Sequential coding schemes for an additive noise channel with a noisy feedback link Technical report, May - Aug. 1966
Sequential coding scheme for additive Gaussian channel with noisy feedback link
CODING SYSTEM↗
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Development of high-accuracy convection schemes for sequential solvers
An exploration is conducted of the applicability of such high resolution schemes as TVD to the resolving of sharp flow gradients using a sequential solution approach borrowed from pressure-based algorithms. It is shown that by extending these high-resolution shock-capturing schemes to a sequential solver that treats the equations as a collection of scalar conservation equations, the speed of signal propagation in the solution has to be coordinated by assigning the local convection speed as the characteristic speed for the entire system. A higher amount of dissipation is therefore needed to eliminate oscillations near discontinuities.
Thakur, Siddharth↗
Analysis of lunar samples for carbon compounds.
Description of one approach to the analysis for carbon compounds in lunar materials from the Apollo 11 mission. The sequential scheme followed generally accepted organic geochemical practices, but was unusual in its application to a single sample. The procedures of the scheme were designed to minimize handling of the solids and extracts or hydrolysates. The solid lunar sample was retained in all steps of the sequential analysis in the vessel in which it was originally placed. Centrifugation was used to separate solid and liquid phases after extraction or refluxing. Liquids were recovered from solids by decantation.
Kvenvolden, K. A.↗
Slightly non-linear estimation with noisy data.
Nonlinear estimation with noisy data, considering least squares fit, sequential /Kalman/ estimate and iterated sequential scheme
Breakwell, J. V.↗
Two-Dimensional Sequential and Concurrent Finite Element Analysis of Unstiffened and Stiffened Aluminum and Composite Panels with Hole
The results of a detailed investigation of the distribution of stresses in aluminum and composite panels subjected to uniform end shortening are presented. The focus problem is a rectangular panel with two longitudinal stiffeners, and an inner stiffener discontinuous at a central hole in the panel. The influence of the stiffeners on the stresses is evaluated through a two-dimensional global finite element analysis in the absence or presence of the hole. Contrary to the physical feel, it is found that the maximum stresses from the glocal analysis for both stiffened aluminum and composite panels are greater than the corresponding stresses for the unstiffened panels. The inner discontinuous stiffener causes a greater increase in stresses than the reduction provided by the two outer stiffeners. A detailed layer-by-layer study of stresses around the hole is also presented for both unstiffened and stiffened composite panels. A parallel equation solver is used for the global system of equations since the computational time is far less than that using a sequential scheme. A parallel Choleski method with up to 16 processors is used on Flex/32 Multicomputer at NASA Langley Research Center. The parallel computing results are summarized and include the computational times, speedups, bandwidths, and their inter-relationships for the panel problems. It is found that the computational time for the Choleski method decreases with a decrease in bandwidth, and better speedups result as the bandwidth increases.
Razzaq, Zia↗
Estimation of Model Error Variances During Data Assimilation
Data assimilation is all about understanding the error characteristics of the data and models that are used in the assimilation process. Reliable error estimates are needed to implement observational quality control, bias correction of observations and model fields, and intelligent data selection. Meaningful covariance specifications are obviously required for the analysis as well, since the impact of any single observation strongly depends on the assumed structure of the background errors. Operational atmospheric data assimilation systems still rely primarily on climatological background error covariances. To obtain error estimates that reflect both the character of the flow and the current state of the observing system, it is necessary to solve three problems: (1) how to account for the short-term evolution of errors in the initial conditions; (2) how to estimate the additional component of error caused by model defects; and (3) how to compute the error reduction in the analysis due to observational information. Various approaches are now available that provide approximate solutions to the first and third of these problems. However, the useful accuracy of these solutions very much depends on the size and character of the model errors and the ability to account for them. Model errors represent the real-world forcing of the error evolution in a data assimilation system. Clearly, meaningful model error estimates and/or statistics must be based on information external to the model itself. The most obvious information source is observational, and since the volume of available geophysical data is growing rapidly, there is some hope that a purely statistical approach to model error estimation can be viable. This requires that the observation errors themselves are well understood and quantifiable. We will discuss some of these challenges and present a new sequential scheme for estimating model error variances from observations in the context of an atmospheric data assimilation system.
