Application of the Theory of Adjustment to Double Theodolite Observations

H. M. De Jong Royal Netherlands Meteorological Institute, De Bilt, Netherlands

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Abstract

The position of a pilot balloon or any other airborne target which is followed by two theodolites is usually computed by means of the known baselength (i.e., the distance between the two theodolite stations) and three observed angle readings. It is to be noted, however, that four angle readings are available. In order to obtain an optimum estimation of the target's location the theory of adjustment of observations should be applied. With this method the estimation of the location is based on making the magnitude of the (root mean square) error a minimum. The method is particularly suitable for high speed electronic computers. The error analysis makes it possible to give some valuable hints in planning specific experiments with two optical or radio theodolites.

Abstract

The position of a pilot balloon or any other airborne target which is followed by two theodolites is usually computed by means of the known baselength (i.e., the distance between the two theodolite stations) and three observed angle readings. It is to be noted, however, that four angle readings are available. In order to obtain an optimum estimation of the target's location the theory of adjustment of observations should be applied. With this method the estimation of the location is based on making the magnitude of the (root mean square) error a minimum. The method is particularly suitable for high speed electronic computers. The error analysis makes it possible to give some valuable hints in planning specific experiments with two optical or radio theodolites.

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