CN104865587B - Quick locating method based on GEO constellation coarse location for Beidou receiver - Google Patents

Abstract

The invention provides a quick locating method based on GEO constellation coarse location for a Beidou receiver by use of the characteristic that the GEO satellite in the hybrid constellation of the Beidou system is high in message rate, and solves the problem that when the outline coordinates of a receiver are unknown, the millisecond recovery algorithm for the traditional GNSS signal transmitting time cannot be applied due to a leap of calculated quantity. When the outline coordinates of the receiver are completely unknown, the GEO satellite of which the signal transmitting time is completely acquired is used at first for coarse location, then the millisecond integer time of the sending time of a non-GEO satellite is recovered according to the outline coordinates acquired by coarse location, and finally, all the visible satellites are utilized for accurate location. The quick locating method can achieve millisecond recovery of the non-GEO satellites which finish capture when the Beidou system only finishes frame alignment of GEO constellation, so that the time to first-time location of the receiver when the satellite ephemeris is known is earlier.

Description

Beidou receiver method for rapidly positioning based on GEO constellation coarse positionings

Technical field

The present invention relates to Beidou navigation satellite system receiver develops field, specifically a kind of Beidou receiver that improves is positioned first The method of time, which is can operate with the concrete research and development of all kinds of Beidou navigation receiving terminals.

Background technology

Primary positioning time (Time to First Fix, TTFF) is the important performance indexes of navigation neceiver, and raising is led Boat receiver primary positioning time is for the experience of the equipment of raising is with important function.

The factor of primary positioning time is affected to include that satellite ephemeris obtain the time and observation pseudorange obtains the time.By receiving Machine storage broadcast ephemeris, expansion type ephemeris or receiver end are autonomously generated the methods such as expansion type ephemeris and can shorten satellite ephemeris The acquisition time.Satellite pseudorange passes through local zone time and satellite-signal launch time and obtains, satellite-signal launch time typically by Two parts are constructed, a part be frame synchronization is completed by navigation message, whole millisecond that bit synchronization (be referred to as text synchronization) determines with Upper time, another part are that the time within the millisecond for obtaining is measured by pseudo-code phase.Position in traditional navigation neceiver In, receiver synchronously obtains satellite-signal launch time by being sequentially completed code phase measuring, text, gives birth to reference to receiver clock Follow-up positioning calculation is realized into pseudorange.Therefore, under ephemeris information known conditions, the principal element for restricting primary positioning time is Satellite completely observes the acquisition time of pseudorange.

Assisted GNSS technology can complete code phase measuring again after by quickly positioned, shorten primary positioning time. Said method has been constrained to user's general location, i.e., be only less than 150km in the general location estimation difference of receiver When, the satellite millisecond integer time could be quickly recovered, amount of calculation is searched in the case where probability positions are unknown can be sharply increased.

Chinese Beidou satellite navigation system (BeiDou Navigation Satellite System, BDS) was in 2012 December formally provides regional service.Compared to GPS system, dipper system is designed using hybrid constellation, ends operation on orbit so far Satellite includes 5 geostationary orbit (GEO) satellites, circle Earth's orbit (MEO) satellite and 5 inclination Geo-synchronous rails in 4 Road (IGSO) satellite.GEO satellite takes the text speed of 500bps, and a frame text persistent period is only 0.6s, and MEO/IGSO Satellite takes the text speed of 50bps, and a frame text persistent period is 6s.Therefore, after signal acquisition, compared to MEO/IGSO Satellite, GEO satellite can quickly finish text frame synchronization, obtain complete signal transmission time.Consumed frame time is only about 1/10th of the frame synchronization time are completed for MEO/IGSO.

The content of the invention

The present invention proposes a kind of Beidou receiver method for rapidly positioning based on GEO constellation coarse positionings.Triones navigation system In have 5 GEO satellites, meet the demand of traditional positioning calculation centre halfback star number at least 4.It is totally unknown in receiver general location In the case of, coarse positioning is carried out first by the GEO satellite for obtaining complete signal x time, then obtained according to coarse positioning Probability positions pseudorange recovery is carried out to the non-GEO satellite x time millisecond integer time, finally entered using all visible satellites Row is accurately positioned.

