CN109613585A - A kind of method of pair of real-time direction finding of antenna for base station ultra-short baseline GNSS double antenna - Google Patents
A kind of method of pair of real-time direction finding of antenna for base station ultra-short baseline GNSS double antenna Download PDFInfo
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- CN109613585A CN109613585A CN201811535344.7A CN201811535344A CN109613585A CN 109613585 A CN109613585 A CN 109613585A CN 201811535344 A CN201811535344 A CN 201811535344A CN 109613585 A CN109613585 A CN 109613585A
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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
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Abstract
The invention discloses the methods of a kind of pair of real-time direction finding of antenna for base station ultra-short baseline GNSS double antenna can determine the two-dimensional attitude of carrier by measuring the vector being fixed on carrier.When the antenna of two receivers is mounted on rigid carrier, the vector of such a reflection carrier two-dimensional attitude is constituted, direction and distance of the vector both ends in space is accurately determined, just can calculate the course angle of carrier.The present invention carries out global solution to basic lineal vector by building double difference model, eliminate the common error of satellite and receiver, while first resolving single poor fuzziness between fixed station, it avoids the occurrence of reference star and replaces frequent problem, it is resolved using EKF, it ensure that the reliability of basic lineal vector, it can guarantee that single epoch is resolved simultaneously, real-time is effectively guaranteed, specifically avoids the various errors influence receiver antenna of inexpensive locating module and antenna in absolute fix in observation and is difficult to obtain high precision position.
Description
Technical field
The present invention relates to heading measure field, in particular to a kind of pair of antenna for base station ultra-short baseline GNSS double antenna is surveyed in real time
To method.
Background technique
Heading measure belongs to one kind of attitude measurement technology, can provide tested carrier in orientation and pitching both direction
Attitude measurement data.Traditional attitude measurement system be based primarily upon photo electricity collimation theodolite (sun sensor, star sensor,
Infrared earth sensor etc.), magnetometer, accelerometer and gyroscope etc., these measuring systems belong to self-contained system, have compared with
Good autonomy, but its disadvantage is also more obvious.Photo electricity collimation theodolite is affected by external environment, in measurement process
It is highly prone to interfere.Based on the inertial navigation system of magnetometer, accelerometer and gyroscope, there is good autonomous characteristic, by
External interference is small, is capable of measuring various high speed attitudes vibrations, but existing measurement drift characteristic itself leads to not carry out persistently
Measurement, inertial navigation system just can guarantee the precision of DATA REASONING through needing to be modified measurement data after a period of time, this
The environment that sample just limits its application reduces the service efficiency of inertial navigation system.
Using GNSS carrier phase measurement principle, GNSS carrier receiver, antenna and the mould with computing function are provided
Block, GNSS direction finding technology have the advantages that easy to carry, flexible for installation, measurement accuracy is high.GNSS system can be global round-the-clock
Real-time measurement, this interference that GNSS survey appearance direction finding technology is generated by extraneous factors such as geography, weather are greatly lowered, and
And the advantage with real-time measurement.These advantages overcome the deficiency of photo electricity collimation theodolite and inertial navigation system, make GNSS
Surveying appearance direction finding technology can be widely applied to aerospace measurement, accurate landing, geographical attitude measurement, car and boat posture or heading measure etc.
Aspect.
It has had already appeared currently on the market and has used the higher high precision double frequency of price mostly using GNSS direction finding technology and lead
Navigate locating module and high-precision measurement type antenna, the pseudorange and carrier wave measured value of outputting high quality, and single measurement module is logical
The pseudorange and carrier wave measured value for crossing high quality carry out absolute fix and find out respective accurate location, then constitute basic lineal vector, most
Direction finding value (angle that basic lineal vector and real north rotate clockwise) is calculated by basic lineal vector afterwards.But due to this kind of survey
The equipment price used to method is excessively high, and inexpensive navigation positioning module and antenna is difficult to obtain precision according to the above method
Preferable direction finding value.
Summary of the invention
The purpose of the present invention is overcoming above-mentioned problems of the prior art, a kind of pair of antenna for base station ultra-short baseline is provided
The precise relative positioning between GNSS antenna may be implemented using antenna arrangement technology in the method for the real-time direction finding of GNSS double antenna, can
To be applied to the navigation positioning module and antenna of low cost, while reliable direction finding value can also be provided for antenna for base station.
