CN102495715B - 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 speed measurement calculating method defined by a double-precision floating point. The deep space Doppler speed measurement calculating method comprises the following steps of: firstly, establishing a Doppler measurement equation according to a Doppler measurement principle; secondly, calculating a light equation of beginning and end time of an integration period by using a Taylor series expansion; and finally, substituting the light equation into a measurement equation to calculate Doppler speed measurement. By utilizing the deep space Doppler speed measurement calculating method disclosed by the invention, the calculation precision and calculation efficiency of the deep space exploration Doppler speed measurement are improved.

Description

Deep space Doppler under double-precision floating point definition tests the speed computing method

Technical field

The invention belongs to technical field of data processing, the deep space Doppler (Doppler) related under the definition of a kind of double-precision floating point tests the speed computing method.

Background technology

In current survey of deep space, the calculating of Doppler adopts " Formulation for observed and computed values of Deep Space Network data types for navigation " method described in a book usually.Utilize the method, calculate light time according to double-precision floating points, due to the impact of round-off error, its computational accuracy is about picoseconds (wherein ^[]expression rounds, R is detection range, unit is hundred million kms), in the process of the detection mission Doppler measurement data of this precision more than 100,000,000 kms, the computational accuracy of 1mm/s (1 second integration period) can only be ensured, obviously can not meet current the 0.1mm/s even accuracy requirement of 0.02mm/s.Common way uses four accuracy floating-point numbers to replace double-precision floating points at calculating light time, to improve computational accuracy, although the method improves computational accuracy, but reduces counting yield.

Summary of the invention

Deep space Doppler under the object of the present invention is to provide a kind of double-precision floating point to define to test the speed computing method, to improve computational accuracy and counting yield.

For achieving the above object, the computing method that test the speed of the deep space Doppler under double-precision floating point provided by the invention definition comprise the following steps:

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

<2> taylor series expansion calculates the light equation in integration period moment at the whole story;

Light equation is substituted into measurement equation calculating Doppler and tests the speed by <3>.

Further, described Doppler measurement equation is as follows:

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

Wherein f _drepresent Doppler frequency offset, f _rrepresent receiving end Received signal strength frequency, f ₀represent ground receiving station local frequency, N _cbe the week counting in an integration period, Δ T is an integration period, and δ f is recording geometry error, and v is observation stochastic error.

The method of described calculating integration period moment at whole story light equation is as follows:

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

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

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

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

Wherein, τ _{s, e}, τ _{s, s}represent that signal transmitting terminal integration period on star terminates respectively corresponding original with initial time, ρ _{sR, e}, ρ _{sR, s}represent that integration terminates the one way geometric distance corresponding with initial time, RLT respectively _e, RLT _srepresent that integration terminates and initial time gravitational deflection, when TDB represents solar system barycenter dynamics, t (τ) represent corresponding former time, [] _e, [] _scorresponding integration terminates and initial time respectively;

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 represents transmitting terminal, and R represents receiving end, and s represents integration start time, and e represents integration finish time.

The present invention calculates the light equation in integration period two moment of the whole story by Taylor series expansion, avoid the shortcoming directly using the observed quantity of difference distance to obtain Doppler, costing bio disturbance precision, eliminate when double-precision floating point defines because the round-off error that produces of word length deficiency is on the impact of computational accuracy, reach the precision that four accuracy floating-point numbers calculate, ensure that counting yield.

Accompanying drawing explanation

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

Embodiment

Deep space Doppler under the double-precision floating point provided by the invention definition computing method that test the speed comprise the following steps:

1. set up Doppler according to Doppler measuring principle and measure equation

The observed quantity of integration Doppler is the side-play amount f of ground station reception signal frequency relative standard frequency _d, counted to get by the week of measuring in an integration period, namely

$f_D=f_R-f_0=\frac{N_C}{\mathrm{\&Delta;T}}+\mathrm{\&delta;f}+v---\left(1\right)$

Wherein f _rrepresent receiving end Received signal strength frequency, f ₀represent ground receiving station local frequency, N _cbe the week counting in an integration period, Δ T is an integration period, and δ f is recording geometry error, and v is observation stochastic error.

