CN107728180A - A kind of GNSS precision positioning methods based on multidimensional particle filter estimation of deviation - Google Patents
A kind of GNSS precision positioning methods based on multidimensional particle filter estimation of deviation Download PDFInfo
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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
- G01S19/42—Determining position
- G01S19/43—Determining position using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
- G01S19/44—Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
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Abstract
The invention discloses a kind of GNSS precision positioning methods based on multidimensional particle filter estimation of deviation, comprise the following steps：Step 1：Data prediction, import satellite ephemeris, current epoch Pseudo-range Observations and current epoch carrier phase observable；Step 2：Set up GNSS double difference observational equations, obtained after linearisation single epoch normal equation or with epoch before add up normal equation；Step 3：Deviation is corresponded to in the particle correction normal equation with multiple particle values, resolves normal equation；Particle filter power is updated, according to cum rights particle, calculates the numerical value and particle root mean square of deviation fractional part between phase system；Step 4：Repeat step 13, after convergence to be filtered, estimation of deviation value and variance corresponding to output；Step 5：According to the estimate of error parameter, deviation is corrected in observation or normal equation, fixed integer ambiguity, realizes precision positioning.This method can realize particle filter to estimating while multiple GNSS straggling parameters, can realize Precise Relative Positioning using less observation satellite.
Description
Technical field
The present invention relates to global position system and positioning measurement technical field, and in particular to one kind is based on multidimensional particle filter
The GNSS precision positioning methods of estimation of deviation.
Background technology
Applications of the GPS GNSS in precision positioning field is more and more extensive；GNSS observations include convection current
Deviation etc. between layer and ionosphere delay error, GLONASS FDMA signals inter-frequency deviation, multisystem GNSS alignment systems.
The Data processing of GNSS precision positionings, these errors in carrier phase observable need to eliminate or estimated.In GNSS phase observations
More than one error unknown parameter is may be simultaneously present in value, such as in the GNS multimodes positioning that GLONSS systems participate in,
GLONASS inter-frequency deviation and can exist simultaneously with deviation between the system of other constellations.When system in combination frequency is more than two groups,
Have straggling parameter between two or more systems；Traditional calculation method is to use the method based on least square method, and this
Certain correlation, such as deviation and the complete phase of fuzziness parameter between phase system be present in a little parameters and GNSS fuzziness parameter
Close.The situation of equation rank defect or approximate rank defect now occurs in resolving, it is necessary to more observation is to strengthen resolving equation,
Or use priori value with eliminate/weaken rank defect.And positioning time can be extended by increasing observation data；Then using the method for priori value
Seeking priori value has a case that very high reliability, it is necessary to measure and the change of more intractable error amount in advance.
The content of the invention
The present invention provide it is a kind of with particle filter simultaneously estimate the how individual error terms of GNSS based on multidimensional particle filter deviation
The GNSS precision positioning methods of estimation.
A kind of GNSS precision positioning methods based on multidimensional particle filter estimation of deviation, comprise the following steps：
Step 1：Satellite navigation data is pre-processed, imports satellite ephemeris, current epoch Pseudo-range Observations and current
Epoch carrier phase observable；
Step 2：Establish the observation equation comprising multiple error parameters simultaneously to linearize, obtain single epoch normal equation or therewith
Preceding epoch adds up normal equation；
Step 3：Deviation is corresponded to in the particle correction normal equation with multiple particle values, resolves normal equation；Pass through
LAMBDA methods carry out fuzziness and fix and export RATIO values, the function on RATIO values are established, with functional value more new particle
Power；According to cum rights particle, the numerical value and particle root mean square of deviation fractional part between phase system are calculated；
Step 4：Repeat step 1-3, after convergence to be filtered, export unknown parameter vector estimate, including two and with
The valuation of upper error parameter；
Step 5：According to the estimate vector of error parameter, deviation, fixed complete cycle are corrected in observation or normal equation
Fuzziness, realize precision positioning.
Further, the detailed process of the step 3 is as follows：
(1) primary collection is produced in M dimension up-samplingDuring for k-th
Carve, particle collection is generated by last moment filter result；Wherein, x is particle numerical value, and w is corresponding weights, and N is particle number, i=
1,2 ... N is particle sequence number；Below willIt is denoted as vector xi 0, corresponding xi kAcute pyogenic infection of finger tip
(2) as error parameter contains straggling parameter between GNSS system, the root mean square of dimensionality of particle corresponding to calculating；For every
One dimension, judges whether root mean square is more than given threshold value stdgroup, clustering analysis then is carried out to particle if greater than threshold value, led to
Cross clustering analysis and integrate sub-clustering particle, other class deviations then skip the step；
(3) for each particle, using the multidimensional value of particle, the corresponding deviation in GNSS observation normal equations is corrected；
Normal equation is resolved, obtains the float-solution of unknown quantity and corresponding covariance matrix；Fuzziness is carried out by LAMBDA methods to fix, and it is defeated
Go out the RATIO values of corresponding particle；
(4) likelihood function on RATIO values is established, carries out particle filter power renewal with functional value, and standardize particle
Weights, as new particle weights；
(5) valuation of the desired value of particle as unknown bias vector is calculated
Calculate the variance of particle
(6) judge whether particle filter restrains, judge whether root mean square is less than given threshold stdthdIf then export phase
The position valuation of deviation and the variance of particle are as valuation result；
(7) if meeting resampling condition, according to the weights resampling of renewal；
(8) estimated subsequent time particle, to the real-time discretization of particle of resampling：
Wherein：For discretization when added random noise；Push away
The particle value of next epoch is calculated, is transferred to step 1.