To solve above-mentioned technical problem, technical scheme proposed by the present invention is：

A kind of Beidou receiver method for rapidly positioning based on GEO constellation coarse positionings, it is characterised in that comprise the following steps：

Step S1, judges whether GEO satellite completes frame synchronization, obtains the satellite launch moment；

Step S2, satellite are carried out slightly to local zone time according to GEO satellite signal x time and all kinds of satellite transmission delays Slightly correct, rough correction here is slightly corrected or slightly corrected using multi-satellite using single GEO satellite；

Step S3, carries out coarse positioning using the GEO constellations for having obtained full pseudoranges, and rough localization method is directly using most A young waiter in a wineshop or an inn takes advantage of, the ridge estimaion that ridge estimaion or Doppler aid in；

Step S4, after outline customer location is obtained, carries out complete puppet to which with reference to the following pseudorange of millisecond of non-GEO satellite Away from recovery；Following form is written as respectively can in the pseudo range observed quantity for finishing receiving frame synchronization and be only completed code phase measuring：

Above formula is only completed the pseudorange of code phase measuring for the full pseudoranges and satellite j of satellite i and represents.Wherein, ρ_iBe through Pseudoranges of the satellite i of pseudorange correction to user, b_uFor the equivalent distances error that user's clock correction is produced.For little below millimeter Number pseudorange value, N_jMillimeter pseudorange fuzzy number is represented, c represents the light velocity, r_iAnd r_jRepresent user to satellite i and the space of satellite j respectively Distance, 1e3 are constant 1000.

I-th satellite is selected to carry out single poor between pseudorange star as reference satellite and satellite j can be obtained by floor operation The computing formula of pseudorange millisecond number be：

Step S5, after non-GEO satellite full pseudoranges are recovered, you can directly entered using all satellites for capturing of hybrid constellation Row least square is positioned；

According to the pseudorange residuals after positioning, step S6, judges that whether reasonable pseudorange recovers；Due to being carried out slightly using GEO constellations Positioning obtains user's general location, if general location deviation causes the pseudorange of non-GEO satellite to recover mistake compared with conference, therefore needs Quick positioning result is tested.Pseudorange is estimated that customer location using least-squares iteration after recovering while can be with The RMS value for calculating the pseudorange residuals value of each satellite, residual values and residual error vector is calculated as follows.In formulaRepresent and estimate what is obtained The space length of customer location and satellite i.

As pseudorange recovers to recover for whole millisecond, if larger puppet occurs after positioning when pseudorange recovers to occur mistake Away from residual error, whether transfinited using the root-mean-square of the pseudorange residuals value after positioning and judge whether method for rapidly positioning is successful, residual error door Limit value is according to certainty of measurement or/and error correction precision setting.The specific setting of residual error threshold value may be referred to receiver-autonomous The thresholding method to set up of integrity monitoring technology (RAIM).

GEO constellation rough localization methods described in step S3 of the present invention：

Coarse positioning is carried out using GEO constellations and can adopt different schemes.Directly can obtain general using least-squares iteration Omit position, it would however also be possible to employ the ridge estimaion method of ridge estimaion and Doppler's auxiliary carries out coarse positioning.

1) ridge estimaion positioning

When pseudorange is positioned, observational equation can be expressed as

Δ ρ=H Δ x+ ε

Skews of the wherein Δ ρ for pseudorange value, Δ x are the skew of the customer location and clock correction relative to linearisation point, and ε is clothes From the error vector of normal distribution, average is 0, and variance is σ²The matrix of I, H for n × 4It is The unit vector of i-th satellite position is pointed to linearisation point, n is the pseudorange number for participating in positioning.Least square is usually used Method carries out customer location iterative, but when being positioned using GEO constellations, due to normal equation coefficient matrix ranks yes The possible very little of absolute value, when coefficient in normal equation and constant term have round-off error and produce change, can cause the very big of solution Difference.Ridge estimaion can effectively solve problems, and its basic thought is the mathematical model using original least-squares estimation, Positive number on the diagonal of normal equation coefficient matrix plus a very little.I.e. using the calculated Δ x valuations of ridge estimaion Mathematic(al) representation is

Wherein k is ridge parameter, and I is unit matrix.

