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At least 577 records · Page 32

Improving Simulated Soil Moisture Fields Through Assimilation of AMSR-E Soil Moisture Retrievals with an Ensemble Kalman Filter and a Mass Conservation Constraint

Model simulated soil moisture fields are often biased due to errors in input parameters and deficiencies in model physics. Satellite derived soil moisture estimates, if retrieved appropriately, represent the spatial mean of soil moisture in a footprint area, and can be used to reduce model bias (at locations near the surface) through data assimilation techniques. While assimilating the retrievals can reduce model bias, it can also destroy the mass balance enforced by the model governing equation because water is removed from or added to the soil by the assimilation algorithm. In addition, studies have shown that assimilation of surface observations can adversely impact soil moisture estimates in the lower soil layers due to imperfect model physics, even though the bias near the surface is decreased. In this study, an ensemble Kalman filter (EnKF) with a mass conservation updating scheme was developed to assimilate the actual value of Advanced Microwave Scanning Radiometer (AMSR-E) soil moisture retrievals to improve the mean of simulated soil moisture fields by the Noah land surface model. Assimilation results using the conventional and the mass conservation updating scheme in the Little Washita watershed of Oklahoma showed that, while both updating schemes reduced the bias in the shallow root zone, the mass conservation scheme provided better estimates in the deeper profile. The mass conservation scheme also yielded physically consistent estimates of fluxes and maintained the water budget. Impacts of model physics on the assimilation results are discussed.

Li, Bailing↗

The error associated with use of various forms of the divergence equation to diagnose geopotential and temperature

This study utilizes a model-generated data set to evaluate the errors associated with the diagnosis of geopotential height using three approximate forms of the divergence equation (DE). The DE was solved on the original sigma-coordinate surfaces of the model to exclude any error produced in the process of interpolating the data from observation points to the coordinate surface of the DE. An inviscid, nonlinear, divergent DE produced rms geopotential height errors as large as 3 m and rms temperature errors of over 26 C in the lower planetary boundary layer (PBL), with minimal errors above 800 mb. Elimination of the isobaric divergence in the velocity field caused additional height errors of 5-6 m and temperature errors of 0.4-1.2 C in the free troposphere. Use of a further-degraded DE without nonlinear terms caused height errors of 10-15 m in the upper troposphere with modestly increased temperature errors. Error fields at all levels had synoptic-scale features, with some mesoalpha structure. No spatial noise was apparent. Use of a temporal spectral filter to eliminate high-frequency modes from the model-generated data did not significantly influence the error associated with use of various forms of the DE.

Modica, George M.↗

Integrating Radio-Over-Fiber Communication System and BOTDR Sensor System

In this paper, we propose and experimentally demonstrate for the first time, the integration of a radio-over-fiber (RoF) communication system and a Brillouin optical time-domain reflectometry (BOTDR) distributed sensor system using a single optical fiber link. In this proof-of-concept integrated system, the communication system is composed of three modulation formats of quadrature phase-shift keying (QPSK), 16-quadrature amplitude modulation (16-QAM) and 64-QAM, which are modulated onto an orthogonal frequency division multiplexing (OFDM) signal. Whereas, the BOTDR sensor system is used for strain and/or temperature monitoring over the fiber distance with a spatial resolution of 5 m using a 25 km single-mode silica fiber. The error vector magnitude (EVM) is analyzed in three modulation formats in the presence of various BOTDR input pump powers. Using QPSK modulation, optimized 18 dBm sensing and 10 dBm data power, the measured EVM values with and without bandpass filter are 3.5% and 14.5%, respectively. The proposed system demonstrates a low temperature measurement error (±0.49 °C at the end of 25 km) and acceptable EVM values, which were within the 3GPP requirements. The proposed integrated system can be effectively applied for practical applications, which significantly reduces the fiber infrastructure cost by effective usage of a single optical fiber link.

42 ENGINEERING↗

Low-dimensional Representation of Error Covariance

Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional representation. A useful measure of forecast/analysis cycle stability is the bound matrix, a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady-state analysis error covariance matrix eigenvalues are derived from the bound matrix. The estimates generalize to time-dependent systems. If much of the steady-state analysis error variance is due to a few dominant modes, the leading eigenvectors of the bound matrix approximate those of the steady-state analysis error covariance matrix. The analytical results are illustrated in two numerical examples where the Kalman filter is carried to steady state. The first example uses the dynamics of a generalized advection equation exhibiting nonmodal transient growth. Failure to observe growing modes leads to increased steady-state analysis error variances. Leading eigenvectors of the steady-state analysis error covariance matrix are well approximated by leading eigenvectors of the bound matrix. The second example uses the dynamics of a damped baroclinic wave model. The leading eigenvectors of a lowest-order approximation of the bound matrix are shown to approximate well the leading eigenvectors of the steady-state analysis error covariance matrix.

