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Differential equations for minimum variance linear filter separating signals from additive correlated noise, using discrete time optimum formulas
It is argued that the design of a single input single output (SISO) control system is simplified if the designer has direct control over the closed loop poles. A space-laser-communications design example utilizing a two-transform algorithm that constructs a generic discrete compensator is presented. The plant in the example has an anti-aliasing filter, a double integrator, a torquer time constant, and a sample-and-hold as continuous elements, and a discrete proportional plus integral module. This fifth-order system is representative of many instrument pointing control systems. Poles resulting from the compensator are placed near the origin of the Z-plane so that the response is dominated by the closed loop poles from the plant. Root locus, time response, and frequency response data are given. Normalization by the sample interval is used to provide a dimensionless example.
A method for calculating the increase in received telemetry signal power required to compensate for the use of a radio frequency interference (RFI) filter in front of the DSN receiving system low-noise amplifier is described. The telemetry system for which the degradation is calculated is an uncoded PCM/PM system in which the NRZ data directly modulates the carrier at a modulation level which leaves a discrete carrier. A phase-locked loop in the RF receiver tracks the discrete carrier and coherently demodulates the PCM data. The RFI filter may be a series of Butterworth, Tchebychev, or Bessel low-pass, high-pass, band-pass, or band-reject filters, each with arbitrary bandwidth, number of poles, and, for band-pass or band-reject filters, resonant frequency. The only restriction is that the RFI filter must have only simple poles. Numerical results are presented for the RFI filters the DSN plans to place in front of the S-band FET, S-band maser, and X-band maser low noise amplifiers. The main conclusion is that the filters will produce negligible degradation at data rates below 4 Mbps.
Controlling the delivery of kHz-class pulsed lasers is of interest in a variety of industrial and scientific applications, from next-generation laser-plasma acceleration to laser-based x-ray emission and high-precision manufacturing. The transverse position of the laser pulse train on the application target is often subject to fluctuations by external drivers (e.g., room cooling and heating systems, motorized optics stages and mounts, vacuum systems, chillers, and/or ground vibrations). For typical situations where the disturbance spectrum exhibits discrete peaks on top of a broad-bandwidth lower-frequency background, traditional PID (proportional-integral-derivative) controllers may struggle, since as a general rule PID controllers can be used to suppress vibrations up to only about 5%–10% of the sampling frequency. Here, a predictive feed-forward algorithm is presented that significantly enhances the stabilization bandwidth in such laser systems (up to the Nyquist limit at half the sampling frequency) by online identification and filtering of one or a few discrete frequencies using optimized Fourier filters. Furthermore, the system architecture demonstrated here uses off-the-shelf CMOS cameras and piezo-electric actuated mirrors connected to a standard PC to process the alignment images and implement the algorithm. To avoid high-end, high-cost components, a machine-learning-based model of the piezo mirror’s dynamics was integrated into the system, which enables high-precision positioning by compensating for hysteresis and other hardware-induced effects. A successful demonstration of the method was performed on a 1 kHz laser pulse train, where externally-induced vibrations of up to 400 Hz were attenuated by a factor of five, far exceeding what could be done with a standard PID scheme.
Here, the accuracy of coarse-grained Euler-Lagrangian simulations of fluidized beds heavily depends on the mesoscale drag models to account for the influences of the unresolved sub-grid structures. Traditional filtered drag models are regressed with mesoscale markers such as voidage and slip velocities. In this research, a filtered drag was regressed with both mesoscale and macro-scale markers using fine grid Computational Fluid Dynamics - Discrete Element Method (CFD-DEM) simulations. The traditional non-linear regression method was compared with machine learning regression using an Artificial Neural Network (ANN) implemented in PyTorch and coupled with MFiX. The new drag showed higher accuracy than the Wen-Yu drag and another filtered drag derived from the two-fluid model. The nonlinear regression shows slightly better results than ANN regression in cases with similar R 2 values. The utilization of the gas inlet velocity as an additional macro-scale marker reduced the errors by up to 55.3% in the tested cases.
