A Simple Perturbation Algorithm for Inverting the Cartesian to Geodetic Transformation

Table 1

List of polynomial coefficients.

Coefficient	Expression
𝐶1	−4ℎ^30+37𝑏^3−66𝑏^2ℎ0+33𝑏ℎ^20
𝐶2	ℎ^30−31𝑏^3+75𝑏^2ℎ0−33𝑏ℎ^20
𝐶3	3𝑏𝑏^2+3ℎ^20−6𝑏ℎ0
𝐶4	139𝑏^3−5ℎ^30+49𝑏ℎ^20−143𝑏^2ℎ0
𝐶5	ℎ^30−127𝑏^3+163𝑏^2ℎ0−45𝑏ℎ^20
𝐶6	4𝑏−10𝑏ℎ0+ℎ^20+5𝑏^2
𝐶7	4ℎ^40+118𝑏^4+198𝑏^2ℎ^20−266𝑏^3ℎ0−54𝑏ℎ^30
𝐶8	−155𝑏^4−2ℎ^40+67𝑏ℎ^30+421𝑏^3ℎ0−315𝑏^2ℎ^20
𝐶9	49𝑏^4−15𝑏ℎ^30−185𝑏^3ℎ0+135𝑏^3ℎ^20
𝐶10	2𝑏^210𝑏ℎ0−5ℎ^20−𝑏^2