CN108205151A - A kind of Low-cost GPS single antenna attitude measurement method - Google Patents
A kind of Low-cost GPS single antenna attitude measurement method Download PDFInfo
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- CN108205151A CN108205151A CN201810020784.2A CN201810020784A CN108205151A CN 108205151 A CN108205151 A CN 108205151A CN 201810020784 A CN201810020784 A CN 201810020784A CN 108205151 A CN108205151 A CN 108205151A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/53—Determining attitude
- G01S19/54—Determining attitude using carrier phase measurements; using long or short baseline interferometry
- G01S19/55—Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
Abstract
The present invention proposes a kind of Low-cost GPS single antenna attitude measurement method.This method establishes double difference carrier phase observation model by using high-precision carrier phase for main observed quantity, then establishes attitude measurement model using relative position of the single antenna in two different moments, devises single antenna attitude measurement method.So as to reduce the cost of attitude measurement, solve the disadvantage that multi-antenna structure is complicated, easily deform upon, effectively expand the application scenarios of GPS attitude measurements.
Description
Technical field
The invention belongs to field of navigation technology, are related to a kind of Low-cost GPS single antenna attitude measurement method.
Background technology
The attitude information of carrier is the important parameter of modern navigation, these parameters are conducive to be better understood by the movement of carrier
State.Posture attitude measurement system based on aeronautical satellite has been widely used for multiple necks such as land, ocean, Aeronautics and Astronautics
Domain.Such as ship, aircraft need quick accurate posture and Position result, no person to influence whether navigation route.
With the development of carrier phase difference technology, realize that attitude measurement becomes possibility using GPS system.Traditional is used
Property navigation system can not be interfered by outside, the attitude of carrier angle accurately asked, have higher concealment.But this method
Changing with time, there are the accumulation of error, it usually needs additional equipment is corrected the attitude angle of output, leads to the posture asked
Angle is not exclusively high-precision.Using the advantage of the distance measuring signal precision of satellite system signals, using the higher carrier wave phase of precision
Attitude measurement is realized in position as the observed quantity that attitude information resolves, and can meet high-precision, error free accumulation, body in modern navigation
Accumulate the demands such as small, at low cost.
By installing more antennas on large-scale ship carrier, realize that attitude of carrier measures under conditions of Long baselines
Through becoming reality.Multiple antennas survey appearance have it is complicated, volume is big, installation difficulty is big, the shortcomings of easily deforming upon, may
Be not suitable for being applied to require antenna volume small scene, such as pilotless automobile, small drone.
Therefore the present invention devises a kind of Low-cost GPS single antenna attitude measurement method, can effectively reduce the body of antenna
Product is so that it is convenient to install, reduce cost.The application scenarios of attitude measurement can be expanded simultaneously, and there is highly important meaning
Justice.
Invention content
It is an object of the invention to overcome above-mentioned existing deficiency, a kind of Low-cost GPS single antenna attitude measurement side is provided
Method, this method take into account that antenna volume when multiple antennas measures is excessive, inconvenient installation when carrying out attitude measurement conducive to GPS,
Easily the shortcomings of deforming upon, is effectively reduced the number of antenna and has selected carrier phase as main observed quantity,
Improve attitude measurement accuracy.
In order to achieve the above objectives, the present invention provides following technical solution：
A kind of Low-cost GPS single antenna attitude measurement method, includes the following steps：
Step 1：Build the initial data of data acquisition platform record GPS boards；
Step 2：Almanac data in the initial data that is acquired in step 1 and observation data are pre-processed；
Step 3：The position of satellite observed using the almanac data calculating receiver in step 2.
Step 4：The position of receiver is calculated using the observation data in step 2.
Step 5：It parses the observation data of two adjacent moments respectively using the observation data in step 2, establishes double difference
Carrier phase observation model.
Step 6：According to the double difference carrier phase observation model established in step 5, derive and be suitable for single antenna attitude measurement
Model.
