Denoising nonlinear dynamical systems
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dynamical system, denoising, kalman filter, koopma↗
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Method and System for Temporal Filtering in Video Compression Systems
Three related innovations combine improved non-linear motion estimation, video coding, and video compression. The first system comprises a method in which side information is generated using an adaptive, non-linear motion model. This method enables extrapolating and interpolating a visual signal, including determining the first motion vector between the first pixel position in a first image to a second pixel position in a second image; determining a second motion vector between the second pixel position in the second image and a third pixel position in a third image; determining a third motion vector between the first pixel position in the first image and the second pixel position in the second image, the second pixel position in the second image, and the third pixel position in the third image using a non-linear model; and determining a position of the fourth pixel in a fourth image based upon the third motion vector. For the video compression element, the video encoder has low computational complexity and high compression efficiency. The disclosed system comprises a video encoder and a decoder. The encoder converts the source frame into a space-frequency representation, estimates the conditional statistics of at least one vector of space-frequency coefficients with similar frequencies, and is conditioned on previously encoded data. It estimates an encoding rate based on the conditional statistics and applies a Slepian-Wolf code with the computed encoding rate. The method for decoding includes generating a side-information vector of frequency coefficients based on previously decoded source data and encoder statistics and previous reconstructions of the source frequency vector. It also performs Slepian-Wolf decoding of a source frequency vector based on the generated side-information and the Slepian-Wolf code bits. The video coding element includes receiving a first reference frame having a first pixel value at a first pixel position, a second reference frame having a second pixel value at a second pixel position, and a third reference frame having a third pixel value at a third pixel position. It determines a first motion vector between the first pixel position and the second pixel position, a second motion vector between the second pixel position and the third pixel position, and a fourth pixel value for a fourth frame based upon a linear or nonlinear combination of the first pixel value, the second pixel value, and the third pixel value. A stationary filtering process determines the estimated pixel values. The parameters of the filter may be predetermined constants.
Lu, Ligang↗
Experimental parameters, combined dynamics, and nonlinearity of a magnonic-opto-electronic oscillator (MOEO)
We report the construction and characterization of a comprehensive magnonic-opto-electronic oscillator (MOEO) system based on 1550-nm photonics and yttrium iron garnet (YIG) magnonics. The system exhibits a rich and synergistic parameter space because of the ability to control individual photonic, electronic, and magnonic components. Taking advantage of the spin wave dispersion of YIG, the frequency self-generation as well as the related nonlinear processes becomes sensitive to the external magnetic field. Besides being known as a band-pass filter and a delay element, the YIG delay line possesses spin wave modes that can be controlled to mix with the optoelectronic modes to generate higher-order harmonic beating modes. With the high sensitivity and external tunability, the MOEO system may find usefulness in sensing applications in magnetism and spintronics beyond optoelectronics and photonics.
47 OTHER INSTRUMENTATION↗
Encoding and decoding of color information using two-dimensional spatial filtering.
Spatial frequency encoding is described as it applies to both photographic and television systems. In each case, color separations amplitude modulate spatial frequency carriers. The photographic system separates the carriers in the two-dimensional Fourier transform plane using coherent optics; the television system employs a two-dimensional electrical filter to perform the same separation. These filters are synthesized so that the two-dimensional bandwidths of the television camera are used efficiently. Nonlinear processing techniques are also described to minimize crosstalk between channels.
Schaefer, L. F.↗
Normal Mode Initialization
The objective of this research is the development and implementation of normal mode procedures for use with the GLAS analysis/forecast system. Specific tasks of this work include: (1) high latitude filtering of model fields to preserve the GLAS GCM's linear stability during integration; (2) development of nonlinear normal mode initialization (NLNMI) processes, both adiabatic and diabatic. Using NLNMI to initialize GLAS analyses; investigation of the impact of normal mode initialization on the GLAS analysis/forecast system, especially in regard to data assimilation; and (3) diagnosis of the 1-3 day systemic forecast errors of the GLAS GCM.
Bloom, S. C.↗
Angular-Rate Estimation Using Delayed Quaternion Measurements
This paper presents algorithms for estimating the angular-rate vector of satellites using quaternion measurements. Two approaches are compared one that uses differentiated quaternion measurements to yield coarse rate measurements, which are then fed into two different estimators. In the other approach the raw quaternion measurements themselves are fed directly into the two estimators. The two estimators rely on the ability to decompose the non-linear part of the rotas rotational dynamics equation of a body into a product of an angular-rate dependent matrix and the angular-rate vector itself. This non unique decomposition, enables the treatment of the nonlinear spacecraft (SC) dynamics model as a linear one and, thus, the application of a PseudoLinear Kalman Filter (PSELIKA). It also enables the application of a special Kalman filter which is based on the use of the solution of the State Dependent Algebraic Riccati Equation (SDARE) in order to compute the gain matrix and thus eliminates the need to compute recursively the filter covariance matrix. The replacement of the rotational dynamics by a simple Markov model is also examined. In this paper special consideration is given to the problem of delayed quaternion measurements. Two solutions to this problem are suggested and tested. Real Rossi X-Ray Timing Explorer (RXTE) data is used to test these algorithms, and results are presented.
