uncertainty

The problem of convergence of uncertainties to their true values is of great interest in adaptive control. It is desirable as it facilitates accurate online modeling of structured uncertainties and robust adaptation to disturbances. The adaptation law based on the classical gradient method requires the restrictive persistent excitation (PE) condition to be satisfied for parameter convergence. This paper deals with the relaxation of this PE condition for a class of nonlinear systems in the presence of unmatched uncertainty. The design of the proposed adaptive backstepping controller involves multiple filtered models that translate the restrictive PE condition to linear independence of the filtered regressor models. The proposed controller guarantees asymptotic convergence of the tracking and parameter estimation errors globally in the presence of unmatched uncertainty. Numerical simulations show the efficacy of the proposed controller.

Composite Adaptive Control for Anti-Unwinding Attitude Maneuvers: An Exponential Stability Result Without Persistent Excitation

This paper provides an exponential stability result for the adaptive anti-unwinding attitude tracking problem of a rigid body with uncertain inertia parameters, without the need for a persistent excitation (PE) condition. Specifically, a composite adaptive control scheme with guaranteed parameter convergence is proposed by integrating the dynamic regressor extension and mixing (DREM) technique into the dynamically scaled immersion and invariance adaptive control framework, wherein we modify the scaling factor so that the algorithm design does not involve any dynamic gains. To avoid the unwinding problem, a barrier function is introduced as the attitude error function, along with the establishment of two key algebraic properties for exponential stability analysis. Aiding by an linear time-varying filter, the scalar regressor of DREM is extended to generate an exciting counterpart. In this manner, the derived controller is shown to permit closed-loop exponential stability under a strictly weaker interval excitation condition than PE, in the sense that both the output-tracking and parameter estimation errors exponentially converge to zero. Furthermore, the composite adaptive law is also augmented to achieve finite/fixed-time parameter convergence in a time-synchronized manner. Simulation results are presented to verify our theoretical findings.

On exponentially convergent parameter estimation with lack of persistency of excitation

Given a linear regression model, the problem of exponentially convergent identification of a vector of p constant parameters is addressed, without the assumption that the regressor is persistently exciting. A new definition of lack of persistency of excitation of order q , with 0 ≤ q ≤ p , is introduced, which reduces to the well-known persistency of excitation condition in the special case q = 0 . This definition implies that the kernel of the Gram matrix of the regressor has constant dimension q . Gradient and least squares identification algorithms may be modified on the basis of such a kernel computation, so that exponential convergence and robustness of parameter estimation errors is achieved both for gradient and least squares algorithms, even without persistency of excitation.

Linear Motor Command Tracking: A Novel Immersion and Invariance Adaptive Control Method with Arctangent-Function-Based Parameter Projection

This paper innovates an adaptive control law that unifies the Immersion and Invariance (I&I) principle and a novel arctangent-function-based smooth projection operator. Such an adaptive controller is exploited to accomplish the command tracking task of a parametric uncertain linear motor system. The uniqueness and advantage of the proposed method lie twofold. First and foremost, the novel nonaffine I&I scheme ensures the asymptotical convergence of the parameter estimation error despite the reference command's persistency of excitation conditions. Second, the arctangent-function-based smooth projection operator is a one-piece infinitely differentiable (C∞) function that requires no boundary layer construction nor piecewise-defined functions compared to existing smooth projection techniques. Simulation results are presented to examine the proposed adaptive controller. Furthermore, its performance (especially the transient one) is compared against a certainty-equivalence-based method.