Further, it is as follows by clustering analysis integration sub-clustering particle process in the step (2)：
S1：Two minimum and maximum particles of particle value are selected to calculate other particles to initiating particle as initiating particle
Distance, particle is divided into two groups according to apart from size；
S2：Calculate the center of gravity g of two particle groups1, g2, it is defined as follows：
Wherein, h=1,2 be group number, and Nh is the particle number of each group；Particle group centroidal distance is：
D=| g1-g2|；
S3：Difference between judging distance d and carrier wavelength lambda is less than eps, if | d- λ | ＜ eps are set up, will wherein one
Group particle is transferred to another group by increasing or subtracting a wavelength on dimension m, realizes that two particle groups are closed on dimension m
And m=1,2 ..., M；Wherein eps is usually a minimum value；
S4：If unknown parameter vectorEither element be deviation between phase system, then to the element
Corresponding dimensionality of particle value repeat step S1-S3.
Further, particle filter power renewal process is as follows in the step (4)：
S11：The functional relation established between likelihood function and RATIO：
In formula：F (RATIO) is the function on RATIO values；
S12：According to RATIO values RATIO corresponding to the functional relation established in step S11 and i-th of particleiCalculate corresponding
The likelihood function value of particle
S13：Likelihood function value is multiplied with the weights of corresponding particle, the particle power after being updated
S14：Standardize particle weights, will each particle power with all particles weigh sum ratio, as new grain
Sub- weights
Further, resampling process is as follows in the step (7)：
S21：Added up particle weights according to sequence number, obtain the cumulative distribution function value collection of each particle：
S22：Population N needed for calculatingk+1：
In formula：N is particle number corresponding to unit variance,For smallest particles number；
S23：Generate uniform or random cumulative distribution function value：
S24：Cumulative distribution function value corresponding to particle sequence number, and uniform or random cumulative distribution function value are entered successively
Row contrast；For m=1, i=1, such asThen delete i-th of particle, i=i+1, otherwise replicate i-th of particle to new
Particle collection, m=m+1；Until m=Nk+1, obtaining new particle collection is
S25：New particle collection is set to be weighed to wait：
Obtain new particle collection and weights.
Further, single epoch normal equation or as follows with epoch summation establishing equation process before in the step 2：
GNSS system pseudorange non-difference observation equation is：
GNSS system phase non-difference observation equation is：
In formula：I is satellite sequence number, and a is observation station sequence number, and P is the non-poor Pseudo-range Observations of GNSS satellite, and Φ defends for GNSS
The non-poor carrier phase observable of star, c are the light velocity, δ taFor GNSS observation stations receiver clock-offsets, ρ is observation station between GNSS satellite
Distance, δ tiFor GNSS satellite clock correction, di aFor receiver end pseudorange hardware delay, diFor GNSS satellite end pseudorange hardware delay,
I is ionosphere delay error, and T is tropospheric delay error, and ε is the observation noise of Pseudo-range Observations, μi aFor receiver end phase
Hardware delay, μiPostpone for GNSS satellite end phase hardware, λiFor the carrier wavelength of i-th satellite, Ni aFor integer ambiguity, ζ
For the observation noise of carrier phase observable；
Double difference combination is carried out for GNSS system pseudorange un-differenced observation and GNSS system phase un-differenced observation, elimination is defended
Star clock correction, receiver clock-offsets, correct ionosphere delay error and tropospheric delay error；Double difference pseudorange in GNSS system is obtained to see
Survey equation：
Double difference carrier phase observational equation in GNSS system：
In formula：s1For any satellite system, swFor s1Outside another satellite system, w=2,3 ... W, wherein W for combination
Landsat band number, b be double difference observation another survey station survey station number, j be composition double difference observation another GNSS satellite
Satellite number, d deviations between pseudorange system, μ deviations between phase system, (kj-ki)ΔγabTo there is GLONASS systems
Inter-frequency deviation during FDMA observations, k are satellite number, and Δ γ is inter-frequency deviation rate；
Can after the linearisation of double difference carrier phase observational equation in double difference pseudorange observation equation and GNSS system in GNSS system
It is converted into：
V=Ax+Db+Cz+l
In formula：X is the vector that other unknown quantitys include survey station coordinate components composition in addition to fuzziness and inter-frequency deviation, and b is
Single poor fuzziness unknown number vector between receiver, z are the unknown vector comprising multiple deviations, and A, D and C are respectively that unknown quantity is corresponding
Coefficient matrix, l are constant term vector, and P is weight matrix, and v is observation residual error vector；
According to lienarized equation cocoa single epoch normal equation or with epoch before add up normal equation：
The beneficial effects of the invention are as follows：
(1) present invention can be achieved to estimate while straggling parameter how individual to GNSS using particle filter, including GLONSS phases
Deviation, tropospheric delay etc., realize GNSS precision positionings between position inter-frequency deviation, multimode GNSS phase systems；
(2) for the present invention in GNSS multimode integrated positionings, this method can utilize the fuzziness complete cycle between GNSS system
Characteristic, the solution of deviation between phase system is realized when satellite number is less, reach the purpose of precision positioning.
