Unknown Amplitude Research Articles

Virtual Impedance Method for Mutual Coupling Compensation

The radiation pattern of an antenna within an array environment is modified by mutual coupling to neighboring elements, which can create unknown phase and amplitude variation on the order of 10° and 5 dB. This uncertainty in the element patterns results in beamforming errors, which can be particularly problematic for applications requiring precise pattern control. A new approach is reported to compensate for the mutual coupling of single-mode radiators using only the measured S-parameters and received signal from several far-field sources. The technique relies on the fact that dominant mode scattering from each antenna can be removed by terminating it with the proper impedance. Optimized beamforming weights are derived that compensate for mutual coupling. It is shown that implementing these optimized weights is equivalent to terminating all elements with a “virtual” impedance that cancels scattering from neighboring antenna elements (i.e., mutual coupling). Simulations of perfectly uniform and nonuniform linear dipole arrays show that compensating for mutual coupling using the proposed technique reduces the variation of the embedded element patterns by an order of magnitude compared to more conventional techniques. The proposed approach could be useful for a wide variety of antenna arrays and may even lend itself to self-calibration in the field using signals of opportunity.

A New Measurement Method for High Voltages Applied to an Ion Trap Generated by an RF Resonator.

A new method is proposed to measure unknown amplitudes of radio frequency (RF) voltages applied to ion traps, using a pre-calibrated voltage divider with RF shielding. In contrast to previous approaches that estimate the applied voltage by comparing the measured secular frequencies with a numerical simulation, we propose using a pre-calibrated voltage divider to determine the absolute amplitude of large RF voltages amplified by a helical resonator. The proposed method does not require measurement of secular frequencies and completely removes uncertainty caused by limitations of numerical simulations. To experimentally demonstrate our method, we first obtained a functional relation between measured secular frequencies and large amplitudes of RF voltages using the calibrated voltage divider. A comparison of measured relations and simulation results without any fitting parameters confirmed the validity of the proposed method. Our method can be applied to most ion trap experiments. In particular, it will be an essential tool for surface ion traps which are extremely vulnerable to unknown large RF voltages and for improving the accuracy of numerical simulations for ion trap experiments.

Recovering the instantaneous images of underwater objects distorted by surface waves

ABSTRACT Method for recovering the single instantaneous images of underwater objects distorted by surface waves is presented. This method consists of a combination of two independent parts. In the first part, the algorithm for the determination of an instantaneous relief of waved sea surface from sunglints characteristics has been developed. The instantaneous relief is presented as a sum of harmonics with unknown amplitudes, wavenumbers and phases. To find those unknowns, a system of nonlinear equations that includes the parameters of sunglints, such as the coordinates of glints and their sizes, was derived. The number of unknowns depends on a number of harmonics in a sum, approximating the instantaneous surface relief. In the second part, the algorithm for recovering of the instantaneous image of an underwater object distorted by surface waves is developed. The correctness of the method is tested by a natural experiment.

Experimental Validation of a Nonlinear Wave Encounter Frequency Estimator Onboard a Wave-Propelled USV

Abstract Knowledge of the amplitude and frequency of sea waves is useful to characterize the sea state, and increases the situational awareness as perceived by unmanned marine crafts. The ability to adapt navigation control parameters according to the current sea state is an essential feature for vehicles whose motion is mainly governed by environmental forces. From a control perspective, an estimate of the wave encounter frequency (WEF) can be used to filter out first-order wave-induced motions that cause undesired rudder control action and servo wear and deterioration. In this work we consider a nonlinear second-order observer capable of computing the approximate frequency of a sinusoidal signal with unknown amplitude and phase. This work presents the first experimental validation of the nonlinear estimator, which is tested for the first time on a five meters long wave-propelled unmanned surface vehicle (USV). Moreover, this article shows the estimator’s ability to characterize the dominant frequency of wave spectra across different sea states and discusses two applications of the WEF estimation: sea state estimation and wave-filtered steering control. Theoretical considerations are supported with both simulation and experimental results.

