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The cosmic ray telescopes on Pioneer 10 and 11 are used to examine solar cosmic ray events out to a distance about 5 AU from the sun. A detailed error analysis of the cosine fit to the anisotropy is presented. The anisotropy and intensity time characteristics during solar events are discussed as a function of radial distance.
It is shown that high-resolution low-uncertainty temperature-height profiles cannot be deduced from pressure-height data alone because the relative uncertainty in pressure data cannot be expected to be smaller than 1% or 2% in present-day practical instrumentation. The basic equations relating temperature to pressure-height or density-height data are subjected to error analysis to determine the uncertainty introduced into computed temperature-height values by observed data. The results show that the use of density data is much more preferable than the use of pressure data if atmospheric temperature is to be determined as a function of height with a fine height resolution and a small uncertainty from the height profiles of pressure or density and if pressures and densities can be measured with comparable accuracies.
Estimation theory has been applied to a wide range of aerospace problems. Application of this expertise outside the aerospace field has been extremely limited, however. This paper describes the use of covariance error analysis techniques in evaluating the accuracy of pollution estimates obtained from a variety of concentration measuring devices. It is shown how existing software developed for aerospace applications can be applied to the estimation of pollution through the processing of measurement types involving a range of spatial and temporal responses. The modeling of pollutant concentration by meandering Gaussian plumes is described in some detail. Time averaged measurements are associated with a model of the average plume, using some of the same state parameters and thus avoiding the problem of state memory. The covariance analysis has been implemented using existing batch estimation software. This usually involves problems in handling dynamic noise; however, the white dynamic noise has been replaced by a band-limited process which can be easily accommodated by the software.
Covariance error analysis techniques were applied to investigate estimation strategies for the high-low SST mission for accurate local recovery of gravitational fine structure, considering the aliasing effects of unsolved for parameters. Surface density blocks of 5 deg x 5 deg and 2 1/2 deg x 2 1/2 deg resolution were utilized to represent the high order geopotential with the drag-free GRAVSAT configured in a nearly circular polar orbit at 250 km. altitude. GEOPAUSE and geosynchronous satellites were considered as high relay spacecraft. It is demonstrated that knowledge of gravitational fine structure can be significantly improved at 5 deg x 5 deg resolution using SST data from a high-low configuration with reasonably accurate orbits for the low GRAVSAT. The gravity fine structure recoverability of the high-low SST mission is compared with the low-low configuration and shown to be superior.
The gimballed Ku-band antenna system for communication with TDRS was studied. By means of an error analysis it was demonstrated that the antenna cannot be open loop pointed to TDRS by an onboard programmer, but that an autotrack system was required. After some tradeoffs, a two-axis, azimuth-elevation type gimbal configuration was recommended for the antenna. It is shown that gimbal lock only occurs when LANDSAT-D is over water where a temporary loss of the communication link to TDRS is of no consequence. A preliminary gimbal control system design is also presented. A digital computer program was written that computes antenna gimbal angle profiles, assesses percent antenna beam interference with the solar array, and determines whether the spacecraft is over land or water, a lighted earth or a dark earth, and whether the spacecraft is in eclipse.
A solution is presented to the radiative transfer of the solar irradiation through a turbid atmosphere, based on the single-scattering approximation, i.e., an assumption that a photon that underwent scattering either leaves the top of the atmosphere or strikes the surface. The solution depends on a special idealization of the scattering phase function of the aerosols. The equations developed are subsequently applied to analyze quantitatively the enhancement of the surface irradiation and the enhancement of the scattered radiant emittance as seen from above the atmosphere, caused by the surface reflectance and atmospheric back scattering. An order of magnitude error analysis is presented.
Fourier techniques have been exhaustively calibrated using Unno's (1956) results for the absorption profile of a simple Zeeman triplet. If a simple transformation is applied to the normalized line depths, then magnetic-field strengths and inclination angles can be measured very accurately from noisy saturated line profiles. Systematic errors caused by saturation effects can be estimated and reduced by varying one parameter. When a significant fraction of the line profile is unsplit and unpolarized, large errors may be made in measurements of low fields, unless the line is sufficiently weak. For a weak line, a vertical field of 1600 gauss can be measured to 10% accuracy even when 70% of the line profile is stray light. These stray-light errors are troublesome in measuring fields of gaps and pores but not sunspots. Numerical results of the error analysis are presented graphically.
During the summer of 1976, the two Viking spacecraft, each consisting of an orbiter-lander combination, were inserted into orbit about Mars. The paper describes the experiences of the Viking Satellite Orbit Determination Team in determining Mars centered ephemerides of the orbiters and positions of the landers from the two-way Doppler and range data, and synthesizes the different phases of the navigation plan which involves pre-flight modeling and error analysis for all Viking navigation functions from launch through landing. The problem of initial orbit convergence is solved by using DPODP's (Double Precision Orbit Determination Program) square-root batch data filter, and gravity models for both Viking I and Viking II were produced from the combination of short arc estimates. The importance of synchronous Viking orbits (with the rotational period of Mars) is stressed and future extended missions of the spacecraft are outlined.
In this paper it is supposed that the variables x sub 1,...,x sub n each have finite range with the variable x sub i taking on p sub i possible values and that the values of the variables are changing with time. It is supposed further that it is desired to detect occurrences in which some subset of the variables achieve particular values. Finally, it is supposed that the problem involves the detection of a large number of combined occurrences for a large number of changes of values of variables. Two efficient solutions for this problem are described. Both methods have the unusual property of being faster for systems where the sum p sub 1 +...+ p sub n is larger. The first solution is error-free and suitable for most cases. The second solution is slightly more elegant and allows negation as well as conjunction, but is subject to the possibility of errors. An error analysis is given for the second method and an empirical study is reported.