Azor, R.↗
Extended Decentralized Linear-Quadratic-Gaussian Control
A straightforward extension of a solution to the decentralized linear-Quadratic-Gaussian problem is proposed that allows its use for commonly encountered classes of problems that are currently solved with the extended Kalman filter. This extension allows the system to be partitioned in such a way as to exclude the nonlinearities from the essential algebraic relationships that allow the estimation and control to be optimally decentralized.
Carpenter, J. Russell↗
A simple dynamic engine model for use in a real-time aircraft simulation with thrust vectoring
A simple dynamic engine model was developed at the NASA Ames Research Center, Dryden Flight Research Facility, for use in thrust vectoring control law development and real-time aircraft simulation. The simple dynamic engine model of the F404-GE-400 engine (General Electric, Lynn, Massachusetts) operates within the aircraft simulator. It was developed using tabular data generated from a complete nonlinear dynamic engine model supplied by the manufacturer. Engine dynamics were simulated using a throttle rate limiter and low-pass filter. Included is a description of a method to account for axial thrust loss resulting from thrust vectoring. In addition, the development of the simple dynamic engine model and its incorporation into the F-18 high alpha research vehicle (HARV) thrust vectoring simulation. The simple dynamic engine model was evaluated at Mach 0.2, 35,000 ft altitude and at Mach 0.7, 35,000 ft altitude. The simple dynamic engine model is within 3 percent of the steady state response, and within 25 percent of the transient response of the complete nonlinear dynamic engine model.
Johnson, Steven A.↗
A simulation study of turbofan engine deterioration estimation using Kalman filtering techniques
Deterioration of engine components may cause off-normal engine operation. The result is an unecessary loss of performance, because the fixed schedules are designed to accommodate a wide range of engine health. These fixed control schedules may not be optimal for a deteriorated engine. This problem may be solved by including a measure of deterioration in determining the control variables. These engine deterioration parameters usually cannot be measured directly but can be estimated. A Kalman filter design is presented for estimating two performance parameters that account for engine deterioration: high and low pressure turbine delta efficiencies. The delta efficiency parameters model variations of the high and low pressure turbine efficiencies from nominal values. The filter has a design condition of Mach 0.90, 30,000 ft altitude, and 47 deg power level angle (PLA). It was evaluated using a nonlinear simulation of the F100 engine model derivative (EMD) engine, at the design Mach number and altitude over a PLA range of 43 to 55 deg. It was found that known high pressure turbine delta efficiencies of -2.5 percent and low pressure turbine delta efficiencies of -1.0 percent can be estimated with an accuracy of + or - 0.25 percent efficiency with a Kalman filter. If both the high and low pressure turbine are deteriorated, the delta efficiencies of -2.5 percent to both turbines can be estimated with the same accuracy.
Lambert, Heather H.↗
Nonlinear time-series analysis of current signal in cathodic contact glow discharge electrolysis
In the standard two-electrode configuration employed in electrolytic process, when the control dc voltage is brought to a critical value, the system undergoes a transition from conventional electrolysis to contact glow discharge electrolysis (CGDE), which has also been referred to as liquid-submerged micro-plasma, glow discharge plasma electrolysis, electrode effect, electrolytic plasma, etc. The light-emitting process is associated with the development of an irregular and erratic current time-series which has been arbitrarily labelled as “random,” and thus dissuaded further research in this direction. Here, we examine the current time-series signals measured in cathodic CGDE configuration in a concentrated KOH solution at different dc bias voltages greater than the critical voltage. We show that the signals are, in fact, not random according to the NIST SP. 800-22 test suite definition. We also demonstrate that post-processing low-pass filtered sequences requires less time than the native as-measured sequences, suggesting a superposition of low frequency chaotic fluctuations and high frequency behaviors (which may be produced by more than one possible source of entropy). Using an array of nonlinear time-series analyses for dynamical systems, i.e., the computation of largest Lyapunov exponents and correlation dimensions, and re-construction of phase portraits, we found that low-pass filtered datasets undergo a transition from quasi-periodic to chaotic to quasi-hyper-chaotic behavior, and back again to chaos when the voltage controlling-parameter is increased. The high frequency part of the signals is discussed in terms of highly nonlinear turbulent motion developed around the working electrode.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Crystalline Colloidal Arrays in Polymer Matrices