The technical scheme is that the method for a kind of pair of real-time direction finding of antenna for base station ultra-short baseline GNSS double antenna, packet
Include following steps:
1) data are imported and is pre-processed
The t moment epoch observation data and navigation ephemeris for reading receiver r and b in real time, calculate co-ordinates of satellite, by code
It tests to remove with the non-poor residual error of carrier phase and can not participate in resolving and second-rate satellite data；
2) double-difference equation model is constructed
Initially set up the basic observational equation of carrier phase: in the identical t moment of two receiver epoch times, receiver r and b
L1 frequency point pseudorange and carrier phase observational equation between satellite j are as follows:
In formula, λ is carrier wavelength, and c is carrier wave spread speed,It is receiver r, pseudorange of the b for satellite j
Observation,It is receiver r, b is for the carrier observations of satellite j, and N is integer ambiguity, and ρ is receiver and satellite
Between geometric distance, dt is satellite clock correction, dr,ion, db,ionFor ionosphere delay, dr,trop, db,tropFor tropospheric delay, ε is
Phase error caused by receiver noise and multipath；
Pseudorange is obtained after making difference and carrier phase observes single eikonal equation:
Two receivers observation satellite k simultaneously is enabled again, obtains two receivers to single eikonal equation of satellite k:
Establish double difference variance: it is poor that formula (3) and formula (4) are made, and obtains pair of pseudorange and carrier phase measurement relative positioning
Eikonal equation:
It after above-mentioned double-difference equation is established, tests to the residual error of the double-difference equation of pseudorange and carrier phase, if examining logical
Cross carry out next step resolving；If the test fails, it is believed that there are rough errors is unavailable for Current observation data, directly abandons, and returns to step
The rapid data for 1) reading in next epoch and calculating；
3) EKF filter resolves
Vector to be estimated is handled using EKF filter (Extended Kalman Filter, EKF), and is updated
Kalman correlation matrix parameter；
4) Carrier Phase Ambiguity Resolution
Using continuous fuzziness fixed model, single poor fuzziness is located with following without mode between carrier phase station
Reason: under updating by the time of EKF, the value of single poor fuzziness is inherited in next epoch.It is detected by LLI (losing lock detector)
Cycle slip, if having found cycle slip in measurement data, corresponding single poor ambiguity state resets to initial value, process noise matrix
Sufficiently large value (10 is set4㎡)；
State vector to be asked is calculated by above-mentioned EKF, wherein single poor float ambiguities can be converted between state vector station
It is double difference integer ambiguity to improve convergence time and convergence precision.Firstly, their association side of estimated state vector sum to be asked
Poor matrix can be converted to double difference form by following formula:
Wherein,
G is single poor transition matrix for turning double difference, can eliminate reception by the way that single poor fuzziness is converted to double difference fuzziness
Itself existing deviation between machine, at the same also can avoid occurring reference star replacement frequently and to cause EKF filtering to be difficult to convergent
Problem, it is assumed that integer ambiguity isCorresponding covariance matrix puppet QN, it is closest to fuzziness true valueThus it constructs
The least square problem (ILS) of one fuzziness complete cycle solution
In order to solve the least square problem of fuzziness complete cycle solution, using general MLAMBDA method, in order to examine solution
Reliability is adjudicated using significant threshold ratio；
After double difference fuzziness is fixed successfully, it is then converted into single poor fuzziness, the status information of each matrix of EKF is updated, mentions
The high estimation accuracy for resolving state vector to be asked to epoch later.