The Doppler week counting N of accumulation in an integration period Δ T of ground receiving station _cchange can derive Doppler observed quantity f _d.For given ground survey station, continuous print Doppler observation has continuous print integration period.Integration period can be short to 0.1s, also can grow to half a day (43200s), and typical integration period is several seconds intervals to a few kilosecond.

For N _chave

$N_C={\&Integral;}_{t_s}^{t_e}(f_R-f_0)\mathrm{dt}={\&Integral;}_{t_s}^{t_e}{f}_R\mathrm{dt}-f_0\mathrm{\&Delta;T}---\left(2\right)$

$={\&Integral;}_{{\mathrm{\&tau;}}_s}^{{\mathrm{\&tau;}}_e}{f}_S\mathrm{d\&tau;}-f_0\mathrm{\&Delta;T}$

Wherein f ₀for the local frequency of ground receiving station, the subscript s of small letter, e represent integration starting and ending, and t represents the ground survey station time, general adopt Coordinated Universal Time(UTC) UTC time system, when τ represents signal transmitting terminal former.

Consider more satisfactory state, i.e. emission standard frequency f _sbe a constant, then have:

f _RΔT＝f _S(τ _e-τ _s)＝f _SΔτ (3)

Conveniently distinguish, Δ T is receiving end integration period, and Δ τ is the former time difference of the transmitting terminal that receiving end integration period is corresponding.

2. the light equation in integration period moment at the whole story is calculated with taylor series expansion

Consider that in survey of deep space, light time is generally set up under general relativity solar system geocentric coordinate system, the former time difference can by lower formulae discovery:

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

$=\frac{({\mathrm{\&rho;}}_{\mathrm{SR},e}-{\mathrm{\&rho;}}_{\mathrm{SR},s})}{c}+{\mathrm{RLT}}_e-{\mathrm{RLT}}_s$ $\left(4\right)$

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

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

Wherein, τ _{s, e}, τ _{s, s}represent that signal transmitting terminal integration period on star terminates respectively corresponding original with initial time, ρ _{sR, e}, ρ _{sR, s}represent that integration terminates the one way geometric distance corresponding with initial time, RLT respectively _e, RLT _srepresent that integration terminates and initial time gravitational deflection, when TDB represents solar system barycenter dynamics, t (τ) represent corresponding former time, [] _e, [] _scorresponding integration terminates and initial time respectively.

For survey of deep space (as mars exploration), the numerical value that (4) formula right-hand member is the 1st is between 200-1300s, and the 2nd, 3 is relativistic effect item, and numerical value is about 10 ^-6s magnitude, and the numerical value of the 4th, 5 is 10 ^-9s magnitude.Therefore, under double-precision floating point definition, calculate light time according to formula (4), the round-off error that right-hand member Section 1 is introduced is about 3 × 10 ^-12the Doppler measuring error of the X-band of s, corresponding 8.4GHz is 1mm/s (1s integration period), far below current measuring accuracy.Therefore, in order to meet the accuracy requirement of double-precision floating point system, need the calculating of above formula right-hand member Section 1 be changed into following:

${\mathrm{\&rho;}}_{\mathrm{SR},e}-{\mathrm{\&rho;}}_{\mathrm{SR},s}\&ap;-(\frac{{\&PartialD;\mathrm{\&rho;}}_{\mathrm{SR},e}}{\&PartialD;{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR},e}}\mathrm{\&Delta;}{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR}}+\frac{1}{2}{\mathrm{\&Delta;}}^T{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR}}\frac{{\&PartialD;}^2{\mathrm{\&rho;}}_{\mathrm{SR},e}}{\&PartialD;{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR},e}^2}\mathrm{\&Delta;}{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR}})---\left(5\right)$

Here,

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

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

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

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

If Doppler integration period relatively short (< 100s), can ignore the impact of relativistic revision item in formula, the error introduced thus more than 0.3mm, can not can be better than the computational accuracy requirement of 1ps.

