Adaptive Estimation Scheme Research Articles

Transient Response of Linear Systems Under Integral Constraints

Abstract The requirement of satisfying an integral constraint imposed on a linear system's transient step-response is considered in this paper. The problem is first analyzed to determine the specific structure of a system's transfer function that helps satisfy such constraints. Analytical results are derived for a class of second-order systems with an additional zero. The results are extended to higher order transfer functions. Subsequently, a standard compensation consisting of a combination of feedforward and feedback actions is proposed to transform a given transfer function to the desired structure. Necessary and sufficient conditions to guarantee stability of the resulting closed-loop system are derived. Next, the problem of satisfying integral constraints in the presence of parametric uncertainty is addressed by augmenting adaptive estimation strategies to the feedforward and feedback compensation structure. Simulation results are provided for validation. The theory presented here is an abstraction from power management algorithms for hybrid power systems, such as a fuel cell hybridized with an ultracapacitor. Further work is ongoing to extend the theory to nonlinear systems.

Towards a revised framework of modified time series InSAR for mapping land deformation

Interferometric synthetic aperture radar (InSAR) time series technique has been widely applied to map the ground deformation over the past two decades. One of the key steps of InSAR time series approach is to select appropriate measurement scatterer (MS) pixels to build the triangulated irregular network (TIN). In order to build a stable TIN, there are four criteria need to be satisfied: (1) working from whole to the part, (2) hierarchical network, step-by-step control, (3) with sufficient accuracy, and (4) with appropriate spatial density. The effectiveness of Geodesy and Earth Observing Systems-PSI (GEOS-PSI) and GEOS-Advance Time Series Analysis (GEOS-ATSA) approaches have met the first three criteria above. Nevertheless, it is noteworthy to mention that higher sparseness of the TIN may lead to unwrapping failures, while having more evenly distributed of MS offers a higher chance to eliminate such effect and include more additional pixels during the adaptive processing. In this work, we proposed a revised MS pixels selection approach to satisfy the fourth criterion, in combination with the GEOS-PSI and GEOS-ATSA processing chain: the modified GEOS-ATSA (GEOS-MATSA). As compared to the conventional MS pixels selection criterion, the proposed approach has three advantages: (1) the MS pixels are added into the main network with control through an adaptive estimation strategy, (2) isolated sub-networks have better chances of including into the main network, and (3) the computing workload can be decreased by reducing the iteration times. The case study area is selected in Beijing–Langfang region, while the ideal threshold settings for the initial reference network are discussed for both persistent scatterer and distributed scatterer pixels in this work.

Optimal probes and error-correction schemes in multi-parameter quantum metrology

We derive a necessary and sufficient condition for the possibility of achieving the Heisenberg scaling in general adaptive multi-parameter estimation schemes in presence of Markovian noise. In situations where the Heisenberg scaling is achievable, we provide a semidefinite program to identify the optimal quantum error correcting (QEC) protocol that yields the best estimation precision. We overcome the technical challenges associated with potential incompatibility of the measurement optimally extracting information on different parameters by utilizing the Holevo Cramér-Rao (HCR) bound for pure states. We provide examples of significant advantages offered by our joint-QEC protocols, that sense all the parameters utilizing a single error-corrected subspace, over separate-QEC protocols where each parameter is effectively sensed in a separate subspace.

Integrated fault estimation and fault tolerant control for systems with generalized sector input nonlinearity

This paper presents a Fault Tolerant Control (FTC) scheme for systems with L2-bounded disturbances and generalized sector nonlinearity at the input. An adaptive observer-based fault estimation (FE) scheme is used to estimate the fault. The nonlinearity causes the control input (the measurable controller output, which is injected into the FE scheme) to differ from the actuator output (which enters the plant); this mismatch (together with the disturbances) causes interactions between the FE and FTC schemes, violating the separation principle and hence they cannot be designed separately. We introduce a method that integrates both FE and FTC schemes, and design them simultaneously (thus overcoming the violation of the separation principle), guaranteeing bounded stability. To obtain the sufficient conditions for stability and minimum L2-gain performance for disturbance rejection, we use the Sector Condition (SC) and successfully re-casted the design as Linear Matrix Inequalities (LMIs) which can be performed in a single step and yield tractable solutions. Through a numerical example, we demonstrate the effectiveness of the proposed method.