Above-mentioned steps 3) described in EKF filter method it is as follows:
The wherein state vector of unknown model parametersAnd its covariance matrix P tkThe observation vector y at momentk,
It is obtained by calculation:
Pk=(I-KkHk)PK, k-1 (7)
Wherein I is unit battle array；Pk,k-1Respectively one-step prediction value and its variance-covariance battle array；KkFor gain square
Battle array；In order to reduce filtering algorithm to the sensibility for calculating rounding error, guarantee PkSymmetric positive definite, with improve filtering numerical value
Stability prevents filtering divergence, needs formula (7) being rewritten as following form in practical calculating
Assuming that movement station and receiving station all use GNSS single frequency receiving, estimative unknown state vector X is defined as follows:
Wherein,It broadcasts TV programs by satellite for L1 frequency point border singly poor fuzziness of standing (unit is week).Use list
Poor fuzziness can avoid the problem of reference star is frequently replaced in double difference fuzziness without the use of double difference fuzziness well；
Observation vector y is defined with double difference carrier phase and pseudo-range measurements
Wherein,
Measurement model vector h (x), partial derivative matrix (observing matrix factor arrays) H (x) and measurement error covariance matrix Rk
It respectively indicates as follows:
Wherein,For single poor side
Journey,
For L1Frequency point carrier wave measurement error standard deviation (m),For L1The standard deviation of frequency point pseudo-range measurements error
Poor (m).
In application EKF, need to state-transition matrix Φk,k-1, process noise Qk-1It is defined, is thought of as ultrashort base
Line and be static state, Φk,k-1, Qk-1Therefore it is defined as following formula:
EKF is used by above-mentioned matrix, it is single between the carrier phase station in the state vector of this epoch movement station to be estimated
Poor fuzziness can be found out, the search for double difference fuzziness.
Above-mentioned steps 4) described in significant threshold ratio to adjudicate its method as follows:
Wherein, when Ratio is greater than the threshold value of predetermined set, this paper threshold settings are 3, if then judging corresponding double
Poor integer ambiguity combination is unique correct.In order to guarantee fixed correctness, ambiguity information is stored, if continuous 10 are gone through
First continuous fixed, then fuzziness fixed inspection passes through, the higher fixed solution of output accuracyIt is needed under if examining failure
Formula calculates float-solution
Basic lineal vector between two antennas can accurately be calculated by crossing above-mentioned steps, may then pass through basic lineal vector meter
Calculate course angle.In user's local coordinate, the antenna coordinate of two receivers constitutes basic lineal vector, when the load where direction-finding system
When body is rigid body, which can reflect the real-time two-dimensional attitude of carrier.
In the antenna 1 and 2 of carrier y direction installation receiver r and b, seat of the antenna 1 and 2 in user's local coordinate
Mark is respectively (x1,y1,z1) and (x2,y2,z3), basic lineal vector is accurately determined by GNSS carrier wave relative positioningVector
Amount along change in coordinate axis direction is respectively as follows:
Assuming that yaw angle ψ isThe angle of projection and x-axis in xoy plane, pitching angle theta are vectorIt is flat with xoy
The angle in face, specific formula for calculation are as follows:
The value range of yaw angle ψ is 0-360 ° in formula, and the value range of pitching angle theta is -90-90 °.Because of local coordinate system
System is northeast day coordinate system, and x-axis is directed toward the positive east of carrier position, so yaw angle indicates carrier movement direction and due east
The angle of side, and the definition of course angle is the angle in carrier movement direction and the positive north, when calculating the course angle in carrier, is needed
The benchmark of yaw angle is rotated by 90 ° counterclockwise, the course angle of carrier.Therefore, the accurate baseline obtained by the above method
The course of carrier can be calculated in vector in real time.
Beneficial effects of the present invention: the present invention provides a kind of pair of real-time direction findings of antenna for base station ultra-short baseline GNSS double antenna
Method the two-dimensional attitude of carrier can be determined by measuring the vector that be fixed on carrier.When the day of two receivers
When line is mounted on rigid carrier, the vector of such a reflection carrier two-dimensional attitude is constituted, accurately determines that the vector both ends exist
Direction and distance in space, just can calculate the course angle of carrier.The present invention by building double difference model to basic lineal vector into
Row global solution eliminates the common error of satellite and receiver, while first resolving single poor fuzziness between fixed station, avoids the occurrence of ginseng
It examines star and replaces frequent problem, during single poor fuzziness building double difference fuzziness, eliminate the error between receiver, select
Maximum as reference star with elevation angle, MLAMBDA searches for double difference fuzziness, examines ambiguity resolution using Ratio value later
Success rate, judging that continuous 10 epoch fuzzinesses successfully fix, fixed solution then exported, so that output be effectively guaranteed
As a result in addition high-precision is resolved using EKF, can fully play the state vector relationship at front and back moment, ensure that baseline
The reliability of vector, while can guarantee that single epoch is resolved, the real-time of this method is effectively guaranteed.It specifically avoids
The various errors influence receiver antenna of inexpensive locating module and antenna in absolute fix in observation is difficult to obtain high-precision
Position is spent, by the measured value for the baseline vector procession that this method is handled, is verified by practical direction-finding system, precision is reachable
Within 3 °.