WhereinFor least-squares estimation.Estimate that average and variance are.

It is identical with method of least square iterative, using ridge estimaion solve customer location when parameter to be asked be customer location and The side-play amount of clock correction, due to the process that customer location is continuous iterative approach real user position clock correction.And ridge estimaion and true value Between the expectation of distance can be expressed as：

Wherein λ_iFor matrix H^TThe eigenvalue of H.λ_i/(λ_i+k)²≤ 1/ (4 × k), and Δ x is changed with kth -1 during kth time estimation For the skew of rear customer location clock correction and true value.If iterative process restrains, even if eigenvalue is less, suitable k value is still selected, is made Obtain position error and be less than 150km.

2) Doppler's auxiliary ridge estimaion

The pseudorange observation equation and Doppler's observational equation of user's observation satellite can be written as equation below：

Wherein, ρ_iFor i-th satellite Pseudo-range Observations,For position under i-th satellite ECEF coordinate system,For position under user's ECEF coordinate systems, b represents receiver clock-offsets,For i-th satellite Speed under ECEF coordinate systems,For user velocity,Represent receiver clock rate of change, ε_ρ,iWithDistribution Represent pseudorange and pseudorange rate of change observation noise.If ρ_{I, 0}、Forb₀、Correspondence pseudorange and pseudorange rate of change.Equation In linearisation pointb₀、Linearisation can be obtained

Wherein x_u,0,y_u,0,z_u,0The respectively initial three-dimensional position of user, v_xu,0,v_yu,0,v_zu,0For the initial three-dimensional speed of user Degree, symbolRepresent definition, that is to say, that willIt is denoted as It is denoted asIt is denoted asIt is denoted asIt is denoted asIt is denoted as (δx,δy,δz) (δ v_x,δv_y,δv_z) receiver location and the skew between the true value and linearisation point of speed are represented respectively.

Therefore, when Doppler aids in, linear equation can be written as

Wherein n and m represent that pseudorange is seen and pseudorange rate of change observation number respectively.

During due to coarse positioning, GEO constellation set configurations are poor, at the same Doppler observation to customer location resolve contribution compared with Little, solution process is likely to occur the problem of normal equation coefficient matrix morbid state, equally can mitigate matrix disease using ridge estimaion method State problem.When aiding in coarse positioning using Doppler, lienarized equation can be expressed as

WhereinWithThe respectively vector representation of pseudorange value and the skew of pseudorange rate of change,It is relative to linearisation point Customer location, time deviation, the vector representation of the side-play amount of speed and clock rate of change, the calculated Δ x of ridge estimaion The mathematic(al) representation of valuation is

(2) non-GEO satellite pseudorange recovers

The pseudorange of satellite i is represented by receivers

Wherein,For signal transmission time, t^rFor local zone time, c is the light velocity,Represent the milli of integer signal x time Second integer part,The millisecond fractional part of signal x time is represented,RepresentThe satellite i and t at moment^rMoment The space length of user,For the local clock correction of receiver, ε (t^r) represent round-off error, N_iThe whole millisecond number of pseudorange is represented,Represent The following pseudorange of millisecond.

When by pseudo-code phase measurement acquisitionAfter value, you can obtain the following pseudorange value of millisecond Wherein mod is modulo operation, and 1e-3 is constant 0.001.Therefore to completing frame synchronization and being only completed the pseudorange sight of code phase measuring Measurement can be written as following form respectively：

The computing formula that single after the recovery can obtain pseudorange integers millisecond number between pseudorange star is：

The method have the benefit that：

The present invention can be in the case where dipper system be only completed GEO constellation frame synchronization, to the non-GEO satellite for completing to capture Millisecond recovery is carried out, reduces the receiver primary positioning time under satellite ephemeris known conditions.

