Recursive formulas for the evaluation of certain complex integrals
Recursive formulas for stability tests and quadratic loss functions evaluation for linear discrete time dynamical systems
Astroem, K. J.↗
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Interplanetary shock normals
A scheme has been developed to improve the estimate of an interplanetary shock normal by using both magnetic field and plasma data from a single spacecraft. Calculation of the basic shock model employs a subset of the eight magnetohydrodynamic conservation relations for a shock in an isotropic medium. This subset consists of six equations that are devoid of pressure and temperature terms. A sigma-weighted least squares loss function technique is used to best fit the overdetermination equations with respect to the eleven parameters of the system. This procedure usually yields a normal much more accurate than the one obtained using magnetic field values alone. An example is given of the use of the technique on the data for the Pioneer 7 shock of 29 August 1966.
Lepping, R. P.↗
Analytic expression for the energy-transfer rate from photoelectrons to thermal-electrons.
An analytic form is given for the energy-transfer rate from photoelectrons to thermal electrons. The expression fits the classical formulation of Itakawa and Aono (1966) at low energies and gives a smooth transition to fit the quantum mechanical equation of Schunk and Hays (1971) at higher energies. The corresponding loss function or stopping power has a form that is convenient in auroral and dayglow calculations.
Swartz, W. E.↗
Low-energy auroral electrons
A measurement of the low-energy auroral electron flux distribution between 0.5 and 80 eV reveals structure between 0.5 and 10.0 eV. The structure is due to the thermal electron Maxwellian distribution and electron energy loss to thermal electrons, molecular nitrogen, and atomic oxygen. Some physical process in the auroral plasma causes the deduced loss function to differ from theory. Reasonable agreement is obtained between calculated and measured N2 second positive emission.
Sharp, W. E.↗
Ion temperatures in HIP-1 and SUMMA from charge-exchange neutral optical emission spectra
Ion temperatures were obtained from observations of the H sub alpha, D sub alpha, and He 587.6 nm lines emitted from hydrogen, deuterium, and helium plasmas in the SUMMA and HIP-1 mirror devices at Lewis Research Center. Steady state discharges were formed by applying a radially inward dc electric field between cylindrical or annular anodes and hollow cathodes located at the peaks of the mirrors. The ion temperatures were found from the Doppler broadening of the charge-exchange components of spectral lines. A statistical method was developed for obtaining scaling relations of ion temperature as a function of current, voltage, and magnetic flux density. Derivations are given that take into account triangular monochromator slit functions, loss cones, and superimposed charge-exchange processes. In addition, the Doppler broadening was found to be sensitive to the influence of drift on charge-exchange cross section. The effects of finite ion-cyclotron radius, cascading, and delayed emission are reviewed.
Patch, R. W.↗
Ambiguity resolution for satellite Doppler positioning systems
A test for ambiguity resolution was derived which was the most powerful in the sense that it maximized the probability of a correct decision. When systematic error sources were properly included in the least squares reduction process to yield an optimal solution, the test reduced to choosing the solution which provided the smaller valuation of the least squares loss function. When systematic error sources were ignored in the least squares reduction, the most powerful test was a quadratic form comparison with the weighting matrix of the quadratic form obtained by computing the pseudo-inverse of a reduced rank square matrix. A formula is presented for computing the power of the most powerful test. A numerical example is included in which the power of the test is computed for a situation which may occur during an actual satellite aided search and rescue mission.
Argentiero, P. D.↗
On least squares collocation
It is shown that the least squares collocation approach to estimating geodetic parameters is identical to conventional minimum variance estimation. Hence, the least squares collocation estimator can be derived either by minimizing the usual least squares quadratic loss function or by computing a conditional expectation by means of the regression equation. When a deterministic functional relationship between the data and the parameters to be estimated is available, one can implement a least squares solution using the functional relation to obtain an equation of condition. It is proved the solution so obtained is identical to what is obtained through least squares collocation. The implications of this equivalance for the estimation of mean gravity anomalies are discussed.
