CN107807373A - GNSS high-precision locating methods based on mobile intelligent terminal - Google Patents

GNSS high-precision locating methods based on mobile intelligent terminal Download PDF

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CN107807373A
CN107807373A CN201710977413.9A CN201710977413A CN107807373A CN 107807373 A CN107807373 A CN 107807373A CN 201710977413 A CN201710977413 A CN 201710977413A CN 107807373 A CN107807373 A CN 107807373A
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mrow
msub
msubsup
satellite
intelligent terminal
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潘树国
王帅
张建
胡惠卿
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Southeast University
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Southeast University
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S19/00Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39Determining 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
    • G01S19/42Determining position
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S19/00Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39Determining 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
    • G01S19/40Correcting position, velocity or attitude
    • G01S19/41Differential correction, e.g. DGPS [differential GPS]

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Position Fixing By Use Of Radio Waves (AREA)

Abstract

The invention discloses a kind of GNSS high-precision locating methods based on mobile intelligent terminal, belong to technical field of satellite.The localization method of the present invention comprises the following steps:Under Android7.0 systems, GNSS raw observation data are obtained by LocationManager interfaces;Raw observation data are analyzed, the Differential positioning model based on mobile intelligent terminal is designed, calculates Pseudo-range Observations;Scheme is weighed using elevation angle surely, the weight of corresponding observation is determined according to the elevation angle size of every satellite;Correlation epoch is filtered out using kalman filter method, the sub_meter position result based on mobile intelligent terminal can be obtained.Using localization method proposed by the present invention, it can realize that plane is better than 0.8 1m on mobile intelligent terminal, elevation is better than 1m positioning precision.

Description

GNSS high-precision locating methods based on mobile intelligent terminal
Technical field
The invention belongs to technical field of satellite, and in particular to a kind of high-precision locating method of mobile intelligent terminal.
Background technology
With the rapid development and popularization of the mobile intelligent terminal equipment such as smart mobile phone, and based on mobile intelligent terminal Called a taxi on line, for the rise for driving and sharing the Newly Sprouted Things such as bicycle, the popular positioning precision for outdoor location service proposes to get over Carry out higher requirement.The outdoor positioning technology of current mobile intelligent terminal mainly has two kinds, and one kind is to be based on carrier network, Using mobile intelligent terminal the position of terminal is determined with respect to the range measurement of base station;Another kind is to be based on global navigational satellite System (GNSS), positioned using the locating module in mobile intelligent terminal with interacting for satellite to realize.But traditional intelligence Terminal device can only provide about 15m positioning precision by both localization methods, can not meet high accuracy positioning demand and standard True location-based service requirement, therefore high-precision locating method of the research based on mobile intelligent terminal is significant and city Field value.
GNSS provides positioning for the whole world or spatial user, navigates and time service information, at present the GNSS with construction in orbit Mainly there are GPS, GLONASS, Galileo and BDS.Traditional intelligent terminal based on Android operation system utilizes GNSS satellite The targeting scheme of location technology mainly directly obtains position by the LocationManager classes for calling application layer packaged Information, this can not meet the requirements for high precision of user;However, in some other positioning measurement fields, have been realized in centimetre Level, or even millimetre-sized positioning precision, all tend to be ripe in terms of theory and practice, this is high-precision for mobile intelligent terminal Degree positioning provides possibility.Google is claimed in the I/O conferences in May, 2016 to be in Android7.0 and the above Open original observed data in system, wherein just include pseudorange and carrier data, for Android intelligent terminals meter level even Centimeter-level positioning provides feasibility.
The content of the invention
Goal of the invention:Based on information above, the present invention proposes a kind of GNSS high accuracy positionings based on mobile intelligent terminal Method, solve the problems, such as that smart mobile phone positioning precision is relatively low, the positioning precision of sub-meter grade can be provided the user.