Dee, Dick↗
The TRMM Multi-satellite Precipitation Analysis (TMPA): Quasi-Global Precipitation Estimates at Fine Scales
The TRMM Multi-satellite Precipitation Analysis (TMPA) provides a calibration-based sequential scheme for combining multiple precipitation estimates from satellites, as well as gauge analyses where feasible, at fine scales (0.25 degrees x 0.25 degrees and 3-hourly). It is available both after and in real time, based on calibration by the TRMM Combined Instrument and TRMM Microwave Imager precipitation products, respectively. Only the after-real-time product incorporates gauge data at the present. The data set covers the latitude band 50 degrees N-S for the period 1998 to the delayed present. Early validation results are as follows: The TMPA provides reasonable performance at monthly scales, although it is shown to have precipitation rate dependent low bias due to lack of sensitivity to low precipitation rates in one of the input products (based on AMSU-B). At finer scales the TMPA is successful at approximately reproducing the surface-observation-based histogram of precipitation, as well as reasonably detecting large daily events. The TMPA, however, has lower skill in correctly specifying moderate and light event amounts on short time intervals, in common with other fine-scale estimators. Examples are provided of a flood event and diurnal cycle determination.
Huffman, George J.↗
Computational aspects of helicopter trim analysis and damping levels from Floquet theory
Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.
Gaonkar, Gopal H.↗
Helicopter trim analysis by shooting and finite element methods with optimally damped Newton iterations
Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used, and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.
Achar, N. S.↗
Estimation in nonlinear systems with transport delay.
The problem of estimation of state in nonlinear dynamical systems containing time delays is studied. The plant is specified by a set of nonlinear differential-difference equations. Observations are a nonlinear function of current and/or delayed states. Both contain additive disturbances. The criterion used for the optimal estimates is the integral of the weighted squared error. Using the theory of the calculus of variations, equations are developed for the estimation. They are first expressed in the form of a split boundary value problem, which is then converted to an initial value problem for on-line estimation. The result yields a sequential estimation scheme in which filtered and smoothed estimates are computed in a sequential manner. The applicability of the procedure is demonstrated by a practical example.
Stoller, R. L.↗
Node synchronization of viterbi decoders using state metrics
The concept of node synchronization using state metrics is investigated. The branch metrics are integrated over a fixed time interval and the results are compared to the detection threshold. If the threshold is exceeded, the out-of-sync hypothesis is accepted; otherwise, the in-sync hypothesis is accepted. It is shown that the detection threshold can be chosen independent of any particular convolutional code with fixed code rate and constant length if the code has reasonably good bit error rate performance. Three node synchronization schemes are compared: (1) a scheme using the syndrome; (2) a scheme using the frame-sync patterns; and (3) a scheme using the state metrics. At very low signal to noise ratios (SNR), scheme 2 can be faster than scheme 1. For Voyager's rate 1/2 and constraint length 7 convolutional code, this happens for SNRs of less than 0.7 dB. This result is obtained by assuming that the code frame-sync pattern has good aperiodic autocorrelation properties. For a fixed false alarm probability, the sequential detection scheme based on the syndrome is faster than scheme 3 with fixed integration time. A sequential detection technique is needed to improve the speed of scheme 3.
Cheng, U.↗
Practical sequential decoding and a simple hybrid scheme.
Simple decoding properties of Reed-Solomon codes for erasure channels combined with sequential coding for complex channels
Huband, F. L.↗
A scheme for tracking and pointing at small celestial bodies during high velocity encounters
A scheme has been developed and verified for closed-loop tracking and pointing space-borne science instruments at small celestial bodies, such as comets and asteroids, during high velocity encounters. To overcome ephemeris uncertainties for these bodies, the scheme involves sequential estimation of flyby model parameters. The design consists of a two-axis gimballed platform mounted on a three-axis stabilized spacecraft. A platform-mounted optical tracker provides closed-loop target measurements and precision micro-step actuators enable high-rate platform slewing. For comet missions which involve dust particle impact disturbances, a dual-mode attitude control scheme is presented for minimizing transient response time.