Step 7：Rapidly searching for integer cycle is carried out based on least-squares algorithm, it is further to solve integer ambiguity
Improve baseline vector estimated accuracy.
Step 8：Attitude angle is solved according to the conversion of baseline vector and coordinate system.
Further, in step 1, the specific side of the initial data for building data acquisition platform record GPS boards
Method is：GPS boards are driven by microcontroller and pass through the accurate Control card output frequency of timer；Acquisition GPS is defended in real time
The initial data that star is broadcast, each collected 1 epoch data are encapsulated as a frame data；Pass through bluetooth after the completion of data encapsulation
Interface outwardly exports.
Further, in step 2, the data that GPS boards are acquired are done pretreatment and are included according to databook pair
Initial data carries out Conversion of measurement unit.
Further, in step 3, the sub-step that the position that data calculate satellite is observed in the utilization is：
Step 3 (one) calculates satellite mean angular velocity n0
In formula, μ is the Gravitational coefficient of the Earth under the earth coordinates of the earth's core, and A is the major semiaxis number that almanac data provides.
Step 3 (two) calculating observation epoch to reference to epoch time difference tk
tk=t-toe
In formula, t receives almanac data time, t for receiveroeThe reference time provided for almanac data.
Step 3 (three) calculates correction average angular rate n
N=n0+Δn
In formula, n0For satellite mean angular velocity, Δ n be almanac data the satellite mean motion speed and calculated value that provide it
Difference.
Step 3 (four) calculating observation epoch tkMean anomaly Mk
Mk=M0+n·tk
In formula, n is the correction average angular rate being computed, M0For reference time toeFlat nearly angle.
Step 3 (five) calculates eccentric anomaly Ek
Ek=Mk-e·sinEk
In formula, MkFor the epoch of observation t being computedkMean anomaly, e are to provide eccentricity by almanac data.
Step 3 (six) calculates true anomaly vk
In formula, e is eccentricity, is provided by almanac data.EkFor the eccentric anomaly calculated.
Step 3 (seven) calculates latitude argument parameter phik
φk=vk+ω
In formula, vkFor the true anomaly being computed.ω is with reference to moment toePerigee of orbit angular distance, is carried by almanac data
For.
Step 3 (eight) calculates correction member
uk=φk+δuk
rk=A (1-ecosEk)+δrk
ik=i0+IDOT·tk+δik
In formula, δ uk、δrk、δikRespectively latitude argument phikCorrection member, radial direction correction member and orbit inclination angle correction member, ukFor
Latitude argument after correction, rkFor the mirror image after correction, ikFor the orbit inclination angle after correction, IDOT is orbit inclination angle change rate.
Step 3 (nine) calculates coordinate of the satellite in orbit plane
In formula, ukFor the latitude argument after correction, rkFor the mirror image after correction.
Step 3 (ten) calculates position of the satellite in the earth coordinates of the earth's core
In formula, Ω0To refer to epoch toeThe red diameter of ascending node,To refer to epoch toeRed diameter perturbation change rate.
In formula, xk, ykThe coordinate for being the satellite that has been computed in orbit plane, ikFor the rail after the correction that has been computed
Road inclination, ΩkFor the red diameter of epoch ascending node.
Further, in step 4, the specific method that observation data calculate receiver location is：If Pseudo-range Observations are ρ,
The actual distance of receiver to satellite is R, and receiver clock-offsets are the light velocity for δ t, c, can establish pseudorange observation equation：
ρ=R+c δ t
If a certain moment observes n satellite altogether, then n pseudorange observation equation can be established.Above formula can be carried out linear
Change, obtain equation below group：
In formula, l, m, n are unit vector of the satellite relative to receiver.
Rough coordinates are asked using the realization of pseudorange One-Point Location during initial calculation, the geometric distance R of receiver to satellite is not
Accurately, therefore the result and true receivers position coordinates gap that are calculated are larger.It is calculated, obtained accurate by iterating
Positioning result.There is electricity in also needing to establish observation error model during actually measuring to GPS signal communication process
Absciss layer, troposphere, satellite clock correction equal error are modified.