Crystalline Colloidal Arrays (CCA, also known as colloidal crystals), composed of aqueous or nonaqueous dispersions of self-assembled nanosized polymer colloidal spheres, are emerging toward the development of advanced optical devices for technological applications. The spontaneous self assembly of polymer spheres in a dielectric medium results from the electrostatic repulsive interaction between particles of uniform size and charge distribution. In a way similar to atomic crystals that diffract X-rays, CCA dispersions in thin quartz cells selectively and efficiently Bragg diffract the incident visible light. The reason for this diffraction is because the lattice (body or face centered cubic) spacing is on the order of the wavelength of visible light. Unlike the atomic crystals that diffract a fixed wavelength, colloidal crystals in principle, depending on the particle size, particle number and charge density, can diffract W, Vis or IR light. Therefore, the CCA dispersions can be used as laser filters. Besides, the diffraction intensity depends on the refractive index mismatch between polymer spheres and dielectric medium; therefore, it is possible to modulate incident light intensities by manipulating the index of either the spheres or the medium. Our interest in CCA is in the fabrication of all-optical devices such as optical switches, limiters, and spatial light modulators for optical signal processing. The two major requirements from a materials standpoint are the incorporation of suitable nonlinear optical materials (NLO) into polymer spheres which will allow us to alter the refractive index of the spheres by intense laser radiation, and preparation of solid CCA filters which can resist laser damage. The fabrication of solid composite filters not only has the advantage that the films are easier to handle, but also the arrays in solid films are more robust than in liquid media. In this paper, we report the photopolymerization process used to trap CCA in polymer matrices, the factors which affect the optical diffraction qualities of resulting polymer films, and methods to improve the efficiencies of solid optical filters. Before this, we also present the experimental demonstration, of controlling the optical diffraction intensities from aqueous CCA dispersions by varying the temperature, which establishes the feasibility of fabricating all-optical switching devices with nonlinear periodic array structures.
Sunkara, Hari B.↗
Magneto-ballistic transport in GaN nanowires
The ballistic filtering property of nanoscale crosses was used to investigate the effect of perpendicular magnetic fields on the ballistic transport of electrons on wide band-gap GaN heterostructures. The straight scattering-less trajectory of electrons was modified by a perpendicular magnetic field which produced a strong non-linear behavior in the measured output voltage of the ballistic filters and allowed the observation of semi-classical and quantum effects, such as quenching of the Hall resistance and manifestation of the last plateau, in excellent agreement with the theoretical predictions. A large measured phase coherence length of 190 nm allowed the observation of universal quantum fluctuations and weak localization of electrons due to quantum interference up to ∼25 K. This work also reveals the prospect of wide band-gap GaN semiconductors as a platform for basic transport and quantum studies, whose properties allow the investigation of ballistic transport and quantum phenomena at much larger voltages and temperatures than in other semiconductors.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Model reference adaptive control using only input and output signals
It is shown how globally stable model reference adaptive control systems may be designed using only the plant's input and output signals. Controllers for single input-single output, nonlinear, nonautonomous plants are developed based on Liapunov's direct method and the Meyer-Kalman-Yacubovich lemma. Filtered derivatives of the plant output replace pure derivatives which are normally required in these systems. An augmented error signal replaces the error previously used which is the difference between the model and plant outputs. However, global stability is assured in the sense that this difference approaches zero asymptotically.
Monopoli, R. V.↗
Neuromorphic learning of continuous-valued mappings from noise-corrupted data. Application to real-time adaptive control
The ability of feed-forward neural network architectures to learn continuous valued mappings in the presence of noise was demonstrated in relation to parameter identification and real-time adaptive control applications. An error function was introduced to help optimize parameter values such as number of training iterations, observation time, sampling rate, and scaling of the control signal. The learning performance depended essentially on the degree of embodiment of the control law in the training data set and on the degree of uniformity of the probability distribution function of the data that are presented to the net during sequence. When a control law was corrupted by noise, the fluctuations of the training data biased the probability distribution function of the training data sequence. Only if the noise contamination is minimized and the degree of embodiment of the control law is maximized, can a neural net develop a good representation of the mapping and be used as a neurocontroller. A multilayer net was trained with back-error-propagation to control a cart-pole system for linear and nonlinear control laws in the presence of data processing noise and measurement noise. The neurocontroller exhibited noise-filtering properties and was found to operate more smoothly than the teacher in the presence of measurement noise.
