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Ranjit M. Passi

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Ranjit M. Passi

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The Omega navigation system will be used during FGGE to derive vertical profiles of horizontal wind field. The aircraft dropsonde system and the shipboard Omega system will be used for the purpose. Since considerable effort and money will be spent it is only natural that these systems be optimally deployed. For this, Michael Olson of NCAR and M. C. Poppe of Cambridge Engineering have independently derived Omega wind error predictions. Both have made use of a smoothing improvement factor (resulting from superior phase smoothing techniques) over a quadratic phase model. This paper gives a theoretical justification for the use of such a smoothing improvement factor and empirical evaluation of it.

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Ranjit M. Passi

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A procedure for determining vertical wind profiles using Omega signal phase information from any number of Omega stations (at least three) is given. A statistical method of smoothing the phase data is presented and weighted least-square solutions are derived to estimate the position of the Omegasonde, and the U (east-west) and V (north-south) components of the wind. The technique is then applied to the data collected at Wallops Island by the National Oceanic and Atmospheric Administration in December 1972.

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Ranjit M. Passi

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A simple arithmetic mean, when the observations are correlated, is not the optimum estimate of the population mean. Such is usually the case when the observations are taken from a stationary time series. The variances of the optimally weighted and the unweighted means, for different sample sizes, were compared when the data follow a second-order autoregressive scheme, and it was observed that, for small samples, much is to be gained if the observations are optimally weighted. In this paper, optimal weights are derived for the general case when the data follow an autoregressive scheme of order k, where k is any positive integer. These optimal weights are simple closed expressions in terms of the autoregressive coefficients.

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Ranjit M. Passi

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This paper derives formulas for the application of nonlinear least squares. The need for doing statistical error analyses before undertaking any system development is pointed and formulas are derived to compute the covariance matrix of the estimated parameters. The technique is illustrated with application to three systems developed by the GAMP Group at NCAR, namely the GHOST sun angle tracking system, the use of Omega navigation system in the Carrier Balloon System, and the Safesonde, a Doppler wind measuring radiosonde system. The techniques developed are general enough for a universal application of nonlinear least squares.

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Ranjit M. Passi

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A generalized hyperbolic navigation system using Omega signals is defined. For three stations this system is shown to be equivalent to the ordinary hyperbolic navigation system. It is shown that the velocity and position determination are independent of the station selected to be the common station. Furthermore, a formula is given to combine several estimates of the wind vector into a single optimum estimate. The efficiency of using three frequencies instead of a single frequency to derive the wind vector is derived.

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Ranjit M. Passi

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During GARP Atlantic Tropical Experiment (GATE), temporal and cospatial measurements on meteorological parameters were made. it is necessary that such measurements be pooled to obtain an optimal estimate. This paper presents formulas for both univariate and multivariate cases to optimally combine correlated estimates (or observations) yielding a single estimate which is better. Applications to a linear autoregressive scheme and Omega windfinding are given.

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Ranjit M. Passi and Claude Morel

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It has been known that the Loran (Long Range Navigation) system can accurately provide a finescale structure of winds. However, this capability could not be widely adopted because of the limited coverage of this system in the continental United States and other parts of the world. Recently there has been a remarkable expansion of Loran chains throughout the Northern Hemisphere. In addition, the cross-chain navigation concept has virtually eliminated the gap through the midcontinent of the United States. The CLASS (cross-chain Loran atmospheric sounding system) developed at the National Center for Atmospheric Research has demonstrated the capability of measuring the finescale winds so necessary for mesoscale research. This paper provides the expected accuracy of the winds derived using the existing and planned worldwide Loran network.

Appendices include derivation of the basic equations used to determine winds from CLASS and study the impact on noise of averaging winds beyond 30 seconds.

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Claude-Morel and Ranjit M. Passi

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The National Center for Atmospheric Research has developed a new radiosonde system CLASS (Cross-chain LORAN Atmospheric Sounding System). The sounding data acquired by this system are nonstationary with time dependent mean and variance. Real-time analysis is required to determine winds, pressure, temperature and humidity. Before such computations we must carry out an editing step to remove wild data points or outliers. It is paper presents a new data-editing algorithm using adaptive polynomials. This algorithm is amenable for real-time editing of nonstationary data because of its (i) data-adaptive nature, (ii) computing efficiency, and (iii) simplicity of implementation. Its implementation is demonstrated on a set of pressure data collected by CLASS.

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H. Jean Thiebaux and Ranjit M. Passi

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Properties of the optimal combination scheme for several vector estimates are developed for correlated estimates having common ensemble mean. Classic optimality properties of a linear combination of estimates from separate sources are established as corollaries of the more general optimization criterion. simultaneous minimization of variance components.

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