Brief description of the drawings
Fig. 1 is the schematic flow sheet of the present invention.
Fig. 2 is RAITO distribution maps deviation is estimated between two phase systems of GNSS in the embodiment of the present invention simultaneously when.
Fig. 3 is the convergence process of full constellation in the embodiment of the present invention, wherein figure a is followed successively by first epoch to the to d is schemed
The particle distribution map and error estimate position, background of four epoch is each epoch RATIO distribution maps, and grainy dots are each particle position
Put, five-pointed star is estimation of deviation value position.
Fig. 4 is No. PRN of six satellites used in the embodiment of the present invention.
Fig. 5 is estimated result deviation is estimated between two, the satellite phase systems of GNSS six in the embodiment of the present invention simultaneously when
Sequence number.
Fig. 6 is Baselines Comparative result after correction for deflection between two phase systems in the embodiment of the present invention.
Embodiment
The present invention will be further described with specific embodiment below in conjunction with the accompanying drawings.
As shown in figure 1, a kind of GNSS precision positioning methods based on multidimensional particle filter estimation of deviation, including following step
Suddenly：
Step 1：Satellite navigation data is pre-processed, imports satellite ephemeris, current epoch Pseudo-range Observations and current
Epoch carrier phase observable；
It is generally pretreated to be handled including Data Format Transform, Detection of Gross Errors and rejecting, cycle-slip detection and repair etc..
Step 2：Establish the observation equation comprising multiple error parameters simultaneously to linearize, obtain single epoch normal equation or therewith
Preceding epoch adds up normal equation.
GNSS system pseudorange non-difference observation equation is：
GNSS system phase non-difference observation equation is：
Wherein：I is satellite sequence number, and a is observation station sequence number, and P is the non-poor Pseudo-range Observations of GNSS satellite, and Φ defends for GNSS
The non-poor carrier phase observable of star, c are the light velocity, δ taFor GNSS observation stations receiver clock-offsets, ρ is observation station between GNSS satellite
Distance, δ tiFor GNSS satellite clock correction, di aFor receiver end pseudorange hardware delay, diFor GNSS satellite end pseudorange hardware delay,
I is ionosphere delay error, and T is tropospheric delay error, and ε is the observation noise of Pseudo-range Observations, μi aFor receiver end phase
Hardware delay, μiPostpone for GNSS satellite end phase hardware, λiFor the carrier wavelength of i-th satellite, Ni aFor integer ambiguity, ζ
For the observation noise of carrier phase observable.
Double difference combination is carried out for GNSS system pseudorange and GNSS system phase un-differenced observation, is obtained double in GNSS system
Dual carrier difference phase observations equation in poor pseudorange observation equation and GNSS system：
In formula：s1For any satellite system, swFor another satellite system, w=1,2,3 ... W, wherein W are the satellite of combination
Frequency band number, b are the survey station number of another survey station of double difference observation, and j is defending for another GNSS satellite of composition double difference observation
Asterisk, d deviations between pseudorange system, μ between phase system deviation, it is necessary to accurately estimate, (kj-ki)ΔγabTo have
Inter-frequency deviation during GLONASS system FDMA observations, k are satellite number, and Δ γ is inter-frequency deviation rate, in no GLONASS systems
This is zero during FDMA observations of uniting, may when the frequency of combination is more, it is necessary to estimate deviation between multiple phase systems simultaneously
GLONASS inter-frequency deviation, also need to estimate troposphere, ionosphere delay deviation etc. when baseline is longer.