Argentiero, P. D.↗
Approximate algorithms for fast optimal attitude computation
Fast accurate algorithms are presented for computing an optimal attitude which minimizes a quadratic loss function. These algorithms compute an optimal rotation which carries a set of reference vectors into a set of corresponding observation vectors. Simplifications of these algorithms are obtained for the case of small rotation angles. Applications to the Magsat mission are discussed.
Shuster, M. D.↗
Ambiguity resolution for satellite Doppler positioning systems
The implementation of satellite-based Doppler positioning systems frequently requires the recovery of transmitter position from a single pass of Doppler data. The least-squares approach to the problem yields conjugate solutions on either side of the satellite subtrack. It is important to develop a procedure for choosing the proper solution which is correct in a high percentage of cases. A test for ambiguity resolution which is the most powerful in the sense that it maximizes the probability of a correct decision is derived. When systematic error sources are properly included in the least-squares reduction process to yield an optimal solution the test reduces to choosing the solution which provides the smaller valuation of the least-squares loss function. When systematic error sources are ignored in the least-squares reduction, the most powerful test is a quadratic form comparison with the weighting matrix of the quadratic form obtained by computing the pseudoinverse of a reduced-rank square matrix. A formula for computing the power of the most powerful test is provided. Numerical examples are included in which the power of the test is computed for situations that are relevant to the design of a satellite-aided search and rescue system.
Argentiero, P.↗
Contextual classification of multispectral image data
A general method is presented for exploiting both spatial and spectral information when classifying multispectral image data. This statistical classification algorithm utilizes the tendency of certain ground cover classes to be more likely to occur in some contexts than others. The theoretical model assumes the two-dimensional array of random observations and a 0-1 loss function, a distribution of the p-context array that is spatially invariant, and class-conditional independence for the observations. The problems that prevent the immediate use of this context classifier are the need for a generally applicable method for making adequate estimates of the context distribution and a reduction in the computational intensivity of the classifier. The former problem is being approached by a method that raises the relative frequency value for each class configuration to a power and uses the result as the context distribution estimate. The second is being approached by searching for a less computationally intensive algorithm.
Tilton, J. C.↗
Radiating properties of solar plasmas
Using a series of 14 previously obtained empirical emission measure distributions and a number of spectral lines observed by the SMM and P78-1 instruments, the total power radiated by a hot plasma is compared to that radiated by individual spectrum lines. Results are presented for different choices of ionization balance and power loss functions. The results indicate that for some lines such as the C IV resonance doublet at 1548 A and 1550 A, the ratio of the line intensity to the total radiated power varied only over a factor of 2, suggesting that well-calibrated measurements of a single line intensity may provide a fairly good estimation of the total radiated power output from the solar plasma.
Bruner, M. E.↗
Attitude determination and parameter estimation using vector observations
Procedures for attitude determination based on Wahba's loss function are generalized to include the estimation of parameters other than the attitude, such as sensor biases. Optimization with respect to the attitude requires either the singular value decomposition of a 3x3 matrix or finding the maximum eigenvalue and corresponding eigenvector of a 4x4 symmetric matrix, but does not require an a priori estimate of the attitude. Optimization with respect to the other parameters employs an iterative approach, which does require an a priori estimate of these parameters. Conventional state estimation methods require a priori estimates of both the parameters and the attitude, while the algorithms presented in this paper always compute the exact optimal attitude for given values of the parameters. The proposed method is shown to give the correct solution of an example problem. An expression for the covariance of the attitude and parameter estimates is derived.
Markley, F. Landis↗
Algorithm for in-flight gyroscope calibration
An optimal algorithm for the in-flight calibration of spacecraft gyroscope systems is presented. Special consideration is given to the selection of the loss function weight matrix in situations in which the spacecraft attitude sensors provide significantly more accurate information in pitch and yaw than in roll, such as will be the case in the Hubble Space Telescope mission. The results of numerical tests that verify the accuracy of the algorithm are discussed.