Antenna Array Calibration Using a Sparse Scene

In radar systems, antenna arrays acquire direction-dependent information to localize targets or create images of the environment. However, because of unknown complex amplitudes per channel and mutual coupling, a calibration is necessary for good performance. Common calibration approaches measure to targets under known angles in a multipath-free far-field environment, which often can only be provided by anechoic chambers. Therefore, this process is not suitable for low-cost and frequent calibration. To overcome these limitations, this paper proposes a novel calibration approach using an unknown but sparse target scene. Multiple measurements at known relative positions of the radar are combined to a synthetic aperture. Then, the full mutual coupling matrix is estimated simultaneously with the unknown target scene. The method requires neither target position information, far-field conditions, nor an anechoic chamber because multipath propagation can be suppressed easily for targets located in the near-field. The proposed calibration approach is validated by measurements of a commercial 77GHz radar. The performance is evaluated by comparing the achieved image quality using the calibration results of this work and the radar’s ex-factory calibration data. The proposed novel calibration procedure improves the image quality, while considerably lowering the demands on the calibration measurements and environment.

FLUID INHOMOGENEITY INFLUENCING WAVE MOTION

This article deals with a problem that describes the propagation of surface waves in a layer of an inhomogeneous fluid. The authors present a mathematical model that describes wave motions on the surface of an ideal exponentially stratified fluid. In the equations and boundary conditions, the transition to dimensionless variables and quantities has been completed. Next, a linear version of the problem follows, the solution of which is in the form of progressive waves of a steady-state form with unknown amplitude coefficients. This type of solution is substituted into the equations and boundary conditions of the linear problem, which makes it possible to reduce the determination of unknown quantities to the problem of solving a system of ordinary differential equations. Solving the system has allowed identifying two areas of physical parameters with different nature of wave motion. Expressions are obtained for the unknown components of the fluid velocity, pressure, free surface shape, and wave frequency. This article contains the analysis of the influence of various parameters of the problem on the wave motion: graphs of the dependence of the phase velocity of the wave on the stratification parameter are constructed for different layer depths and wavelengths. For a better understanding of the nature of wave motion, the expressions for the trajectories of liquid particles are determined. This has required writing the equations of motion of particles using the obtained expressions for the components of the velocity vector; these equations are solved with the method of asymptotic approximations. A graphical analysis of the effect of the stratification parameter value on the particle trajectory shape is carried out. The results have revealed that an increase in stratification leads to a compression of the trajectory in the vertical direction.

Adaptive Consensus and Parameter Estimation of Multiagent Systems With an Uncertain Leader

In this article, the problem of simultaneous leader-following consensus and parameter estimation is studied for a class of multiagent systems subject to an uncertain leader system. The leader system is described by a sum of sinusoids with unknown amplitudes, frequencies, and phases. A fully distributed adaptive observer is established for each agent to estimate the unknown frequencies of the leader without using any global information. It is shown that if the signal of the leader is sufficiently rich, the estimation errors of the unknown frequencies converge to zero asymptotically for all the agents. Based on the designed distributed adaptive observer, a distributed adaptive control law is synthesized for each agent to solve the leader-following consensus problem.

Scattering and diffraction of a uniform complex-source beam by a slit in a perfectly conducting plane screen

Abstract. A new multipole solution in plane-polar coordinates for the scattering of an arbitrary TE- or TM-polarized incident field by an infinitely extended slit in a plane screen is derived. To this end a classical three-domain problem with a complete multipole expansion in each of the domains is formulated. The unknown multipole amplitudes are found from the continuity conditions of the tangential electric and magnetic field components. Finally an infinite system of linear equations is derived which can be approximated by a numerically tractable finite one leading to a solution with an arbitrary accuracy. The results are numerically successfully compared to those ones obtained by classically solving the strip problem using Mathieu functions and by a subsequent application of the rigorous form of the Babinet principle. Numerical results include the comparison of the scattered fields obtained for an incident uniform complex-source beam and for an incident plane wave.

