CN102495715A - Deep space Doppler speed measurement calculating method defined by double-precision floating point - Google Patents

Abstract

The invention belongs to the technical field of data processing, and discloses a deep-space Doppler velocity measurement calculation method defined by double-precision floating points. The method first establishes the Doppler measurement equation based on the Doppler measurement principle; then uses the Taylor series expansion to calculate the light travel time difference at the beginning and end of the integration period; finally, the light travel time difference is substituted into the measurement equation to calculate the Doppler velocity measurement. The invention improves the calculation accuracy and efficiency of Doppler speed measurement for deep space exploration.

Description

Calculation Method of Deep Space Doppler Velocimetry Under the Definition of Double Precision Floating Point

technical field

The invention belongs to the technical field of data processing, and relates to a deep-space Doppler (Doppler) velocity measurement calculation method defined by double-precision floating points.

Background technique

皮秒左右(其中^[]表示取整，R为探测距离，单位为亿千米)，此精度在1亿千米以上的探测任务Doppler测量数据的处理中，只能保证1mm/s(1秒积分周期)的计算精度，显然不能满足当前0.1mm/s甚至0.02mm/s的精度要求。通常的做法是在计算光行时使用四精度浮点数代替双精度浮点数，以提高计算精度，但该方法虽然提高了计算精度，却降低了计算效率。At present, the calculation of Doppler in deep space exploration usually adopts the method described in the book "Formulation for observed and computed values of Deep Space Network data types for navigation". Using this method, if double-precision floating-point numbers are used to calculate light lines, due to the influence of rounding errors, the calculation accuracy is about

About picoseconds (where ^[] means rounding, R is the detection distance, and the unit is 100 million kilometers), this accuracy can only guarantee 1mm/s (1 second The calculation accuracy of integration period) obviously cannot meet the current accuracy requirement of 0.1mm/s or even 0.02mm/s. The usual practice is to use quadruple-precision floating-point numbers instead of double-precision floating-point numbers when calculating light lines to improve calculation accuracy, but this method reduces calculation efficiency although it improves calculation accuracy.

Contents of the invention

The object of the present invention is to provide a deep-space Doppler velocity measurement calculation method under the definition of double-precision floating point, so as to improve calculation accuracy and calculation efficiency.

In order to achieve the above object, the deep space Doppler speed measurement calculation method under the double-precision floating-point definition provided by the present invention comprises the following steps:

<1>Establish the Doppler measurement equation according to the Doppler measurement principle;

<2> Use the Taylor series expansion to calculate the light travel time difference at the beginning and end of the integration period;

<3> Substitute the travel time difference into the measurement equation to calculate the Doppler speed measurement.

Further, the Doppler measurement equation is as follows:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="f"\; filenames="HSA00000629336800011.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}}{\mathrm{<span\; class="notranslate">\; \&Delta;T</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;\; f</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; v</span>}$

where f _D represents the Doppler frequency offset, f _R represents the signal frequency received by the receiving end, f ₀ represents the local oscillator frequency of the ground receiving station, N _C is the cycle count in one integration period, ΔT is an integration period, and δf is the observation system Error, v is the observation random error.

The method for calculating the light travel time difference at the beginning and end of the integration period is as follows:

$\mathrm{<span\; class="notranslate">\; \&Delta;\&tau;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}$

$<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; RLT</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; RLT</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}$

$<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \{</span>{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; TDB</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; TDB</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \}</span>$

$<span\; class="notranslate">\; +</span><span\; class="notranslate">\; \{</span>{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; TDB</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; TDB</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \}</span>$

Among them, τ _{S, e} , τ _{S, s} respectively represent the original points corresponding to the end of the integration period and the start time of the signal transmitting end on the star, and ρ _{SR, e} , ρ _{SR, s} respectively represent the one-way geometry corresponding to the end of the integration period and the start time Distance, RLT _e , RLT _s represent the gravitational bending at the end of integration and the beginning moment, TDB represents the dynamic time of the center of mass of the solar system, t(τ) represents the corresponding original time, [] _e , [] _s correspond to the end and start time of integration respectively;

in:

${\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&ap;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{<span\; class="notranslate">\; \&PartialD;</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; SR</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; SR</span>}}\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{<span\; class="notranslate">\; \&PartialD;</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="e"\; filenames="HSA00000629336800011.png"\; state="\{\{state\}\}">e</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; SR</span>}}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; SR</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; [</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; TDB</span>}}_{\mathrm{<span\; class="notranslate">\; SC</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; TDB</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; [</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; TDB</span>}}_{\mathrm{<span\; class="notranslate">\; SC</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; TDB</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; e</span>}}$