Troudet, Terry↗
PSC algorithm description
An overview of the performance seeking control (PSC) algorithm and details of the important components of the algorithm are given. The onboard propulsion system models, the linear programming optimization, and engine control interface are described. The PSC algorithm receives input from various computers on the aircraft including the digital flight computer, digital engine control, and electronic inlet control. The PSC algorithm contains compact models of the propulsion system including the inlet, engine, and nozzle. The models compute propulsion system parameters, such as inlet drag and fan stall margin, which are not directly measurable in flight. The compact models also compute sensitivities of the propulsion system parameters to change in control variables. The engine model consists of a linear steady state variable model (SSVM) and a nonlinear model. The SSVM is updated with efficiency factors calculated in the engine model update logic, or Kalman filter. The efficiency factors are used to adjust the SSVM to match the actual engine. The propulsion system models are mathematically integrated to form an overall propulsion system model. The propulsion system model is then optimized using a linear programming optimization scheme. The goal of the optimization is determined from the selected PSC mode of operation. The resulting trims are used to compute a new operating point about which the optimization process is repeated. This process is continued until an overall (global) optimum is reached before applying the trims to the controllers.
Nobbs, Steven G.↗
Angular-Rate Estimation Using Star Tracker Measurements
This paper presents algorithms for estimating the angular-rate vector of satellites using quaternion measurements. Two approaches are compared, one that uses differentiated quatemion measurements to yield coarse rate measurements which are then fed into two different estimators. In the other approach the raw quatemion measurements themselves are fed directly into the two estimators. The two estimators rely on the ability to decompose the non-linear rate dependent part of the rotational dynamics equation of a rigid body into a product of an angular-rate dependent matrix and the angular-rate vector itself This decomposition, which is not unique, enables the treatment of the nonlinear spacecraft dynamics model as a linear one and, consequently, the application of a Pseudo-Linear Kalman Filter (PSELIKA). It also enables the application of a special Kalman filter which is based on the use of the solution of the State Dependent Algebraic Riccati Equation (SDARE) in order to compute the Kalman gain matrix and thus eliminates the need to propagate and update the filter covariance matrix. The replacement of the elaborate rotational dynamics by a simple first order Markov model is also examined. In this paper a special consideration is given to the problem of delayed quatemion measurements. Two solutions to this problem are suggested and tested. Real Rossi X-Ray Timing Explorer (RXTE) data is used to test these algorithms, and results of these tests are presented.
Azor, R.↗
Angular-Rate Estimation using Star Tracker Measurements
This paper presents algorithms for estimating the angular-rate vector of satellites using quaternion measurements. Two approaches are compared, one that uses differentiated quaternion measurements to yield coarse rate measurements which are then fed into two different estimators. In the other approach the raw quaternion measurements themselves are fed directly into the two estimators. The two estimators rely on the ability to decompose the non-linear rate dependent part of the rotational dynamics equation of a rigid body into a product of an angular-rate dependent matrix and the angular-rate vector itself. This decomposition, which is not unique, enables the treatment of the nonlinear spacecraft dynamics model as a linear one and, consequently, the application of a Pseudo-Linear Kalman Filter (PSELIKA). It also enables the application of a special Kalman filter which is based on the use of the solution of the State Dependent Algebraic Riccati Equation (SDARE) in order to compute the Kalman gain matrix and thus eliminates the need to propagate and update the filter covariance matrix. The replacement of the elaborate rotational dynamics by a simple first order Markov model is also examined. In this paper a special consideration is given to the problem of delayed quaternion measurements. Two solutions to this problem are suggested and tested. Real Rossi X-Ray Timing Explorer (RXTE) data is used to test these algorithms, and results of these tests are presented.
Azor, R.↗
Mesosphere Dynamics with Gravity Wave Forcing: Diurnal and Semi-Diurnal Tides - 1
We present results from a nonlinear, 3D, time dependent numerical spectral model (NSM), which extends from the ground up into the thermosphere and incorporates Hines' Doppler Spread Parameterization for small-scale gravity waves (GW). Our focal point is the mesosphere that is dominated by wave interactions. We discuss diurnal and semi-diurnal tides ill the present paper (Part 1) and planetary waves in the companion paper (Part 2). To provide an understanding of the seasonal variations of tides, in particular with regard to gravity wave processes, numerical experiments are performed that lead to the following conclusions: 1. The large semiannual variations in tile diurnal tide (DT), with peak amplitudes observed around equinox, are produced primarily by GW interactions that involve, in part, planetary waves. 2. The DT, like planetary waves, tends to be amplified by GW momentum deposition, which reduces also the vertical wavelength. 3.Variations in eddy viscosity associated with GW interactions tend to peak in late spring and early fall and call also influence the DT. 4. The semidiurnal semidiurnal tide (SDT), and its phase in particular, is strongly influenced by the mean zonal circulation. 5. The SDT, individually, is amplified by GW's. But the DT filters out GW's such that the wave interaction effectively reduces the amplitude of the SDT, effectively producing a strong nonlinear interaction between the DT and SDT. 6.) Planetary waves generated internally by baroclinic instability and GW interaction produce large amplitude modulations of the DT and SDT.
Mayr, H. G.↗