There has been strong motivation to produce numerically stable formulations of the Kalman filter algorithms because it has long been known that the original discrete-time Kalman formulas are numerically unreliable. Numerical instability can be avoided by propagating certain factors of the estimate error covariance matrix rather than the covariance matrix itself. This paper documents filter algorithms that correspond to the covariance factorization P = UDU(T), where U is a unit upper triangular matrix and D is diagonal. Emphasis is on computational efficiency and numerical stability, since these properties are of key importance in real-time filter applications. The history of square-root and U-D covariance filters is reviewed. Simple examples are given to illustrate the numerical inadequacy of the Kalman covariance filter algorithms; these examples show how factorization techniques can give improved computational reliability.
One approach to the problem of simplifying complex nonlinear filtering algorithms is through using stratified probability approximations where the continuous probability density functions of certain random variables are represented by discrete mass approximations. This technique is developed in this paper and used to simplify the filtering algorithms developed for the optimum receiver for signals corrupted by both additive and multiplicative noise.
We present the Tucker tensor DFT (TTDFT) code which uses a tensor-structured algorithm with graphic processing unit (GPU) acceleration for conducting ground-state DFT calculations on large-scale systems. The Tucker tensor DFT algorithm uses a localized Tucker tensor basis computed from an additive separable approximation to the Kohn-Sham Hamiltonian. The discrete Kohn-Sham problem is solved using Chebyshev filtered subspace iteration method that relies on matrix-matrix multiplications of a sparse symmetric Hamiltonian matrix and a dense wavefunction matrix, expressed in the localized Tucker tensor basis. These matrix-matrix multiplication operations, which constitute the most computationally intensive step of the solution procedure, are GPU accelerated providing ~8-fold GPU-CPU speedup for these operations on the largest systems studied. In conclusion, the computational performance of the TTDFT code is presented using benchmark studies on aluminum nano-particles and silicon quantum dots with system sizes ranging up to ~7,000 atoms.
Attitude estimation of earth orbiting satellites (including Large Space Telescope) subjected to environmental disturbances and noises was investigated. Modern control and estimation theory is used as a tool to design an efficient estimator for attitude estimation. Decomposed linear recursive filters for both continuous-time systems and discrete-time systems are derived. By using this accurate estimation of the attitude of spacecrafts, state variable feedback controller may be designed to achieve (or satisfy) high requirements of system performance.
A computational fluid dynamics code has been developed for large-eddy simulations (LES) of turbulent flow. The code uses high-order of accuracy and high-resolution numerical methods to minimize solution error and maximize the resolution of the turbulent structures. Spatial discretization is performed using explicit central differencing. The central differencing schemes in the code include 2nd- to 12th-order standard central difference methods as well as 7-, 9-, 11- and 13-point dispersion relation preserving schemes. Solution filtering and high-order shock capturing are included for stability. Time discretization is performed using multistage Runge-Kutta methods that are up to 4th order accurate. Several options are available to model turbulence including: Baldwin-Lomax and Spalart-Allmaras Reynolds-averaged Navier-Stokes turbulence models, and Smagorinsky, Dynamic Smagorinsky and Vreman sub-grid scale models for LES. This report presents the theory behind the numerical and physical models used in the code and provides a user's manual to the operation of the code.
The Ormsby model of human dynamic orientation, a discrete time computer program, was used to provide a vestibular explanation for observed differences between two washout schemes. These washout schemes, a linear washout and a nonlinear washout, were subjectively evaluated. It was found that the linear washout presented false rate cues, causing pilots to rate the simulation fidelity of the linear scheme much lower than the nonlinear scheme. By inputting these motion histories into the Ormsby model, it was shown that the linear filter causes discontinuities in the pilot's perceived angular velocity, resulting in the sensation of an anomalous rate cue. This phenomenon does not occur with the use of the nonlinear filter.