SQP-based Power Allocation Strategy for Target Tracking in MIMO Radar Network with Widely Separated Antennas

MIMO radar with widely separated antennas enhances detection and estimation resolution by utilizing the diversity of the propagation path. Each antenna of this type of radar can steer its beam independently towards any direction as an independent transmitter. However, the joint processing of signals for transmission and reception differs this radar from the multistatic radar. There are many resource optimization problems which improve the performance of MIMO radar. But power allocation is one of the most interesting resource optimization problems. The power allocation finds an optimum strategy to assign power to transmit antennas with the aim of minimizing the target tracking errors under specified transmit power constraints. In this study, the performance of power allocation for target tracking in MIMO radar with widely separated antennas is investigated. Therefore, a MIMO radar with distributed antennas is configured and a target motion model using the constant velocity (CV) method is modeled. Then Joint Cramer Rao bound (CRB) for target parameters (joint target position and velocity) estimation error is calculated. This is utilized as a power allocation problem objective function. Since the proposed power allocation problem is nonconvex. Therefore, a SQP-based power allocation algorithm is proposed to solve it. In simulation results, the performance of the proposed algorithm in various conditions such as a different number of antennas and antenna geometry configurations is examined. Results affirm the accuracy of the proposed algorithm.

Про один алгоритм ідентифікації лінійних обʼєктів на основі найменшого ексцесу

Розглянуто задачу ідентифікації параметрів лінійного обʼєкта за наявності негауссівських завад. Алгоритм ідентифікації є градієнтною процедурою мінімізації критерію найменшого середнього ексцесу. Використання такого функціоналу дозволяє отримати оцінки з робастними властивостями. Алгоритм ідентифікації — це градієнтна процедура. Визначено умови збіжності процедури, що застосовується, в середньому і середньоквадратичному за наявності негауссівських завад вимірів. Крім того, отримано оцінки для визначення оптимального значення параметра алгоритму, що забезпечують його максимальну швидкість збіжності. На основі цих оцінок визначено асимптотичні та неасимптотичні значення похибок оцінювання параметрів та похибок ідентифікації. У звʼязку з цим отримані вирази містять невідомі параметри (значення дисперсій сигналів і завад). Для їх застосування слід використовувати оцінки цих параметрів. Отримані співвідношення досить громіздкі, однак їх спрощення дозволяє провести якісний аналіз сталості. Слід зазначити, що всі отримані в роботі оцінки залежать від низки параметрів, проблема визначення яких залишається відкритою. Вони дозволяють досліднику попередньо оцінити можливості алгоритму ідентифікації та ефективність його використання при вирішенні практичних задач.

The robust minimum cost consensus model with risk aversion

Due to the uncertain circumstances in which decisions are made, the moderator may be unable to provide an accurate unit adjustment cost to each decision maker, making the unit adjustment cost uncertain. This paper formulates a consensus approach to reduce the adverse effects of parameter uncertainty and estimation errors. First, the mean–variance (MV) theory is employed to build the risk minimum cost consensus model (RMCCM) to reflect the risk preference of the moderator in the consensus progress. Second, due to existing estimation errors of the mean and covariance matrix of unit adjustment cost in RMCCM, new RMCCM variants are proposed using robust optimization. To identify a solution that performs best in the worst case, the robust counterpart RMCCM problem is equivalent to a tractable problem. Finally, a case study of urban housing demolition in China is used to verify the feasibility and applicability of the proposed method, and then sensitivity analysis and comparative analysis are presented.

An effective PSO-based power allocation for target tracking in MIMO radar with widely separated antennas

In MIMO radar with widely separated antennas, the antennas are spaced far from each other and the target is seen from different angles. In this type of radars, each receiver collects all transmit signals and transmits them to the central processor unit. Power allocation is an important part of military operations. Therefore, it is a primary factor that requires to be taken into account in the designing of target tracking problems in MIMO radar. In fact, the power allocation finds an optimum strategy to allot power to transmit antennas with the goal of minimizing the target tracking errors under specified transmit power constraints. In this paper, the performance of power allocation for target tracking in MIMO radar with widely separated antennas is investigated. For this purpose, first, a MIMO radar with distributed antennas is configured and a target motion model using the constant velocity (CV) method is modeled. Then Joint Cramer Rao bound (CRB) for target parameters (joint target position and velocity) estimation error is computed. This is applied as a power allocation problem objective function. Because a complex Gaussian model is considered for target radar cross-section (RCS), this function becomes complicated. Due to the nonlinearity of this objective function, the proposed power allocation problem is nonconvex. Therefore, a particle swarm optimization (PSO) -based power allocation algorithm is proposed to solve it. In simulation experiments, the performance of the proposed algorithm in different conditions such as a different number of antennas and antenna geometry configurations is evaluated. Results prove the validity of the proposed algorithm.