$\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{<span\; class="notranslate">\; \&PartialD;</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; =</span>\frac{{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}$

$\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{<span\; class="notranslate">\; \&PartialD;</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}\left[\begin{array}{ccc}\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& \frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}& \frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\\ \frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}& \frac{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& \frac{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\\ \frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}& \frac{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}& \frac{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$

Among them, X, Y, and Z represent the position components of the aircraft in the barycentric coordinate system of the general relativity solar system, the subscript S represents the transmitting end, R represents the receiving end, s represents the integration start time, and e represents the integration end time.

The present invention calculates the light travel time difference between the beginning and the end of the integration period through Taylor series expansion, avoids the shortcomings of directly using the difference distance observation to obtain Doppler and loss of calculation accuracy, and eliminates the lack of word length when defining double-precision floating points The impact of the rounding error generated on the calculation accuracy reaches the accuracy of four-precision floating-point number calculation, which ensures the calculation efficiency.

Description of drawings

Fig. 1 Mars probe uses the conventional method to compare the result with the Doppler calculated by the present invention.

Detailed ways

The deep-space Doppler velocity measurement calculation method under the double-precision floating-point definition provided by the present invention comprises the following steps:

1. Establish the Doppler measurement equation according to the Doppler measurement principle

The observation value of the integrated Doppler is the offset f _D of the received signal frequency of the ground station relative to the standard frequency, which is obtained by measuring the cycle count in an integration period, that is,

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="f"\; filenames="HSA00000629336800011.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}}{\mathrm{<span\; class="notranslate">\; \&Delta;T</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;\; f</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, f _R represents the signal frequency received by the receiving end, f ₀ represents the local oscillator frequency of the ground receiving station, N _C is the cycle count in an integration period, ΔT is an integration period, δf is the observation system error, and v is the observation random error.

The Doppler observation f _D can be derived from the change of the accumulated Doppler cycle count N _C within an integration period ΔT at the ground receiving station. For a given surface station, successive Doppler observations have successive integration periods. The integration period can be as short as 0.1s or as long as half a day (43200s), and the typical integration period is in the range of a few seconds to several thousand seconds.

For N _C there is

${\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}^{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}^{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="f"\; filenames="HSA00000629336800011.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;T</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}^{{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}\mathrm{<span\; class="notranslate">\; d\&tau;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="f"\; filenames="HSA00000629336800011.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;T</span>}$

Where f ₀ is the local oscillator frequency of the ground receiving station, the lowercase subscript s, e represent the start and end of the integration, t represents the time of the ground station, generally using the Coordinated Universal Time (UTC) time system, and τ represents the original time of the signal transmitter.

Considering the ideal state, that is, the emission standard frequency f _S is a constant, then:

f _R ΔT = f _S (τ _e -τ _s ) = f _S Δτ (3)

For the convenience of distinction, ΔT is an integration period of the receiving end, and Δτ is the original time difference of the transmitting end corresponding to one integration period of the receiving end.

2. Use the Taylor series expansion to calculate the light travel time difference at the beginning and end of the integration period

Considering that light travel time in deep space exploration is generally established in the barycentric coordinate system of the general relativity solar system, the original time difference can be calculated by the following formula:

$\mathrm{<span\; class="notranslate">\; \&Delta;\&tau;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}$

$<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; RLT</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; RLT</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}$ $<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \{</span>{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; TDB</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; TDB</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \}</span>$

$<span\; class="notranslate">\; +</span><span\; class="notranslate">\; \{</span>{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; TDB</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; TDB</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \}</span>$

Among them, τ _{S, e} , τ _{S, s} respectively represent the original points corresponding to the end of the integration period and the start time of the signal transmitting end on the star, and ρ _{SR, e} , ρ _{SR, s} respectively represent the one-way geometry corresponding to the end of the integration period and the start time Distance, RLT _e , RLT _s represent the gravitational bending at the end and the beginning of the integration, TDB represents the dynamic time of the center of mass of the solar system, t(τ) represents the corresponding original time, [] _e , [] _s correspond to the end and the beginning of the integration respectively.

