CN102590830A - Method for estimating Doppler frequency of global positioning system (GPS) signal source - Google Patents

Abstract

The invention belongs to the field of parameter estimation of satellite navigation signal source and provides a method for estimating Doppler frequency of a GPS signal source. The method includes calculating satellite position information at the moment, user position information at a next moment, and satellite position information at next moment according to user speed at the moment, position information and a navigation almanac; calculating relative distances between a user and a satellite at the moment and at the next moment respectively by using the position information; calculating a relative distance variation quantity between the user and the satellite at the moment and at the next moment; calculating a relative transmission delay variation quantity between the user and the satellite; estimating an average value of the Doppler frequency from the moment to the next moment; and the like. The method reduces the amount of calculation, and is more suitable for continuous estimation of the Doppler frequency.

Description

A kind of method that is used for the Doppler frequency of estimating GPS signal source

Technical field

The present invention relates to the parameter estimation field of satellite navigation signal source, be specifically related to a kind of method that is used for the Doppler frequency of estimating GPS signal source.

Background technology

The gps signal source can provide repeatably simulating signal for studies, emulation and the test in satellite navigation field, helps the propelling of research work.Simultaneously, in the environment that is not easy to erect a television antenna, like the area of remote mountain areas and awful weather, the gps signal source also can guarantee the operate as normal of navigation terminal, greatly reduces the construction cost and the maintenance cost that erect a television antenna.

When simulation produced the GPS navigation signal in the gps signal source, accurately estimating Doppler frequency was one of them important step, is the basis of correct simulating GPS signal.Method at present commonly used is, utilizes the velocity information of user and selected satellite, calculates satellite and user's relative velocity, and based on the Doppler frequency parameter f of this signal calculated _d, promptly

$f_d=f_T\×\frac{v_{u}g{v}_s}{c}$

Wherein, f _TBe the carrier frequency of gps signal, c is the light velocity, v _uAnd v _sBe respectively the user of current time t and the velocity of satellite, v _uV _sWhat calculate is current time satellite and user's relative velocity.

When actual computation, above method mainly comprises the steps:

Step 1: the navigation almanac of input user state information and selected satellite, and set Doppler frequency and upgrade interval T _u

User state information comprises: current time time t and corresponding ECEF (heart solid) customer position information p _u=[x _u, y _u, z _u] ^TWith velocity information v _u=[v _Ux, v _Uy, v _Uz] ^TIf customer location and the velocity information of input are not ECEF (heart consolidate) coordinates, then need carry out coordinate conversion to it, conversion method is a content well known to those of ordinary skill in the art.

The navigation almanac can be the almanac of putting down in writing on the GPS navigation technical manual, also can be the actual almanac that receives through the GPS navigation terminal.Navigation almanac parameters commonly used comprises: satellite orbit eccentricity e, almanac generate t constantly _Oe, satellite orbit and equator inclination angle i ₀, right ascension of ascending node rate of change ' Ω, satellite orbit major semi-axis a, weekly epoch Ω _e, perigee arc angle ω, with reference to constantly mean anomaly M ₀, orbit inclination rate of change di/dt, mean angular velocity correction value delta n, to the corrected value C of latitude amplitude cosine _Uc, to the sinusoidal corrected value C of latitude argument _Us, to the corrected value C of orbit radius cosine _Rc, to the sinusoidal corrected value C of orbit radius _Rs, to the corrected value C of orbit inclination cosine _Ic, to the sinusoidal corrected value C of orbit inclination _IsDeng.

Step 2: utilize current time t and navigation almanac, calculate the satellite position of current time, specifically comprise the steps:

Step 2-1: calculate the normalization time:

t _k＝t-t _oe

Step 2-2: the mean angular velocity n that calculates satellite transit _k

$n_k=n_0+\mathrm{\Δn}=\sqrt{G/a^3}+\mathrm{\Δn}$

Wherein, G=3.986005 * 10 ¹⁴Be geocentric gravitational constant, a is the elliptical orbit major semi-axis, and Δ n is the corrected value of mean angular velocity, all from the navigation almanac.

Step 2-3: calculate satellite at t _kMean anomaly M constantly _k

M _k＝n _k×t _k+M ₀

Wherein, M ₀Be the reference moment t that provides in the almanac _OeMean anomaly.