State of charge estimation for lithium-ion battery using Transformer with immersion and invariance adaptive observer

Accurate state-of-charge (SOC) estimation lays the foundation for lithium-ion batteries’ long-life and safe services. This paper exploits a new machine-learning method and an adaptive observer to estimate the battery's SOC. First, a Transformer neural-network is employed to predict the SOC with the sequence of current, voltage, and temperature data as inputs. Second, an innovative immersion and invariance (I&I) adaptive observer is applied to reduce the oscillations of the Transformer's prediction. The lead of the Transformer network lies in that it has an overview of the entire input sequence and obtains richer information than other conventional neural networks. Besides, the I&I adaptive observer is competent for correcting possible learning fluctuations and ensuring that the battery parameter estimation error is confined within an invariant manifold. The proposed methods are validated with experimental data. The results demonstrate their higher SOC estimation accuracy than a popular baseline method.

Estimation of the Equivalent Circuit Parameters of Induction Motors by Laboratory Test

The determination of equivalent circuit parameters for AC induction motors represents an important task in an electrical machine laboratory. Frequently used open-circuit and short current tests answer these requirements. However, the results have a low accuracy. This becomes especially obvious when the equivalent circuit is applied for the motor current and power prediction. The main obstacles in this circumstance lie in the difficulty of providing a pristine open-circuit test, the lack of which causes errors in parameter estimation. A much more accurate approach can be carried out with a test including several output points with measurements of the motor torque, velocity, current, and power magnitudes. Nevertheless, a relatively simple and accurate method to ensure determining parameters for such tests does not exist. This article tries to provide such a method by an approach based on Kloss’s simplified equation and the Thevenin theorem. The significant novelty of the method is the specially selected synergetic interaction between the analytical and numerical approaches, which give a relatively simple algorithm with a good accuracy and a convergence of the parameters’ estimation.

Noisy multimodal brain image registration using markov random field model

In this paper, a new scheme is proposed to register brain Magnetic Resonance (MR) and Computed Tomography (CT) images under a noisy environment. The scheme is developed based on the notion of mutual information and this is extended to the feature space-based registration. The 2D joint histogram of the noisy MR and CT images has been computed and this is assumed to be the degraded version of the true 2D joint histogram that corresponds to the CT and MR images. The true 2D joint histogram is modeled as Markov Random Field (MRF) model and is estimated from the degraded one by formulating the problem in Maximum A Posterior (MAP) estimation framework. The MAP estimates are obtained by the combination of Simulated Annealing (SA) and Iterated Conditioned Mode (ICM) algorithms. The Mutual Information (MI) at different values of the parameter vector θ are computed from the estimated joint histogram and is maximized to determine the optimal registration parameter. The MI curve is modeled as multivariate Gaussian distribution and the registration parameter vector is obtained with a confidence interval. The scheme has been tested with the slices of patients from the Retrospective Image Registration Evaluation (RIRE) database. The efficacy of the scheme on MR and CT volumes is demonstrated by rendering the registered slices. The proposed algorithm is successfully tested with different degrees of Gaussian, Rician and Rayleigh noise conditions. Performance measures such as parameter estimation errors, error statistics and landmark based validation are used to demonstrate the efficacy of the proposed algorithm. The scheme is found to exhibit improved performance, especially at high noisy conditions as compared to the existing schemes.