Technical scheme:A kind of GNSS high-precision locating methods based on mobile intelligent terminal of the present invention, including with Lower step:1) under the system of Android7.0 and the above, using the API based on location-based service of system offer, original is got The observation Value Data of beginning;2) by analyzing raw observation data, the Differential positioning based on mobile intelligent terminal is designed Model, calculate pseudorange value;3) elevation angle sequence, the scheme weighed surely using elevation angle, selection height are carried out to obtained satellite The larger satellite in angle participates in resolving;4) high-precision positioning result is obtained using the pseudo range difference scheme based on Kalman filtering.
The API that the present invention is provided using the android.location bags of android system is location-based to realize Service.Location bags mainly include two components of Geocoder and LocationManager, and the present invention uses LocationManager interfaces.Specifically, step 1) comprises the following steps:
11) the registerGnssMeasurementsCallback methods registration in LocationManager is used to see The callback object GnssMeasurementsEvent.Callback of measured value data;
12) the onGnssMeasurementsReceived methods of monitoring reception observation data are override in callback object, Obtain receiving the event class GnssMeasurementsEvent of observation Value Data;
13) GNSS observation class GnssMeasurements are obtained by the getMeasurements methods in event class, The observation Value Data of correlation can be obtained by such, includes time that pseudorange rates, carrier wave, data are launched etc..
The present invention uses pseudo range difference targeting scheme, and step 2) specifically includes:
21) satellite j and receiver k non-poor Pseudo-range Observations are calculated according to below equation (2-1):
Wherein r is the distance between satellite and receiver, and c is the light velocity, δ tkIt is receiver clock relative to the standard time Deviation, δ tjIt is deviation of the satellite clock relative to the standard time,It is troposphere correction member,It is ionosphere correction ,It is remaining error;
22) satellite i, j and receiver a, the b interspace double difference Pseudo-range Observations in station border are calculated according to below equation (2-2):
WhereinBe stand star away from double difference value,It is the double difference value of tropospheric delay,It is The double difference value of ionosphere delay,It is the double difference value of other errors, each double difference value is specifically by step 21) herein In corresponding non-differential make the difference and obtain.
Mode is weighed using elevation angle surely in location model of the present invention, when movement station observes that the elevation angle of satellite is more than 30 Its weights is just set to 1 by degree, and when elevation of satellite is less than 30 degree, satellite weights are set to sin2E, E are elevation angle, simultaneously The threshold value of elevation of satellite is set to 10 degree, gives up the satellite data less than threshold value.
Beneficial effect:A kind of GNSS high-precision locating methods based on mobile intelligent terminal proposed by the present invention, divide in detail The high accuracy positioning scheme under data acquisition and pure GNSS based on location-based service under Android operation system is analysed, completely The locating module carried using smart mobile phone can be obtained by the positioning precision of sub-meter grade, with mobile intelligent terminals such as mobile phones The rapid development and popularization of equipment, and called a taxi on the line based on mobile intelligent terminal, generation drive and share the new industries such as bicycle Rise, the popular positioning precision for outdoor location service puts forward higher requirement, therefore based on mobile intelligent terminal High-precision locating method is significant and market value.
Brief description of the drawings
Fig. 1 is the GPS high-precision locating method flow charts based on mobile intelligent terminal;
Fig. 2 is the flow chart of the acquisition raw observation data of the present invention;
Fig. 3 is the GNSS satellite observation Value Data that Android application programs can obtain;
Fig. 4 is the time that Android application programs can be obtained about GNSS satellite;
Fig. 5 is that Android application programs can obtain GNSS satellite navigation message data;
Fig. 6 is the satellite visibility obtained according to an embodiment of the invention;
Fig. 7 is the satellite carrier-to-noise ratio obtained according to an embodiment of the invention;
Fig. 8 is the elevation of satellite obtained according to an embodiment of the invention;
Fig. 9 is the zero base line positioning result figure obtained according to an embodiment of the invention;
Figure 10 is the short baseline positioning result figures of the 10km obtained according to an embodiment of the invention;
Figure 11 is the short baseline positioning result figures of the 25km obtained according to an embodiment of the invention.
Embodiment
Technical scheme is described further below in conjunction with the accompanying drawings.