Can after the linearisation of dual carrier difference phase observations equation in double difference pseudorange observation equation and GNSS system in GNSS system
It is converted into：
V=Ax+Db+Cz+l
In formula：X is the vector that other unknown quantitys include survey station coordinate components composition in addition to fuzziness and inter-frequency deviation, and b is
Single poor fuzziness unknown number vector between receiver, z is deviation unknown quantity vector, and A, D and C are respectively unknown quantity coefficient of correspondence square
Battle array, l is constant term vector, and P is weight matrix, and v is observation residual error vector；
According to lienarized equation can obtain single epoch normal equation or with epoch before add up normal equation：
Step 3：Deviation is corresponded to in the particle correction normal equation with multiple particle values, resolves normal equation；Pass through
LAMBDA methods carry out fuzziness and fix and export RATIO values, the function on RATIO values are established, with functional value more new particle
Power；According to cum rights particle, the numerical value and particle root mean square of deviation fractional part between phase system are calculated；If particle root mean square is small
In a certain threshold value, filtering is exited, detailed process is as follows：
(1) primary collection is produced in M dimension up-samplingDuring for k-th
Carve, particle collection is generated by last moment filter result；Wherein, x is particle numerical value, and w is corresponding weights, and N is particle number, i=
1,2 ... N is particle sequence number；Below willIt is denoted as vector xi 0, corresponding xi kAcute pyogenic infection of finger tip
(2) as error parameter contains straggling parameter between GNSS system, the root mean square of dimensionality of particle corresponding to calculating；For every
One dimension, all carries out following computing：Judge whether corresponding root mean square is more than given threshold value stdgroup, it is then right if greater than threshold value
Particle carries out clustering analysis, and particle is divided into two groups；If the distance between particle center of gravity is similar to a carrier wavelength,
Merge two populations, the step is skipped for other deviations.
It is as follows that sub-clustering particle process is integrated by clustering analysis：
S1：Two minimum and maximum particles of particle value are selected to calculate other particles to initiating particle as initiating particle
Distance, particle is divided into two groups according to apart from size；
S2：Calculate the center of gravity g of two particle groups1, g2, it is defined as follows：
Wherein, h=1,2 be group number, and Nh is the particle number of each group；Particle group centroidal distance is：
D=| g1-g2|；
S3：Difference between judging distance d and carrier wavelength lambda is less than a smaller value eps, if | d- λ | ＜ eps are set up,
One of which particle is then transferred to another group by increasing or subtracting a wavelength on dimension m, realizes that two particle groups exist
Merge on dimension m, m=1,2 ..., M；Wherein eps is one relative to the less value of carrier wavelength；
S4：If unknown parameter vectorEither element be deviation between phase system, then to the element
Corresponding dimensionality of particle value repeat step S1-S3.
(3) for each particle, using the multidimensional value of particle, the corresponding deviation in GNSS observation normal equations is corrected；
Normal equation is resolved, obtains the float-solution of unknown quantity and corresponding covariance matrix；Fuzziness is carried out by LAMBDA methods to fix, and it is defeated
Go out the RATIO values of corresponding particle；
(4) likelihood function on RATIO values is established, carries out particle filter power renewal with functional value, and standardize particle
Weights, as new particle weights；
Particle filter power renewal process is as follows：
S11：The functional relation established between likelihood function and RATIO：
In formula：F (RATIO) is the function on RATIO values；
S12：According to RATIO values RATIO corresponding to the functional relation established in step S11 and i-th of particleiCalculate corresponding
The likelihood function value of particle
S13：Likelihood function value is multiplied with the weights of corresponding particle, the particle power after being updated
S14：Standardize particle weights, will each particle power with all particles weigh sum ratio, as new grain
Sub- weights
(5) valuation of the desired value of particle as unknown bias vector is calculated
Calculate the variance of particle
(6) judge whether particle filter restrains, judge whether root mean square is less than given threshold stdthdIf then export phase
The position valuation of deviation and the variance of particle are as valuation result；
(7) if meeting resampling condition, according to the weights resampling of renewal；
Resampling process is as follows：
S21：Added up particle weights according to sequence number, obtain the cumulative distribution function value collection of each particle：
S22：Population N needed for calculatingk+1：
In formula：N is particle number corresponding to unit variance,For smallest particles number；
S23：Generate uniform or random cumulative distribution function value：
S24：Cumulative distribution function value corresponding to particle sequence number, and uniform or random cumulative distribution function value are entered successively
Row contrast；For m=1, i=1, such asThen delete i-th of particle, i=i+1, otherwise replicate i-th of particle to new
Particle collection, m=m+1；Until m=Nk+1, obtaining new particle collection is
S25：New particle collection is set to be weighed to wait：
New particle collection and weights is obtained, the new particle collection and its weights of generation are output to next step.
(8) estimated subsequent time particle, to the real-time discretization of particle of resampling：
Wherein：For discretization when added random noise；Push away
The particle value of next epoch is calculated, is transferred to step 1.