Консистентнiсть оцiнки найменших квадратiв параметрiв тригонометричної моделi регресiї у присутностi лiнiйного випадкового шуму

Регресiйний аналiз є iстотною частиною математичної та прикладної статистики. Нелiнiйний регресiйний аналiз є значним розширенням та ускладненням класичного лiнiйного регресiйного аналiзу, завдяки використанню нелiнiйних або частково нелiнiйних за параметрами моделей, якi адекватнiше описують, нiж лiнiйнi моделi, явища, що потребують статистичного аналiзу. Велика кiлькiсть прикладних проблем у численних наукових, технiчних та гуманiтарних галузях знань дають поштовх розвитку нелiнiйного регресiйного аналiзу. Задача оцiнювання векторного параметра сигналу в моделях спостереження «сигнал + шум» є добре вiдомою проблемою статистики випадкових процесiв, та у випадку нелiнiйного параметра сигналу – задачею нелiнiйного регресiйного аналiзу. Серед рiзноманiтностi задач нелiнiйного регресiйного аналiзу оцiнювання амплiтуд та кутових частот суми гармонiчних коливань, що спостерiгається на фонi випадкового шуму, займає значне мiсце, завдяки її численним застосуванням. Статистичнi моделi такого типу називаються тригонометричними моделями регресiї, а проблема статистичного оцiнювання її параметрiв називається задачею виявлення прихованих перiодичностей. Статтю присвячено вивченню тригонометричної моделi регресiї, в якiй випадковий шум є лiнiйним Левi-керованим стацiонарним четвертого порядку випадковим процесом iз нульовим середнiм, iнтегровную та iнтегровную з квадратом iмпульсною перехiдною функцiєю. Це припущення призводить до iнтегровностi коварiацiйної функцiї та кумулянтної функцiї 4-го порядку. Для оцiнювання амплiтуд та кутових частот такої тригонометричної моделi ми використовуємо оцiнки найменших квадратiв у сенсi Уолкера, тобто розглянуто спецiальну множину параметрiв, щоб розрiзнити належним чином рiзнi кутовi частоти в сумi гармонiчних коливань. У статтi доведено теорему про сильну консистентнiсть оцiнки найменших квадратiв за описаними вище припущеннями щодо випадкового шуму. Для отримання такого результату було доведено дуже важливу лему про рiвномiрну збiжнiсть майже напевно середнього значення перетворення Фурьє лiнiйного Левi-керованого випадкового процеса. Ця лема є головним iнструментом доведення теореми про сильну консистентнiсть. Для доведення теореми, по-перше, знаходимо деякi представлення оцiнок найменших квадратiв амплiтуд через вiдповiднi оцiнки кутових частот. По-друге, ми пiдставляємо цi формули у функцiонал методу найменших квадратiв. Останнiй крок доведення полягає у перетвореннi L2-норми рiзницi мiж емпiричною тригонометричною функцiєю регресiї та iстиною функцiєю регресiї таким чином, що ця норма прямує до нуля майже напевно тодi i тiльки тодi, коли оцiнки є сильно консистентними.

A new parametric adaptive detector with mismatched signals rejection capability in AR model interference

This paper addresses the multichannel adaptive detection of signal with unknown amplitude in the presence of coloured Gaussian interference. The interference is modelled as an autoregressive (AR) process with regard to its spatial and temporal correlation. We propose a new parametric detector in which the ability to reject fictitious targets is considered by including a mismatched signal in the null hypothesis at the design stage. Simulation results and comparison with the well-known methods show that the proposed detector has proper performance at detecting the mainlobe targets especially in cases with less or even no secondary data. Also, the proposed detector can effectively reject the fictitious or sidelobe targets while the previous detectors based on AR model interference do not have such a capability.

Generalized Beam Theory for Thin-Walled Beams with Curvilinear Open Cross-Sections

The use of the Generalized Beam Theory (GBT) is extended to thin-walled beams with curvilinear cross-sections. After defining the kinematic features of the walls, where their curvature is consistently accounted for, the displacement of the points is assumed as linear combination of unknown amplitudes and pre-established trial functions. The latter, and specifically their in-plane components, are chosen as dynamic modes of a curved beam in the shape of the member cross-section. Moreover, the out-of-plane components come from the imposition of the Vlasov internal constraint of shear indeformable middle surface. For a case study of semi-annular cross-section, i.e., constant curvature, the modes are analytically evaluated and the procedure is implemented for two different load conditions. Outcomes are compared to those of a FEM model.