Further, in step 5 double difference carrier phase observation model is established using the observation data of two different moments.
Specific choice method is：
Carrier phase in Satellite Observations initially sets up carrier phase observation model and is represented by：
In formula,For receiver tkThe carrier phase value actually measured at the position i at moment；For tkWhen
Carve the actual range of satellite p and receiver location i；δi(tk) for the receiver clock-offsets at the i of position；Complete cycle mould for satellite p
Paste degree；δp(tk) be satellite p clock correction；For ionospheric error；For tropospheric error；C is the light velocity, and λ is carrier wave
Wavelength.
If receiver is in tkThe apparent position at moment isIts correction is [δ Xi(tk)δYi
(tk)δZi(tk)], above formula is existedLocate Taylor series expansion, and first approximation expression formula is taken to have：
In formula,[l m n]
Satellite is expressed as to the unit vector of receiver：
Then the list of different location can be obtained by receiver being made the difference in the carrier phase observation model of position i and position j
Difference carries phase observations model and is linearized according to above formula, can obtain equation below：
In formula, δij(Δ t)=δi(tk)-δj(tm),It is arrived for satellite p
The unit vector of receiver j,For receiver the rough coordinates of position j correction,
Δ t is receiver respectively in the time difference of position i and position j, tmIt is receiver at the time of the j of position.
Finally on the basis of single poor carrier phase observation model, carry out that the list between satellite p and satellite q is poor to be obtained
Double difference carrier phase observation model can be expressed as：
In formulaFor the complete cycle after double difference
Fuzziness.
It further,, can when selecting 4 satellites and being resolved according to double difference carrier phase observation model in step 6
6 double difference observational equations are established, so as to derive single antenna attitude measurement model.The satellite of selection elevation angle maximum is defended as reference
Star, the equation group after being simplified：
Formula is abbreviated as：
Y=AX
In formula：Y is the observation data of receiver；A is the design matrix that the unit vector of receiver to satellite is formed, and X is
Baseline vector to be asked and solution of fuzzy degree.
According to least square resolution principle, X can be acquired：
X=(AT·P·A)-1·AT·P·Y
Ignore the integer characteristic of double difference integer ambiguity, enable double difference integer ambiguity vectorBase correction vector b=[δ Xj δYj δZj]T, the result that least square acquires can represent
For：
Commonly known as float-solution, variance-covariance matrix Q are：
In formula,For the auto-covariance matrix of b,For the auto-covariance matrix of a,WithCross covariance for a and b
Matrix, P are weight matrix.
Further, in step 7, the specific method that rapidly ambiguity search is carried out based on least square is：By whole
Integer ambiguity resolution obtains double difference integer ambiguity vectorUsing the integer characteristic of fuzziness, further improve baseline vector and estimate
Count precision.It is searched for by least squareIt can obtain：
In formula,For the fixed solution of baseline vector correction,ForCorresponding covariance matrix.
Further, in step 8, the specific method that attitude angle is solved according to the conversion of baseline coordinate and coordinate system is：By
InFor the correction of baseline vector, if coordinates of the position i of receiver under the earth coordinates of the earth's core is [Xm Ym Zm]T, then
Coordinate of the receiver in position j be relative to the coordinate of position i：
In formula,For the receiver that has been computed position j coordinate correction amount.It is receiver in position i
Coordinate.
Assuming that using the position i of receiver as coordinate origin, then receiver changes in the coordinate correction amount of position j with baseline vector
Positive numberEquivalence, i.e.,：
Due to baselineIt is to be based on the earth's core earth coordinates, it willIt is transformed under topocentric coordinate system, obtains
In formula, λ is longitude of the receiver in position j, and φ is latitude of the receiver in position j.
Since the coordinate vector in the coordinate vector in topocentric coordinate system and the earth's core earth coordinates has following conversion to close
System：
In formula,For the coordinate vector in topocentric coordinate system,For the coordinate vector in the earth coordinates of the earth's core,
For topocentric coordinate system and the transition matrix of the earth's core earth coordinates.