Detailed description of the invention
Fig. 1 is the real-time direction finding technology program flow chart of antenna for base station ultra-short baseline GNSS double antenna of the invention；
Fig. 2 is double antenna building double-difference equation model schematic；
Fig. 3 is double antenna baseline vector procession course schematic diagram.
Specific embodiment
With reference to the accompanying drawing, the specific embodiment of the present invention is described in detail, it is to be understood that of the invention
Protection scope be not limited by the specific implementation.
Referring to figures 1-3, the invention discloses the sides of a kind of pair of real-time direction finding of antenna for base station ultra-short baseline GNSS double antenna
Method specifically includes the following contents:
1) double-difference equation model is constructed
Calculate the observation requirement in carrier course in real time in single epoch, the present invention uses double difference method, that is, utilizes carrier phase
Observation data do second difference between different satellites and different receivers.When the antenna of two GNSS receivers is not far from one another
The signal of (within 1m), same satellite are almost the same for the propagation path of receiving end, the propagated error that signal is subject to
Also approximately equal, most of error concealment in measurement process can be made by way of making difference.It is built using the method integrally resolved
Vertical double-difference equation, can accurately calculate relative distance between two antennas, and then can solve accurate direction finding value.
Initially set up the basic observational equation of carrier phase.As can be seen from FIG. 2, it is received under normal conditions using double antenna GNSS
Orientating function can be realized in unit, and usually in identical epoch time t moment, the L1 frequency point between receiver r and b and satellite j is pseudo-
Away from can be written as with carrier phase observational equation:
In formula, λ is carrier wavelength, and c is carrier wave spread speed,It is receiver r, pseudorange of the b for satellite j
Observation,It is receiver r, b is for the carrier observations of satellite j, and N is integer ambiguity, and ρ is receiver and satellite
Between geometric distance, dt is satellite clock correction, dr,ion, db,ionFor ionosphere delay, dr,trop, db,tropFor tropospheric delay, ε is
Phase error caused by receiver noise and multipath.
Due to two antennas be separated by it is not far, in observation process, ionosphere suffered by the signal of the satellite j received and right
Fluid layer influences almost phase, and satellite clock correction is identical, and can also be approximately considered by the error that multipath effect generates be it is identical,
Pseudorange is obtained after making difference and carrier phase observes single eikonal equation.
It can be seen that error almost all relevant to satellite is eliminated in single eikonal equation after making difference, remaining error parameter
Middle major part is related with receiver, has also comprised multipath and receiver noise error that part is not eliminated, withIt indicates.
Two receivers observation satellite k simultaneously is enabled again, obtains two receivers to single eikonal equation of satellite k:
Establish double-differential carrier phase variance.It is poor that formula (3) and formula (4) are made, because in two equations between receiver
Clock deviation Δ TrbIt is identical, it is considered that substantially eliminating after making difference；When using the receiver of same type, the noise of receiver
It is also assumed that it is approximately uniform, so very small numerical value can be reduced to when making difference second, thus obtain pseudorange
With the double-difference equation of carrier phase measurement relative positioning:
It ensure that the epoch time of two receiver observations is identical in single poor building process between standing in this method, but by
It cannot be guaranteed that two receiver times are fully synchronized in the crystal oscillator that the receiver of low cost uses, therefore in order to more preferably guarantee border of standing
Single poor synchronism has been selected a kind of standard in this method to determine one group of measured value, that is, has been selected and the moving station measuring value time
Identical or last group of measured value more ahead of time.Epoch time difference between movement station and base station is referred to as " time difference ".