Fig. 1 is the GNSS high-precision locating method flow charts based on mobile intelligent terminal, and one kind is based on mobile intelligent terminal GNSS high-precision locating methods, first under the system of Android7.0 and the above, utilize system provide based on position take The API of business, gets original observation Value Data, and pseudorange value is calculated by observation data analysis;Then defended to what is obtained Star carries out elevation angle sequence, the scheme weighed surely using elevation angle, selects the larger satellite of elevation angle to participate in resolving;Finally utilize Pseudo range difference scheme based on Kalman filtering obtains high-precision positioning result.Detailed process described below.
It is primarily based on mobile intelligent terminal and obtains raw observation data, the present invention is devised by Android7.0 LocationManager interfaces obtain the scheme of GNSS raw observation data, and Fig. 2, which is shown, obtains raw observation data Flow chart.Specific steps include:The first step is used in LocationManager The callback object of registerGnssMeasurementsCallback methods registration observation Value Data GnssMeasurementsEvent.Callback, second step override monitoring reception observation data in callback object OnGnssMeasurementsReceived methods, obtain receiving the event class of observation Value Data GnssMeasurementsEvent, the 3rd step obtain GNSS observation classes by the getMeasurements methods in event class GnssMeasurements, the observation Value Data of correlation can be finally obtained by such, include pseudorange rates, carrier wave, data hair Time penetrated etc..Fig. 3-Fig. 5 respectively illustrates the GNSS satellite observation Value Data that Android application programs can obtain, relevant The time of GNSS satellite and GNSS satellite navigation message data, the wherein explanation of key data item are respectively such as table 1, table 2 and table Shown in 3.
Table 1GNSS moonscope Value Datas
The Time Correlation Data of table 2GNSS satellites
Table 3GNSS satellite navigation message data
Next according to raw observation data, using pseudo range difference targeting scheme, Pseudo-range Observations are calculated, specific step It is rapid as follows:
(1) non-poor Pseudo-range Observations are calculated
The time propagated by measuring GNSS satellite signal between satellite j and receiver k, pseudorange value is calculated so as to ask:
ρ=Δ tc (1)
Wherein Δ t is the propagation time between satellite and receiver, and c is the light velocity, and Δ t can be by the time of satellite launch data The time that data are received with receiver asks difference to obtain:
Δ t=tk-tj (2)
Wherein tkBe receiver receive data time, tjIt is the time of satellite launch data, can be asked by initial data :
tk=T-tfullbias-tbias (3)
tj=tallweek+treceivedsv (4)
Wherein T is GNSS receiver internal hardware clock getTimeNanos (), tfullbiasIt is the GPS in hardware clock Difference getFullBiasNanos () between receiver and true gps time, tbiasIt is the biasing getBiasNanos of clock (); tallweekIt is total complete cycle number time, can calculates to obtain by current time, represent from 1980.6.1 to current time Between complete cycle number, treceivedsvIt is time getReceivedSvTimeNanos () of satellite launch data.
Satellite j and receiver k pseudorange non-difference observation equation is constructed, obtains non-poor Pseudo-range Observations:
Wherein r is the distance between satellite and receiver, δ tkIt is deviation of the receiver clock relative to the standard time, δ tj It is deviation of the satellite clock relative to the standard time,It is troposphere correction member,It is ionosphere correction member,It is remaining error.
(2) double difference Pseudo-range Observations are calculated
According to non-poor Pseudo-range Observations, construction satellite i, j and receiver a, the b interspace double-difference equation in station border:
WhereinBe stand star away from double difference value,It is the double difference value of tropospheric delay,It is The double difference value of ionosphere delay,It is the double difference value of other errors.Specific every double difference Pseudo-range Observations be by Above-mentioned corresponding non-poor Pseudo-range Observations make the difference calculating, can so eliminate common error.