Davenport, P. B.↗
Attitude determination and parameter estimation using vector observations - Theory
Procedures for attitude determination based on Wahba's loss function are generalized to include the estimation of parameters other than the attitude, such as sensor biases. Optimization with respect to the attitude is carried out using the q-method, which does not require an a priori estimate of the attitude. Optimization with respect to the other parameters employs an iterative approach, which does require an a priori estimate of these parameters. Conventional state estimation methods require a priori estimates of both the parameters and the attitude, while the algorithm presented in this paper always computes the exact optimal attitude for given values of the parameters. Expressions for the covariance of the attitude and parameter estimates are derived.
Markley, F. Landis↗
Human tolerance to space flight
Medical studies of astronauts and cosmonauts before, during, and after space missions have identified several effects of weightlessness and other factors that influence the ability of humans to tolerate space flight. Weightlessness effects include space motion sickness, cardiovascular abnormalities, reduction in immune system function, loss of red blood cells, loss of bone mass, and muscle atrophy. Extravehicular activity (EVA) increases the likelihood that decompression sickness may occur. Radiation also gives reason for concern about health of crewmembers, and psychological factors are important on long-term flights. Countermeasures that have been used include sensory preadaptation, prebreathing and use of various air mixtures for EVA, loading with water and electrolytes, exercise, use of pharmacological agents and special diets, and psychological support. It appears that humans can tolerate and recover satisfactorily from at least one year of space flight, but a number of conditions must be further ameliorated before long-duration missions can be considered routine.
Huntoon, C. L.↗
Simultaneous quaternion estimation (QUEST) and bias determination
Tests of a new method for the simultaneous estimation of spacecraft attitude and sensor biases, based on a quaternion estimation algorithm minimizing Wahba's loss function are presented. The new method is compared with a conventional batch least-squares differential correction algorithm. The estimates are based on data from strapdown gyros and star trackers, simulated with varying levels of Gaussian noise for both inertially-fixed and Earth-pointing reference attitudes. Both algorithms solve for the spacecraft attitude and the gyro drift rate biases. They converge to the same estimates at the same rate for inertially-fixed attitude, but the new algorithm converges more slowly than the differential correction for Earth-pointing attitude. The slower convergence of the new method for non-zero attitude rates is believed to be due to the use of an inadequate approximation for a partial derivative matrix. The new method requires about twice the computational effort of the differential correction. Improving the approximation for the partial derivative matrix in the new method is expected to improve its convergence at the cost of increased computational effort.
Markley, F. Landis↗
A comparison between bright points in a coronal hole and a quiet-sun region
A comparison is made of the morphological structure and temporal behavior of the emission from coronal bright points in a coronal hole and a quiet region, using data from the Harvard EUV experiment on Skylab. It is found that, in both regions, coronal bright points are located at network boundaries and cover a range of sizes from 10 to 40 in in linear extent. In a given bright pint, the peaks of emission in the six different lines, measured simultaneously through the same instrument slit, are not always cospatial, implying that bright points consist of a complex of small-scale loops at different temperatures. The intensity of bright points in both regions is also characterized by a significant temporal variability in all the wavelengths measured. This variability exhibits no regular periodicity. Yet the ratio of the varying (ac) to the constant (dc) components of the emission, in all the bright points studied, has a local maximum at 1-2 x 10 to the 5th k which coincides with the peak of the radiative loss function, and another local maximum at Mg x (1.4 x 10 to the 6th K). It is found that coronal bright points in a coronal hole or a quiet region are indistinguishable structures, and, therefore, conclude that they are independent of the overlying background corona.
Habbal, Shadia Rifai↗
Attitude determination and parameter estimation using vector observations - Application
This paper presents tests of a new method for the simultaneous estimation of spacecraft attitude and sensor biases, based on a quaternion estimation algorithm minimizing Wahba's loss function. The new method is compared with a conventional batch least-squares differential correction algorithm. The estimates are based on data from strapdown gyros and star trackers, simulated with varying levels of Gaussian noise for both inertially-fixed and earth-pointing attitudes. Both algorithms solve for the spacecraft attitude and the gyro drift rate biases. In the majority of tests performed, the two methods converge to the same estimates in the same number of iterations, but the new algorithm requires about 60 percent more computational effort. Some cases were found in which the new method converges in fewer iterations than the differential correction, and some for which the differential correction requires fewer iterations.
Markley, F. Landis↗