CN109738926A - A kind of GNSS multipath effect correcting method based on BP neural network technology - Google Patents
A kind of GNSS multipath effect correcting method based on BP neural network technology Download PDFInfo
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Abstract
The present invention provides a kind of GNSS multipath effect correcting method based on BP neural network technology successively includes Multipath Errors extractions, sample pre-selection, sample preprocessing, sample training, network topology structure determination, data preservation, Data Post and model modification；By being modeled using the signal forward-propagating of BP neural network algorithm and the backpropagation of error to Multipath Errors, multipath effect error caused by motion conditions, elevation of satellite, signal-to-noise ratio and the monitoring point ambient environmental conditions of satellite can effectively be weakened, the cyclic fluctuation in tri- direction result monitoring station X, Y, Z trained simultaneously be improved significantly, and dynamic update can be carried out to model according to newly-increased Multipath Errors data, can utmostly weaken multipath effect periodic error caused by monitoring point.
Description
Technical field
The present invention relates to multipath effect technical fields, particularly, are related to a kind of GNSS based on BP neural network technology
Multipath effect correcting method.
Background technique
GNSS(Global Navigation Satellite System) be various navigation system general designation, comprising:
The navigation system such as GPS, BDS, GLONASS, Galileo.With the rapid development of satellite navigation system, GNSS technology is being led
It is got a lot of applications in the multiple fields such as boat, deformation monitoring, positioning, time service.Due to GNSS it is round-the-clock, it is full-automatic, be not necessarily to people
The characteristics of work is intervened is widely used in deformation monitoring.
GNSS obtains the deformation of monitored object in real time in deformation monitoring using short baseline relative positioning technology, due to
Baseline is shorter, and most error has been effectively eliminated by filtering and differential technique.However multipath effect can not pass through
These means effectively eliminate.Multipath effect seriously damages the precision of GNSS measurement, and the losing lock of signal can be also caused when serious, is
A kind of important error source in GNSS measurement.
There are mainly three types of the existing effective ways for weakening Multipath Errors: (1) selecting to block when acquiring data less
Place；(2) algorithm for inhibiting multipath effect is added in GNSS receiver or using the antenna for having choke coil；(3) it adopts
Multipath effect is rejected with post-processing algorithm.The position of general monitoring point is determining in the project, can not be had highly desirable
Spacious environment, so first method and being not suitable for；Second method needs to improve within hardware, needs receiver manufacturer
To optimize；Application in the project generally can weaken Multipath Errors using the third method.
Simplest post-processing algorithm is to select star method, using it is commonplace be to establish multiple path routing model method.Two kinds of sides
Method is being affected, based on this principle smaller to the image of carrier observations to Pseudo-range Observations first by multipath effect
Calculate the multipath effect of different satellites；Star method is wherein selected mainly to defend according to the Multipath Errors Select Error being calculated is lesser
Star participates in resolving；Modelling establishes the multipath effect model of every satellite according to more days Multipath Errors, then according to model
The Pseudo-range Observations of each satellite are corrected.Currently, multipath modeling method mainly pass through fitting of a polynomial,
Kalman filter technology, spectrum analysis, signal-to-noise ratio-Multipath Errors, elevation angle-Multipath Errors realize that multipath changes to model
Just.
Above-mentioned multipath mitigation method has some limitations: selecting star method fairly simple, but this method is being seen
Measure satellite number it is less in the case where, rejecting excessive observation data can be such that calculation accuracy reduces, and can be used only in satellite situation very
Good place；For modelling, although since multipath effect has certain periodicity, its numerical value and satellite motion feelings
Condition, receiver ambient enviroment have a much relations, rule performance it is more complicated, can not by simply filtering, signal-to-noise ratio, height
It spends angle and models accurate modeling, so the above modeling method equally exists very big difficulty for multipath correction, and can be used only in
In post-processing, it can not be used in real time data processing.
It is badly in need of a kind of new technique of GNSS multipath effect correcting method based on BP neural network technology in the industry.