A redundant strapdown inertial navigation system for integrated flight control/navigation use is described. Design of the system, which consists of four tuned-gimbal gyros, eight accelerometers, and four processors, is discussed, with emphasis on its compact configuration (13 by 13 by 14 in.), based on symmetry properties of an octahedron. A matrix operator for least-squares combination of data from an arbitrary number of two-degree-of-freedom gyros is derived, and general parity equations for error analysis are given. Self-contained detection and isolation of a two-axis gyro failure is considered; system failure probability, which depends on component failure rates and self-correction capacities, is analyzed. Test data, including typical parity equation responses during motion and simulated gyro and accelerometer failures, are also presented.
Absolute line-center frequencies for eleven lines of ammonia in near coincidence with CO2-laser transitions have been determined to accuracies of + or -3 MHz by infrared heterodyne detection. These results were obtained by heterodyning a blackbody with a stable grating-tuned CO2 gas laser. A discussion of the apparatus and method of calculation, including error analysis, is presented. With these accurately determined line-center positions, the ammonia molecule will be a useful secondary-frequency standard for diode-laser spectroscopy in the 11-micron wavelength region.
The feasibility of recovering parameters from one-way range rate between two earth orbiting spacecraft during occultation of the tracking signal by the earth's lower atmosphere. The tracking data is inverted by an integral transformation (Abel transform) to obtain a vertical refractivity profile above the point of closest approach of the ray connecting the satellites. Pressure and temperature distributions can be obtained from values of dry refractivity using the hydrostatic equation and perfect gas law. Two methods are investigated for recovering pressure and temperature parameters. Results show that recovery is much more sensitive to satellite velocity errors than to satellite position errors. An error analysis is performed. An example is given demonstrating recovery of parameters from radio occultation data obtained during satellite-to-satellite tracking of Nimbus 6 by the ATS 6 satellite.
The calibration coefficients of existing water vapor radiometers are dependent upon meteorology profiles. This is shown to be due mainly to incorrect frequency pairs. By properly selecting an optimum frequency pair, the dependency can be reduced to a relatively small amount which can be handily adjusted by surface measurement alone. Hence, a universal calibration equation is applicable to all environmental conditions - site, seasonal and diurnal variations. Optimum frequency pairs are systematically searched. Error analysis indicates that calibration for the water vapor phase delay accurate to less than 2 cm is possible at all elevation angles greater than 15 degrees.
An efficient numerical method of multiple quadratures, the Conroy method, is applied to the problem of computing multiple scattering contributions in the radiative transfer through realistic planetary atmospheres. A brief error analysis of the method is given and comparisons are drawn with the more familiar Monte Carlo method. Both methods are stochastic problem-solving models of a physical or mathematical process and utilize the sampling scheme for points distributed over a definite region. In the Monte Carlo scheme the sample points are distributed randomly over the integration region. In the Conroy method, the sample points are distributed systematically, such that the point distribution forms a unique, closed, symmetrical pattern which effectively fills the region of the multidimensional integration. The methods are illustrated by two simple examples: one, of multidimensional integration involving two independent variables, and the other, of computing the second order scattering contribution to the sky radiance.
The following topics are discussed: (1) the Unified Model of Lunar Translation/Rotation (UMLTR); (2) the effect of figure-figure interactions on lunar physical librations; (3) the effect of translational-rotational coupling on the lunar orbit; and(4) an error analysis for estimating lunar inertias from LURE (Lunar Laser Ranging Experiment) data.
A simple relationship has been established between the vertical ozone profile above the ozone maximum and satellite measured radiances for wavelengths shorter than 3000 A. The method is based on the computation of the penetration depths for solar radiation entering the atmosphere at wavelengths employed by the BUV satellite. Suitably defined penetration depths are shown to be linear functions of the normalized intensities for typical conditions, eliminating the requirement for iterative solutions and considerably simplifying the error analysis for the system. For ozone distributions which depart significantly from the exponential form, a noniterative extension of the analysis procedure has been developed and tested through application to simulated intensities.
The nitric oxide mixing ratio between 43 km and 61 km was directly measured with a rocket-borne chemiluminescent detector. The ozone-generated background signal was monitored throughout the flight (in 1976) by periodically interrupting the atmospheric sample flow with a pure-N2 bias-supply gas. An error analysis of the 1976 results showed the need to correct results obtained from an earlier flight (in 1975). The corrected 1975 results are reported and compared with the 1976 results.
A statistical technique is developed for inferring the optimum values of the ground albedo and the effective imaginary term of the complex refractive index of atmospheric particulates. The procedure compares measurements of the ratio of the hemispheric diffuse to directly transmitted solar flux density at the earth's surface with radiative transfer computations of the same as suggested by Herman et al. (1975). A detailed study is presented which shows the extent to which the ratio of diffuse to direct solar radiation is sensitive to many of the radiative transfer parameters. Results indicate that the optical depth and size distribution of atmospheric aerosol particles are the two parameters which uniquely specify the radiation field to the point where ground albedo and index of absorption can be inferred. Varying the real part of the complex refractive index of atmospheric particulates as well as their vertical distribution is found to have a negligible effect on the diffuse-direct ratio. The statistical procedure utilizes a semi-analytic gradient search method from least-squares theory and includes a detailed error analysis.