In order to improve navigation and positioning accuracy, it is necessary to be rejected to invalid observation Value Data.Adopted in location model of the present invention Mode is weighed surely with elevation angle, selects the larger satellite of elevation angle to participate in resolving, when movement station observes that the elevation angle of satellite is more than 30 degree, its weights is just set to 1, when elevation of satellite is less than 30 degree, satellite weights are set to sin2E, E are elevation angle.Simultaneously The threshold value of elevation of satellite is set to 10 degree, gives up the satellite data less than the threshold value.
Correlation epoch is filtered out finally by kalman filter method, obtains accurate positioning result.Karr The calculating process of graceful filtering can be divided into prediction, filtering gain and Filtering Estimation three parts.
(1) predict
Assuming that current system mode is k, current predicted value is calculated according to a preceding filter result (or initial value):
Xk,k-1k,k-1Xk-1 (7)
Wherein, Xk,k-1It is to utilize the current results of laststate optimal value prediction, Φk,k-1It is equation of motion coefficient, Xk-1 It is the optimal result of laststate.
Predicted value is calculated according to the error covariance matrix (or initial value) of a preceding filter result and system dynamic noise variance matrix Error covariance matrix:
Wherein, Qk,k-1It is to utilize the error current variance matrix of last covariance optimal value prediction, Qk-1,k-1Be it is preceding once The error covariance matrix of filter result,It is Φk,k-1Transposed matrix, QwkIt is system dynamic noise variance matrix.
(2) filtering gain
In order to obtain least mean-square error, optimal kalman gain matrix is calculated:
Wherein, KkIt is the optimal estimation value of current state, AkIt is the coefficient of observational equation,It is AkTransposed matrix, Rk It is the noise variance matrix of measurement.
(3) Filtering Estimation
Calculate this filter result:
Xk,k=Xk,k-1+Kk(Lk-AkXk,k-1) (10)
Wherein, Xk,kIt is this filter result, LkIt is observation.
Calculate the error covariance matrix of this filter result:
Qk.k=(I-KkAk)Qk,k-1 (11)
Wherein, Qk,kIt is the error covariance matrix of this filter result, I is unit matrix.
Storage filtering estimation, waits subsequent time to obtain new observation, repeats aforementioned process.
Kalman filtering fully account for the stochastic behaviour of unknown parameter, be particularly suited for compared with least square adjustment The real-time positioning calculations of GNSS, computational efficiency are also higher.In Kalman filtering process, the setting of model parameter is extremely important, sets Filtering divergence is easily caused if improper, makes positioning result substantial deviation true value.The filtering parameter of usual static immobilization can root Set according to empirical value, dynamic positioning needs to be adjusted according to actual conditions.System dynamic noise under dynamic condition of the present invention Battle array QwkOnly acceleration is handled, and position and speed not handled.The error covariance matrix Q equally predictedk,k-1 Time difference that can be before and after between epoch is handled speed and acceleration.
Embodiment:
Android mobile intelligent terminals used in experiment are Huawei's P9 mobile phones, and model is EVA-AL00, and version number is EVA-AL00C00B377, EMUI version are 5.0, and operating system is Android7.0.Mobile phone terminal is placed on Southeast China University Near hall, the time using experimental data is 03 second April 26 day 09 point 38 minute in 2017, and time span is 900 seconds, base Quasi- station is using laboratory base station, and data sampling was at intervals of 1 second.Because the accurate coordinates of mobile phone are unknown, so first by Moving station measuring goes out the accurate coordinates of the point, and mobile phone then is placed into this point.
By the parsing to raw observation data, satellite data is obtained.Fig. 6 shows the visibility of satellite, wherein Gps satellite is stablized at 9 always, and GLONASS satellite starts a period of time as 9, is reduced to 7 afterwards.GPS satellites it is visible Degree is good, participates in resolving using GPS satellite data, satellite number is respectively:G10、G14、G15、 G22、G25、G26、G29、 G31、G32.The gps satellite carrier-to-noise ratio that handset receiver receives is shown in Fig. 7, from figure 7, it is seen that gps satellite carrier-to-noise ratio More than 40 normally are maintained, only G18 satellites carrier-to-noise ratio is very poor;From the gps satellite elevation angle shown in Fig. 8, G18 Number elevation of satellite is very low, always below 10 degree, and is gradually reducing, therefore give up G18 satellites in solution process Data.Other elevation of satellite are all more than 20 degree, and average height angle is at 45 degree or so, it is seen that what handset receiver received Gps satellite signal quality is good.