Description of the drawings

Fig. 1 illustrates the method for rapidly positioning flow process based on GEO constellation coarse positionings

Fig. 2 diagram satellite full pseudoranges recover flow process；

Specific embodiment

Below in conjunction with the accompanying drawings, describe the present invention：

Fig. 1 is the principle process schematic diagram of technical solution of the present invention, as illustrated, comprising the following steps：

Step S1, judges whether GEO satellite completes frame synchronization, obtains the satellite launch moment.In navigation signal capture, tracking Afterwards, bit synchronization and frame synchronization process to be carried out to signal so as to obtain signal transmission time, and realizes final positioning.

The present invention is can quickly to be positioned after GEO satellite realizes frame synchronization.Bit synchronization method can be using tradition Histogram method, frame synchronization algorithm can also adopt four conventional step methods of inspection check whether to complete frame synchronization：1st, search frame is same Step code；2nd, verify whether frame swynchronization code is normal with verification；3rd, after verifying synchronous code, whether subframe numbers and week interior second count information close Reason；4th, etc., after collecting next sub-frame data, check whether subframe numbers and week interior second information are matched with a upper sub-frame data.

Step S2, satellite are carried out slightly to local zone time according to GEO satellite signal x time and all kinds of satellite transmission delays Slightly correct, correction can be slightly to be corrected using single GEO satellite, it is also possible to slightly be corrected using multi-satellite.GEO is defended Star orbital road is about 35786 kms, therefore satellite-signal is about 119~139ms to the propagation time scope of terrestrial user.Therefore, Local zone time is modified using 129ms as the pseudorange transfer time, local zone time error precision is better than 10ms.

Step S3, carries out coarse positioning using the GEO constellations for having obtained full pseudoranges, and rough localization method directly can make The ridge estimaion aided in least square, ridge estimaion or Doppler.Introduce separately below and aided in using ridge estimaion and Doppler Ridge estimaion concrete methods of realizing：

1st, coarse positioning is carried out using ridge estimaion, concrete grammar is as follows：

When pseudorange is positioned, observational equation is expressed as

Δ ρ=H Δ x+ ε

Skews of the wherein Δ ρ for pseudorange value, Δ x are the skew of the customer location and clock correction relative to linearisation point, and ε is clothes From the error vector of normal distribution, average is 0, and variance is σ²I；

Using the mathematic(al) representation of the calculated Δ x valuations of ridge estimaion it is

Wherein k is ridge parameter, and I is unit matrix；

WhereinFor least-squares estimation；Estimate that average and variance are：

Between ridge estimaion and true value, the Expectation-based Representation for Concepts of distance is：

Wherein λ_iFor matrix H^TThe eigenvalue of H.

2nd, coarse positioning is carried out using Doppler's auxiliary ridge estimaion, concrete grammar is as follows：

The pseudorange observation equation and Doppler's observational equation of user's observation satellite is written as equation below：

Wherein, ρ_iFor i-th satellite Pseudo-range Observations,For position under i-th satellite ECEF coordinate system,For position under user's ECEF coordinate systems, b represents receiver clock-offsets,For i-th satellite Speed under ECEF coordinate systems,For user velocity,Represent receiver clock rate of change, ε_ρ,iWithDistribution table Show pseudorange and pseudorange rate of change observation noise；If ρ_{I, 0}、Forb₀、Correspondence pseudorange and pseudorange rate of change；Equation existsb₀、Linearisation can be obtained

Wherein

Therefore, when Doppler aids in, linear equation can be written as

Wherein n and m represent that pseudorange is seen and pseudorange rate of change observation number respectively；

When aiding in coarse positioning using Doppler, lienarized equation is expressed as

The mathematic(al) representation of the calculated Δ x valuations of ridge estimaion is

Step S4, after outline customer location is obtained, can have been carried out to which with reference to the following pseudorange of the millisecond of non-GEO satellite Whole pseudorange recovers.Idiographic flow can be found in flow process Fig. 2.