When baseline is overlapped with the y-axis of carrier, the course angle of carrier can be measuredIn this case, baseline is carrying
Normalized vector under body coordinate system is represented by [010]T, roll angle is set as 0 °.
Course angle can be acquired by above formula：
The beneficial effects of the present invention are：A kind of Low-cost GPS single antenna attitude measurement method is provided, this method passes through
High-precision carrier phase is used to establish double difference carrier phase observation model for main observed quantity, is then devised based on Dan Tian
The attitude measurement model of line.The cost of attitude measurement is reduced, solves that multi-antenna structure is complicated, lacking of easily deforming upon
Point effectively expands the application scenarios of GPS attitude measurements.
Description of the drawings
To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention is made below in conjunction with attached drawing into
The detailed description of one step, wherein：
Fig. 1 is GPS single antenna attitude measurement method flow diagrams；
Fig. 2 is carrier phase observation model schematic diagram；
Fig. 3 is carrier phase list difference model schematic；
Fig. 4 is double-differential carrier phase model schematic；
Specific embodiment
In order to which those skilled in the art is made to be better understood when the purpose of the present invention, technical solution and advantageous effect, below
It is completely described with attached drawing is illustrated in conjunction with specific embodiments.
Fig. 1 is GPS single antenna attitude measurement method flow diagrams；
Step 1：GPS boards are driven using microcontroller and pass through the accurate Control card output frequency of timer；It is real
When the initial data broadcast of acquisition GPS satellite, each collected 1 epoch data are encapsulated as a frame data；Data have encapsulated
It is outwardly exported by blue tooth interface into rear.
Step 2：Conversion of measurement unit is carried out to initial data according to databook.
Step 3：The position of satellite is calculated according to almanac data, the sub-step of the step is as follows：
Step 3 (one) calculates satellite mean angular velocity n0
In formula, μ is the Gravitational coefficient of the Earth under the earth coordinates of the earth's core, and A is the major semiaxis number in Almanac parameter.
Step 3 (two) calculating observation epoch to reference to epoch time difference tk
tk=t-toe
In formula, t is receiver time when receiving the almanac data, toeFor the reference time provided by almanac data.
Step 3 (three) calculates correction average angular rate n
N=n0+Δn
In formula, n0For satellite mean angular velocity, Δ n is Almanac parameter
Step 3 (four) calculating observation epoch tkMean anomaly Mk
Mk=M0+n·tk
In formula, n is corrects average angular rate, M0For the reference time t provided in almanac dataoeFlat nearly angle.
Step 3 (five) calculates eccentric anomaly Ek
Ek=Mk-e·sinEk
In formula, MkFor the epoch of observation t being computedkMean anomaly, e are eccentricity, are provided by almanac data.
Step 3 (six) calculates true anomaly vk
In formula, e is eccentricity, is provided by almanac data.EkFor the eccentric anomaly calculated
Step 3 (seven) calculates latitude argument parameter phik
φk=vk+ω
In formula, ω is with reference to moment toePerigee of orbit angular distance.vkFor the true anomaly being computed.
Step 3 (eight) calculates correction member δ uk, δ rk, δ ik
uk=φk+δuk
rk=A (1-ecosEk)+δrk
ik=i0+IDOT·tk+δik
In formula, δ uk、δrk、δikRespectively latitude argument phikCorrection member, radial direction correction member and orbit inclination angle correction member, ukFor
Latitude argument after correction, rkFor the mirror image after correction, ikFor the orbit inclination angle after correction, IDOT is orbit inclination angle change rate.
Step 3 (nine) calculates coordinate of the satellite in orbit plane
In formula, ukFor the latitude argument after correction, rkFor the mirror image after correction.
Step 3 (ten) calculates position of the satellite in the earth coordinates of the earth's core, calculates the red diameter Ω of epoch ascending node firstk
In formula, Ω0To refer to epoch toeThe red diameter of ascending node,To refer to epoch toeRed diameter perturbation change rate.