With the increase of time difference, due to the ionospheric delay of satellite clock drift and variation, precision dying down gradually.Use broadcast
Single aberration measurements between satellite clock parameters corrigendum station compensate satellite clock drift with this.Maximum " time difference " is in present treatment
Threshold value 30 is set in the process.Single eikonal equation between constructing star, each epoch choose the maximum satellite of elevation of satellite as reference
Satellite.Satellite between different navigation system cannot construct single eikonal equation between star as GPS and GLONASS.It is primarily due to pair
In the signal of different navigation system, even if they, which possess identical carrier frequency receiver, generally also has different group delays.
Using the double-difference equation of pseudorange and carrier phase measurement relative positioning, public mistake relevant to satellite and receiver is eliminated
Difference greatly improves last positioning accuracy significantly in this way to ensure that last direction finding value reaches the precision within 3 °
2) it is resolved using EKF filter
In this method use EKF filter (Extended Kalman Filter, EKF) processing it is to be estimated to
Amount, can make full use of the status information of the estimation of previous moment to correct current status information in this way, to guarantee each to go through
Member can export accurate direction finding value.EKF filter principle is generally as follows: the state vector X of unknown model parameters with
And its covariance matrix P can use tkThe observation vector y at momentkIt is calculated:
Pk=(I-KkHk)Pk,k-1 (7)
I is unit battle array；Pk,k-1Respectively one-step prediction value and its variance-covariance battle array；KkFor gain matrix point
It Wei not Filtering Estimation and its variance-covariance battle array.In order to reduce filtering algorithm to the sensibility for calculating rounding error, guarantee Pk's
Symmetric positive definite prevents filtering divergence to improve the numerical stability of filtering, it is practical calculate in need for formula (7) to be rewritten as
Lower form
Assuming that movement station and receiving station all use GNSS single frequency receiving, estimative unknown state vector X is defined as follows:
Wherein,It broadcasts TV programs by satellite for L1 frequency point border singly poor fuzziness of standing (unit is week).Use list
Poor fuzziness can avoid the problem of reference star is frequently replaced in double difference fuzziness without the use of double difference fuzziness well.
Observation vector y is defined with double difference carrier phase and pseudo-range measurements
Wherein,
Measurement model vector h (x), partial derivative matrix (observing matrix factor arrays) H (x) and measurement error covariance matrix Rk
It respectively indicates as follows:
Wherein,For single poor side
Journey,
For L1Frequency point carrier wave measurement error standard deviation (m),For L1The standard deviation of frequency point pseudo-range measurements error
Poor (m).
In application EKF, need to state-transition matrix Φk,k-1, process noise Qk-1It is defined, considers in this method
It for ultra-short baseline and is static state, Φk,k-1, Qk-1Therefore it is defined as following formula:
EKF is used by above-mentioned matrix, the receiver location of movement station to be estimated can be found out, and need exist for explanation
It is the accurate coordinate for needing the accurate location of base station that can just find out movement station in traditional relative positioning technology, and it is herein
Base station only needs to input the coordinate value that common One-Point Location calculates, and the error of coordinate of base station is then transmitted to movement station and is sat
Mark, station coordinates mobile in this way and benchmark station coordinates, which make the difference, can eliminate the error of coordinate of base station in turn not when constituting basic lineal vector
It will affect direction finding value.
3) Carrier Phase Ambiguity Resolution
This method uses under continuous fuzziness fixed model, between carrier phase station single poor fuzziness can with it is following not
It is handled with mode: under updating by the time of EKF, the value of single poor fuzziness is inherited in next epoch.By LLI, (losing lock is visited
Survey device) cycle slip is detected, if having found cycle slip in measurement data, corresponding single poor ambiguity state resets to initial value,
The sufficiently large value (10 of process noise arranged in matrix4㎡)。
State vector to be asked is calculated by EKF, single poor float ambiguities can be converted to double difference integer ambiguity between standing
To improve convergence time and convergence precision.Firstly, their covariance matrix of estimated state vector sum to be asked can be by following public affairs
Formula is converted to double difference form:
Wherein,
G is single poor transition matrix for turning double difference, can eliminate reception by the way that single poor fuzziness is converted to double difference fuzziness
Itself existing deviation between machine, it is assumed that integer ambiguity isCorresponding covariance matrix puppet QN, true closest to fuzziness
Value isThus the least square problem (ILS) of a fuzziness complete cycle solution is constructed
In order to solve the least square problem of fuzziness complete cycle solution, this method uses general MLAMBDA method, in order to
The reliability of solution is examined, significant threshold ratio is used and adjudicates, significant threshold ratio decision method is as follows:
Wherein, when Ratio is greater than the threshold value of predetermined set, this paper threshold settings are 3, if then judging corresponding double
Poor integer ambiguity combination is unique correct.In order to guarantee fixed correctness, ambiguity information is stored, if continuous 10 are gone through
First continuous fixed, then fuzziness fixed inspection passes through, the straight higher fixed solution of output accuracyIt is needed under if examining failure
Formula calculates float-solution
After double difference fuzziness is fixed successfully, it is then converted into single poor fuzziness, the status information of each matrix of EKF is updated, mentions
The high valuation for resolving state vector to be asked to epoch later.