Summary of the invention
It is an object of that present invention to provide a kind of GNSS multipath effect correcting method based on BP neural network technology, with solution
Certainly the complicated difficult of Multipath Errors can not be calculated with accurate modeling and in real time to resolve multipath effect and correct the technology of error and be asked
Topic.
To achieve the above object, a kind of GNSS multipath effect correction based on BP neural network technology provided by the invention
Method is implemented on the basis of BP neural network technical application, and BP neural network algorithm is implied including an input layer, one
Layer and an output layer, 2 times wherein to stand on the basis of input layer number with the common number of satellites in monitoring station, output layer has
Three neurons, respectively the coordinate time sequence in tri- direction of base station and monitoring station X, Y, Z；BP neural network activation primitive is adopted
With Sigmoid function:
Specifically includes the following steps:
(1), Multipath Errors extract；The almanac data, carrier wave and pseudorange of continuous acquisition one period base station and monitoring station
1) observation handles the data of acquisition as the following formula, extract the Multipath Errors MP of base station and monitoring station difference satellite
Sequence；MP sequence is by several epochMultipath Errors value composition；Simultaneously to formula 1) be calculatedMultipath Errors value carries out sample pre-selection, obtains the Multipath Errors MP sequence not comprising ambiguity information；
；
Formula 1) inFor the frequency of carrier phase observation data；For carrier phase observation data；For Pseudo-range Observations；For Multipath Errors value；
Sample pre-selection in step (1), specifically: 1. according to formula 1) acquire each satellite current epoch
The mean value of Multipath Errors value；2. will be according to formula 1) subsequent each epoch for being calculatedMultipath misses
1. mean value that step calculates is individually subtracted in difference, obtains not comprising ambiguity informationMultipath Errors value；
To obtain by several epoch and not include ambiguity informationThe MP sequence of Multipath Errors value composition
Data.
(2), sample preprocessing: the multichannel that will be calculated in step (1) by the method for the multiple fitting of a polynomial of unitary
Elimination of rough difference in diameter error MP sequence obtains the clean MP sequence data not comprising rough error；
The multiple fitting of a polynomial of unitary is the fitting of unitary cubic polynomial, specifically carries out elimination of rough difference as follows:
(2.1), assume polynomial equation are as follows:
(2.2), the sum of square of deviations of Multipath Errors are as follows:
(2.3), basisMinimum principle finds out polynomial coefficient:
(2.4), the fitting Multipath Errors value of various time points is found out using multinomial, and by the Multipath Errors value after fitting
By formula 2) processing, it will be greater than the data rejecting of 3 times of Multipath Errors values；
；
Formula 2) inFor coefficientThe match value at j moment after fitting,For j
The Multipath Errors value at moment, 3V are 3 times of Multipath Errors values.
Double deference processing is carried out to the MP sequence data after the excluding gross error of satellite common in monitoring station and base station, is obtained
The Double deference time series data of Multipath Errors, then Double deference time series data is normalized；
Double deference processing includes single poor processing and double difference processing, single poor processing are as follows: by common satellite each in monitoring station and base station
Excluding gross error afterData press formula 3) processing；
；
Formula 3) inThe monitoring station being calculated for step (1) and benchmark
It stands i-th satelliteThe Multipath Errors of frequency range；For i-th satelliteFrequency range
Single difference Multipath Errors value；
Double difference processing are as follows: by what is obtained after single poor processingSingle difference Multipath Errors value and reference satellite
Multipath Errors value makees difference processing, forms Double deference Multipath Errors value；Reference satellite is selected as base station or monitoring station monitoring
The maximum satellite of the elevation angle arrived；It selects base station or the maximum satellite of elevation angle of monitoring station monitoring as reference satellite, is
Since the elevation angle of satellite is bigger, the signal strength of satellite is higher, and the signal of satellite launch is by ionosphere and tropospheric influences
It is small, it is more accurate true.
；
Formula 4) inFor i-th satellite and reference satellite j momentThe Double deference of frequency range is more
Tracking error value.