In formula, xk, ykThe coordinate for being the satellite that has been computed in orbit plane, ikFor the rail after the correction that has been computed
Road inclination, ΩkFor the red diameter of epoch ascending node.
Step 4：If Pseudo-range Observations are ρ, the actual distance of receiver to satellite is R, and receiver clock-offsets are δ t.It can build
Vertical pseudorange observation equation：
ρ=R+c δ t
If a certain moment observes n satellite altogether, then n pseudorange observation equation can be established, and linearized, obtained
Equation below group：
In formula, l, m, n are unit vector of the satellite relative to receiver.It can be solved by above formula：
Rough coordinates are asked using the realization of pseudorange One-Point Location during initial calculation, the geometric distance R of receiver to satellite is not
Accurately, therefore the result and true receivers position coordinates gap that are calculated are larger.It is calculated, obtained accurate by iterating
Positioning result.There is electricity in also needing to establish observation error model during actually measuring to GPS signal communication process
Absciss layer, troposphere, satellite clock correction equal error are modified.
Step 5：Carrier phase observation model is initially set up, in t0To tkIn this period, between satellite p and receiver
Signal transmission schematic diagram is as shown in Figure 2.In t0Reception machine can only measureThat is fractional part, signal communication process
In integer partIt can not measure.From t0Moment, receiver start continuous counter, as long as signal not losing lock, can survey
It obtains in t0To tkThe complete cycle number that satellite-signal is propagated in this periodAnd fractional partTherefore, in t0Afterwards
Any epoch carrier phase total variation is represented by：
In formula,It is receiver reference signal in tkThe phase at moment, you can be considered the phase of the moment satellite-signal
Position；It is receiver in tkReception machine receives the phase of satellite-signal；It is receiver from t0Moment start to
tkThe carrier phase variable quantity of moment record and the actual observation amount of receiver output；It is t0Moment carrier wave integral circumference ambiguity
Degree.
If receiver observes satellite p in two different positions i and position j, the load of two such as above formulas can be established
Wave phase observational equation, carrier phase list difference model schematic are as shown in Figure 3.
Since two receiver locations are spaced closely together, the signal of satellite p can be approximately considered to receiver location i and position
The transmission path of j is consistent.Therefore, the propagateds error such as most of ionosphere and tropospheric error can be eliminated by making difference.It is single
Equation below can be obtained after difference：
In formula,Represent the value after carrier phase observed quantity list difference.It is receiver t in position ikWhen
The carrier phase variable quantity of record is engraved,It is receiver t in position jmThe carrier phase variable quantity of moment record,
In single poor carrier phase observation model, it is assumed that receiver position i coordinate it is known that receiver position j's
Rough coordinates areExist to above formulaPlace carries out Taylor expansion, obtains linearizing the poor load of later list
Wave phase observational equation：
In formula, δij(Δ t)=δi(tk)-δj(tm),It is arrived for satellite p
The unit vector of receiver j,For receiver the rough coordinates of position j correction,
Δ t is receiver respectively in the time difference of position i and position j, tmIt is receiver at the time of the j of position.
In above formula, single poor carrier phase model has eliminated most of error, but receiver clock-offsets still have.
On the basis of single differential mode type, double difference carrier phase model, double-differential carrier phase mould are can obtain as difference again for different satellites
Type schematic diagram schematic diagram is as shown in Figure 4.Assuming that satellite p is reference satellite, by receiver in position i and position j respectively to satellite p
It is single poor to make with satellite q, obtains the poor carrier phase observation model of list between different location first, then carries out between different satellites
List poor can obtain double difference carrier phase observation model, equation below：
In formula,It is whole after double difference
All fuzzinesses.
Step 6：According to double difference carrier phase modular concept, when selecting 4 satellites and being resolved, establish 6 double differences and see
Survey equation, the equation group after being simplified：
Formula is abbreviated as：
Y=AX
In formula：Y is the observation data of receiver；A is the design matrix that the unit vector of receiver to satellite is formed；X is
Baseline vector to be asked and solution of fuzzy degree.