Step 4：Repeat step 1-3, after convergence to be filtered, export unknown parameter vector estimate, including two and with
The valuation of upper error parameter；
Step 5：According to the estimate of error parameter, deviation, fixed integral circumference ambiguity are corrected in observation or normal equation
Degree, realizes precision positioning.
Using deviation between two GNSS phase systems of method while estimation of the present invention, a short baseline is handled,
The observation of baseline includes GPS system L5, Galieo system E5a and QZSS system L5；Need to estimate GPS L5- simultaneously
Straggling parameter between Galileo E5a and GPS L5-QZSS two phase systems of L5；Deviation is simultaneously between two phase systems of GNSS
The RAITO distribution maps of estimation are as shown in Figure 2, it can be seen that RATIO values can map out the value of two parameters simultaneously；With whole
Observation satellite estimates the convergence process of deviation between two phase systems as shown in figure 3, particle can successfully be restrained using this method,
And two parameter values are estimated, the half cycle problem of deviation is successfully solved (shown in Fig. 3 c) between the phase system in one of dimension
Certainly (shown in Fig. 3 d)；Simulate six situations of the observation satellite from three constellations, No. PRN such as figure of six satellites used
Shown in 4；For simulating the satellite received, the data message used is given；Bias contribution is such as between the two systems estimated
Shown in Fig. 5, it is seen that using respectively from a small amount of of three GNSS constellations, this method remains able to realize deviation between two systems
Correct estimation；Thus the baseline result of calculation obtained eventually using positioning result after this law inventive method as shown in fig. 6, had clearly
Improve, fuzziness fixed proportion also brings up to 99.7% by 19.3%.
The inventive method estimates while can realizing straggling parameter how individual to GNSS using particle filter, including
GLONASS phase inter-frequency deviations, deviation, tropospheric delay etc. between multimode GNSS phase systems, realize GNSS precision positionings；
In GNSS multimode integrated positionings, this method can be using the fuzziness complete cycle characteristic between GNSS system, when satellite number is less
The solution of deviation between phase system is realized, reaches the purpose of precision positioning.
Wen Zhong：LAMBDA is Least-squares AMBiguity Decorrelation Adjustment abbreviation,
Refer to least square fuzziness decorrelation adjustment；RATIO singly refers to reliability inspection when integer ambiguity is fixed in GNSS fields
Test index；PRN is Pseudo Random Noise abbreviation, refers to pseudo noise.
Claims (6)
1. a kind of GNSS precision positioning methods based on multidimensional particle filter estimation of deviation, it is characterised in that comprise the following steps：
Step 1：Satellite navigation data is pre-processed, imports satellite ephemeris, current epoch Pseudo-range Observations and current epoch
Carrier phase observable；
Step 2：Establish the observation equation comprising multiple error parameters and linearize, obtain single epoch normal equation or with going through before
The cumulative normal equation of member；
Step 3：Deviation is corresponded to in the particle correction normal equation with multiple particle values, resolves normal equation；By LAMBDA side
Method carries out fuzziness and fixes and export RATIO values, establishes the function on RATIO values, is weighed with functional value more new particle；According to band
Particle is weighed, calculates the numerical value and particle root mean square of deviation fractional part between phase system；
Step 4：Repeat step 1-3, after convergence to be filtered, export the estimate of unknown parameter vector, including two and above mistake
The valuation of poor parameter；
Step 5：According to the estimate of error parameter, deviation is corrected in observation or normal equation, fixed integer ambiguity is real
Existing precision positioning.