Step 2-4: the iterative computation satellite is at t _kEccentric anomaly F constantly _k,

(1) puts initial value, make E _K0=M _k

(2) iterative computation makes i=1, calculates as follows:

E _ki＝M _k+esin?E _k(i-1)，ΔE _k＝|E _ki-E _k(i-1)|

Judge, if Δ E _kThresholding less than setting in advance then stops iteration, E _k=E _Ki

Otherwise, make i=i+1, returned for (2) step.

Step 2-5: calculate satellite at t _kTrue anomaly f constantly _k,

$f_k={\cos }^{-2}\left(\frac{{\cos E}_k-e}{1-{e\cos E}_k}\right)\×\mathrm{sign}\left(\frac{\sqrt{1-e^2}\sin E_k}{1-{e\cos E}_k}\right)$

Wherein, satellite orbit eccentricity e is provided by the navigation almanac.

Step 2-6: calculate unregulated ascending node angular distance Φ _k

Φ _k＝f _k+ω

Wherein, ω is the perigee arc angle that provides in the almanac.

Step 2-7: calculate perturbation correction term δ _μ, δ _rAnd δ _i

δ μ, δ r and δ i are respectively ascending node angular distance Φ _k, satellite loses footpath r _kWith orbit inclination i _kThe perturbation amount, its concrete computing method are shown below:

δ _u＝C _uc?cos?2Φ _k+C _us?sin?2Φ _k

δ _r＝C _rc?cos?2Φ _k+C _rs?sin?2Φ _k

δ _i＝C _ic?cos?2Φ _k+C _is?sin?2Φ _k

On this basis, calculate the ascending node angular distance Φ that corrects through perturbation _k, satellite loses footpath r _kAnd orbit inclination i _d, concrete computing formula is:

Φ _k＝Φ _k+δ _u，r _k＝a(1-ecos?E _k)+δ _r，i _k＝i ₀+(di/dt)×t _k+δ _i

Wherein, i ₀Be inclination of satellite orbit, di/dt is the rate of change of orbit inclination, provides by almanac.

Step 2-8: calculate satellite at t _kRight ascension of ascending node Ω constantly _k

Ω _k＝Ω _e+′Ω×t _k

Wherein, Ω _eBe that the reference right ascension of ascending node constantly provide in the almanac, ' Ω are the rate of change of the right ascension of ascending node that provides of almanac.

As consider also need carry out earth rotation earth rotation and proofread and correct to it

Ω _k＝Ω _e+(′Ω-ω _e)t _k-ω _et _oe＝Ω _e+′Ωt _k-ω _et _in

Wherein, ω _eBe earth rotation speed, value is ω _e=7.2921151467 * 10 ^-5(rad/s).

Step 2-9: calculate t _kConstantly satellite is at the coordinate of ECEF (heart solid) coordinate system

Step 2-9-1: calculate the position coordinates of satellite in the elliptical orbit rectangular coordinate system

_xk＝r _kcosΦ _k，y _k＝r _ksinΦ _k

Step 2-9-2: calculate the coordinate p of satellite in the ECEF coordinate system _s=[x _s, y _s, z _s] ^T:

$\left[\begin{array}{c}{x}_s\\ y_s\\ z_s\end{array}\right]=\left[\begin{array}{c}{x}_k{\cos \mathrm{\Ω}}_k-y_k{\cos i}_k\×{\sin \mathrm{\Ω}}_k\\ x_k{\sin \mathrm{\Ω}}_k+y_k{\cos i}_k\×{\cos \mathrm{\Ω}}_k\\ y_k{\sin i}_k\end{array}\right]$

Step 3: the positional information p that utilizes the current time satellite _s, it is carried out differentiate, calculate the velocity information v of current time satellite _s

$v_s=\left[\begin{array}{c}{v}_{\mathrm{sx}}\\ v_{\mathrm{sy}}\\ v_{\mathrm{sz}}\end{array}\right]=\left[\begin{array}{c}{-y}_s{\mathrm{\Ω}}_k^{\′}-(y_k^{\′}{\cos i}_k-z_s{i}_k^{\′})\·{\sin \mathrm{\Ω}}_k+x_k^{\′}{\cos \mathrm{\Ω}}_k\\ x_s{\mathrm{\Ω}}_k^{\′}+(y_k^{\′}{\cos i}_k-z_s{i}_k^{\′})\·{\cos \mathrm{\Ω}}_k+x_k^{\′}{\sin \mathrm{\Ω}}_k\\ y_k^{\′}{\sin i}_k+y_k{i}_k^{\′}{\cos i}_k\end{array}\right]$