Normalized are as follows: by the data in Double deference time seriesBy formula 5) processing, simultaneously
After normalizationDouble deference Multipath Errors data save respectively；
；
It is the Double deference Multipath Errors value of i-th satellite,It is
The minimum value of data in Double deference Multipath Errors,It is that i-th satellite Double deference multipath misses
The maximum value of data in difference,It is the Double deference Multipath Errors data after normalization.
The input data obtained after sample preprocessing is the matrix data of n row 2m column, such as formula 6) shown in；Wherein n is
The epoch number of difference Multipath Errors data, station, the common number of satellites in monitoring station on the basis of m；It is each to be classified as an input data,
So the input layer of neural network is 2m；
；
In formulaRepresent tnThe Double deference Multipath Errors of moment (epoch) the m satellite p1 frequency range；Represent tnThe Double deference Multipath Errors of the m satellite p2 frequency range of moment.
(3), sample training and post-processing: being arranged corresponding training parameter, pre- to sample using BP neural network algorithm
Treated, and data are trained, wherein input is formula 6) shown in data in n row 2m column matrix, export and resolve software for GNSS
Read the coordinate time sequence in tri- directions monitoring station X, Y, Z that training obtains；Software, which is resolved, by GNSS reads trained obtain
Tri- directions monitoring station X, Y, Z coordinate time sequence, multipath corrected value is predicted, and correct tri- sides X, Y, Z
To coordinate value.
Preferably, network topology structure determines specifically: according to sample data training as a result, calculating root-mean-square error
Rmse adjusts different hidden layer neuron numbers, network weight, then recalculates rmse, after repeating repeatedly, selection
The smallest neuron number of rmse and network weight are as optimum network topological structure；
；
Formula 7) in n be prediction points, o be network desired output, p be network reality output.
(4), model modification: when data of monitoring point length reaches a period in step (1), by newly-increased observation number
It has been obtained before being merged into according to the Double deference Multipath Errors data after the normalization obtained by step (1) and step (2) processing
To normalization after Double deference Multipath Errors data in form the Double deference Multipath Errors data after new normalization, and
Again new samples data are trained, according to the training result of new samples data, update model parameter；Model parameter is BP mind
Through the network weight and biasing coefficient in network.
The invention has the following advantages:
A kind of GNSS multipath effect correcting method based on BP neural network technology of the present invention, by being calculated using BP neural network
The signal forward-propagating of method and the backpropagation of error model Multipath Errors, can effectively weaken the movement feelings of satellite
Multipath effect error caused by condition, elevation of satellite, signal-to-noise ratio and monitoring point ambient environmental conditions, while training
As a result the cyclic fluctuation in tri- direction monitoring station X, Y, Z be improved significantly, and can be according to newly-increased Multipath Errors number
Dynamic update is carried out according to model, can utmostly weaken multipath effect periodic error caused by monitoring point.
It is more three times using unitary in a kind of GNSS multipath effect correcting method based on BP neural network technology of the present invention
Item formula carries out Multipath Errors fitting, is conducive to Multipath Errors and the satellite motion period of each satellite Pseudo-range Observations of monitoring
Periodically correlation is presented, so that error curve is relatively smooth, regression criterion is relatively small.
A kind of GNSS multipath effect correcting method based on BP neural network technology of the present invention, by using at Double deference
Can effectively eliminate the common error to satellite monitoring of monitoring station and base station, at the same double difference treated Multipath Errors into
Row difference more meets the carrier phase difference algorithm of GNSS software resolving, so as to reach better Correction of Errors effect.
A kind of GNSS multipath effect correcting method based on BP neural network technology of the present invention, passes through normalized energy
It is enough that the value range of Double deference treated Multipath Errors data is effectively contracted to (0,1), greatly promote subsequent BP nerve
The training operation efficiency of network model and the resolving efficiency of GNSS software.
Other than objects, features and advantages described above, there are also other objects, features and advantages by the present invention.
