Papers by James Van Zandt
73 new cubature rules are found for three standard multidimensional integrals with spherically sy... more 73 new cubature rules are found for three standard multidimensional integrals with spherically symmetric regions and weights, using direct search with a numerical zero-finder. All but four of the new rules have fewer integration points than known rules of the same degree, and twenty are within three points of Möller's lower bound. Most have all positive coefficients and most have some symmetry, including some supported by one or two concentric spheres. They include degree 7 formulas for integration over the sphere and Gaussian-weighted integrals over all space, each in 6 and 7 dimensions, with 127 and 183 points, respectively.
We describe, optimize, and compare covariance encoding sch emes. Several current systems encode t... more We describe, optimize, and compare covariance encoding sch emes. Several current systems encode three dimensional covariances in terms of their eigenvalue s and Euler angles. We generalize this method to n dimensions. We precondition covariances to ensure that rec onstructed matrices will be positive definite. We propose a new scalar measure of merit for covaria nce encodings, the Bhattacharyya distance. We compare the schemes in terms of the encoding error and the e ncoding length in bits. We recommend using enough bits to make the encoding error small compared t o the error described by the covariance itself. The most e fficient scheme uses logarithmic encoding of the variances and linear encoding of the Cholesky factor of the correlation matrix.
Time-resolved measurements were made of the shifts of the ionized helium lines at 1,640 A (n = 3 ... more Time-resolved measurements were made of the shifts of the ionized helium lines at 1,640 A (n = 3 approaches 2) and 1,215 A (n = 4 approaches 2), and of the Stark profile of the 1,215 A wavelength line. An electromagnetic shock tube was used as a light source. The plasma conditions corresponded to electron temperatures of approximately 3.5 eV
ETNA - Electronic Transactions on Numerical Analysis
67 new cubature rules are found for three standard multidimensional integrals with spherically sy... more 67 new cubature rules are found for three standard multidimensional integrals with spherically symmetric regions and weight functions, using direct search with a numerical zerofinder. 63 of the new rules have fewer integration points than known rules of the same degree, and 20 are within three points of Möller's lower bound. Most have all positive coefficients and most have some symmetry, including some supported by one or two concentric spheres. They include degree 7 formulas for integration over the sphere and Gaussian-weighted integrals over all space, each in 6 and 7 dimensions, with 127 and 183 points, respectively.
ABSTRACT Planning an airborne search for a relocatable target involves minimizing the risk to the... more ABSTRACT Planning an airborne search for a relocatable target involves minimizing the risk to the crew while maximizing the estimated likelihood of finding targets. When the number of potential sites is small, the problem reduces to finding the best (usually the shortest) route connecting them. When the number of sites is larger, however, the planner must also decide which of them are to be visited. This report presents a genetic algorithm f or selecting both an appropriate set of sites to visit and an appropriate routing pattern. The procedure also accounts for the finite turning radius of the aircraft.
Time-resolved measurements were made of the shifts of the ionized helium lines at 1,640 A (n = 3 ... more Time-resolved measurements were made of the shifts of the ionized helium lines at 1,640 A (n = 3 approaches 2) and 1,215 A (n = 4 approaches 2), and of the Stark profile of the 1,215 A wavelength line. An electromagnetic shock tube was used as a light source. The plasma conditions corresponded to electron temperatures of approximately 3.5 eV
We describe, optimize, and compare covariance encoding schemes. Several current systems encode th... more We describe, optimize, and compare covariance encoding schemes. Several current systems encode three dimensional covariances in terms of their eigenvalues and Euler angles. We generalize this method to n dimensions. We precondition covariances to ensure that reconstructed matrices will be positive definite. We propose a new scalar measure of merit for covariance encodings, the Bhattacharyya distance. We compare the schemes in terms of the encoding error and the encoding length in bits. We recommend using enough bits to make the encoding error small compared to the error described by the covariance itself. The most efficient scheme uses logarithmic encoding of the variances and linear encoding of the Cholesky factor of the correlation matrix.
AIAA SPACE 2013 Conference and Exposition, 2013
We investigate ways of harnessing the relative motion of two asteroids by means of a tether that ... more We investigate ways of harnessing the relative motion of two asteroids by means of a tether that is connected at their time of closest approach, and later released. We estimate the frequency of suitable asteroid conjunctions and assess the feasibility of possible applications of this slingshot maneuver, including artificial gravity, electric power generation, payload launch, and orbit transfer of an asteroid.
Signal and Data Processing of Small Targets 2012, 2012
ABSTRACT Steady-state performance of a tracking filter is traditionally evaluated immediately aft... more ABSTRACT Steady-state performance of a tracking filter is traditionally evaluated immediately after a track update. However, there is commonly a further delay (e.g., processing and communications latency) before the tracks can actually be used. We analyze the accuracy of extrapolated target tracks for four tracking filters: Kalman filter with the Singer maneuver model and worst-case correlation time, with piecewise constant white acceleration, and with continuous white acceleration, and the reduced state filter proposed by Mookerjee and Reifler. Performance evaluation of a tracking filter is significantly simplified by appropriate normalization. For the Kalman filter with the Singer maneuver model, the steady-state RMS error immediately after an update depends on only two dimensionless parameters. By assuming a worst case value of target acceleration correlation time, we reduce this to a single parameter without significantly changing the filter performance (within a few percent for air tracking).4 With this simplification, we find for all four filters that the RMS errors for the extrapolated state are functions of only two dimensionless parameters. We provide simple analytic approximations in each case.
Physical Review A, 1976
ABSTRACT Time-resolved photoelectric measurements were made of the shifts of helium plasma lines ... more ABSTRACT Time-resolved photoelectric measurements were made of the shifts of helium plasma lines at 1640 A and 1215 A and of the Stark profile of the 1215 A line, using an electromagnetic shock tube as a light source. These red shifts are consistent with a plasma polarization shift, where the interaction energy between the radiating ion and the perturbing plasma electrons corresponds to the Coulomb interaction near the excited state Bohr radius. No significant shifts were observed for the 1640 A line, while the 1215 A line underwent a red shift of about 0.5 A. The measured Stark width of the 1215 A line was 10-45% greater than the calculated width based on the measured width of the 4686 A line.
The unscented transformation is extended to use extra test points beyond the minimum necessary to... more The unscented transformation is extended to use extra test points beyond the minimum necessary to determine the second moments of a multivariate normal distribution. The additional test points can improve the estimated mean and variance of the transformed distribution when the transforming function of its derivatives have discontinuities.
Signal and Data Processing of Small Targets 2002
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Papers by James Van Zandt