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Use of a least squares with conditional equations method in positioning a tramway track in the Gdansk agglomeration

Czaplewski K., Specht C., Dąbrowski P., Specht M., Wiśniewski Z., Koc W., Wilk A., Karwowski K., Chrostowski P., Szmagliński J.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

2019

Vol. 13. no. 4

895--900

Satellite measurement techniques have been used for many years in different types of human activity, including work related to staking out and making use of rail infrastructure. First and foremost, satellite techniques are applied to determine the tramway track course and to analyse the changes of its position during its operation. This paper proposes using the least squares with conditional equations method, known in geodesy (LSce). When applied, this method will allow for improvement of the final determination accuracy. This paper presents a simplified solution to the LSce alignment problem. The simplification involves replacement of the parameter binding equations with equivalent observational equations with properly selected weights. The results obtained with such a solution were demonstrated with a randomly selected section of a tramway track in Gdańsk. The article presents the theoretical foundations of the test method, the experiment organisation and the results obtained with MathCad Prime 3.0 software. It also presents the outcome of a study associated with the execution of the project No POIR.04.01.01-00-0017/17 entitled “Developing an innovative method of precision determination of a rail vehicle trajectory” executed by a consortium of the Gdańsk University of Technology and Gdynia Maritime University.

Some New Dimensions in Sextant-Based Celestial Navigation Aspects of Position Solution Reliability with Multiple Sights

Zevering K. H.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

2008

Vol. 2, no. 3

271--278

The traditional approach relying on sight reduction tables, a non-programmatic location of the position fix and an inadequate allowance for observation errors is still widely pursued and advocated. In the late 1970s the programmatic Least Squares method (LSQ) was introduced which determines a random error fix (FixQ) for any multiple sights combination. B.D Yallop & C.Y Hohenkerk (1985) expanded LSQ to incorporate the computation of the random error margin of a fix. Several marketed PDA-based programs apply LSQ, but none have fully incorporated the random error margin as a guide for the navigator. All existing LSQ applications have two drawbacks. One is, all observation error is attributed to random sources, whereas the possibility of systematic error has in fact a long theoretical and practical background in celestial navigation. Systematic error represents a bias in statistical random error theory and can and should be allowed for. A major drawback is that existing LSQ program applications incorporate the running fix technique (RFT) traditionally applied in coastal navigation. It has no general validity in celestial navigation. The position circle of an earlier celestial sight can only be mathematically correctly transferred when its Geometric Position (GP) is transferred for the run data. A final aspect of reliability is the strategy adopted at the sight planning stage. At least during twilight observations, navigators should aim at getting three or four sights with a total azimuth angle >180o, with three successive subsights on each body. In such configurations FixQ and FixS will be relatively close together, generally obviating the need to process the sights for possible systematic error.