Design, implementation, and evaluation of a backstepping control algorithm for an active ankle–foot orthosis

Active ankle–foot orthoses are used to assist patients suffering from stroke, multiple sclerosis, cerebral palsy etc. through providing them an external force supply to track normal gait cycles. In this paper, an active ankle–foot orthosis prototype is developed and an adaptive backstepping control algorithm is proposed for tracking desired gait trajectories while reducing the effects of unknown disturbances. A prototype of the orthosis, which is composed of a series elastic actuator, a lever mechanism and an orthotic shoe, is developed. The prototype is mathematically modeled as a two-degree-of-freedom mass–spring system. The unknown disturbances are modeled as a finite sum of sinusoidal signals with unknown amplitudes, frequencies and phases, and an unknown constant. The backstepping control algorithm is designed for the force input supplied to the system, and the stability of the equilibrium point is proved. The proposed algorithm is implemented in a real-time operating system to control the developed ankle–foot orthosis prototype. Numerical simulations and physical experiments on healthy human subjects are performed to show the superiority of the proposed design over a PID controller in trajectory tracking of the prototype. As a further development, an embedded system is designed to bring portability to the ankle–foot orthosis prototype. Experiments are performed to observe the execution performance and power consumption of the embedded system.

Detecting a radio signal with the unknown parameters and inexactly known envelope shape

The new quasi-likelihood algorithm is considered for detecting a radio signal with the unknown amplitude, duration, initial phase and inexactly known envelope shape against Gaussian white noise. The structure and the statistical characteristics of the introduced detection algorithm are found. The influence is studied of the difference in the envelope shapes of the received and reference signals upon detection efficiency.

Adaptive synchronization for surface vessels with disturbances and saturated thruster dynamics

This work investigates the adaptive synchronization for the surface vessels with disturbances and saturated thruster dynamics. The vessel movement model becomes the three-order equation with mismatched disturbances due to the inclusion of saturated thruster dynamics. The marine disturbances are described as the multiple harmonic disturbances with unknown frequencies, unknown amplitudes and unknown phases. By fusions of the nonlinear observer and the adaptive technique, the marine disturbance estimation and rejection are transformed into the adaptive problem. The auxiliary dynamic filter generates the state vectors to represent the filtered versions of the non-achievable portions of the vessel’s positions and velocities. The state vectors on-line correct the control errors for avoiding disturbance rejection performance compromise under thruster saturation. The synchronization controller is derived via the adaptive command filtered backstepping. The surface vessel closed-loop control system is guaranteed stable. The adaptive synchronization scheme is validated by simulations with comparisons in different cases.

Modelling and simulation studies on adaptive controller for alt-azimuth telescopes despite unknown wind disturbance and mass

Numerous ground-based observatories are using small sized ground telescopes for scientific research purposes. The telescopes that are available on the market have three main problems. These issues can be listed as: positioning repeatability, tuning requirement according to different wind speeds for different seasons, and the mass changing via different scientific equipments added to the telescope. This study is aimed at resolving these issues for ground based small alt-azimuth telescopes. Establishing of a set and forget system is performed by designing an adaptive controller. Motor dynamics are taken into consideration for a realistic mathematical model. The Wind-Gust model that consists of a sum of sinusoidal disturbances with unknown phase, amplitude and frequency is used for the wind model. The purposed controller cancels the disturbance effects on the plant while operational positioning and also the makes the plant insensitive to mass changes. The Lyapunov approach is utilised when proving the asymptotic stability. The proposed controller’s success is illustrated with thorough numerical evaluation.

Adaptive disturbance estimation and cancelation for ships under thruster saturation

SummaryThis work addresses the problem of disturbance estimation and cancelation for ships with ocean disturbances and modeling uncertainties under thruster saturation effects. The ocean disturbances are expressed as the multiple sinusoidal disturbances with unknown frequencies, amplitudes, and phases. By means of a parametric exogenous system and a canonical model with unknown disturbances being inputs, the ocean disturbances are represented as the multivariate regression model with unavailable regressors and regression parameters. An observer is employed to provide the regressor estimation, such that the disturbance estimation and cancelation are converted to the adaptive control problem. The robust control term with the adaptive technique attenuates the modeling uncertainties. The thruster saturation effects are reduced using the state vectors from the auxiliary dynamic filter to online correct the control errors. The ship disturbance cancelation controller is derived via the adaptive backstepping. The closed‐loop tracking system is guaranteed to be uniformly ultimately stable and the ship's position and heading navigate along with desired trajectories. The proposed adaptive control scheme is validated by simulations with comparisons on a 1:70 scaled model ship CyberShip II in different cases.

