Astronomical Fixes Without an Assumed Position

Spencer, B.

doi:10.1017/s0373463300014090

Cited by 6 publications

(12 citation statements)

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“…Although other literatures [5,6,[9][10][11][12][13] found useful formulae in AVP solving procedures, most of them are complex and tedious compared to our suggested optimal formulae. Discussions on Optimal Formulae.…”

Section: O M M E N T S O N C O N V E N T I O N a L M E T H O D S F mentioning

confidence: 87%

“…As for the work of Kotlaric [6], transformation of the Haversine function, Hav x= sin 2 x 2 , is adopted in steps 1 and 5 and the half angle formula is adopted in steps 2, 3, and 6. Other related papers can also be found [9][10][11][12][13]. Further analysis show that except for step 4, any one of the spherical triangle formulae used in the above steps shows the relationship of three sides and one angle.…”

Section: O M M E N T S O N C O N V E N T I O N a L M E T H O D S F mentioning

confidence: 91%

“…For instance, one can find that in Chiesa's work [5], spherical triangle equations such as the side cosine formula, four-part formula, half angle formula, sine formula and Napier's analogies, are adopted in steps 1, 2, 3, 5, and 6, respectively. Other related papers can also be found [9][10][11][12][13]. Other related papers can also be found [9][10][11][12][13].…”

Section: O M M E N T S O N C O N V E N T I O N a L M E T H O D S F mentioning

confidence: 94%

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New Computational Methods for Solving Problems of the Astronomical Vessel Position

Hsu

Chen

Chang³

2005

J. Navigation

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In this paper, a simplified and direct computation method formulated by the fixed coordinate system and relative meridian concept in conjunction with vector algebra is developed to deal with the classical problems of celestial navigation. It is found that the proposed approach, the Simultaneous Equal-altitude Equation Method (SEEM), can directly calculate the Astronomical Vessel Position (AVP) without an additional graphical procedure. The SEEM is not only simpler than the matrix method but is also more straightforward than the Spherical Triangle Method (STM). Due to tedious computation procedures existing in the commonly used methods for determining the AVP, a set of optimal computation procedures for the STM is also suggested. In addition, aimed at drawbacks of the intercept method, an improved approach with a new computation procedure is also presented to plot the celestial line of position without the intercept. The improved approach with iteration scheme is used to solve the AVP and validate the SEEM successfully. Methods of solving AVP problems are also discussed in detail. Finally, a benchmark example is included to demonstrate these proposed methods.K E Y W O R D S 1. Astronomical vessel position.2. Spherical trigonometry. 3. Intercept method.

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Section: O M M E N T S O N C O N V E N T I O N a L M E T H O D S F mentioning

confidence: 87%

Section: O M M E N T S O N C O N V E N T I O N a L M E T H O D S F mentioning

confidence: 91%

Section: O M M E N T S O N C O N V E N T I O N a L M E T H O D S F mentioning

confidence: 94%

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New Computational Methods for Solving Problems of the Astronomical Vessel Position

Hsu

Chen

Chang³

2005

J. Navigation

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“…Exact solutions to a two-body fix, such as those by Chiesa and Chiesa (1990), Spencer (1990) These methods can be applied to any number of observations ≥ 2. Traditional hand-calculation and chart-based methods fall into this category, as does the least-squares method by DeWitt (1974), which was independently derived by Yallop and Hohenkerk (1990) and described in the Nautical Almanac and used in HMNAO's NavPac software.…”

Section: Direct Computation Methods For Celestial Navigation Fixmentioning

confidence: 99%

Celestial Navigation Fix Based on Particle Swarm Optimization

Tsou

2015

Polish Maritime Research

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“…Either the assumed position is not needed or the knowledge of an approximate position is sufficient. Some researchers have studied a two-body fix [2,3,5,6,12,14]. It is proposed that at a given time, the astronomical vessel position can be determined by observing circles of equal altitude of two celestial bodies.…”

Section: Spherical Triangle Methods (Stm) and Vector-matrix Methodsmentioning

confidence: 99%

Genetic algorithm for solving celestial navigation fix problems

Tsou¹

2012

Polish Maritime Research

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As we enter the 21st century and advance further into the information age, traditional methods for computing a celestial navigation fix can no longer meet the requirements of modern vessels in terms of calculation speed and precision. Study of precise, rapid, and convenient celestial navigation computational methods and the application of information technology to modern celestial navigation is especially meaningful, considering the current push for e-Navigation. In this work, we employ a genetic algorithm, from the field of artificial intelligence, due to its superior search ability that mimics the natural process of biological evolution. Unique encodings and genetic operators designed in this study, in combination with the fix principle of celestial circles of equal altitude in celestial navigation, allow the rapid and direct attainment of accurate optimum vessel position. Test results indicate that this method has more flexibility, and avoids tedious and complicated computation and graphical procedures.

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Astronomical Fixes Without an Assumed Position

Abstract: have drawn attention to a method of obtaining an astronomical fix without an assumed position. The present writer further encourages use of the principle, and the writing of programs for the purpose on small computers.

Cited by 6 publications

References 1 publication

New Computational Methods for Solving Problems of the Astronomical Vessel Position

New Computational Methods for Solving Problems of the Astronomical Vessel Position

Celestial Navigation Fix Based on Particle Swarm Optimization

Genetic algorithm for solving celestial navigation fix problems

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