2. a kind of GNSS precision positioning methods based on multidimensional particle filter estimation of deviation according to claim 1, it is special
Sign is that the detailed process of the step 3 is as follows：
(1) primary collection is produced in M dimension up-samplingFor k-th of moment, grain
Subset is generated by last moment filter result；Wherein, x is particle numerical value, and w is corresponding weights, and N is particle number, i=1,2 ... N
For particle sequence number；Below willIt is denoted as vectorAccordinglyAcute pyogenic infection of finger tip(2)
As error parameter contains straggling parameter between GNSS system, the root mean square of dimensionality of particle corresponding to calculating；For each dimension, sentence
Whether disconnected root mean square is more than given threshold value stdgroup, clustering analysis then is carried out to particle if greater than threshold value, passes through clustering analysis
Sub-clustering particle is integrated, other class deviations then skip the step；
(3) for each particle, using the multidimensional value of particle, the corresponding deviation in GNSS observation normal equations is corrected；Resolve
Normal equation, obtain the float-solution of unknown quantity and corresponding covariance matrix；Fuzziness is carried out by LAMBDA methods to fix, and output pair
Answer the RATIO values of particle；
(4) likelihood function on RATIO values is established, particle filter power renewal is carried out with functional value, and standardizes particle weights,
As new particle weights；
(5) valuation of the desired value of particle as unknown bias vector is calculated
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3. a kind of GNSS precision positioning methods based on multidimensional particle filter estimation of deviation according to claim 2, it is special
Sign is, as follows by clustering analysis integration sub-clustering particle process in the step (2)：
S1：Minimum and maximum two particles of particle value are selected as initiating particle, calculate other particles to initiating particle away from
From particle is divided into two groups according to apart from size；
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<msub>
<mi>N</mi>
<mi>h</mi>
</msub>
</msubsup>
<msubsup>
<mi>x</mi>
<mi>k</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>m</mi>
</mrow>
</msubsup>
<msubsup>
<mi>w</mi>
<mi>k</mi>
<mi>i</mi>
</msubsup>
</mrow>
<mrow>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<msub>
<mi>N</mi>
<mi>h</mi>
</msub>
</msubsup>
<msubsup>
<mi>w</mi>
<mi>k</mi>
<mi>i</mi>
</msubsup>
</mrow>
</mfrac>
<mo>;</mo>
</mrow>
Wherein, h=1,2 be group number, and Nh is the particle number of each group；Particle group centroidal distance is：
D=| g1-g2|；
S3：Difference e ps between judging distance d and carrier wavelength lambda, if | d- λ | ＜ eps are set up, and one of which particle is led to
Crossing on dimension m, which increases or subtract a wavelength, is transferred to another group, realizes that two particle groups merge on dimension m, m=1,
2 ..., M；
S4：If unknown parameter vectorEither element be deviation between phase system, then it is corresponding to the element
Dimensionality of particle value repeat step S1-S3.
4. a kind of GNSS precision positioning methods based on multidimensional particle filter estimation of deviation according to claim 2, it is special
Sign is that particle filter power renewal process is as follows in the step (4)：
S11：The functional relation established between likelihood function and RATIO：
<mrow>
<mi>p</mi>
<mrow>
<mo>(</mo>
<msub>
<mover>
<mi>b</mi>
<mo>~</mo>
</mover>
<mi>k</mi>
</msub>
<mo>|</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>R</mi>
<mi>A</mi>
<mi>T</mi>
<mi>I</mi>
<mi>O</mi>
<mo>)</mo>
</mrow>
</mrow>
In formula：F (RATIO) is the function on RATIO values；
S12：According to RATIO values RATIO corresponding to the functional relation established in step S11 and i-th of particleiCalculate corresponding particle
Likelihood function value
<mrow>
<mi>p</mi>
<mrow>
<mo>(</mo>
<msub>
<mover>
<mi>b</mi>
<mo>~</mo>
</mover>
<mi>k</mi>
</msub>
<mo>|</mo>
<msup>
<mi>x</mi>
<mi>i</mi>
</msup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>RATIO</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
S13：Likelihood function value is multiplied with the weights of corresponding particle, the particle power after being updated
<mrow>
<msubsup>
<mover>
<mi>w</mi>
<mo>&OverBar;</mo>
</mover>
<mi>k</mi>
<mi>i</mi>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>w</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mi>i</mi>
</msubsup>
<mi>p</mi>
<mrow>
<mo>(</mo>
<msub>
<mover>
<mi>b</mi>
<mo>~</mo>
</mover>
<mi>k</mi>
</msub>
<mo>|</mo>
<msubsup>
<mi>x</mi>
<mi>k</mi>
<mi>i</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
S14：Standardize particle weights, will each power of particle and all particles power sum ratio, as new particle power
Value
<mrow>
<msubsup>
<mi>w</mi>
<mi>k</mi>
<mi>i</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<msubsup>
<mover>
<mi>w</mi>
<mo>&OverBar;</mo>
</mover>
<mi>k</mi>
<mi>i</mi>
</msubsup>
<mrow>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</msubsup>
<msubsup>
<mover>
<mi>w</mi>
<mo>&OverBar;</mo>
</mover>
<mi>k</mi>
<mi>j</mi>
</msubsup>
</mrow>
</mfrac>
<mo>.</mo>
</mrow>
5. a kind of GNSS precision positioning methods based on multidimensional particle filter estimation of deviation according to claim 2, it is special
Sign is that resampling process is as follows in the step (7)：
S21：Added up particle weights according to sequence number, obtain the cumulative distribution function value collection of each particle：
<mrow>
<msubsup>
<mrow>
<mo>{</mo>
<msubsup>
<mi>x</mi>
<mi>k</mi>
<mi>i</mi>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>W</mi>
<mi>k</mi>
<mi>i</mi>
</msubsup>
<mo>}</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</msubsup>
<mo>;</mo>
</mrow>
S22：Population N needed for calculatingk+1：
In formula：N is particle number corresponding to unit variance,For smallest particles number；
S23：Generate uniform or random cumulative distribution function value：
<mrow>
<msubsup>
<mrow>
<mo>{</mo>
<msubsup>
<mi>U</mi>
<mi>k</mi>
<mi>i</mi>
</msubsup>
<mo>}</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<msub>
<mi>N</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</msubsup>
<mo>;</mo>
</mrow>
S24：Successively by cumulative distribution function value corresponding to particle sequence number, and uniform or random cumulative distribution function value is carried out pair
Than；For m=1, i=1, such asI-th of particle is then deleted, i=i+1, otherwise replicates i-th of particle to new particle
Collection, m=m+1；Until m=Nk+1, obtaining new particle collection is
S25：New particle collection is set to be weighed to wait：
<msubsup>
<mrow>
<mo>{</mo>
<msubsup>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mi>k</mi>
<mi>i</mi>
</msubsup>
<mo>,</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>N</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mfrac>
<mo>}</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<msub>
<mi>N</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</msubsup>
Obtain new particle collection and weights.