The pseudorange of satellite i is expressed as in receivers

Wherein,For signal transmission time, t^rFor local zone time, c is the light velocity,Represent the milli of integer signal x time Second integer part,The millisecond fractional part of signal x time is represented,RepresentThe satellite i and t at moment^rMoment The space length of user,For the local clock correction of receiver, ε (t^r) represent round-off error, N_iThe whole millisecond number of pseudorange is represented,Represent The following pseudorange of millisecond；

When by pseudo-code phase measurement acquisitionAfter value, you can obtain the following pseudorange value of millisecond Wherein mod is modulo operation；Therefore the pseudo range observed quantity to completing frame synchronization be only completed code phase measuring is written as follows respectively Form：

The computing formula that single after the recovery obtains pseudorange integers millisecond number between pseudorange star is：

Step S5, after non-GEO satellite full pseudoranges are recovered, you can directly entered using all satellites for capturing of hybrid constellation Row least square is positioned.The pseudorange of satellite can be expressed as with the relation of space length

V in formula_jFor revised pseudorange error, (x_u,y_u,z_u) and (x_j,y_j,z_j) be respectively user and satellite j (j=1, 2 ..., the n) position coordinateses in ECEF coordinate systems, ρ_cjBe through pseudorange correction satellite j to user pseudorange, b_uFor user The equivalent distances error that clock correction is produced, observation satellite number are n.

If approx knowing the position of subscriber computer, can be with Position Corrections amount (Δ x_u,Δy_u,Δz_u) representing true Position (x_u,y_u,z_u) and apparent positionBetween deviate.By pseudorange observation equation in user's general location coordinateAnd estimate clock correctionPlace carries out Taylor series expansion, Position Corrections amount can be represented general location coordinate and pseudorange The linear function of measured value.By least-squares iteration, the final position of user can be obtained.

According to the pseudorange residuals after positioning, step S6, judges that whether reasonable pseudorange recovers.Due to being carried out slightly using GEO constellations Positioning obtains user's general location, if general location deviation causes the pseudorange of non-GEO satellite to recover mistake compared with conference, therefore needs Quick positioning result is tested.As pseudorange recovers to recover for whole millisecond, when pseudorange recovers mistake, positioning can go out Existing larger pseudorange residuals, it is possible to use whether the root-mean-square of the pseudorange residuals after positioning transfinites whether judge method for rapidly positioning Success, threshold value can be arranged according to certainty of measurement, error correction precision etc..

In sum, although the present invention is disclosed above with preferred embodiment, so which is not limited to the present invention, any Those of ordinary skill in the art, without departing from the spirit and scope of the present invention, when can make it is various change with retouching, therefore this Bright protection domain is defined when the scope defined depending on claims.

Claims (4)

1. a kind of Beidou receiver method for rapidly positioning based on GEO constellation coarse positionings, it is characterised in that comprise the following steps：

Step S1, judges whether GEO satellite completes frame synchronization, obtains the satellite launch moment；

Step S2, satellite carry out rough school to local zone time according to GEO satellite signal x time and all kinds of satellite transmission delays Just, rough correction is slightly corrected or is slightly corrected using multi-satellite using single GEO satellite here；

Step S3, carries out coarse positioning using the GEO constellations for having obtained full pseudoranges, and rough localization method directly uses a most young waiter in a wineshop or an inn Take advantage of, ridge estimaion or Doppler auxiliary ridge estimaion；

Step S4, after outline customer location is obtained, with reference to the following pseudorange of millisecond of non-GEO satellite, to carry out full pseudoranges to which extensive It is multiple；Following form is written as respectively can in the pseudo range observed quantity for finishing receiving frame synchronization and be only completed code phase measuring：

$\left\{\begin{array}{c}{\mathrm{\ρ}}_i=r_i+b_u\\ N_{j}c/1e3+{\mathrm{\ρ}}_j^{frca}=r_j+b_u\end{array}\right.$