According to least square resolution principle, X can be acquired：
X=(AT·P·A)-1·AT·P·Y
Ignore the integer characteristic of double difference integer ambiguity, enable double difference integer ambiguity vectorBase correction vector b=[δ Xj δYj δZj]T, the result that least square acquires can represent
For：
Commonly known as float-solution, variance-covariance matrix Q are：
In formula,For the auto-covariance matrix of b,For the auto-covariance matrix of a,WithCross covariance for a and b
Matrix, P are weight matrix.
Step 7：The specific method that rapidly ambiguity search is carried out based on least-squares algorithm is：Pass through integral circumference ambiguity
Degree solves and obtains double difference integer ambiguity vectorUsing the integer characteristic of fuzziness, baseline vector estimation essence is further improved
Degree.It is searched for by least squareIt can obtain：
In formula,For the fixed solution of baseline vector correction,ForCorresponding covariance matrix,Auto-covariance for a
Matrix,WithFor the Cross-covariance of a and b, P is weight matrix.
Step 8：The specific method that attitude angle is solved according to the conversion of baseline coordinate and coordinate system is：Due toIt is sweared for baseline
The correction of amount, if coordinates of the position i of receiver under the earth coordinates of the earth's core is [Xm Ym Zm]T, then receiver is in position
The coordinate of j is relative to the coordinate of position i：
In formula,For the receiver that has been computed position j coordinate correction amount,It is receiver position i's
Coordinate.
Assuming that using the position i of receiver as coordinate origin, then receiver changes in the coordinate correction amount of position j with baseline vector
Positive numberEquivalence, i.e.,：
Due to baselineIt is to be based on the earth's core earth coordinates, it willIt is transformed under topocentric coordinate system, obtains
In formula, λ is longitude of the receiver in position j, and φ is latitude of the receiver in position j.
Since the coordinate vector in the coordinate vector in topocentric coordinate system and the earth's core earth coordinates has following conversion to close
System：
In formula,For the coordinate vector in topocentric coordinate system,For the coordinate vector in the earth coordinates of the earth's core,
For topocentric coordinate system and the transition matrix of the earth's core earth coordinates.
When baseline is overlapped with the y-axis of carrier, the course angle of carrier can be measuredIn this case, baseline is carrying
Normalized vector under body coordinate system is represented by [010]T, roll angle is set as 0 °.
Course angle can be acquired by above formula：
Claims (9)
1. a kind of Low-cost GPS single antenna attitude measurement method, it is characterised in that：It comprises the steps of：
Step 1: build the initial data of data acquisition platform record GPS boards；
Step 2: the almanac data in the initial data that is acquired in step 1 and observation data are pre-processed；
Step 3: the position of satellite observed using the almanac data calculating receiver in step 2.
Step 4: the position of receiver is calculated using the observation data in step 2.
Step 5: parsing the observation data of two adjacent moments respectively using the observation data in step 2, double difference load is established
Wave phase observation model.
Step 6: according to the double difference carrier phase observation model established in step 5, derive and be suitable for single antenna attitude measurement mould
Type.
Step 7: carrying out rapidly ambiguity search based on least-squares algorithm, solve fuzziness and further improve baseline vector
Estimated accuracy.
Step 8: attitude angle is solved according to the conversion of baseline vector and coordinate system.
2. a kind of Low-cost GPS single antenna attitude measurement method method according to claim 1, it is characterised in that：In step
In rapid one, GPS boards are driven by microcontroller and pass through the accurate Control card output frequency of timer；Acquisition GPS in real time
The initial data that satellite is broadcast, each collected 1 epoch data are encapsulated as a frame data；Pass through indigo plant after the completion of data encapsulation
Tooth interface outwardly exports.
3. a kind of Low-cost GPS single antenna attitude measurement method method according to claim 2, it is characterised in that：In step
In rapid two, the data that GPS boards are acquired do pretreatment and include carrying out unit turn to initial data according to databook
It changes.