6. a kind of GNSS precision positioning methods based on multidimensional particle filter estimation of deviation according to claim 1, it is special
Sign is, single epoch normal equation or as follows with epoch summation establishing equation process before in the step 2：
GNSS system pseudorange non-difference observation equation is：
<mrow>
<msubsup>
<mi>P</mi>
<mi>a</mi>
<mi>i</mi>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>&rho;</mi>
<mi>a</mi>
<mi>i</mi>
</msubsup>
<mo>-</mo>
<mi>c</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&delta;t</mi>
<mi>a</mi>
</msub>
<mo>-</mo>
<msup>
<mi>&delta;t</mi>
<mi>i</mi>
</msup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msubsup>
<mi>d</mi>
<mi>a</mi>
<mi>i</mi>
</msubsup>
<mo>-</mo>
<msup>
<mi>d</mi>
<mi>i</mi>
</msup>
<mo>+</mo>
<msubsup>
<mi>I</mi>
<mi>a</mi>
<mi>i</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>T</mi>
<mi>a</mi>
<mi>i</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>&epsiv;</mi>
<mi>a</mi>
<mi>i</mi>
</msubsup>
</mrow>
GNSS system phase non-difference observation equation is：
<mrow>
<msup>
<mi>&lambda;</mi>
<mi>i</mi>
</msup>
<msubsup>
<mi>&Phi;</mi>
<mi>a</mi>
<mi>i</mi>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>&rho;</mi>
<mi>a</mi>
<mi>i</mi>
</msubsup>
<mo>-</mo>
<mi>c</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&delta;t</mi>
<mi>a</mi>
</msub>
<mo>-</mo>
<msup>
<mi>&delta;t</mi>
<mi>i</mi>
</msup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msubsup>
<mi>&mu;</mi>
<mi>a</mi>
<mi>i</mi>
</msubsup>
<mo>-</mo>
<msup>
<mi>&mu;</mi>
<mi>i</mi>
</msup>
<mo>+</mo>
<msup>
<mi>&lambda;</mi>
<mi>i</mi>
</msup>
<msubsup>
<mi>N</mi>
<mi>a</mi>
<mi>i</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>I</mi>
<mi>a</mi>
<mi>i</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>T</mi>
<mi>a</mi>
<mi>i</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>&xi;</mi>
<mi>a</mi>
<mi>i</mi>
</msubsup>
</mrow>
In formula：I is satellite sequence number, and a is observation station sequence number, and P is the non-poor Pseudo-range Observations of GNSS satellite, and Φ is GNSS satellite
Non- poor carrier phase observable, c are the light velocity, δ taFor GNSS observation stations receiver clock-offsets, ρ be observation station between GNSS satellite away from
From δ tiFor GNSS satellite clock correction, di aFor receiver end pseudorange hardware delay, diFor GNSS satellite end pseudorange hardware delay, I is
Ionosphere delay error, T are tropospheric delay error, and ε is the observation noise of Pseudo-range Observations, μi aFor receiver end phase hardware
Delay, μiPostpone for GNSS satellite end phase hardware, λiFor the carrier wavelength of i-th satellite, Ni aFor integer ambiguity, ζ is phase
The observation noise of position observation；
Double difference combination is carried out for GNSS system pseudorange un-differenced observation and GNSS system phase un-differenced observation, obtains GNSS systems
Double difference pseudorange and phase observations equation are respectively in system：
<mrow>
<msubsup>
<mi>P</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<msub>
<mi>s</mi>
<mi>w</mi>
</msub>
<mo>,</mo>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>&rho;</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<msub>
<mi>s</mi>
<mi>w</mi>
</msub>
<mo>,</mo>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>d</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<msub>
<mi>s</mi>
<mi>w</mi>
</msub>
<mo>,</mo>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>I</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<msub>
<mi>s</mi>
<mi>w</mi>
</msub>
<mo>,</mo>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>T</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<mi>s</mi>
<mi>w</mi>
<mo>,</mo>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>&epsiv;</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<mi>s</mi>
<mi>w</mi>
<mo>,</mo>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msubsup>
</mrow>
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msup>
<mi>&lambda;</mi>
<mrow>
<msub>
<mi>s</mi>
<mi>w</mi>
</msub>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msup>
<msubsup>
<mi>&Phi;</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mrow>
<msub>
<mi>s</mi>
<mi>w</mi>
</msub>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msubsup>
<mo>-</mo>
<msup>
<mi>&lambda;</mi>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<mi>i</mi>
</mrow>
</msup>
<msubsup>
<mi>&Phi;</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<mi>i</mi>