Tippett, Michael K.↗

Kalman filter divergence and aircraft motion estimators

Kalman filters designed for many aerospace systems turn out to be unsatisfactory. The estimate errors become large compared to the errors predicted by the theory ('divergence'). One of the principal causes of this failure is that the system model contains states or modes that are undisturbed by the modeled process noise, and are neutrally stable (NS). One cure for such problems is periodic restarting of a time-varying Kalman filter. Other cures include minimum variance observers with eigenvalue constraints, added noise, pole-shifting, and destabilization. Several examples are given, including effective time-invariant estimators for the longitudinal and lateral motions of an airplane where several NS modes are undisturbed by wind gusts. An interpretation of these estimators as a 'strapdown IMU' without accelerometers, gimbaled gyros, or servos is given.

Bryson, A. E., Jr.↗

Improving precision and accuracy of genetic mapping with genotyping‐by‐sequencing data in outcrossing species

Abstract Genotyping‐by‐sequencing (GBS) is a widely used strategy for obtaining large numbers of genetic markers in model and non‐model organisms. In crop plants, GBS‐derived marker datasets are frequently used to perform quantitative trait locus (QTL) mapping. In some plant species, however, high heterozygosity and complex genome structure mean that researchers must use care in handling GBS data to conduct QTL mapping most effectively. Such outbred crops include most of the perennial grass and tree species used for bioenergy. To identify strategies for increasing accuracy and precision of QTL mapping using GBS data in outbred crops, we conducted an empirical study of SNP‐calling and genetic map‐building pipeline parameters in a Miscanthus sinensis population, and a complementary simulation study to estimate the relationship between genome‐wide error rate, read depth, and marker number. The bioenergy grass Miscanthus is an obligate outcrossing species with a recent (diploidized) whole‐genome duplication. For the study of empirical M. sinensis data, we compared two SNP‐calling methods (one non‐reference‐based and one reference‐based), a series of depth filters (12×, 20×, 30×, and 40×) and two map‐construction methods (i.e., marker ordering: linkage‐only and order‐corrected based on a reference genome). We found that correcting the order of markers on a linkage map by using a high‐quality reference genome improved QTL precision (shorter confidence intervals). For typical GBS datasets of between 1000 and 5000 markers to build a genetic map for biparental populations, a depth filter set at 30× to 40× applied to outbred populations provided a genome‐wide genotype‐calling error rate of less than 1%, improved accuracy of QTL point estimates and minimized type I errors for identifying QTL. Based on these results, we recommend using a reference genome to correct the marker order of genetic maps and a robust genotype depth filter to improve QTL mapping for outbred crops.

59 BASIC BIOLOGICAL SCIENCES↗

A filtering strategy for the numerical convergence of radiation transport through purely absorbing particle clouds

Radiation transport through particle clouds plays a major role in many engineering applications. Here in this paper, we study this problem by means of solving the radiative transport equation (RTE) on a Eulerian continuous domain. The particle clouds are generated through direct numerical simulation of Navier-Stokes equations coupled with Lagrangian particle transport at different Stokes numbers. We confirm the earlier observation noted in the literature that the solution to the RTE on Eulerian mesh diverges when the Eulerian mesh size is of the order of the particle diameter. This observation is often called the homogenization error stemming from relegation of number density onto the Eulerian domain. In order to circumvent this divergence problem, we propose a filtering strategy that spreads the information of the particles to the neighboring cells in a way that the representation of the particles remains the same even when the mesh size is smaller than that of the particle size. We show through our simulations that our filtering strategy solves the issue of homogenization error for the cases where the Beer-Bouger law is valid.

42 ENGINEERING↗

The Importance of Semi-Major Axis Knowledge in the Determination of Near-Circular Orbits