X in the following formula _k' and y _k' be by x _kAnd y _kThe time differentiate is obtained, promptly

x′ _k＝r′ _k?cos?u _k-r _ku′ _k?sin?u _k，y′ _k＝r′ _k?sin?u _k+r _ku′ _k?cos?u _k

U wherein _k', r _k', i _k' and Ω _k' can be respectively by u _k, r _k, i _kAnd Ω _kThe time differentiate is obtained, promptly

u′ _k＝Φ′ _k+δ′ _u，r′ _k＝aeE′ _ksin?E _k+δ′ _r

i′ _k＝di/dt+δ′ _i，Ω′ _k＝Ω′-ω _e

δ wherein _μ', δ _r' and δ _i' can be respectively by δ _μ, δ _rAnd δ _iThe time differentiate is obtained, promptly

δ′ _u＝2Φ′ _k[C _us?cos(2Φ _k)-C _uc?sin(2Φ _k)]

δ′ _u＝2Φ′ _k[C _rs?cos(2Φ _k)-C _rc?sin(2Φ _k)]

δ′ _u＝2Φ′ _k[C _is?cos(2Φ _k)-C _ic?sin(2Φ _k)]

Φ wherein _k' can be by Φ _kThe time differentiate is obtained, promptly

${\mathrm{\Φ}}_k^{\′}=f_k^{\′}=\frac{\sqrt{1-e^2}{E}_k^{\′}}{1-e\cos E_k}$

E wherein _kCan be by E _kThe time differentiate is obtained, promptly

$E_k^{\′}=\frac{M_k^{\′}}{1-e\cos E_k}$

M wherein _k' can be by M _kThe time differentiate is obtained, promptly

M′ _k＝n _k

Step 4: utilize the velocity information of current time user and satellite, calculate the Doppler frequency of satellite-signal.

$f_d=f_T\×\frac{v_{u}g{v}_s}{c}$

Step 5: upgrade interval T if arrive Doppler frequency _u, then upgrading current time is t=t+T _u, and the customer position information p of current time _uWith velocity information v _u, return step 2.

Said method; What 2007 published in the Electronic Industry Press is outstanding by JAMES BAO-YEN TSUI; Chen Jun etc. translate in the .GPS software receiver basis (the 2nd edition) has write up, during the GPS principle by Xie Gangzhu that 2009 publish in the Electronic Industry Press designs with receiver write up is arranged also.

We find that through analyzing there is following difficult point in above method when concrete the realization:

The Doppler frequency of real satellite navigation signal all is a continually varying, and when using above method that navigation signal is simulated, can only approach its continually varying value with the discrete value of Doppler frequency.Just there is the turnover rate problem of a parameter in this.In theory, the turnover rate of parameter is high more, can approach its real situation of change more.But the turnover rate of parameter is high more, and also just high more to performance and the cost requirement of realizing system, because this requires system in the shorter time, to accomplish CALCULATION OF PARAMETERS, the method for estimation that is about to above-mentioned Doppler frequency recomputates once.In above method, the calculating of Doppler frequency needs satellite and user's velocity information, and the speed of calculating satellite need further obtain the position differentiate after trying to achieve its positional information, and computational complexity is higher.Therefore, the renewal of Doppler frequency parameter is comparatively complicated, and the operand that reduces this parameter update helps the realization difficulty and the cost that reduces its hardware platform of simplified system.

Summary of the invention

The present invention provides a kind of method that is used for the Doppler frequency of estimating GPS signal source.Compare with prior art, this method is more simple, only uses the positional information of user and satellite to come Doppler frequency is estimated, no longer need calculate the velocity information of satellite.

A kind of method that is used for the Doppler frequency of estimating GPS signal source provided by the invention comprises that this satellite of navigation almanac parameters calculating that utilizes satellite is at current time t ₁With next moment t ₂Positional information, be designated as p respectively _S1=[x _S1, y _S1, z _S1] ^TAnd p _S2=[x _S2, y _S2, z _S2] ^T, and utilize the user at current time t ₁Velocity information v _U1=[v _Xu1, v _Yu1, v _Zu1] ^TWith positional information p _U1=[x _U1, y _U1, z _U1] ^T, estimating user is at next moment t ₂Positional information p _U2=[x _U2, y _U2, z _U2] ^T=[x _U1+ v _Xu1* (t ₂-t ₁), y _U1+ v _Yu1* (t ₂-t ₁), z _U1+ y _Zu1* (t ₂-t ₁)] ^T, it is characterized in that also in turn including the following steps:

Step 1:, calculate respectively at current time t according to the positional information of user position information and satellite ₁With next moment t ₂The time, the relative distance of user and satellite

${\mathrm{\ρ}}_1={\left|\right|p_{u1}-p_{s1}\left|\right|}_2=\sqrt{{(x_{u1}-x_{s1})}^2+{(y_{u1}-y_{s1})}^2+{(z_{u1}-z_{s1})}^2}$

${\mathrm{\ρ}}_2={\left|\right|p_{u2}-p_{s2}\left|\right|}_2=\sqrt{{(x_{u2}-x_{s2})}^2+{(y_{u2}-y_{s2})}^2+{(z_{u2}-z_{s2})}^2}$

Step 2: calculate from t ₁The time be carved into t ₂Constantly, the variation delta ρ=ρ of user and satellite relative distance ₂-ρ ₁

Step 3: calculate from t ₁The time be carved into t ₂Constantly, the variation delta τ of user and the relative propagation delay time of satellite=Δ ρ/c, wherein, c is the light velocity;

Step 4: estimate from t ₁The time be carved into t ₂Constantly, the mean value f of Doppler frequency _d=f _T* Δ τ/T _u, wherein, f _TBe the carrier frequency of gps signal, the time interval T that Doppler frequency is upgraded _u=t ₂-t ₁

After said step 4 is accomplished, upgrade the value t of current time ₁=t ₂, the customer position information p of renewal current time _U1=p _U2, renewal speed information v _U1=v _U2, the relative distance ρ of renewal user and satellite ₁=ρ ₂, and calculate next t constantly ₂Customer position information p _U2With satellite position information p _S2, return step 1 then.

Can know through above description technical scheme; The present invention is the method identical with prior art the positional information employing of calculating satellite; Interior at interval average Doppler frequency replaces the instantaneous Doppler frequency on the updated time point but follow-up calculation procedure has adopted update time; Therefore no longer need calculate the satellite instantaneous velocity of updated time, only utilize the satellite position information of updated time just can accomplish the estimation of Doppler frequency, thereby greatly reduce the calculated amount of Doppler frequency.And; Between double Doppler frequency was estimated, " next moment " correlation parameter that calculates for the first time just in time was " current time " correlation parameter of estimating for the second time; Like this; Doublely estimate to such an extent that a lot of parameters just can be shared, operand can further reduce, and is convenient to the flowing water realization.

Compare with prior art, on identical hardware platform, technical scheme of the present invention can be supported higher parameter update rate, thereby approaches the situation that these continuous parameters change more accurately.In other words, require down in identical parameter update rate, the operand of technical scheme needs of the present invention still less can be realized on the lower platform of cost.

Description of drawings

The overview flow chart of the method for a kind of Doppler frequency that is used for the estimating GPS signal source that accompanying drawing 1 proposes for the present invention.

Embodiment

Specify the embodiment of technical scheme of the present invention below.

Step 1: input user state information and navigation almanac.User's current time is t ₁=0s, user ECEF position coordinates is p _u=[x _u, y _u, z _u] ^T, user ECEF speed coordinate is v _u=[0,0,0] ^T, promptly the user remains static; The navigation almanac is the simple and easy almanac of downloading on the website.Set other parameter simultaneously, comprise light velocity c=3 * 10 ⁸M/s, gps signal carrier frequency f _T=1575.42MHz, Doppler frequency is upgraded interval T _u=1ms.

Step 2: utilize user's current time information t ₁, navigation almanac parameters, the positional information p of the selected gps satellite of calculating current time _s=[x _s, y _s, z _s] ^TConcrete computing method adopt the existing computing method of mentioning in the background technology.

Step 3: the positional information p of user and satellite _uAnd p _s, calculate current time t ₁The relative distance ρ of user and satellite ₁:

${\mathrm{\ρ}}_1={\left|\right|p_u-p_s\left|\right|}_2=\sqrt{{(x_u-x_s)}^2+{(y_u-y_s)}^2+{(z_u-z_s)}^2}$

Step 4: the updated time t that calculates Doppler frequency ₂

t ₂＝t ₁+T _u＝0.001s

Step 5: utilize navigation message, calculate t ₂Satellite position constantly still is designated as p _sThree [x _s, y _s, z _s] ^TConcrete computing method adopt the existing computing method of mentioning in the background technology.