Explanatory Cognitive Diagnostic Modeling Incorporating Response Times

AbstractThis study proposes explanatory cognitive diagnostic model (CDM) jointly incorporating responses and response times (RTs) with the inclusion of item covariates related to both item responses and RTs. The joint modeling of item responses and RTs intends to provide more information for cognitive diagnosis while item covariates can be used to predict item parameters when item calibration is not feasible in diagnostic assessments or item parameter estimation errors could be too large due to small sample sizes for calibration. In addition, the inclusion of the item covariates allows the evaluation of cognitive theories underlying the test design in item development. Model parameter estimation is explored using the Bayesian Markov chain Monte Carlo (MCMC) method. A Monte Carlo simulation study is conducted to examine the parameter recovery of the proposed model under different simulated conditions in comparison to alternative competing models. Further, the application of the proposed model is illustrated using the Programme for International Student Assessment (PISA) 2012 problem‐solving items modeling both item response and RT data. The study results indicate that model parameters can be well recovered using the MCMC algorithm and the explanatory CDM jointly incorporating item responses and RTs with item covariates holds promising applications in digital‐based diagnostic assessments.

Cost-effective surveillance of invasive species using info-gap theory

Invasive species can lead to community-level damage to the invaded ecosystem and extinction of native species. Most surveillance systems for the detection of invasive species are developed based on expert assessment, inherently coming with a level of uncertainty. In this research, info-gap decision theory (IGDT) is applied to model and manage such uncertainty. Surveillance of the Asian House Gecko, Hemidactylus frenatus Duméril and Bibron, 1836 on Barrow Island, is used as a case study. Our research provides a novel method for applying IGDT to determine the population threshold (K) so that the decision can be robust to the deep uncertainty present in model parameters. We further robust-optimize surveillance costs rather than minimize surveillance costs. We demonstrate that increasing the population threshold for detection increases both robustness to the errors in the model parameter estimates, and opportuneness to lower surveillance costs than the accepted maximum budget. This paper provides guidance for decision makers to balance robustness and required surveillance expenditure. IGDT offers a novel method to model and manage the uncertainty prevalent in biodiversity conservation practices and modelling. The method outlined here can be used to design robust surveillance systems for invasive species in a wider context, and to better tackle uncertainty in protection of biodiversity and native species in a cost-effective manner.

Fundamentals of turbulent flow spectrum imaging.

PurposeTo introduce a mathematical framework and in‐silico validation of turbulent flow spectrum imaging (TFSI) of stenotic flow using phase‐contrast MRI, evaluate systematic errors in quantitative turbulence parameter estimation, and propose a novel method for probing the Lagrangian velocity spectra of turbulent flows.Theory and MethodsThe spectral response of velocity‐encoding gradients is derived theoretically and linked to turbulence parameter estimation including the velocity autocorrelation function spectrum. Using a phase‐contrast MRI simulation framework, the encoding properties of bipolar gradient waveforms with identical first gradient moments but different duration are investigated on turbulent flow data of defined characteristics as derived from computational fluid dynamics. Based on theoretical insights, an approach using velocity‐compensated gradient waveforms is proposed to specifically probe desired ranges of the velocity autocorrelation function spectrum with increased accuracy.ResultsPractical velocity‐encoding gradients exhibit limited encoding power of typical turbulent flow spectra, resulting in up to 50% systematic underestimation of intravoxel SD values. Depending on the turbulence level in fluids, the error due to a single encoding gradient spectral response can vary by 20%. When using tailored velocity‐compensated gradients, improved quantification of the Lagrangian velocity spectrum on a voxel‐by‐voxel basis is achieved and used for quantitative correction of intravoxel SD values estimated with velocity‐encoding gradients.ConclusionTo address systematic underestimation of turbulence parameters using bipolar velocity‐encoding gradients in phase‐contrast MRI of stenotic flows with short correlation times, tailored velocity‐compensated gradients are proposed to improve quantitative mapping of turbulent blood flow characteristics.

