BUCHBERGER ALGORITHM APPLIED TO PLANAR LATERATION AND INTERSECTION PROBLEMS

Author: Awange, Joseph L.

Source: Survey Review, Volume 37, Number 290, October 2003 , pp. 319-329(11)

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Abstract:

The Buchberger algorithm which is incorporated in algebraic software of MAPLE and MATHEMATICA is here used to derive expressions relating the known coordinates of planar stations P₁ ∈ E² and P₂ ∈ E² (i.e. {X₁, Y₁}_P₁ and {X₂, Y₂}_P₂ respectively) and the observables {S₁, S₂, T₁₀, T₁₂, T₂₀, T₂₁} to the unknown planar coordinates {X₀, Y₀}_p₀ of station P₀ for planar lateration and intersection problems. In the case of lateration, the coordinates {X₀, Y₀}_P₀ of the unknown station P₀ ∈ E² are expressed as quadratic equations in terms of the measured distances {S₂, S₂} to the known station {P₁, P₂} ∈ E² and the coordinates {X₁, Y₁}_P₁ and {X₂, Y₂}_P₂ of these known stations respectively. For intersection, the coordinates {X₀, Y₀}_P₀ of the unknown stations P₀ ∈ E² are expressed in terms of the measured directions {T₁₀, T₁₂, T₂₀, T₂₁} and the coordinates {X₁, Y₁}_P₁} and {X₂, Y₂}_P₂ of known stations {P₁, P₂} ∈ E². These expressions can easily be programmed in laptops or programmable calculators and thus making it feasible for any practitioner with these computing devices to obtain directly planar coordinates once the distances {S_l, S₂} or directions {T₁₀, T₁₂, T₂₀, T₂₁} have been measured.

Document Type: Research Article

DOI: http://dx.doi.org/10.1179/003962603791482569

Publication date: 2003-10-01

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