Below with reference to figure, the present invention is described in further detail.
Detailed description of the invention
The attached drawing constituted part of this application is used to provide further understanding of the present invention, schematic reality of the invention
It applies example and its explanation is used to explain the present invention, do not constitute improper limitations of the present invention.In the accompanying drawings:
Fig. 1 is BP neural network structural schematic diagram of the present invention；
Fig. 2 is difference Multipath Errors figure (a, P1 frequency range difference multichannel in the embodiment of the present invention after the normalization of No. 1 satellite
Diameter error, b, P2 frequency range difference Multipath Errors)；
Fig. 3 is that (a, X-direction model are pre- with initial data comparison diagram for model predication value of the present invention after BP neural network algorithm
Measured value and initial data compare, and b, Y-direction model predication value and initial data compare, c, Z-direction model predication value and original number
According to).
Specific embodiment
The embodiment of the present invention is described in detail below in conjunction with attached drawing, but the present invention can be limited according to claim
Fixed and covering multitude of different ways is implemented.
A kind of GNSS multipath effect correcting method based on BP neural network technology provided by the invention is in BP nerve
Implement on the basis of application of net, BP neural network algorithm includes an input layer, a hidden layer and an output layer
(referring to Fig. 1), 2 times wherein to stand on the basis of input layer number with the common number of satellites in monitoring station, there are three output layers
Neuron, respectively the coordinate time sequence in tri- direction monitoring point X, Y, Z；BP neural network activation primitive uses Sigmoid letter
Number:
A kind of GNSS multipath effect correcting method based on BP neural network technology of the present invention, specifically includes the following steps:
(1), Multipath Errors extract；The almanac data, carrier wave and pseudorange of continuous acquisition one period base station and monitoring station
Observation, to the data (almanac data, carrier wave and Pseudo-range Observations) of acquisition as the following formula 1) it handles, extract base station and prison
The Multipath Errors MP sequence of survey station difference satellite；MP sequence is by several epochMultipath Errors value
Composition；Simultaneously to formula 1) be calculatedMultipath Errors value carries out sample pre-selection, obtains not including fuzzy
Spend the Multipath Errors MP sequence of information；The period acquired in the present embodiment is 30 days；
；
Formula 1) inFor the frequency of carrier phase observation data；For carrier phase observation data；For Pseudo-range Observations；For Multipath Errors value；
Sample pre-selection in step (1), specifically: 1. according to formula 1) acquire each satellite current epoch
The mean value of Multipath Errors value；2. will be according to formula 1) subsequent each epoch for being calculatedMultipath misses
1. mean value that step calculates is individually subtracted in difference, obtains not comprising ambiguity informationMultipath Errors value；
To obtain by several epoch and not include ambiguity informationThe MP sequence of Multipath Errors value composition
Data.
(2), sample preprocessing: the multichannel that will be calculated in step (1) by the method for the multiple fitting of a polynomial of unitary
Elimination of rough difference in diameter error MP sequence obtains the clean MP sequence data not comprising rough error；
The multiple fitting of a polynomial of unitary is the fitting of unitary cubic polynomial, specifically carries out elimination of rough difference as follows:
(2.1), assume polynomial equation are as follows:
(2.2), the sum of square of deviations of Multipath Errors are as follows:
(2.3), basisMinimum principle finds out polynomial coefficient:
(2.4), the fitting Multipath Errors value of various time points is found out using multinomial, and by the Multipath Errors value after fitting
By formula 2) processing, it will be greater than the data rejecting of 3 times of Multipath Errors values；
；
Formula 2) inFor coefficientThe match value at j moment after fitting,For j
The Multipath Errors value at moment, 3V are 3 times of Multipath Errors values.
It is more three times using unitary in a kind of GNSS multipath effect correcting method based on BP neural network technology of the present invention
Item formula carries out Multipath Errors fitting, is conducive to Multipath Errors and the satellite motion period of each satellite Pseudo-range Observations of monitoring
Periodically correlation is presented, so that error curve is relatively smooth, regression criterion is relatively small.