Pseudo range difference positioning experiment have chosen respectively the zero base line of laboratory base station, the short baselines of the 10km of herds of horses base station and The short base-line datas of 25km of six directions base station.Experiment continues to demonstrate the pseudo range difference targeting scheme based on Kalman filtering.Fig. 9- Figure 11 be based on sequential pseudo range difference positioning result figure, table 4 list based on sequential pseudo range difference zero base line, 10km with And error in the positioning of 25km baselines.
Error in the Kalman filtering pseudo range difference zero base line of table 4, the positioning of 10km and 25km baselines
In the case of zero base line, in-plane position error is about 0.75m, and elevation direction is about 0.8m;10km and 25km are short Under baseline case, in-plane position error is 0.8m, and elevation direction is about 1m.It is flat under short baseline from positioning result Face direction is compared zero base line with elevation direction positioning precision and decreased, and final plane positioning precision is better than 0.8-1m, and elevation is fixed Position precision is better than 1m.

Claims (6)

1. a kind of GNSS high-precision locating methods based on mobile intelligent terminal, it is characterised in that comprise the following steps:
1) under the system of Android7.0 and the above, using the API based on location-based service of system offer, it is original to obtain GNSS Observe Value Data;
2) raw observation data are analyzed, designs the Differential positioning model based on mobile intelligent terminal, calculate pseudorange Observation;
3) scheme is weighed using elevation angle surely, the weight of corresponding observation is determined according to the elevation angle size of every satellite;
4) noise is filtered out using kalman filter method, obtains accurate positioning result.
2. the GNSS high-precision locating methods according to claim 1 based on mobile intelligent terminal, it is characterised in that described Step 1) specifically includes following steps:
11) the registerGnssMeasurementsCallback methods registration in LocationManager interfaces is used to see The callback object GnssMeasurementsEvent.Callback of measured value data;
12) the onGnssMeasurementsReceived methods of monitoring reception observation data are override in callback object, are obtained Receive the event class GnssMeasurementsEvent of observation Value Data;
13) GNSS observation class GnssMeasurements are obtained by the getMeasurements methods in event class, by such Related observation Value Data is obtained, includes the time of pseudorange rates, carrier wave, data transmitting.
3. the GNSS high-precision locating methods according to claim 1 based on mobile intelligent terminal, it is characterised in that described Step 2) specifically includes following steps:
21) satellite j and receiver k non-poor Pseudo-range Observations are calculated according to formula (2-1):
<mrow> <mi>&amp;rho;</mi> <mo>=</mo> <mi>r</mi> <mo>+</mo> <msub> <mi>c&amp;delta;t</mi> <mi>k</mi> </msub> <mo>-</mo> <msup> <mi>c&amp;delta;t</mi> <mi>j</mi> </msup> <mo>+</mo> <msubsup> <mi>&amp;delta;&amp;rho;</mi> <mrow> <mi>t</mi> <mi>r</mi> <mi>o</mi> <mi>p</mi> </mrow> <mi>j</mi> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;delta;&amp;rho;</mi> <mrow> <mi>i</mi> <mi>o</mi> <mi>n</mi> </mrow> <mi>j</mi> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;delta;&amp;rho;</mi> <mrow> <mi>o</mi> <mi>t</mi> <mi>h</mi> <mi>e</mi> <mi>r</mi> <mi>s</mi> </mrow> <mi>j</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
Wherein r is the distance between satellite and receiver, and c is the light velocity, δ tkIt is deviation of the receiver clock relative to the standard time, δtjIt is deviation of the satellite clock relative to the standard time,It is troposphere correction member,It is ionosphere correction member,It is remaining error;
22) satellite i, j and receiver a, the b interspace double difference Pseudo-range Observations in station border are calculated according to formula (2-2):