For deep space exploration (such as Mars exploration), the value of the first item on the right side of (4) is about 200-1300 s, and the second and third items are relativistic effect items, and the value is about 10 ^-6 s. However, the values of items 4 and 5 are in the order of 10 ^-9 s. Therefore, under the definition of double-precision floating point, when calculating the light line according to formula (4), the rounding error introduced by the first item on the right end is about 3×10 ^-12 s, and the Doppler measurement error corresponding to the 8.4GHz X-band is 1mm /s (1s integration period), far lower than the current measurement accuracy. Therefore, in order to meet the precision requirements of the double-precision floating-point system, the calculation of the first item on the right side of the above formula needs to be changed to the following:

${\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&ap;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{<span\; class="notranslate">\; \&PartialD;</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; SR</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; SR</span>}}\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{<span\; class="notranslate">\; \&PartialD;</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="e"\; filenames="HSA00000629336800011.png"\; state="\{\{state\}\}">e</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; SR</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

here,

$\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; SR</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; [</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; TDB</span>}}_{\mathrm{<span\; class="notranslate">\; SC</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; TDB</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; [</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; TDB</span>}}_{\mathrm{<span\; class="notranslate">\; SC</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; TDB</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; e</span>}}$

$\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{<span\; class="notranslate">\; \&PartialD;</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; =</span>\frac{{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}$

$\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{<span\; class="notranslate">\; \&PartialD;</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}\left[\begin{array}{ccc}\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& \frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}& \frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\\ \frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}& \frac{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& \frac{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\\ \frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}& \frac{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}& \frac{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; SR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$

Among them, X, Y, and Z represent the position components of the aircraft in the barycentric coordinate system of the general relativity solar system, the subscript S represents the transmitting end, R represents the receiving end, s represents the start time of integration, and e represents the end time of integration.

If the Doppler integration period is relatively short (<100s), the influence of the relativistic correction item in the formula can be ignored, and the error introduced by it will not exceed 0.3mm, which can be better than the calculation accuracy requirement of 1ps.

3. Substitute the light travel time difference into the measurement equation to calculate the Doppler speed measurement

Substituting the above formulas (4)-(5) into formula (1) can obtain the measured value of Doppler in deep space. This calculation method uses Taylor expansion for the calculation of differential one-way distance, avoids the disadvantage of directly using differential distance observations to obtain Doppler, and loses calculation accuracy, and realizes high-precision Doppler calculations using double-precision floating-point numbers, ensuring calculation accuracy , improving the computational efficiency.

The invention has been successfully applied to the orbit calculation of the Mars probe. Fig. 1 is a comparison of the residual error (the difference between the observed value and the calculated value) calculated using the double-precision conventional method and calculated using the present invention. The upper part of Figure 1 is the calculation result of the conventional method, and the lower part is the calculation result of the patented method. It can be seen that the Doppler residual calculated by this method is basically white noise, and the accuracy of the Doppler calculation value is increased by an order of magnitude.

Claims (2)

1. computing method that test the speed of the deep space Doppler under the double-precision floating point definition is characterized in that may further comprise the steps:

< 1>sets up Doppler according to the Doppler measuring principle and measure equation;

< 2>calculate integration period light equation constantly at the whole story with taylor series expansion;

< 3>Equation for Calculating Doppler being measured in the light equation substitution tests the speed.

2. the double-precision floating point as claimed in claim 1 definition deep space Doppler down computing method that test the speed, it is characterized in that: said Doppler measurement equation is following:

$f_D=f_R-f_0=\frac{N_C}{\mathrm{\&Delta;T}}+\mathrm{\&delta;f}+v$

F wherein _DExpression Doppler frequency offset, f _RThe expression receiving end receives signal frequency, f ₀Expression ground receiving station local frequency, N _CThe week counting that integration period is interior, Δ T is an integration period, and δ f is the recording geometry error, and v is the observation stochastic error.