Gridless Underdetermined DOA Estimation of Wideband LFM Signals With Unknown Amplitude Distortion Based on Fractional Fourier Transform

In this article, a wideband Direction-of-Arrival (DOA) estimation method for underdetermined scenarios is proposed, which effectively solves the basis mismatch problem. Based on the fractional Fourier transform (FRFT), the wideband received signal model with a coprime array is first derived by exploiting the aggregation characteristic of wideband linear frequency modulated (LFM) signals in the fractional Fourier (FRF) domain. Then, in order to increase the degree of freedom, an extended uniform linear array is built, and the covariance matrix of the signal is reconstructed by employing the penalized atomic norm minimization with the consecutive spatial dictionary. Meanwhile, without the knowledge of the noise level, the noise variance is estimated from the noisy incomplete data, which is utilized to improve the covariance matrix reconstruction performance. Additionally, for the unconditional model, the Cramér-Rao bound for the wideband DOA estimation based on a coprime array is derived. Different from the existing methods, the proposed method not only can estimate more DOAs of wideband signals than the number of physical sensors in the presence of unknown amplitude distortion but also can obtain more accurate DOA estimation performance without basis mismatch. The effectiveness of the proposed method is verified by our numerical results.

Adaptive Control Algorithms in MIMO Linear Systems with Control Delay

In this paper we present two adaptive state control algorithms for the class of linear multi-input multi-output plants under external disturbances and the presence of control delay. Reference signal and external disturbance are considered as multi-harmonic signals with unknown frequencies, amplitudes, and initial phases. The algorithms are developed using the direct adaptive control method based on the internal model principle and do not require identification of disturbance parameters and/or the reference signal.

Simulating the complexity of the dark matter sheet I: numerical algorithms

ABSTRACT At early times, dark matter has a thermal velocity dispersion of unknown amplitude which, for warm dark matter (WDM) models, can influence the formation of non-linear structure on observable scales. We propose a new scheme to simulate cosmologies with a small-scale suppression of perturbations that combines two previous methods in a way that avoids the numerical artefacts which have so far prevented either from producing fully reliable results. At low densities and throughout most of the cosmological volume, we represent the dark matter phase sheet directly using high-accuracy interpolation, thereby avoiding the artificial fragmentation which afflicts particle-based methods in this regime. Such phase-sheet methods are, however, unable to follow the rapidly increasing complexity of the denser regions of dark matter haloes, so for these we switch to an N-body scheme which uses the geodesic deviation equation to track phase-sheet properties local to each particle. In addition, we present a novel high-resolution force calculation scheme based on an oct-tree of cubic force resolution elements which is well suited to approximate the force field of our combined sheet+particle distribution. Our hybrid simulation scheme enables the first reliable simulations of the internal structure of low-mass haloes in a WDM cosmology.

Statistical Tests for Force Inference in Heterogeneous Environments

We devise a method to detect and estimate forces in a heterogeneous environment based on experimentally recorded stochastic trajectories. In particular, we focus on systems modeled by the heterogeneous overdamped Langevin equation. Here, the observed drift includes a "spurious” force term when the diffusivity varies in space. We show how Bayesian inference can be leveraged to reliably infer forces by taking into account such spurious forces of unknown amplitude as well as experimental sources of error. The method is based on marginalizing the force posterior over all possible spurious force contributions. The approach is combined with a Bayes factor statistical test for the presence of forces. The performance of our method is investigated analytically, numerically and tested on experimental data sets. The main results are obtained in a closed form allowing for direct exploration of their properties and fast computation. The method is incorporated into TRamWAy, an open-source software platform for automated analysis of biomolecule trajectories.