Due to generally using carrier phase difference algorithm in deformation monitoring, it need to be to each total in monitoring station and base station
Double deference processing is carried out with the MP sequence data after the excluding gross error of satellite, obtains the Double deference time series of Multipath Errors,
Then the data in Double deference time series are normalized；Double deference processing includes single poor processing and double difference processing；
Single poor processing are as follows: after the excluding gross error of common satellite each in monitoring station and base stationData are pressed
Formula 3) processing；
；
Formula 3) inThe monitoring station being calculated for step (1) and benchmark
It stands i-th satelliteThe Multipath Errors of frequency range；For i-th satelliteFrequency range
Single difference Multipath Errors value；
Double difference processing are as follows: by what is obtained after single poor processingSingle difference Multipath Errors value and reference satellite
Multipath Errors value makees difference processing, forms Double deference Multipath Errors value；The elevation angle that base station or monitoring station monitor is maximum
Satellite as reference satellite；The maximum satellite of elevation angle for selecting base station or monitoring station to monitor as reference satellite, be by
Bigger in the elevation angle of satellite, the signal strength of satellite is higher, the signal of satellite launch by ionosphere and it is tropospheric influence it is small,
It is more accurate true.
；
Formula 4) inFor i-th satellite and reference satellite j moment (epoch)Pair of frequency range
Difference Multipath Errors value.
By using the common error to satellite monitoring that can effectively eliminate monitoring station and base station at Double deference, simultaneously
Double difference treated Multipath Errors carry out the carrier phase difference algorithm that difference more meets the resolving of GNSS software, so as to reach more
Good Correction of Errors effect.
Normalized are as follows: by the data in Double deference time seriesBy formula 5) processing, simultaneously
After normalizationDouble deference Multipath Errors data save respectively；
；
It is the Double deference Multipath Errors value of i-th satellite,It is
The minimum value of data in Double deference Multipath Errors,It is that i-th satellite Double deference multipath misses
The maximum value of data in difference,It is the Double deference Multipath Errors data after normalization.
Effectively the value range of Double deference treated Multipath Errors data can be contracted to by normalized
(0,1) greatly promotes the training operation efficiency of subsequent BP neural network model and the resolving efficiency of GNSS software, more meets reality
Applicable cases.
The input data obtained after sample preprocessing is the matrix data of n row 2m column, such as formula 6) shown in；Wherein n is
The epoch number of difference Multipath Errors data, station, the common number of satellites in monitoring station on the basis of m；It is each to be classified as an input data,
So the input layer of neural network is 2m；
；
In formulaRepresent tnThe Double deference Multipath Errors of moment (epoch) the m satellite p1 frequency range；Represent tnThe Double deference Multipath Errors of the m satellite p2 frequency range of moment.
(3), sample training and post-processing: being arranged corresponding training parameter, pre- to sample using BP neural network algorithm
Treated, and data are trained, wherein input is formula 6) shown in data in n row 2m column matrix, export and resolve software for GNSS
Read the coordinate time sequence in tri- directions monitoring station X, Y, Z that training obtains；Software, which is resolved, by GNSS reads trained obtain
Tri- directions monitoring station X, Y, Z coordinate time sequence, multipath corrected value is predicted, and correct tri- sides X, Y, Z
To coordinate value.
A kind of GNSS multipath effect correcting method based on BP neural network technology includes that network topology structure determines, tool
Body are as follows: according to sample data training as a result, calculating root-mean-square error rmse, adjusts different hidden layer neuron numbers, net
Network weight, then recalculates rmse, repeat repeatedly after, select the smallest neuron number of rmse and network weight as
Optimum network topological structure；
；
Formula 7) in n be prediction points (epoch number), o is the desired output of network, the i.e. time series in tri- direction monitoring point xyz, p
For the reality output of network.