4. a kind of Low-cost GPS single antenna attitude measurement method method according to claim 3, it is characterised in that：In step
In rapid three, the almanac data in initial data calculates the position of satellite that receiver observes.
5. a kind of Low-cost GPS single antenna attitude measurement method method according to claim 4, it is characterised in that：In step
In rapid four, if Pseudo-range Observations are ρ, the actual distance of receiver to satellite is R, and receiver clock-offsets are δ t, can establish pseudorange sight
Survey equation：
ρ=R+c δ t
If a certain moment observes n satellite altogether, then n pseudorange observation equation can be established, then equation group is solved；
Rough coordinates are asked using the realization of pseudorange One-Point Location during initial calculation, the geometric distance R of receiver to satellite is inaccurate, therefore
The result being calculated and true receivers position coordinates gap are larger；It is calculated by iterating, obtains accurately positioning knot
Fruit.
6. a kind of Low-cost GPS single antenna attitude measurement method method according to claim 5, it is characterised in that：Rapid
In five, the carrier phase in Satellite Observations initially sets up carrier phase observation model and is represented by：
In formula：For receiver tkThe carrier phase value actually measured at the position i at moment,For tkMoment is defended
The actual range of star p and receiver location i, δi(tk) for the receiver clock-offsets at the i of position,For the integer ambiguity of satellite p,
δp(tk) be satellite p clock correction,For ionospheric error,For tropospheric error, c is the light velocity, and λ is the wave of carrier wave
It is long；
Then by receiver is made the difference between the observed quantity of two different moments can must arrive at a station between single poor carrier phase see
Model is surveyed, the satellite that receiver is observed in two different moments is chosen and is used as with reference to measuring, single poor carrier phase is seen between station
Double difference carrier phase observation model can be obtained into list is poor between planet by surveying model.
7. a kind of Low-cost GPS single antenna attitude measurement method method according to claim 6, it is characterised in that：In step
In rapid six, according to double difference carrier phase observation model, when selecting 4 satellites and being resolved, 6 double difference observation sides can be established
Journey so as to derive single antenna attitude measurement model, is shown below：
Y=AX
In formula：Y is known observed quantity, and A is the design matrix that the unit vector of receiver to satellite is formed, and X is base to be asked
Line vector and solution of fuzzy degree；
X can be acquired according to least square resolution principle：
X=(AT·P·A)-1·AT·P·Y
In formula, P is weight matrix；
Ignore the integer characteristic of double difference integer ambiguity, enable double difference integer ambiguity vector
Base correction vector b=[δ Xj δYj δZj]T, the result that least square acquires is represented by：
8. a kind of Low-cost GPS single antenna attitude measurement method method according to claim 7, it is characterised in that：In step
In rapid seven, the specific method that rapidly ambiguity search is carried out based on least-squares algorithm is：It is obtained by Fast integer Ambiguity Resolution
To double difference integer ambiguity vectorUsing the integer characteristic of fuzziness, baseline vector estimated accuracy is further improved, can be represented
For：
In formula：For the auto-covariance matrix of b,For the auto-covariance matrix of a,WithFor the Cross-covariance of a and b,
P is weight matrix,For the fixed solution of baseline vector correction,ForCorresponding covariance matrix.
9. a kind of Low-cost GPS single antenna attitude measurement method method according to claim 8, it is characterised in that：In step
In rapid eight, receiver can be derived in the opposite position of two different moments according to the baseline vector correction solved in step 7
The variation put, in combination with the conversion between the coordinate vector in the coordinate vector and topocentric coordinate system in the earth coordinates of the earth's core
Relationship can derive course angle.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110133702A (en) * | 2019-05-13 | 2019-08-16 | 桂林电子科技大学 | A kind of attitude measurement method and equipment based on orthogonal transformation |
| CN110146050A (en) * | 2019-02-18 | 2019-08-20 | 广东星舆科技有限公司 | A kind of communication base station antenna monitoring method |
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