A new analytical solution of nonlinear geodetic datum transformation
Citations
21 citations
Cites methods from "A new analytical solution of nonlin..."
...The authors presented a new analytical algorithm based on optimization process and the good properties of Rodrigues matrix ([14])....
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19 citations
Cites methods from "A new analytical solution of nonlin..."
...Zeng and Yi (2010) presented a new analytical algorithm based on the good properties of Rodrigues matrix and Gibbs vector....
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14 citations
Cites methods from "A new analytical solution of nonlin..."
...2006a, b; Zeng and Yi 2011), algorithms based on Rodrigues matrix and Gibbs vector see (e.g., Zeng and Huang 2008; Zeng and Yi 2010; Zeng et al. 2016), algorithms based on dual quaternion (see, e....
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...(2006a, b), Zeng and Huang (2008), Han (2010), Zeng and Yi (2010, 2011), Zeng (2015), Závoti and Kalmár (2016), (58)s = 1 2c (B− C)r (59) 1 c ( CT − BT ) (B− C)r − 2 Ar + β1r = 0....
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...2006a, b; Zeng and Yi 2011), algorithms based on Rodrigues matrix and Gibbs vector see (e.g., Zeng and Huang 2008; Zeng and Yi 2010; Zeng et al....
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10 citations
Cites background from "A new analytical solution of nonlin..."
...2006; Zeng and Yi 2011; Závoti and Kalmár 2016), Rodrigues matrix and Gibbs vector see (e.g. Zeng and Huang 2008; Zeng and Yi 2010; Závoti and Kalmár 2016; Zeng et al....
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9 citations
Cites background or methods from "A new analytical solution of nonlin..."
...Zeng and Yi (2010a) presented an analytical algorithm based on Rodrigues matrix....
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...(18) namely R is a matrix with 3 rows and 3 columns, usually represented by rotation angles (see e.g. El-Habiby et al. 2009; Zeng and Yi, 2011), unit quaternion (see e.g. Shen et al. 2006; Zeng and Yi 2011), and Rodrigues matrix (see e.g. Zeng and Yi 2010a)....
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...Pattern search method is a kind of very popular direct search method, and for its more detail, the readers are referred to e.g. Torczon (1997), Lewis, et al. (2000), Dolan, et al. (2003), Al-Sumaita, et al. (2007), Zeng and Yi (2010b)....
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References
80 citations
"A new analytical solution of nonlin..." refers methods in this paper
...By taking the partial derivative of (8) with respect to λ and setting it to be zero, we can derive the solution of λ as...
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72 citations
"A new analytical solution of nonlin..." refers methods in this paper
...Once v is solved, r is got by using (13), and R is obtained by using (12), then λ can be computed by using (9), and lastly t is computed by using (6)....
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...(9) Obviously, if rotation matrix R is solved, we can get the solution of scale parameter λ and translation parameters t by using (9) and (6)....
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17 citations
"A new analytical solution of nonlin..." refers background or methods in this paper
...MATHEMATICS MODEL OF DATUM TRANSFORMATION Usually, 3D datum transformation model uses Bursa-Wolf model, which can be written as [10] , i i Rp t s λ + = (1)...
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...Secondly, compute coordinates in system A (true values) by using (1)....
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..., (1) can be rewritten as follows by using the centrobaric coordinates (namely space vector) form....
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...The transformation residuals is the differences between the calculated values and true values of coordinates in system A, of which the former is obtained by substituting coordinates in system B and solved parameters into (1)....
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9 citations
8 citations
"A new analytical solution of nonlin..." refers background in this paper
...(10) According to the physical meaning of λ , i....
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...i i s p λ = Δ Δ , where the symbol i represents the norm of space vector, (10) can be transformed as...
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