We can accurately calculate the basic lineal vector between two antennas through the above steps, may then pass through baseline
Vector calculates course angle.In user's local coordinate, the antenna coordinate of two receivers constitutes basic lineal vector, when direction-finding system institute
Carrier be rigid body when, which can reflect the real-time two-dimensional attitude of carrier.
The antenna 1 and 2 of two receivers r and b are installed in carrier y direction, antenna 1 and 2 is in user's local coordinate
Coordinate be respectively (x1,y1,z1) and (x2,y2,z3), basic lineal vector is accurately determined by GNSS carrier wave relative positioningVectorAmount along change in coordinate axis direction is respectively as follows:
Assuming that yaw angle ψ isThe angle of projection and x-axis in xoy plane, pitching angle theta are vectorIt is flat with xoy
The angle in face, specific formula for calculation are as follows:
The value range of yaw angle ψ is 0~360 ° in formula, and the value range of pitching angle theta is -90~90 °.Because local sit
Mark system is northeast day coordinate system, and x-axis is directed toward the positive east of carrier position, thus yaw angle indicate carrier movement direction with just
The angle in east, and the definition of course angle is the angle in carrier movement direction and the positive north, when calculating the course angle in carrier,
It needs for the benchmark of yaw angle to be rotated by 90 ° counterclockwise, the course angle of carrier.Therefore, the accurate base obtained by the above method
The course of carrier can be calculated in line vector in real time.
The above examples are only used to illustrate the technical scheme of the present invention and are not limiting, any those skilled in the art can think
Variation should all fall into protection scope of the present invention.
Claims (3)
1. the method for a kind of pair of real-time direction finding of antenna for base station ultra-short baseline GNSS double antenna, which comprises the steps of:
1) data are imported and is pre-processed
The t moment epoch for reading receiver r and b in real time observes data and navigation ephemeris, co-ordinates of satellite is calculated, by code and load
The non-poor residual error of wave phase tests to remove and can not participate in resolving and second-rate satellite data；
2) double-difference equation model is constructed
Initially set up the basic observational equation of carrier phase: in the identical t moment of two receiver epoch times, receiver r and b with defend
L1 frequency point pseudorange and carrier phase observational equation between star j are as follows:
In formula, λ is carrier wavelength, and c is carrier wave spread speed,It is receiver r, pseudorange observation of the b for satellite j
Value,Receiver r, for b for the carrier observations of satellite j, N is integer ambiguity, ρ be receiver with it is intersatellite
Geometric distance, dt are satellite clock correction, dr,ion, db,ionFor ionosphere delay, dr,trop, db,tropFor tropospheric delay, ε is to receive
Phase error caused by machine noise and multipath；
Pseudorange is obtained after making difference and carrier phase observes single eikonal equation:
Two receivers observation satellite k simultaneously is enabled again, obtains two receivers to single eikonal equation of satellite k:
Establish double difference variance: it is poor that formula (3) and formula (4) are made, and obtains the double difference side of pseudorange and carrier phase measurement relative positioning
Journey:
After above-mentioned double-difference equation is established, test to the residual error of the double-difference equation of pseudorange and carrier phase, if upcheck into
Row resolves in next step；If the test fails, it is believed that there are rough errors is unavailable for Current observation data, directly abandons, return step 1)
Read in the data of next epoch and calculating；
3) EKF filter resolves
Vector to be estimated is handled using EKF filter, and updates Kalman correlation matrix parameter；
4) Carrier Phase Ambiguity Resolution
Using continuous fuzziness fixed model, single poor fuzziness is handled with following without mode between carrier phase station: logical
It crosses under the time update of EKF, the value of single poor fuzziness is inherited in next epoch；Cycle slip is detected by losing lock detector LLI, such as