Online friction parameter estimation for machine tools

Accurate description of frictional phenomena is essential in applications that require high‐accuracy control. Online monitoring of friction parameters in machine tools greatly improves the control accuracy making condition‐based feedforward compensation possible and, at the same time, facilitates equipment wear assessment, which enables efficient scheduling of maintenance. Existing friction estimation methods that use detailed dynamical models offer accurate description of friction phenomena, but often rely on a priori knowledge of the static friction parameters, which have to be identified offline. This article suggests an adaptive estimation strategy suitable for online use while the machine works in its normal production cycle. Smooth approximations are introduced to account for stiction, viscous and bidirectional Coulomb friction in order to make online estimation possible. A parallel architecture is used with two adaptive estimators that segregate the frictional phenomena that dominate in different parts of the motion regime. Stability properties are analyzed and performance is experimentally validated on a single‐axis state‐of‐the‐art industrial test rig.

Recursive Least Squares-Based Adaptive Parameter Estimation Scheme for Signal Transformation and Grid Synchronization

Utility-interfaced power electronic systems use a grid synchronizing framework, known as phase-locked loop and need a transformation of sinusoidal signals to rotating dq reference frame for control purposes. The voltage or current signal parameters, including instantaneous fundamental frequency, phase angle, and amplitude, need to be captured in the presence of harmonics, noise, and dc offset. This article proposes an adaptive estimation scheme for the same, using recursive least squares with time-varying covariance gains. Proposed adaptation of gain presents faster transient response and noise-tolerant steady-state response, achieving optimal tradeoff between the two. The covariance resetting mechanism is presented for a better dynamic profile during step changes in the signal. The scheme for the single-phase signal transformation is extended for transforming three-phase unbalanced sinusoids to the decoupled double synchronous reference frame. Stability analysis, design guidelines, and discrete-time realization of proposed methods are provided for reproducibility. Theoretical deductions of the proposed method are supported with several comparative test cases simulated in MATLAB/Simulink and the experimental results.

Sparse SIR: Optimal rates and adaptive estimation

Sliced inverse regression (SIR) is an innovative and effective method for sufficient dimension reduction and data visualization. Recently, an impressive range of penalized SIR methods has been proposed to estimate the central subspace in a sparse fashion. Nonetheless, few of them considered the sparse sufficient dimension reduction from a decision-theoretic point of view. To address this issue, we in this paper establish the minimax rates of convergence for estimating the sparse SIR directions under various commonly used loss functions in the literature of sufficient dimension reduction. We also discover the possible trade-off between statistical guarantee and computational performance for sparse SIR. We finally propose an adaptive estimation scheme for sparse SIR which is computationally tractable and rate optimal. Numerical studies are carried out to confirm the theoretical properties of our proposed methods.

Distributed adaptive state estimation and tracking by using active‐passive sensor networks

SummaryHeterogeneous sensor networks (HSN) find a wide range of applications in the field of military and civilian environments, where sensor nodes are utilized to estimate the position of a target with both dynamics and control input being unknown for the purposes of tracking. In the HSN, nodes are considered active depending upon their ability to sense the target output while the others are taken passive. Accurate estimation requires local information exchange among the spatially located sensor nodes, so that the active nodes as well as the passive nodes converge simultaneously to the same value. The local information exchange among the nodes is dictated by a connected graph. By using the criterion of collective observability, a novel distributed adaptive estimation scheme is introduced via adaptive observer where the nodes are allowed to have different sensor modalities. Using the estimated information, a subset of active and passive nodes, referred to as mobile nodes, can track the moving target. By using a constant state feedback controller at each mobile node, the state and parameter estimation as well as the tracking errors are shown to be uniformly ultimately bounded. Simulation results verify theoretical claims.