Modem orbit determination has mostly been accomplished using Cartesian coordinates. This usage has carried over in recent years to the use of GPS for satellite orbit determination. The unprecedented positioning accuracy of GPS has tended to focus attention more on the system's capability to locate the spacecraft's location at a particular epoch than on its accuracy in determination of the orbit, per se. As is well-known, the latter depends on a coordinated knowledge of position, velocity, and the correlation between their errors. Failure to determine a properly coordinated position/velocity state vector at a given epoch can lead to an epoch state that does not propagate well, and/or may not be usable for the execution of orbit adjustment maneuvers. For the quite common case of near-circular orbits, the degree to which position and velocity estimates are properly coordinated is largely captured by the error in semi-major axis (SMA) they jointly produce. Figure 1 depicts the relationships among radius error, speed error, and their correlation which exist for a typical low altitude Earth orbit. Two familiar consequences are the relationship Figure 1 shows are the following: (1) downrange position error grows at the per orbit rate of 3(pi) times the SMA error; (2) a velocity change imparted to the orbit will have an error of (pi) divided by the orbit period times the SMA error. A less familiar consequence occurs in the problem of initializing the covariance matrix for a sequential orbit determination filter. An initial covariance consistent with orbital dynamics should be used if the covariance is to propagate well. Properly accounting for the SMA error of the initial state in the construction of the initial covariance accomplishes half of this objective, by specifying the partition of the covariance corresponding to down-track position and radial velocity errors. The remainder of the in-plane covariance partition may be specified in terms of the flight path angle error of the initial state. Figure 2 illustrates the effect of properly and not properly initializing a covariance. This figure was produced by propagating the covariance shown on the plot, without process noise, in a circular low Earth orbit whose period is 5828.5 seconds. The upper subplot, in which the proper relationships among position, velocity, and their correlation has been used, shows overall error growth, in terms of the standard deviations of the inertial position coordinates, of about half of the lower subplot, whose initial covariance was based on other considerations.

Carpenter, J. Russell↗

Data Fusion of In-Flight Aerothermodynamic Heating Measurements Using Kalman Filtering

On February 18th, 2021, the Mars 2020 entry system successfully delivered the Perseverance rover to the surface of Mars at Jezero Crater. The entry capsule carried instrumentation installed on the heatshield and backshell, named the Mars Entry, Descent, and Landing Instrumentation 2. The instruments included pressure transducers, thermocouples, heat flux gauges, and a radiometer to measure the aerodynamic and aerothermodynamic performance of the entry vehicle. Three of these sensors, a thermocouple plug, heat flux gauge, and a radiometer, were co-located on the backshell. The sensors were exposed to roughly the same aerodynamic heating, but measured these environments in different ways, each with its own set of modeling and measurement error complications. This paper develops a method for blending each of these measurements together in a single algorithm to produce estimates of the aerothermodynamic environments at that backshell location. The approach makes use of the Kalman-Schmidt filter/smoother methodology, where systematic measurement error parameters are modeled as multiplicative states that are estimated by the filter along with the aerothermal states. The results indicate peak convective and radiative heating values of 0.86 and 5.16 W/cm2, respectively, compared to the filter predictive model values of 0.67 and 4.83 W/cm2.

Christopher D Karlgaard↗

Data Fusion of In-Flight Aerothermodynamic Heating Measurements Using Kalman Filtering

On February 18th, 2021, the Mars 2020 entry system successfully delivered the Perseverance rover to the surface of Mars at Jezero Crater. The entry capsule carried instrumentation installed on the heatshield and backshell, named the Mars Entry, Descent, and Landing Instrumentation 2. The instruments included pressure transducers, thermocouples, heat flux gauges, and a radiometer to measure the aerodynamic and aerothermodynamic performance of the entry vehicle. Three of these sensors, a thermocouple plug, heat flux gauge, and a radiometer, were co-located on the backshell. The sensors were exposed to roughly the same aerodynamic heating, but measured these environments in different ways, each with its own set of modeling and measurement error complications. This paper develops a method for blending each of these measurements together in a single algorithm to produce estimates of the aerothermodynamic environments at that backshell location. The approach makes use of the Kalman-Schmidt filter/smoother methodology, where systematic measurement error parameters are modeled as multiplicative states that are estimated by the filter along with the aerothermal states. The results indicate peak convective and radiative heating values of 0.86 and 5.16 W/cm$^2$, respectively, compared to the filter predictive model values of 0.67 and 4.83 W/cm$^2$.

Christopher D Karlgaard↗

Two novel automatic frequency tracking loops

Two automatic-frequency-control (AFC) loops are introduced and analyzed in detail. The algorithms are generalizations of the well known cross-product AFC loop with improved performance. The first estimator uses running overlapping discrete Fourier transforms to create a discriminator curve proportional to the frequency estimation error, whereas the second one preprocesses the received data and then uses an extended Kalman filter to estimate the input frequency. The algorithms are tested by computer simulations in a highly dynamic environment at low carrier/noise ratio (CNR). The algorithms are suboptimum tracking schemes with a larger frequency-error variance compared to an optimum strategy, but they offer simplicity of mechanization and a CNR with a very low operating threshold.