Burdick, G. M.↗
Modern control concepts in hydrology
Two approaches to an identification problem in hydrology are presented based upon concepts from modern control and estimation theory. The first approach treats the identification of unknown parameters in a hydrologic system subject to noisy inputs as an adaptive linear stochastic control problem; the second approach alters the model equation to account for the random part in the inputs, and then uses a nonlinear estimation scheme to estimate the unknown parameters. Both approaches use state-space concepts. The identification schemes are sequential and adaptive and can handle either time invariant or time dependent parameters. They are used to identify parameters in the Prasad model of rainfall-runoff. The results obtained are encouraging and conform with results from two previous studies; the first using numerical integration of the model equation along with a trial-and-error procedure, and the second, by using a quasi-linearization technique. The proposed approaches offer a systematic way of analyzing the rainfall-runoff process when the input data are imbedded in noise.
Duong, N.↗
Modern control concepts in hydrology
Two approaches to an identification problem in hydrology are presented, based upon concepts from modern control and estimation theory. The first approach treats the identification of unknown parameters in a hydrologic system subject to noisy inputs as an adaptive linear stochastic control problem; the second approach alters the model equation to account for the random part in the inputs, and then uses a nonlinear estimation scheme to estimate the unknown parameters. Both approaches use state-space concepts. The identification schemes are sequential and adaptive and can handle either time-invariant or time-dependent parameters. They are used to identify parameters in the Prasad model of rainfall-runoff. The results obtained are encouraging and confirm the results from two previous studies; the first using numerical integration of the model equation along with a trial-and-error procedure, and the second using a quasi-linearization technique. The proposed approaches offer a systematic way of analyzing the rainfall-runoff process when the input data are imbedded in noise.
Duong, N.↗
VLSI Architecture For Viterbi Decoder
"Pipeline" architecture developed for very-large-scale integrated (VLSI) Viterbi decoding circuits for binary convolutional codes of large constraint lengths. In scheme, single sequential processor computes path metrics in trellis diagram (diagram in which paths and nodes represent possible sequences of code states and in which metrics indicate relative likelihoods of sequences). Systolic-array method used to store path information as well as to choose path with best metric. VLSI Viterbi-decoder architecture is compromise between speed and complexity. Size of decoding circuit increases approximately linearly with constraint length of code, and additional circuit chips added with moderate numbers of interconnections.
Hsu, In-Shek↗
Estimating Alpine Snow Depth by Combining Multi-Frequency Passive Radiance Observations with Ensemble Snowpack Modeling
This paper presents a physically-based snow depth retrieval algorithm adapted for deep mountainous snowpack and airborne multifrequency (10.7, 18.7, 37.0 and 89.0 GHz) passive microwave (PM) radiance observations from a single flight. The algorithm employs a single forecast-analysis cycle of a traditional sequential assimilation scheme. It uses an ensemble of multi-layer snowpack model runs to resolve snow microstructure and melt-refreeze crusts, andmicrowave radiative transfer models to relate snow properties to microwave measurements.Snow depth was retrieved at a 120 m spatial resolution over three 1 km2 Intensive Study Area (ISA) within the Rabbit Ears Meso-Cell Study Area (MSA) from the NASA Cold Land Processes Experiment (CLPX) in Colorado (United States) for one date in February 2003. When evaluated against in situ observations, root mean square error (RMSE) of the snow depth from the assimilation was 13.3 cm for areas with low (<5 %) forest cover, which was a reduction of 48 % in the RMSE compared with the modeled snow depth when the PM observations were not assimilated; indicating a ~5% relative error of the posterior snow depth with respect to the average snow depth (200 cm) measured at these pixels. For pixels with forest cover ranging from 5-15% and 15-30%, results were improved (R2 increased from 0.65 to 0.71 and from 0 to 0.38, respectively) by introducing a forest radiative transfer model during the assimilation.
Airborne Multifrequency↗
A high accuracy sequential solver for simulation and active control of a longitudinal combustion instability
A high accuracy convection scheme using a sequential solution technique has been developed and applied to simulate the longitudinal combustion instability and its active control. The scheme has been devised in the spirit of the Total Variation Diminishing (TVD) concept with special source term treatment. Due to the substantial heat release effect, a clear delineation of the key elements employed by the scheme, i.e., the adjustable damping factor and the source term treatment has been made. By comparing with the first-order upwind scheme previously utilized, the present results exhibit less damping and are free from spurious oscillations, offering improved quantitative accuracy while confirming the spectral analysis reported earlier. A simple feedback type of active control has been found to be capable of enhancing or attenuating the magnitude of the combustion instability.
Shyy, W.↗