An Implicit Function-Based Adaptive Control Scheme for Noncanonical-Form Discrete-Time Neural-Network Systems

This article proposes a new implicit function-based adaptive control scheme for the discrete-time neural-network systems in a general noncanonical form. Feedback linearization for such systems leads to the output dynamics nonlinear dependence on the system states, the control input, and uncertain parameters, which leads to the nonlinear parametrization problem, the implicit relative degree problem, and the difficulty to specify an analytical adaptive controller. To address these problems, we first develop a new adaptive parameter estimation strategy to deal with all uncertain parameters, especially, those of nonlinearly parameterized forms, in the output dynamics. Then, we construct a key implicit function equation using available signals and parameter estimates. By solving the equation, a unique adaptive control law is derived to ensure asymptotic output tracking and closed-loop stability. Alternatively, we design an iterative solution-based adaptive control law which is easy to implement and ensure output tracking and closed-loop stability. The simulation study is given to demonstrate the design procedure and verify the effectiveness of the proposed adaptive control scheme.

Per-Subcarrier RLS Adaptive Channel Estimation Combined with Channel Equalization for FBMC/OQAM Systems

Because of the intrinsic imaginary interference in filter bank multicarrier employing offset quadrature amplitude modulation (FBMC/OQAM) systems, accurate channel estimation remains an open issue, which will be studied in this letter. By using the real-time reconstructed pseudo-data as pseudo-pilots, the authors propose a per-subcarrier recursive least squares (RLS) adaptive channel estimation scheme combined with channel equalization (denoted by RLSACE-CE). The proposed RLSACE-CE scheme not only improves channel estimation performance but also achieves high transmission efficiency, which is validated by simulations and analyses in terms of the normalized mean square error (NMSE) of estimated channels and the bit error rate (BER).

Sensor Bias Fault Diagnosis for a Class of Nonlinear Uncertain Hybrid Systems

This paper presents a sensor bias fault diagnosis approach for a class of hybrid systems with nonlinear uncertain discrete-time dynamics, measurement noise, and autonomous and controlled mode transitions. The proposed approach uses an observer based on a modified hybrid automaton framework and a fault detection scheme that employs a filtering method tighter mode-dependent thresholds for the detection of sensor faults (even with small magnitude). An autonomous guard events identification (AGEI) module is also developed and linked with both the fault detection scheme and the hybrid observer to eliminate any false alarms due to autonomous mode transitions and allow effective mode estimation. Finally, an adaptive sensor fault estimation scheme is included, which is activated once a fault is detected to isolate and estimate the sensor bias fault magnitude.

China's First Demonstration of Cobalt-rich Manganese Crust Thickness Measurement in the Western Pacific with a Parametric Acoustic Probe.

Cobalt-rich manganese crusts (CRCs) are important as a potential mineral source that could occur throughout the Pacific on seamounts, ridges, and plateaus. We built a prototype parametric acoustic probe to complete the task of in-situ thickness measurements to estimate the volumetric distribution of deep-sea mineral. The prototype is designed with dual-channels for receiving the primary and secondary signal, which lays a foundation for improving the thickness extraction algorithm. Considering that the signal quality is degraded by the system interference and ambient noise, some improvements to the algorithm are proposed by including the wavelet-based envelope extraction method and the adaptive estimation strategy based on the dual-channel information. Additionally, wavelet regression is applied to reduce the measuring noise assuming that the CRCs have local thickness invariability. The algorithm is suitable for the CRCs with the structure of the multilayers at the top surface and one single layer at the bottom surface. A laboratory experiment is performed to validate the effectiveness of the algorithm. The experiments carried out on the China Ocean 51th voyage in the Western Pacific Ocean on Aug 30, 2018, are described and the data obtained by using the sit-on-bottom stationary measurement are processed to validate the design of the prototype.

Normalized LMS algorithm and data-selective strategies for adaptive graph signal estimation

This work proposes a normalized least-mean-squares (NLMS) algorithm for online estimation of bandlimited graph signals (GS) using a reduced number of noisy measurements. As in the classical adaptive filtering framework, the resulting GS estimation technique converges faster than the least-mean-squares (LMS) algorithm while being less complex than the recursive least-squares (RLS) algorithm, both recently recast as adaptive estimation strategies for the GS framework. Detailed steady-state mean-squared error and deviation analyses are provided for the proposed NLMS algorithm, and are also employed to complement previous analyses on the LMS and RLS algorithms. Additionally, two different time-domain data-selective (DS) strategies are proposed to reduce the overall computational complexity by only performing updates when the input signal brings enough innovation. The parameter setting of the algorithms is performed based on the analysis of these DS strategies, and closed formulas are derived for an accurate evaluation of the update probability when using different adaptive algorithms. The theoretical results predicted in this work are corroborated with high accuracy by numerical simulations.