Fruit has found cycle slip in measurement data, and corresponding single poor ambiguity state resets to initial value；
Calculate state vector to be asked by above-mentioned EKF, wherein between state vector station single poor float ambiguities can be converted to it is double
Poor integer ambiguity is to improve convergence time and convergence precision；Firstly, their covariance square of estimated state vector sum to be asked
Battle array can be converted to double difference form by following formula:
Wherein,
G is single poor transition matrix for turning double difference, by by single poor fuzziness be converted to double difference fuzziness can with cancellation receiver it
Between existing deviation itself, while also can avoid reference star replacement occur frequently EKF filtering being caused to be difficult to the problem of restraining,
Assuming that integer ambiguity isCorresponding covariance matrix puppet QN, it is closest to fuzziness true valueThus one is constructed
The least square problem of fuzziness complete cycle solution:
In order to solve the least square problem of fuzziness complete cycle solution, using general MLAMBDA method, in order to examine the reliable of solution
Property, it is adjudicated using significant threshold ratio；After double difference fuzziness is fixed successfully, it is then converted into single poor fuzziness, updates each square of EKF
The status information of battle array, to improve the estimation accuracy for resolving state vector to be asked to epoch later.
2. the method for a kind of pair of real-time direction finding of antenna for base station ultra-short baseline GNSS double antenna as described in claim 1, feature
It is, the method for EKF filter described in step 3) is as follows:
The state vector of unknown model parametersAnd its covariance matrix P tkThe observation vector y at momentk, pass through calculating
It obtains:
Pk=(I-KkHk)Pk,k-1 (7)
Wherein I is unit battle array；Pk,k-1Respectively one-step prediction value and its variance-covariance battle array；KkFor gain matrix；For
Filtering algorithm is reduced to the sensibility for calculating rounding error, guarantees PkSymmetric positive definite, with improve filtering numerical stability
Property, filtering divergence is prevented, needs formula (7) being rewritten as following form in practical calculating
Assuming that movement station and receiving station all use GNSS single frequency receiving, estimative unknown state vector X is defined as follows:
Wherein,It broadcasts TV programs by satellite for L1 frequency point border singly poor fuzziness of standing, unit is week；Use single differential mode
Paste degree can avoid the problem of reference star is frequently replaced in double difference fuzziness without the use of double difference fuzziness well；
Observation vector y is defined with double difference carrier phase and pseudo-range measurements
Wherein,
Measurement model vector h (x), partial derivative matrix H (x) and measurement error covariance matrix RkIt respectively indicates as follows:
Wherein, For single eikonal equation,
For L1Frequency point carrier wave measurement error standard deviation (m),For L1The standard deviation of frequency point pseudo-range measurements error
(m)；
In application EKF, need to state-transition matrix Φk,k-1, process noise Qk-1Be defined, be thought of as ultra-short baseline and
For static state, Φk,k-1, Qk-1Therefore it is defined as following formula:
EKF, single differential mode between the carrier phase station in the state vector of this epoch movement station to be estimated are used by above-mentioned matrix
Paste degree can be found out, the search for double difference fuzziness.
3. the method for a kind of pair of real-time direction finding of antenna for base station ultra-short baseline GNSS double antenna as described in claim 1, feature
It is, it is as follows to adjudicate its method for significant threshold ratio described in step 4):
Wherein, when Ratio is greater than the threshold value of predetermined set, this paper threshold settings are 3, then judge corresponding double difference complete cycle
Fuzziness combination is unique correct；In order to guarantee fixed correctness, ambiguity information is stored, if continuous 10 epoch are continuous
Fixed, then fuzziness fixed inspection passes through, the higher fixed solution of output accuracyIt needs to be calculated by following formula if examining failure
Float-solution
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