A Digital Video Quality (DVQ) apparatus and method that incorporate a model of human visual sensitivity to predict the visibility of artifacts. The DVQ method and apparatus are used for the evaluation of the visual quality of processed digital video sequences and for adaptively controlling the bit rate of the processed digital video sequences without compromising the visual quality. The DVQ apparatus minimizes the required amount of memory and computation. The input to the DVQ apparatus is a pair of color image sequences: an original (R) non-compressed sequence, and a processed (T) sequence. Both sequences (R) and (T) are sampled, cropped, and subjected to color transformations. The sequences are then subjected to blocking and discrete cosine transformation, and the results are transformed to local contrast. The next step is a time filtering operation which implements the human sensitivity to different time frequencies. The results are converted to threshold units by dividing each discrete cosine transform coefficient by its respective visual threshold. At the next stage the two sequences are subtracted to produce an error sequence. The error sequence is subjected to a contrast masking operation, which also depends upon the reference sequence (R). The masked errors can be pooled in various ways to illustrate the perceptual error over various dimensions, and the pooled error can be converted to a visual quality measure.
Model-based prognostics approaches use domain knowledge about a system and its failure modes through the use of physics-based models. Model-based prognosis is generally divided into two sequential problems: a joint state-parameter estimation problem, in which, using the model, the health of a system or component is determined based on the observations; and a prediction problem, in which, using the model, the stateparameter distribution is simulated forward in time to compute end of life and remaining useful life. The first problem is typically solved through the use of a state observer, or filter. The choice of filter depends on the assumptions that may be made about the system, and on the desired algorithm performance. In this paper, we review three separate filters for the solution to the first problem: the Daum filter, an exact nonlinear filter; the unscented Kalman filter, which approximates nonlinearities through the use of a deterministic sampling method known as the unscented transform; and the particle filter, which approximates the state distribution using a finite set of discrete, weighted samples, called particles. Using a centrifugal pump as a case study, we conduct a number of simulation-based experiments investigating the performance of the different algorithms as applied to prognostics.
The most common technique for the control of structures is modal control. In modal control, the differential equations in terms of actual coordinates are replaced by a set of ordinary differential equations in terms of the modal coordinates known as modal equations. In designing feedback controls in conjunction with the modal equations, one must know the modal states for the modes targeted for control. The sensors measure actual states, however. The modal states can be estimated by means of a Luenberger observer or modal filters. The modal filters produce estimates of the modal states from distributed measurements of the states. If distributed measurements are not available, then they can be reconstructed from measurements at discrete points via interpolation. This paper examines various questions associated with the implementation of modal filters, such as the effect of choice of interpolation functions and sensors locations, as well as of measurement errors, on the state estimation process. The method is demonstrated by means of two numerical examples.
Appendix 4 of the Study of One- and Two-Dimensional Filtering and Deconvolution Algorithms for a Streaming Array Computer discusses coordinate axes, location of origin, and redundancy for the one- and two-dimensional Fourier transform for complex and real data.
Here, we examine the application of neural network-based methods to improve the accuracy of large eddy simulations of incompressible turbulent flows. The networks are trained to learn a mapping between flow features and the subgrid scales, and applied locally and instantaneously—in the same way as traditional physics-based subgrid closures. Models that use only the local resolved strain rate are poorly correlated with the actual subgrid forces obtained from filtering direct numerical simulation data. We see that highly accurate models in a priori testing are inaccurate in forward calculations, owing to the preponderance of numerical errors in implicitly filtered large eddy simulations. A network that accounts for the discretization errors is trained and found to be unstable in a posteriori testing. We identify a number of challenges that the approach faces, including a distribution shift that affects networks that fail to account for numerical errors.
An algorithm for estimating signal to noise ratio and combiner weight parameters for a discrete time series is presented. The algorithm is based upon the joint maximum likelihood estimate of the signal and noise power. The discrete-time series are the sufficient statistics obtained after matched filtering of a biphase modulated signal in additive white Gaussian noise, before maximum likelihood decoding is performed.
This paper is concerned with the vibration control of the SCOLE structure while it undergoes a slewing maneuver. The control law is designed according to the linear quadratic regulator theory. In view of saturation limits on the actuators, the actual implementation is modified so as to observe these limits, resulting in suboptimal control. State estimation is carried out by means of a Kalman filter. The control and state estimation are carried out in discrete time. Numerical simulations for several cases of interest are presented.