Adaptive high‐order sliding mode controller‐observer for MIMO uncertain nonlinear systems

AbstractIn this paper, an adaptive high‐order sliding mode controller‐observer is proposed for multi input–multi output uncertain systems with application to robotic manipulators. Firstly, a type‐2 Takagi‐Sugeno fuzzy system is used to model the original system. Next, with the unavailability of velocity measurement, a fuzzy high‐order sliding mode observer is designed to estimate both the joint velocities and uncertainties. Moreover, based on a super twisting second‐order sliding mode, the proposed robust controller generates smooth control and guarantees finite‐time convergence to the third‐order sliding set with respect to the sliding variable by keeping second‐order sliding mode constraint. The controller gains are generated based on an adaptive estimation scheme without overestimation. The finite‐time stability of the suggested controller is proved by using an homogeneous and strict Lyapunov function. Finally, the obtained simulation results for two‐link robot manipulators demonstrate the effectiveness of the proposed controller.

A brief survey on the choice of parameters for: “Kernel density estimation for time series data”

This paper presents an overview of the empirical performance of some of the common methods for parameter selection in the area of enhanced dynamic kernel density and distribution estimation with exponentially declining weights. It is shown that exponential weighting delivers accurate nonparametric density and quantile evaluations, without common corrections for scale and/or location in most of the financial time series considered, provided that parameters are chosen appropriately with computationally heavy Least-Squares routines. For more time-efficient numerical optimisations and/or simple kernel adaptive estimation strategies, Least-Squares routines may be re-written with exponentially weighted binned kernel estimators. This insures equally effective parameters evaluation under the different choices of kernel functional forms, though binning strategy becomes an important component of estimations. On the other hand, it is also highlighted that if the estimations target is to mine time-varying nonparametric quantiles, kernel functional forms and bandwidths may not be necessary for these evaluations. Combining exponential weights with empirical distribution estimator provides a very similar quantile performance to the kernel enhanced estimator, while parametric specifications may provide a better extreme quantiles outlook.

Dual Quaternions as a Tool for Modeling, Control, and Estimation for Spacecraft Robotic Servicing Missions

In recent years there has been an increasing interest in spacecraft robotic operations in orbit. In fact, several agencies and organizations around the world are investigating satellite proximity operations as an enabling technology for future space missions such as on-orbit satellite inspection, health monitoring, surveillance, servicing, refueling, and optical interferometry, to name a few. Contrary to more traditional satellite applications, robotic servicing requires addressing both the translational and the rotational motion of the satellite at the same time. One of the biggest challenges for these applications is the need to simultaneously and accurately estimate – and track – both relative position and attitude reference trajectories in order to avoid collisions between the satellites and achieve stringent mission objectives. Motivated by our desire to control spacecraft motion during proximity operations for robotic in-orbit servicing missions which do not depend on the artificial separation of translational and rotational motion, we have recently developed a complete theory to describe the 6-DOF motion of the spacecraft using dual quaternions. Dual quaternions emerge as a powerful tool to model the pose (that is, both attitude and position) of the spacecraft during all phases of the mission under a unified framework. In this paper, we revisit the basic theory behind dual quaternions, the associated Clifford algebras, and compare quaternion-based attitude rigid-body control laws and estimation algorithms, to their dual quaternion-based pose counterparts. We also show that the resulting mathematical structure lends itself to the straightforward incorporation of an adaptive estimation scheme known as concurrent learning, which allows us to also estimate on-the-fly the mass properties of the spacecraft.

An Enhanced Optimization Scheme Based on Gradient Descent Methods for Machine Learning

A The learning process of machine learning consists of finding values of unknown weights in a cost function by minimizing the cost function based on learning data. However, since the cost function is not convex, it is conundrum to find the minimum value of the cost function. The existing methods used to find the minimum values usually use the first derivative of the cost function. When even the local minimum (but not a global minimum) is reached, since the first derivative of the cost function becomes zero, the methods give the local minimum values, so that the desired global minimum cannot be found. To overcome this problem, in this paper we modified one of the existing schemes—the adaptive momentum estimation scheme—by adding a new term, so that it can prevent the new optimizer from staying at local minimum. The convergence condition for the proposed scheme and the convergence value are also analyzed, and further explained through several numerical experiments whose cost function is non-convex.