</mrow>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>&rho;</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<msub>
<mi>s</mi>
<mi>w</mi>
</msub>
<mo>,</mo>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>&mu;</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<msub>
<mi>s</mi>
<mi>w</mi>
</msub>
<mo>,</mo>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msubsup>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<msup>
<mi>k</mi>
<mi>j</mi>
</msup>
<mo>-</mo>
<msup>
<mi>k</mi>
<mi>i</mi>
</msup>
</mrow>
<mo>)</mo>
</mrow>
<msub>
<mi>&Delta;&gamma;</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
</msub>
<mo>+</mo>
<msup>
<mi>&lambda;</mi>
<mrow>
<msub>
<mi>s</mi>
<mi>w</mi>
</msub>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msup>
<msubsup>
<mi>N</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mrow>
<msub>
<mi>s</mi>
<mi>w</mi>
</msub>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msubsup>
<mo>-</mo>
<msup>
<mi>&lambda;</mi>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<mi>i</mi>
</mrow>
</msup>
<msubsup>
<mi>N</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<mi>i</mi>
</mrow>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<msubsup>
<mi>I</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<msub>
<mi>s</mi>
<mi>w</mi>
</msub>
<mo>,</mo>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>T</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<msub>
<mi>s</mi>
<mi>w</mi>
</msub>
<mo>,</mo>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>&xi;</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<msub>
<mi>s</mi>
<mi>w</mi>
</msub>
<mo>,</mo>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msubsup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula：s1For any satellite system, swFor another satellite system, w=1,2,3 ... W, wherein W are satellite system number, b
For the survey station number of another survey station of double difference observation, j is the satellite number of another GNSS satellite of composition double difference observation, and d is puppet
Away from deviation between system, μ deviations between phase system, (kj-ki)ΔγabFor the frequency when there is GLONASS system FDMA observations
Between deviation, k is satellite number, and Δ γ is inter-frequency deviation rate；
It can be converted after the linearisation of double difference carrier phase observational equation in double difference pseudorange observation equation and GNSS system in GNSS system
For：
V=Ax+Db+Cz+l
In formula：X is the vector that other unknown quantitys include survey station coordinate components composition in addition to fuzziness and inter-frequency deviation, and b is reception
Single poor fuzziness unknown number vector between machine, z are the unknown vector for including multiple deviations to be estimated, and A, D and C are respectively that unknown quantity is corresponding
Coefficient matrix, l are constant term vector, and P is weight matrix, and v is observation residual error vector；
According to lienarized equation cocoa single epoch normal equation or with epoch before add up normal equation：
<mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<msup>
<mi>A</mi>
<mi>T</mi>
</msup>
<mi>P</mi>
<mi>A</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<msup>
<mi>A</mi>
<mi>T</mi>
</msup>
<mi>P</mi>
<mi>D</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<msup>
<mi>A</mi>
<mi>T</mi>
</msup>
<mi>P</mi>
<mi>C</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow></mrow>
</mtd>
<mtd>
<mrow>
<msup>
<mi>D</mi>
<mi>T</mi>
</msup>
<mi>P</mi>
<mi>D</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<msup>
<mi>D</mi>
<mi>T</mi>
</msup>
<mi>P</mi>
<mi>C</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>s</mi>
<mi>y</mi>
<mi>m</mi>
</mrow>
</mtd>
<mtd>
<mrow></mrow>
</mtd>
<mtd>
<mrow>
<msup>
<mi>C</mi>
<mi>T</mi>
</msup>
<mi>P</mi>
<mi>C</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mi>x</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>b</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>z</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<msup>
<mi>A</mi>
<mi>T</mi>
</msup>
<mi>P</mi>
<mi>l</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mi>D</mi>
<mi>T</mi>
</msup>
<mi>P</mi>
<mi>l</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mi>C</mi>
<mi>T</mi>
</msup>
<mi>P</mi>
<mi>l</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>.</mo>
</mrow>
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
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