Machine learning astrophysics from 21 cm lightcones: impact of network architectures and signal contamination

ABSTRACT Imaging the cosmic 21 cm signal will map out the first billion years of our Universe. The resulting 3D lightcone (LC) will encode the properties of the unseen first galaxies and physical cosmology. Here, we build on previous work using neural networks (NNs) to infer astrophysical parameters directly from 21 cm LC images. We introduce recurrent neural networks (RNNs), capable of efficiently characterizing the evolution along the redshift axis of 21 cm LC images. Using a large database of simulated cosmic 21 cm LCs, we compare the relative performance in parameter estimation of different network architectures. These including two types of RNNs, which differ in their complexity, as well as a more traditional convolutional neural network (CNN). For the ideal case of no instrumental effects, our simplest and easiest to train RNN performs the best, with a mean squared parameter estimation error (MSE) that is lower by a factor of ≳2 compared with the other architectures studied here, and a factor of ≳8 lower than the previously-studied CNN. We also corrupt the cosmic signal by adding noise expected from a 1000 h integration with the Square Kilometre Array, as well as excising a foreground-contaminated ‘horizon wedge’. Parameter prediction errors increase when the NNs are trained on these contaminated LC images, though recovery is still good even in the most pessimistic case (with R2 ≳ 0.5−0.95). However, we find no notable differences in performance between network architectures on the contaminated images. We argue this is due to the size of our data set, highlighting the need for larger data sets and/or better data augmentation in order to maximize the potential of NNs in 21 cm parameter estimation.

Adaptive augmented torque control of a quadcopter with an aerial manipulator

A quadcopter manipulator system is an aerial robot consisting of a quadcopter with a robotic arm attached to it. The system has coupled nonlinear dynamics with uncertain time-varying parameters. The work in this paper focuses on designing an adaptive nonlinear controller to facilitate the uncertain system’s trajectory tracking and stability. The novelty of the proposed work is the design and implementation of an adaptive feedback linearization controller, called adaptive augmented torque (AAT) control, for the aerial robot. The control law is based on a feedback linearization controller with model reference adaptive controller and a tracking error-based augmented term. Using the input-to-state stability concept, a bound on the parameter estimation error is also developed. In the presented methodology, the controller uses estimated values of system parameters obtained from the adaptive mechanism and the tracking error to compute the control input using the AAT control law. An adaptive law for estimating unknown parameters is obtained using the strictly positive real-Lyapunov method. The asymptotic stability of the closed-loop system is analyzed via the Lyapunov theory. Simulations implemented in MATLAB and ROS/Gazebo and preliminary hardware experiments are presented to validate the theoretical results and to corroborate the performance of the AAT control law.

Parameter estimation for closed-loop lumped parameter models of the systemic circulation using synthetic data

Physics-based models can be applied to describe mechanisms in both health and disease, which has the potential to accelerate the development of personalized medicine. The aim of this study was to investigate the feasibility of personalizing a model of systemic hemodynamics by estimating model parameters.We investigated the feasibility of estimating model parameters for a closed-loop lumped parameter model of the left heart and systemic circulation using the step-wise subset reduction method. This proceeded by first investigating the structural identifiability of the model parameters. Secondly, we performed sensitivity analysis to determine which parameters were most influential on the most relevant model outputs. Finally, we constructed a sequence of progressively smaller subsets including parameters based on their ranking by model output influence. The model was then optimized to data for each set of parameters to evaluate how well the parameters could be estimated for each subset. The subsequent results allowed assessment of how different data sets, and noise affected the parameter estimates.In the noiseless case, all parameters could be calibrated to less than 10−3% error using time series data, while errors using clinical index data could reach over 100%. With 5% normally distributed noise the accuracy was limited to be within 10% error for the five most sensitive parameters, while the four least sensitive parameters were unreliably estimated for waveform data. The three least sensitive parameters were particularly challenging to estimate so these should be prioritized for measurement. Cost functions based on time series such as pressure waveforms, were found to give better parameter estimates than cost functions based on standard indices used in clinical assessment of the cardiovascular system, for example stroke volume (SV) and pulse pressure (PP). Averaged parameter estimate errors were reduced by several orders of magnitude by choosing waveforms for noiseless synthetic data. Also when measurement data were noisy, the parameter estimation procedure based on continuous waveforms was more accurate than that based on clinical indices. By application of the stepwise subset reduction method we demonstrated that by the addition of venous pressure to the cost function, or conversely fixing the systemic venous compliance parameter at an accurate value improved all parameter estimates, especially the diastolic filling parameters which have least influence on the aortic pressure.