On a Novel, Simplified Model Framework Describing Ascorbic Acid Concentration Dynamics.

Ascorbic acid is an essential aminoacid which interacts in several parts of the human body metabolism. The ascorbic acid concentration is controlled by homeostasis, a biological, autonomous control function in the body. Humans are not able to produce ascorbic acid, and the ascorbic acid concentration is maintained by daily oral digestion. Ascorbic acid is buffered in various tissues, such as the adrenal glands, brain, muscles, and other. Excessive ascorbic acid is extracted from the body through urine and intestines. Measuring ascorbic acid concentration in the body is challenging, and special procedures must be followed when extracting a blood sample and performing a concentration analysis. This paper presents a novel, simplified model framework of the ascorbic acid homeostasis in the human body plasma and tissues, including tissues such as adrenal glands, brain, liver, muscles and bone marrow. These tissues also act as ascorbic acid concentration buffers, in case of low oral supply. The dynamic model framework is based on mass balances of ascorbate acid in various tissues, including tissue buffer terms involving the intestine, kidney, adrenal glands, and other critical and noncritical tissues. The interaction between buffer tissues and fluids is maintained by the body homeostasis using chemical transport protein molecules. Additional usage terms describing energy metabolism, body growth, and immune system response are also included. This dynamic model framework, including the ascorbic acid concentration control system, is simulated with assumed parameters based on available literature. The results indicates that further investigations using experiments, in addition to adaptive model parameter estimation schemes and additional model verification tests are needed in order to identify the various model framework parameters to fit the human body ascorbic acid homeostasis and pharmacokinetics.

PRECISE DISPARITY ESTIMATION FOR NARROW BASELINE STEREO BASED ON MULTISCALE SUPERPIXELS AND PHASE CORRELATION

Abstract. With the rapid development of subpixel matching algorithms, the estimation of image shifts with an accuracy of higher than 0.05 pixels is achieved, which makes the narrow baseline stereovision possible. Based on the subpixel matching algorithm using the robust phase correlation (PC), in this work, we present a novel hierarchical and adaptive disparity estimation scheme for narrow baseline stereo, which consists of three main steps: image coregistration, pixel-level disparity estimation, and subpixel refinement. The Fourier-Mellin transform with subpixel PC is used to co-register two input images. Then, the pixel-level disparities are estimated in an iterative manner, which is achieved through multiscale superpixels. The pixel-level PC is performed with the window sizes and locations adaptively determined according to superpixels, with the disparity values calcualted. Fast weighted median filtering based on edge-aware filter is adopted to refine the disparity results. At last, the accurate disparities are calculated via a robust subpixel PC method. The combination of multiscale superpixel hierarchy, adaptive determination of the window size and location of correlation, fast weighted median filtering and subpixel PC make the proposed scheme be able to overcome the issues of either low-texture areas or fattening effect. Experimental results on a pair of UAV images and the comparison with the fixed-window PC methods, the iterative scheme with fixed variation strategy, and a sophisticated implementation using global optimization demonstrate the superiority and reliability of the proposed scheme.

Adaptive high order sliding mode controller/observer based terminal sliding mode for MIMO uncertain nonlinear system

ABSTRACT In this paper, an adaptive super twisting high order sliding mode controller observer is investigated for multi input–multi output uncertain system, with application to robotic manipulator based only on position measurement. First, a type-2 Takagi–Sugeno fuzzy system is used to model the original system. Next, by combining thefuzzy model with third order sliding mode observer, a novel fuzzy observer is designed to estimate both the joint velocities and uncertainties. Moreover, based on super twisting algorithm the proposed controller generates a smooth control signal and guarantees the finite time stabilisation of second order sliding mode. The controller gains are generated based on adaptive estimation scheme, in which the gains overestimation problem and the prior knowledge of the upper boundaries of uncertainties can be avoided. The stability of proposed controller/ observer scheme is discussed using Lyapunov approach. Finally, the obtained simulation results for two link robot manipulator demonstrate the effectiveness of the proposed controller.