Step 6: utilize user's position and velocity information, calculate t ₂=0.001s customer location constantly still is designated as p _u, because the user is static, so the position remains unchanged.

p _u＝p _u+v _u×T _u＝[x _u?y _u?z _u] ^T

Step 7: the positional information p of user and satellite _uAnd p _s, calculation time t ₂The relative distance ρ of=0.001s user and satellite ₂:

${\mathrm{\ρ}}_2={\left|\right|p_u-p_s\left|\right|}_2=\sqrt{{(x_u-x_s)}^2+{(y_u-y_s)}^2+{(z_u-z_s)}^2}$

Step 8: be carved into t when calculating from t ₁Constantly, the variable quantity of user and satellite relative distance

Δρ＝ρ ₂-ρ ₁

Step 9: be carved into t when calculating from t ₁Constantly, the variable quantity of user and the relative propagation delay time of satellite

Δτ＝Δρ/c＝Δρ/(3×10 ⁸)

Step 10: estimate from t ₁The time be carved into t ₂Constantly, the mean value of Doppler frequency

f _d＝f _T×Δτ/T _u＝1575.42MHz×Δτ/1ms

Step 11: upgrade interval T if arrive Doppler frequency _u, then upgrading current time is t ₂=t ₁+ T _u, and the user velocity information v of current time _u=[0,0,0] ^T, simultaneously, make ρ ₁=ρ ₂, returning step 4, can estimate continuously Doppler frequency.

Can be found out that by foregoing description between double Doppler frequency was estimated, a lot of parameters can be shared, operand can further reduce like this, is convenient to flowing water simultaneously and realizes.

Claims (2)

1. a method that is used for the Doppler frequency of estimating GPS signal source comprises that this satellite of navigation almanac parameters calculating that utilizes satellite is at current time t ₁With next moment t ₂Positional information, be designated as p respectively _S1=[x _S1, y _S1, z _S1] ^TAnd p _S2=[x _S2, y _S2, z _S2] ^T, and utilize the user at current time t ₁Velocity information v _U1=[v _X1, v _Yu1, v _Zu1] ^TWith positional information p _U1=[x _U1, y _U1, z _U1] ^T, estimating user is at next moment t ₂Positional information p _U2=[x _U2, y _U2, z _U2] ^T=[x _U1+ v _Xu1* (t ₂-t ₁), y _U1+ v _Yu1* (t ₂-t ₁), z _U1+ v _Zu1* (t ₂-t ₁) ^T, it is characterized in that also in turn including the following steps:

Step 1:, calculate respectively at current time t according to the positional information of user position information and satellite ₁With next moment t ₂The time, the relative distance of user and satellite

${\mathrm{\ρ}}_1={\left|\right|p_{u1}-p_{s1}\left|\right|}_2=\sqrt{{(x_{u1}-x_{s1})}^2+{(y_{u1}-y_{s1})}^2+{(z_{u1}-z_{s1})}^2}$

${\mathrm{\ρ}}_2={\left|\right|p_{u2}-p_{s2}\left|\right|}_2=\sqrt{{(x_{u2}-x_{s2})}^2+{(y_{u2}-y_{s2})}^2+{(z_{u2}-z_{s2})}^2}$

Step 2: calculate from t ₁The time be carved into t ₂Constantly, the variation delta ρ=ρ of user and satellite relative distance ₂-ρ ₁

Step 3: calculate from t ₁The time be carved into t ₂Constantly, the variation delta τ of user and the relative propagation delay time of satellite=Δ ρ/c, wherein, c is the light velocity;

Step 4: estimate from t ₁The time be carved into t ₂Constantly, the mean value f of Doppler frequency _d=f _T* Δ τ/T _u, wherein, f _TBe the carrier frequency of gps signal, the time interval T that Doppler frequency is upgraded _u=t ₂-t ₁

2. a kind of method that is used for the Doppler frequency of estimating GPS signal source according to claim 1 is characterized in that: after said step 4 is accomplished, upgrade the value t of current time ₁=t ₂, the customer position information p of renewal current time _U1=p _U2, renewal speed information v _U1=v _U2, the relative distance ρ of renewal user and satellite ₁=ρ ₂, and calculate next t constantly ₂Customer position information p _U2With satellite position information p _S2, return step 1 then.

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