(4), model modification: when data of monitoring point length reaches 30 days, newly-increased observation data by step (1) and are walked
Suddenly the double difference after the normalization that the Double deference Multipath Errors data after the normalization that (2) processing obtains have obtained before being merged into
Form the Double deference Multipath Errors data after new normalization in point Multipath Errors data, and again to new samples data into
Row training, the training result according to new samples data calculate root-mean-square error rmse, readjust the model ginseng of BP neural network
Number, model parameter are network weight and biasing coefficient in BP neural network.
15 common satellites observation in 30 days in base station and monitoring station measurement gnss big-dipper satellite is selected in the present embodiment
The basic data that base station and monitoring station are observed successively is carried out step (1) and step by basic data of the data as the present embodiment
Suddenly the processing (formula 1) of (2), formula 2), formula 3), formula 4), 5) processing), the Double deference multipath after obtaining the normalization of each satellite misses
Difference data；Double deference Multipath Errors data after normalization (since satellite is more, only show No. 1 Beidou as shown in Figure 2 here
P1, P2 frequency range Double deference Multipath Errors time series of satellite)；The input layer nerve of BP neural network algorithm in the present embodiment
First number is 2 × 15=30；Output layer neuron number is three, is the coordinate time sequence in tri- directions monitoring station X, Y, Z
Column；Double deference Multipath Errors data after the normalization of each satellite are subjected to sample training, setting convergence error is 2mm, training
Number 5000；It is black shown in solid in result such as Fig. 3 after training.
As can be drawn from Figure 3, through a kind of GNSS multipath effect correction side based on BP neural network technology of the present invention
After method, the cyclic fluctuation that GNSS resolves the coordinate time sequence in tri- directions monitoring station X, Y, Z that software calculates is more original
Data have clear improvement, and illustrate that it is effective that multipath correction is carried out using BP neural network algorithm；Also illustrate this hair
It is bright by being modeled using the signal forward-propagating of BP neural network algorithm and the backpropagation of error to Multipath Errors, can
Effectively weaken multipath caused by motion conditions, elevation of satellite, signal-to-noise ratio and the monitoring point ambient environmental conditions of satellite to imitate
The cyclic fluctuation in tri- direction result monitoring station X, Y, Z answering error, while training is obviously improved, and being capable of root
Dynamic update is carried out to model according to newly-increased Multipath Errors data, can utmostly weaken multipath effect and monitoring point is made
At periodic error.
Claims (7)
1. a kind of GNSS multipath effect correcting method based on BP neural network technology, which comprises the following steps:
(1), Multipath Errors extract: the almanac data, carrier wave and pseudorange of continuous acquisition one period base station and monitoring station
Observation handles the data of acquisition, extracts the Multipath Errors MP sequence of base station and each satellite in monitoring station；MP sequence
Column are by several epochMultipath Errors value composition；Simultaneously in MP sequenceIt is more
Tracking error value carries out sample pre-selection, obtains the Multipath Errors MP sequence not comprising ambiguity information；
(2), sample preprocessing: the multipath being calculated in step (1) is missed by the method for the multiple fitting of a polynomial of unitary
Elimination of rough difference in poor MP sequence obtains the clean MP sequence data not comprising rough error；
Double deference processing is carried out to the MP sequence data after the excluding gross error of satellite common in monitoring station and base station, obtains multichannel
The Double deference time series data of diameter error, then Double deference time series data is normalized；
(3), sample training and post-processing: being arranged corresponding training parameter, using BP neural network algorithm to sample preprocessing
Data afterwards are trained, and obtain the coordinate time sequence in tri- directions monitoring station X, Y, Z；Software, which is resolved, by GNSS reads instruction
The coordinate time sequence in tri- directions monitoring station X, Y, the Z got, predicts multipath corrected value, and correct X, Y, Z
The coordinate value in three directions；
(4), model modification: when data of monitoring point length reaches a period in step (1), newly-increased observation data are led to
What the Double deference Multipath Errors data after crossing step (1) and the obtained normalization of step (2) processing had obtained before being merged into
Double deference Multipath Errors data after forming new normalization in Double deference Multipath Errors data after normalization, and again
New samples data are trained, model parameter is updated.