3. light equation is substituted into measurement equation calculating Doppler to test the speed

Above-mentioned (4)-(5) formula is substituted into formula (1) deep space Doppler measured value can be obtained.The calculating of these computing method to difference one way distance employs Taylor expansion, avoid and directly use the observed quantity of difference distance to obtain Doppler, the shortcoming of costing bio disturbance precision, achieve and use double-precision floating points to carry out high-precision Doppler calculating, ensure that computational accuracy, improve counting yield.

The present invention has been successfully applied in the orbit computation of Mars probes.Fig. 1 uses double precision conventional method to carry out calculating and compare with the residual error using the present invention the to calculate difference of calculated value (observed reading with).Fig. 1 the first half is conventional method result of calculation, and the latter half is the result of calculation using this patented method, and can see that the Doppler residual error using the method to calculate is white noise substantially, the calculated value precision of Doppler improves a magnitude.

Claims (1)

1. the deep space Doppler under double-precision floating point definition tests the speed computing method, it is characterized in that comprising the following steps:

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

<2> taylor series expansion calculates the light equation in integration period moment at the whole story;

Light equation is substituted into measurement equation calculating Doppler and tests the speed by <3>;

Wherein:

It is as follows that described Doppler measures equation:

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

Wherein f _drepresent Doppler frequency offset, f _rrepresent receiving end Received signal strength frequency, f ₀represent ground receiving station local frequency, N _cbe the week counting in an integration period, Δ T is an integration period, and δ f is recording geometry error, and v is observation stochastic error.

The method of described calculating integration period moment at whole story light equation is as follows:

$\begin{array}{c}\mathrm{\&Delta;\&tau;}={\mathrm{\&tau;}}_{S,e}-{\mathrm{\&tau;}}_{S,s}\\ =\frac{({\mathrm{\&rho;}}_{\mathrm{SR},e}-{\mathrm{\&rho;}}_{\mathrm{SR},s})}{c}+\mathrm{RL}{T}_e-{\mathrm{RLT}}_s\\ -\{{[\mathrm{TD}{B}_R-t\left({\mathrm{\&tau;}}_R\right)]}_e-{[{\mathrm{TDB}}_R-t\left({\mathrm{\&tau;}}_R\right)]}_s\}\\ +\{{[{\mathrm{TDB}}_S-t\left({\mathrm{\&tau;}}_S\right)]}_e-{[{\mathrm{TDB}}_S-t\left({\mathrm{\&tau;}}_S\right)]}_s\}\end{array}$

Wherein, τ _{s, e}, τ _{s, s}represent respectively signal transmitting terminal integration period on star terminate with initial time corresponding former time, ρ _{sR, e}, ρ _{sR, s}represent that integration terminates the one way geometric distance corresponding with initial time, RLT respectively _e, RLT _srepresent that integration terminates and initial time gravitational deflection, when TDB represents solar system barycenter dynamics, t (τ) represent corresponding former time, [] _e, [] _scorresponding integration terminates and initial time respectively;

Wherein:

$\begin{array}{c}{\mathrm{\&rho;}}_{\mathrm{SR},e}-{\mathrm{\&rho;}}_{\mathrm{SR},s}\&ap;-(\frac{{\&PartialD;\mathrm{\&rho;}}_{\mathrm{SR},e}}{\&PartialD;{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR},e}}\mathrm{\&Delta;}{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR}}+\frac{1}{2}{\mathrm{\&Delta;}}^T{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR}}\frac{{\&PartialD;}^2{\mathrm{\&rho;}}_{\mathrm{SR},e}}{\&PartialD;{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR},e}^2}\mathrm{\&Delta;}{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR}})\\ \mathrm{\&Delta;}{\stackrel{\&RightArrow;}{r}}_{\mathrm{SR}}={[{\stackrel{\&RightArrow;}{r}}_{S/C}\left({\mathrm{TDB}}_{\mathrm{SC}}\right)-{\stackrel{\&RightArrow;}{r}}_R\left({\mathrm{TDB}}_R\right)]}_s-{[{\stackrel{\&RightArrow;}{r}}_{S/C}\left({\mathrm{TDB}}_{\mathrm{SC}}\right)-{\stackrel{\&RightArrow;}{r}}_R\left({\mathrm{TDB}}_R\right)]}_e\end{array}$