Above formula is only completed the pseudorange of code phase measuring for the full pseudoranges and satellite j of satellite i and represents；Wherein, ρ_iIt is to change through pseudorange Pseudoranges of the positive satellite i to user, b_uFor the equivalent distances error that user's clock correction is produced；For the decimal pseudorange below millimeter Value, N_jMillimeter pseudorange fuzzy number is represented, c represents the light velocity, r_iAnd r_jRepresent user to satellite i and the space length of satellite j respectively； 1e3 is constant 1000；

I-th satellite is selected to carry out single puppet poor and that satellite j can be obtained by floor operation between pseudorange star as reference satellite Computing formula away from millisecond number is：

$N_j=round\left(\right({\mathrm{\ρ}}_i-r_i+r_j-{\mathrm{\ρ}}_j^{frca})\·1e3/c)$

Step S5, after non-GEO satellite full pseudoranges are recovered, you can directly carried out most using all satellites for capturing of hybrid constellation A young waiter in a wineshop or an inn takes advantage of positioning；

According to the pseudorange residuals after positioning, step S6, judges that whether reasonable pseudorange recovers；Due to carrying out coarse positioning using GEO constellations User's general location is obtained, if general location deviation causes the pseudorange of non-GEO satellite to recover mistake compared with conference, it is therefore desirable to right Quick positioning result is tested；Pseudorange is estimated that customer location using least-squares iteration while can calculate after recovering The RMS value for going out the pseudorange residuals value of each satellite, residual values and residual error vector is calculated as follows；In formulaRepresent the user for estimating to obtain Position and the space length of satellite i；

$v_i={\mathrm{\ρ}}_i-{\hat{r}}_i-b_u$

$RMS\left(v\right)=\sqrt{\left(\underset{i=1}{\overset{n}{\Σ}}{v}_i^2\right)/n}$

As pseudorange recovers to recover for whole millisecond, if occurring that larger pseudorange is residual after positioning when pseudorange recovers to occur mistake Whether difference, transfinited using the root-mean-square of the pseudorange residuals value after positioning and judge whether method for rapidly positioning is successful, residual error threshold value According to survey

Accuracy of measurement or/and error correction precision setting.

2. the Beidou receiver method for rapidly positioning based on GEO constellation coarse positionings according to claim 1, its feature exist In, coarse positioning is carried out using ridge estimaion in step S3, concrete grammar is as follows：

When pseudorange is positioned, observational equation is expressed as

Δ ρ=H Δ x+ ε

Skews of the wherein Δ ρ for pseudorange value, Δ x is the skew of the customer location and clock correction relative to linearisation point, and ε is just to obey The error vector of state distribution, average is 0, and variance is σ²I；Matrixes of the H for n × 4 It is The unit vector of i-th satellite position is pointed to linearisation point, n is the pseudorange number for participating in positioning；

Using the mathematic(al) representation of the calculated Δ x valuations of ridge estimaion it is

$\begin{array}{c}\mathrm{\Δ}\hat{x}\left(k\right)={(H^{T}H+kI)}^{-1}{H}^T\mathrm{\Δ}\mathrm{\ρ}\\ ={(H^{T}H+kI)}^{-1}\left(H^{T}H\right){\left(H^{T}H\right)}^{-1}{H}^T\mathrm{\Δ}\mathrm{\ρ}\\ ={(H^{T}H+kI)}^{-1}\left(H^{T}H\right)\mathrm{\Δ}\hat{x}\\ =(I-k{\left(H^{T}H+kI\right)}^{-1})\mathrm{\Δ}\hat{x}\end{array}$

Wherein k is ridge parameter, and I is unit matrix；

WhereinFor least-squares estimation；Estimate that average and variance are：

$E\left(\mathrm{\Δ}\hat{x}\right(k\left)\right)=(I-k{\left(H^{T}H+kI\right)}^{-1})\mathrm{\Δ}x$