2. a kind of GNSS multipath effect correcting method based on BP neural network technology according to claim 1, special
Sign is, in step (1) the MP sequenceMultipath Errors value is by formula 1) it is calculated:
；
Formula 1) inFor the frequency of carrier phase observation data；For carrier phase observation data；
For Pseudo-range Observations；For Multipath Errors value；
Sample pre-selection in step (1), specifically: 1. according to formula 1) acquire each satellite current epoch
The mean value of Multipath Errors value；2. will be according to formula 1) subsequent each epoch for being calculatedMultipath misses
1. mean value that step calculates is individually subtracted in difference, obtains not comprising ambiguity informationMultipath Errors value；
To obtain by several epoch and not include ambiguity informationThe MP sequence of Multipath Errors value composition
Data.
3. a kind of GNSS multipath effect correcting method based on BP neural network technology according to claim 1, special
Sign is, the multiple fitting of a polynomial of unitary in the step (2) is the fitting of unitary cubic polynomial, specifically as follows into
Row elimination of rough difference:
(2.1), assume polynomial equation are as follows:
(2.2), the sum of square of deviations of Multipath Errors are as follows:
(2.3), basisMinimum principle finds out polynomial coefficient:
(2.4), the fitting Multipath Errors value of various time points is found out using multinomial, and by the Multipath Errors value after fitting
By formula 2) processing, it will be greater than the data rejecting of 3 times of Multipath Errors values；
；
Formula 2) inFor coefficientThe match value at j moment after fitting,For j
The Multipath Errors value at moment, 3V are 3 times of Multipath Errors values.
4. a kind of GNSS multipath effect correcting method based on BP neural network technology according to claim 1, special
Sign is that the Double deference processing in the step (2) includes single poor processing and double difference processing；
Single poor processing are as follows: after the excluding gross error of common satellite each in monitoring station and base stationData are pressed
Formula 3) processing；
；
Formula 3) inThe monitoring station being calculated for step (1) and benchmark
It stands i-th satelliteThe Multipath Errors of frequency range；For i-th satelliteFrequently
Single difference Multipath Errors value of section；
Double difference processing are as follows: by what is obtained after single poor processingSingle difference Multipath Errors value and reference satellite
Multipath Errors value make difference processing, formed Double deference Multipath Errors value；Reference satellite is selected as base station or monitoring station prison
The maximum satellite of the elevation angle measured；
；
Formula 4) inFor i-th satellite and reference satellite j momentThe Double deference of frequency range is more
Tracking error value.
5. a kind of GNSS multipath effect correcting method based on BP neural network technology according to claim 1, special
Sign is, normalized in the step (2) are as follows: by the data in Double deference time seriesBy formula
5) it handles, while will be after normalizationDouble deference Multipath Errors data save respectively；
；
It is the Double deference Multipath Errors value of i-th satellite,It is double
The minimum value of data in difference Multipath Errors,It is i-th satellite Double deference Multipath Errors
The maximum value of middle data,It is the Double deference Multipath Errors data after normalization.
6. a kind of GNSS multipath effect correcting method based on BP neural network technology according to claim 1, special
Sign is that BP neural network algorithm includes an input layer, a hidden layer and an output layer；Input layer number is
2 times of common number of satellites in base station and monitoring station；Output layer totally three neurons, respectively tri- sides monitoring station X, Y, Z
To coordinate time sequence；BP neural network activation primitive uses Sigmoid function.
7. a kind of GNSS multipath effect correcting method based on BP neural network technology according to claim 1, special
Sign is, further includes that network topology structure determines before the step (4), specifically: according to sample data training as a result,
Root-mean-square error rmse is calculated, different hidden layer neuron numbers, network weight is adjusted, then recalculates rmse, is repeated
After carrying out repeatedly, select the smallest neuron number of rmse and network weight as optimum network topological structure；
；
Formula 7) in n be prediction points, o be network desired output, p be network reality output.
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