Author： Awange Joseph L.
Publisher： Maney Publishing
ISSN： 1752-2706
Source： Survey Review, Vol.37, Iss.290, 2003-10, pp. : 319-329
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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 {Sl, S2} or directions {T10, T12, T20, T21} have been measured.
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