$Var\left(\mathrm{\Δ}\hat{x}\right(k\left)\right)={\mathrm{\σ}}^2{(H^{T}H+kI)}^{-1}\left(H^{T}H\right){(H^{T}H+kI)}^{-1}$

Between ridge estimaion and true value, the Expectation-based Representation for Concepts of distance is：

$\begin{array}{c}E\left(S_k^2\right)=E\[{\left(\mathrm{\Δ}\hat{x}\right(k)-\mathrm{\Δ}x)}^T\left(\mathrm{\Δ}\hat{x}\right(k)-\mathrm{\Δ}x)\]\\ ={\mathrm{\σ}}^2\underset{i=1}{\overset{4}{\Σ}}{\mathrm{\λ}}_i/{({\mathrm{\λ}}_i+k)}^2+k^2{\mathrm{\Δx}}^T{(H^{T}H+kI)}^{-2}\mathrm{\Δ}x\end{array}$

Wherein λ_iFor matrix H^TThe eigenvalue of H.

3. the Beidou receiver method for rapidly positioning based on GEO constellation coarse positionings according to claim 1, its feature exist In, coarse positioning is carried out using Doppler's auxiliary ridge estimaion in step S3, concrete grammar is as follows：

The pseudorange observation equation and Doppler's observational equation of user's observation satellite is written as equation below：

${\mathrm{\ρ}}_i=\left|\right|{\stackrel{\→}{p}}_i-{\stackrel{\→}{p}}_u\left|\right|+b+{\mathrm{\ϵ}}_{\mathrm{\ρ},i}$

Wherein, ρ_iFor i-th satellite Pseudo-range Observations,For position under i-th satellite ECEF coordinate system,For position under user's ECEF coordinate systems, b represents receiver clock-offsets,For i-th satellite Speed under ECEF coordinate systems,For user velocity,Represent receiver clock rate of change, ε_ρ,iWithDistribution Represent pseudorange and pseudorange rate of change observation noise；If ρ_{I, 0}、Forb₀、Correspondence pseudorange and pseudorange rate of change；Equation In linearisation pointb₀、Linearisation can be obtained

$\begin{array}{c}{\mathrm{\ρ}}_i={\mathrm{\ρ}}_{i,0}+\frac{(x_{u,0}-x_i)}{r_{i,0}}\mathrm{\δ}x+\frac{(y_{u,0}-y_i)}{r_{i,0}}\mathrm{\δ}y+\frac{(z_{u,0}-z_i)}{r_{i,0}}\mathrm{\δ}z+\mathrm{\δ}b\\ \stackrel{\mathrm{\Δ}}{=}{\mathrm{\ρ}}_{i,0}+(-l_x^{\left(i\right)})\mathrm{\δ}x+(-l_y^{\left(i\right)})\mathrm{\δ}y+(-l_z^{\left(i\right)})\mathrm{\δ}z+\mathrm{\δ}b\end{array}$

$\begin{array}{c}{\stackrel{\·}{\mathrm{\ρ}}}_i={\stackrel{\·}{\mathrm{\ρ}}}_{i,0}+(\frac{(v_{xu,0}-v_{xi})}{r_{i,0}}+\frac{{\stackrel{\·}{r}}_{i,0}\·(x_{i0}-x_{u,0})}{r_{i,0}^2})\mathrm{\δ}x\\ +(\frac{(v_{yu,0}-v_{yi})}{r_{i,0}}+\frac{{\stackrel{\·}{r}}_{i,0}\·(x_i-x_{u,0})}{r_{i,0}^2})\mathrm{\δ}y\\ +(\frac{(v_{xu,0}-v_{xi})}{r_{i,0}}+\frac{{\stackrel{\·}{r}}_{i,0}\·(x_i-x_{u,0})}{r_{i,0}^2})\mathrm{\δ}z\\ +\frac{(x_{u,0}-x_i)}{r_{i,0}}{\mathrm{\δv}}_x+\frac{(y_{u,0}-y_i)}{r_{i,0}}{\mathrm{\δv}}_y\\ +\frac{(z_{u,0}-z_i)}{r_{i,0}}{\mathrm{\δv}}_z+\mathrm{\δ}\stackrel{\·}{b}\\ \stackrel{\mathrm{\Δ}}{=}{\stackrel{\·}{\mathrm{\ρ}}}_{i,0}+(-k_x^{\left(i\right)})\mathrm{\δ}x+(-k_y^{\left(i\right)})\mathrm{\δ}y+(-k_z^{\left(i\right)})\mathrm{\δ}z\\ +(-l_x^{\left(i\right)}){\mathrm{\δv}}_x+(-l_y^{\left(i\right)}){\mathrm{\δv}}_y+(-l_z^{\left(i\right)}){\mathrm{\δv}}_y+\mathrm{\δ}\stackrel{\·}{b}\end{array}$