Aguirre, Sergio↗

Global mesoscale variability from the Geosat Exact Repeat Mission - Correlation with ocean depth

A simple derivative filter technique for extracting mesoscale variability from satellite altimeter data having large-amplitude, long-wavelength errors, with no data adjustments necessary, is presented. The method is applied to the first year of Geosat Exact Repeat Mission data. The main advantage over previous filter methods is that the derivative filter is only two points long, so that it produces no edge effects. Short profiles can thus be included in the analysis. The derivative filter also transforms a dynamic height profile into a dynamic slope profile. The dynamic slope of the sea surface is a parameter that can be measured independently. Moreover, if the ocean current is in geostrophic balance, then the dynamic gradient of the sea surface is proportional to the current velocity.

Sandwell, David T.↗

Dynamic model with scale-dependent coefficients in the viscous range

The standard dynamic procedure is based on the scale-invariance assumption that the model coefficient C is the same at the grid and test-filter levels. In many applications this condition is not met, e.g. when the filter-length, delta, approaches the Kolmogorov scale, and C(delta approaches eta) approaches O. Using a priori tests, we show that the standard dynamic model yields the coefficient corresponding to the test-filter scale (alpha delta) instead of the grid-scale (delta). Several approaches to account for scale dependence are examined and/or tested in large eddy simulation of isotropic turbulence: (a) take the limit alpha approaches 1; (b) solve for two unknown coefficients C(Delta) and C(alpha delta) in the least-square-error formulation; (c) the 'bi-dynamic model', in which two test-filters (e.g. at scales 2(delta) and 4(delta) are employed to gain additional information on possible scale-dependence of the coefficient, and an improved estimate for the grid-level coefficient is obtained by extrapolation, (d) use theoretical predictions for the ratio C(alpha delta)/C(delta) and dynamically solve for C(delta). None of these options is found to be entirely satisfactory, although the last approach appears applicable to the viscous range.

Meneveau, C.↗

Sensor filter designs for large flexible spacecraft

Traditional control methods may excite flexible modes causing degraded performance or instability of large flexible space structures (LFSS). Control techniques developed for control of LFSS requires a numerical model of the structure and some knowledge of model error. This will be increasingly difficult with the complex space structures planned for the future. If filters could be used to condition the sensor output, control design would be less demanding. This paper is presented in viewgraph format.

Nimmo, Nancy A.↗

Terminal guidance and navigation for comet and asteroid rendezvous

A terminal guidance and navigation scheme developed in earlier work was modified and evaluated for a solar electric propulsion rendezvous mission to comet Encke. The scheme is intended for autonomous, on-board use. The guidance algorithm is based on optimal control theory and minimizes the time integrated square of thrust acceleration. The navigation algorithm employs a modified Kalman filter set in measurement variables. Random sequences were generated to simulate measurement errors, and the evaluation was conducted with detailed numerical computations which include actual motions of spacecraft and comet. The evaluations showed that the scheme attains rendezvous and maintains station after rendezvous within less than 10 km for estimated best measurements and within less than 100 km for estimated worst measurements. The measurements required are angles, range, and range rate. Angles and range appear to be absolutely necessary; range rate is not as strong a measurement type, and further modifications of the filter will allow a scheme that does not require the rate measurements.

Bennett, A. G.↗

Compatibility check of measured aircraft responses using kinematic equations and extended Kalman filter

An extended Kalman filter smoother and a fixed point smoother were used for estimation of the state variables in the six degree of freedom kinematic equations relating measured aircraft responses and for estimation of unknown constant bias and scale factor errors in measured data. The computing algorithm includes an analysis of residuals which can improve the filter performance and provide estimates of measurement noise characteristics for some aircraft output variables. The technique developed was demonstrated using simulated and real flight test data. Improved accuracy of measured data was obtained when the data were corrected for estimated bias errors.

Klein, V.↗

Comparison and testing of extended Kalman filters for attitude estimation of the Earth Radiation Budget Satellite

This paper presents the testing and comparison of two extended Kalman filters (EKFs) developed for the Earth Radiation Budget Satellite (ERBS). One EKF updates the attitude quaternion using a four-component additive error quaternion. This technique is compared to that of a second EKF, which uses a multiplicative error quaternion. Brief developments of the algorithms are included. The convergence properties, singularity problems, and normalization techniques of the two filters are addressed. Both filters are tested with simulated ERBS sensor data in addition to real ERBS sensor data. The results of the two filters are also compared to those from the ERBS operational ground support software, which uses a batch differential correction algorithm to estimate attitude and gyro biases.

Bar-Itzhack, Itzhack Y.↗

A numerical extension of the spatially-filtered Euler equations for contact discontinuities

Solving the spatially-filtered Euler equations with a kinetic energy-preserving centered discretization is an efficient framework for simulating shock-dominated flows. Here, the present work describes a numerical treatment of the spatially-filtered Euler equations to minimize oscillations when simulating contact discontinuities. To counteract dispersive errors inherent to centered schemes, a WENO-like correction term is applied to the enthalpy transport in the energy equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