The method of the said calculating integration period moment at whole story light equation is following:

$\mathrm{\&Delta;\&tau;}={\mathrm{\&tau;}}_{S,e}-{\mathrm{\&tau;}}_{S,s}$

$=\frac{({\mathrm{\&rho;}}_{\mathrm{SR},e}-{\mathrm{\&rho;}}_{\mathrm{SR},s})}{c}+{\mathrm{RLT}}_e-{\mathrm{RLT}}_s$

$-\{{[{\mathrm{TDB}}_R-t\left({\mathrm{\&tau;}}_R\right)]}_e-{[{\mathrm{TDB}}_R-t\left({\mathrm{\&tau;}}_R\right)]}_s\}$

$+\{{[{\mathrm{TDB}}_S-t\left({\mathrm{\&tau;}}_S\right)]}_e-{[{\mathrm{TDB}}_S-t\left({\mathrm{\&tau;}}_S\right)]}_s\}$

Wherein, τ _{S, e}, τ _{S, s}Represent that respectively signal transmitting terminal integration period on the star finishes original with correspondence of the initial moment, ρ _{SR, e}, ρ _{SR,, s}Represent the one way geometric distance that integration finishes and the initial moment is corresponding respectively, RLT _e, RLT _sThe expression integration finishes and initial moment gravitational deflection, when TDB representes solar system barycenter dynamics, and during t (τ) expression correspondence former, [] _e, [] _sRespectively corresponding integration finishes and the initial moment;

Wherein:

${\mathrm{\&rho;}}_{\mathrm{SR},e}-{\mathrm{\&rho;}}_{\mathrm{SR},s}\&ap;-(\frac{{\&PartialD;\mathrm{\&rho;}}_{\mathrm{SR},e}}{\&PartialD;{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR},e}}\mathrm{\&Delta;}{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR}}+\frac{1}{2}{\mathrm{\&Delta;}}^T{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR}}\frac{{\&PartialD;}^2{\mathrm{\&rho;}}_{\mathrm{SR},e}}{\&PartialD;{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR},e}^2}\mathrm{\&Delta;}{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR}})$

$\mathrm{\&Delta;}{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR}}={[{\stackrel{\&RightArrow;}{r}}_{S/C}\left({\mathrm{TDB}}_{\mathrm{SC}}\right)-{\stackrel{\&RightArrow;}{r}}_R\left({\mathrm{TDB}}_R\right)]}_s-{[{\stackrel{\&RightArrow;}{r}}_{S/C}\left({\mathrm{TDB}}_{\mathrm{SC}}\right)-{\stackrel{\&RightArrow;}{r}}_R\left({\mathrm{TDB}}_R\right)]}_e$

$\frac{{\&PartialD;\mathrm{\&rho;}}_{\mathrm{SR},e}}{\&PartialD;{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR},e}}=\frac{{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR},e}}{{\mathrm{\&rho;}}_{\mathrm{SR},e}}$

$\frac{{\&PartialD;}^2{\mathrm{\&rho;}}_{\mathrm{SR},e}}{\&PartialD;{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR},e}^2}=-\frac{1}{{\mathrm{\&rho;}}_{\mathrm{SR},e}}\left[\begin{array}{ccc}\frac{X_{\mathrm{SR},e}^2}{{\mathrm{\&rho;}}_{\mathrm{SR},e}^2}-1& \frac{X_{\mathrm{SR},e}{Y}_{\mathrm{SR},e}}{{\mathrm{\&rho;}}_{\mathrm{SR},e}^2}& \frac{X_{\mathrm{SR},e}{Z}_{\mathrm{SR},e}}{{\mathrm{\&rho;}}_{\mathrm{SR},e}^2}\\ \frac{X_{\mathrm{SR},e}{Y}_{\mathrm{SR},e}}{{\mathrm{\&rho;}}_{\mathrm{SR},e}^2}& \frac{Y_{\mathrm{SR},e}^2}{{\mathrm{\&rho;}}_{\mathrm{SR},e}^2}-1& \frac{Y_{\mathrm{SR},e}{Z}_{\mathrm{SR},e}}{{\mathrm{\&rho;}}_{\mathrm{SR},e}^2}\\ \frac{X_{\mathrm{SR},e}{Z}_{\mathrm{SR},e}}{{\mathrm{\&rho;}}_{\mathrm{SR},e}^2}& \frac{Y_{\mathrm{SR},e}{Z}_{\mathrm{SR},e}}{{\mathrm{\&rho;}}_{\mathrm{SR},e}^2}& \frac{Z_{\mathrm{SR},e}^2}{{\mathrm{\&rho;}}_{\mathrm{SR},e}^2}-1\end{array}\right]$

Wherein, X, Y, Z represent the location components of aircraft under general relativity solar system geocentric coordinate system respectively, and subscript S representes transmitting terminal, and R representes receiving end, and s representes to represent integration zero hour, e integration finish time.

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