Wherein x_u,0,y_u,0,z_u,0The respectively initial three-dimensional position of user, v_xu,0,v_yu,0,v_zu,0For the initial three-dimensional velocity of user, SymbolRepresent definition, that is to say, that willIt is denoted as It is denoted as It is denoted as It is denoted as It is denoted as It is denoted as (δ x, δ y, δ z) and (δ v_x,δv_y,δv_z) receiver location and the skew between the true value and linearisation point of speed are represented respectively；

Therefore, when Doppler aids in, linear equation can be written as

Wherein n and m represent that pseudorange is seen and pseudorange rate of change observation number respectively；

When aiding in coarse positioning using Doppler, lienarized equation is expressed as

WhereinWithThe respectively vector representation of pseudorange value and the skew of pseudorange rate of change,It is the use relative to linearisation point The vector representation of the side-play amount of family position, time deviation, speed and clock rate of change, ridge estimaion are calculatedValuation Mathematic(al) representation be

4. the Beidou receiver method for rapidly positioning based on GEO constellation coarse positionings according to claim 1, its feature exist In, in step S4, outline customer location obtain after, full pseudoranges are carried out to which with reference to the following pseudorange of millisecond of non-GEO satellite The concrete grammar of recovery is：

The pseudorange of satellite i is expressed as in receivers

${\mathrm{\ρ}}_i=c(t^r-t_i^s)=c(t^r-t_i^{ms,s}-t_i^{chip,s})=r_i(t_i^s,t^r)+{\mathrm{ct}}_d^r+{\mathrm{\ϵ}}_i\left(t^r\right)=N_i\·c/1e3+{\mathrm{\ρ}}_i^{frca}$

Wherein,For signal transmission time, t^rFor local zone time, c is the light velocity,Represent that the millisecond of integer signal x time is whole Fractional part,The millisecond fractional part of signal x time is represented,RepresentThe satellite i and t at moment^rMoment user Space length,For the local clock correction of receiver, ε (t^r) represent round-off error, N_iThe whole millisecond number of pseudorange is represented,Represent milli Second following pseudorange；

When by pseudo-code phase measurement acquisitionAfter value, you can obtain the following pseudorange value of millisecond Wherein mod is modulo operation, and 1e-3 is constant 0.001；Therefore to completing frame synchronization and being only completed the pseudorange sight of code phase measuring Measurement is written as following form respectively：

$\left\{\begin{array}{c}{\mathrm{\ρ}}_i=r_i(t_i^s,t^r)+{\mathrm{ct}}_d^r+{\mathrm{\ϵ}}_i\left(t^r\right)\\ {\mathrm{\ρ}}_j=N_j\·c/1e3+{\mathrm{\ρ}}_j^{frca}=r_j(t_j^s,t^r)+{\mathrm{ct}}_d^r+{\mathrm{\ϵ}}_j\left(t^r\right)\end{array}\right.$

The computing formula that single after the recovery obtains pseudorange integers millisecond number between pseudorange star is：

$N_j\≈({\mathrm{\ρ}}_i-r_i(t_i^s,t^r\left)r_j\right(t_j^s,t^r)-{\mathrm{\ρ}}_j^{frca})\·1e3/c.$