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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク GNSS positioning calculation ： ウィキペディア英語版 GNSS positioning calculation The global navigation satellite system (GNSS) positioning for receiver's position is derived through the calculation steps, or algorithm, given below. In essence, a GNSS receiver measures the transmitting time of GNSS signals emitted from four or more GNSS satellites and these measurements are used to obtain its position (i.e., spatial coordinates) and reception time. ==Calculation steps== # A global-navigation-satellite-system (GNSS) receiver measures the apparent transmitting time, $\backslash scriptstyle\; \backslash tilde\_i$, or "phase", of GNSS signals emitted from four or more GNSS satellites ($\backslash scriptstyle\; i\; \backslash ;=\backslash ;\; 1,\backslash ,\; 2,\backslash ,\; 3,\backslash ,\; 4,\backslash ,\; ..,\backslash ,\; n$ ), simultaneously.〔Misra, P. and Enge, P., Global Positioning System: Signals, Measurements, and Performance, 2nd, Ganga-Jamuna Press, 2006.〕 # GNSS satellites broadcast the messages of satellites' ephemeris, $\backslash scriptstyle\; \backslash boldsymbol\_i\; (t)$, and intrinsic clock bias (i.e., clock advance), $\backslash scriptstyle\backslash delta\; t\_\; (t)$ as the functions of (atomic) standard time, e.g., GPST.〔(The interface specification of NAVSTAR GLOBAL POSITIONING SYSTEM )〕 # The transmitting time of GNSS satellite signals, $\backslash scriptstyle\; t\_i$, is thus derived from the non-closed-form equations $\backslash scriptstyle\; \backslash tilde\_i\; \backslash ;=\backslash ;\; t\_i\; \backslash ,+\backslash ,\; \backslash delta\; t\_\; (t\_i)$ and $\backslash scriptstyle\; \backslash delta\; t\_\; (t\_i)\; \backslash ;=\backslash ;\; \backslash delta\; t\_\; (t\_i)\; \backslash ,+\backslash ,\; \backslash delta\; t\_\; (\backslash boldsymbol\_i,\backslash ,\; \backslash dot,i\}\; (\backslash boldsymbol\_i,\backslash ,\; \backslash dot\_i\; \backslash ;=\backslash ;\; \backslash boldsymbol\_i\; (t\_i)$ and $\backslash scriptstyle\; \backslash dot\}\_i\; (t\_i)$. # In the field of GNSS, "geometric range", $\backslash scriptstyle\; r(\backslash boldsymbol\_A,\backslash ,\; \backslash boldsymbol\_B)$, is defined as straight range, or 3-dimensional distance,〔3-dimensional distance is given by $\backslash scriptstyle\; r(\backslash boldsymbol\_A,\backslash ,\; \backslash boldsymbol\_B)\; =\; |\backslash boldsymbol\_A\; -\; \backslash boldsymbol\_B|\; =\; \backslash sqrt$ where $\backslash scriptstyle\backslash boldsymbol\_A\; =\; (x\_A,\; y\_A,\; z\_A)$ and $\backslash scriptstyle\backslash boldsymbol\_B\; =\; (x\_B,\; y\_B,\; z\_B)$ represented in inertial frame.〕 from $\backslash scriptstyle\backslash boldsymbol\_A$ to $\backslash scriptstyle\backslash boldsymbol\_B$ in inertial frame (e.g., Earth Centered Inertial (ECI) one), not in rotating frame.〔 # The receiver's position, $\backslash scriptstyle\; \backslash boldsymbol\_\}$, satisfy the light-cone equation of $\backslash scriptstyle\; r(\backslash boldsymbol\_i,\backslash ,\; \backslash boldsymbol\_\})\; \backslash ;=\backslash ;\; 0$ in inertial frame, where $\backslash scriptstyle\; c$ is the speed of light. The signal transit time is $\backslash scriptstyle\; -(t\_i\; \backslash ,-\backslash ,\; t\_\_i,\backslash ,\; \backslash boldsymbol\_\})\; \backslash ,+\backslash ,\; \backslash delta\; t\_\; \backslash ,-\backslash ,\; \backslash delta\; t\_\; \backslash ;=\backslash ;\; 0$, where $\backslash scriptstyle\; \backslash delta\; t\_$ is atmospheric delay (= ionospheric delay + tropospheric delay) along signal path and $\backslash scriptstyle\; \backslash delta\; t\_$ is the measurement error. # The Gauss–Newton method can be used to solve the nonlinear least-squares problem for the solution: $\backslash scriptstyle\; (\backslash hat\},\backslash ,\; \backslash hat\_\_\}\; )$, where $\backslash scriptstyle\; \backslash phi\; (\; \backslash boldsymbol\_\}\; )\; \backslash ;=\backslash ;\; \backslash sum\_^n\; (\; \backslash delta\; t\_\; /\; \backslash sigma\_\; \}\; )^2$. Note that $\backslash scriptstyle\; \backslash delta\; t\_$ should be regarded as a function of $\backslash scriptstyle\; \backslash boldsymbol\_\}$. # The posterior distribution of $\backslash scriptstyle\; \backslash boldsymbol\_\}$ is proportional to $\backslash scriptstyle\; \backslash exp\; (\; -\backslash frac\; \backslash phi\; (\; \backslash boldsymbol\_\}\; )\; )$, whose mode is $\backslash scriptstyle\; (\backslash hat\},\backslash ,\; \backslash hat\_\_^\backslash infty\; \backslash exp\; (\; -\backslash frac\; \backslash phi\; (\; \backslash boldsymbol\_\}\; )\; )\; \backslash ,\; d\; t\_\{\backslash text\{rec\}\}$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「GNSS positioning calculation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.