<mrow> <msubsup> <mi>V&amp;Delta;&amp;rho;</mi> <mrow> <mi>a</mi> <mo>,</mo> <mi>b</mi> </mrow> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>V&amp;Delta;R</mi> <mrow> <mi>a</mi> <mo>,</mo> <mi>b</mi> </mrow> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msubsup> <mo>+</mo> <mo>&amp;dtri;</mo> <msubsup> <mi>&amp;Delta;&amp;delta;&amp;rho;</mi> <mrow> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mi>t</mi> <mi>r</mi> <mi>o</mi> <mi>p</mi> </mrow> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msubsup> <mo>+</mo> <mo>&amp;dtri;</mo> <msubsup> <mi>&amp;Delta;&amp;delta;&amp;rho;</mi> <mrow> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mi>i</mi> <mi>o</mi> <mi>n</mi> </mrow> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msubsup> <mo>+</mo> <mo>&amp;dtri;</mo> <msubsup> <mi>&amp;Delta;&amp;delta;&amp;rho;</mi> <mrow> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mi>o</mi> <mi>t</mi> <mi>h</mi> <mi>e</mi> <mi>r</mi> <mi>s</mi> </mrow> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
WhereinBe stand star away from double difference value,It is the double difference value of tropospheric delay,It is ionization The double difference value of layer delay,It is the double difference value of other errors.
4. the GNSS high-precision locating methods according to claim 1 based on mobile intelligent terminal, it is characterised in that described Elevation angle weighs scheme and is specially surely in step 3):
When the elevation angle of satellite is more than 30 degree, its weights is set to 1;
When elevation of satellite is less than 30 degree, satellite weights are set to sin2E, E are elevation angle;
When elevation of satellite is less than preset height angle threshold value, give up the observation data of the satellite.
5. the GNSS high-precision locating methods according to claim 4 based on mobile intelligent terminal, it is characterised in that described Preset height angle threshold value is 10 degree.
6. the GNSS high-precision locating methods according to claim 1 based on mobile intelligent terminal, it is characterised in that described The calculating process of Kalman filtering includes in step 4):
4.1) assume that current system mode is k, current predicted value is calculated according to a preceding filter result:
Xk,k-1k,k-1Xk-1 (4-1)
Wherein, Xk,k-1It is to utilize the current results of laststate optimal value prediction, Φk,k-1It is equation of motion coefficient, Xk-1It is upper one The result of state optimization;
4.2) error covariance matrix of filter result and system dynamic noise variance matrix calculate the error side of predicted value before Poor battle array:
<mrow> <msub> <mi>Q</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;Phi;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>Q</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msubsup> <mi>&amp;Phi;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>T</mi> </msubsup> <mo>+</mo> <msub> <mi>Q</mi> <mrow> <mi>w</mi> <mi>k</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
Wherein, Qk,k-1It is to utilize the error current variance matrix of last error variance prediction, Qk-1,k-1It is a preceding filter result Error covariance matrix,It is Φk,k-1Transposed matrix, QwkIt is system dynamic noise variance matrix;
4.3) in order to obtain least mean-square error, optimal kalman gain matrix is calculated:
<mrow> <msub> <mi>K</mi> <mi>k</mi> </msub> <mo>=</mo> <msub> <mi>Q</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mi>k</mi> </msub> <msup> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mi>k</mi> </msub> <msub> <mi>Q</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msubsup> <mi>A</mi> <mi>k</mi> <mi>T</mi> </msubsup> <mo>+</mo> <msub> <mi>R</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>-</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
Wherein, KkIt is the optimal estimation value of current state, AkIt is the coefficient of observational equation,It is AkTransposed matrix, RkIt is measurement Noise variance matrix;
4.4) this filter result is calculated:
Xk,k=Xk,k-1+Kk(Lk-AkXk,k-1) (4-4)
Wherein, Xk,kIt is this filter result, LkIt is observation;
4.5) error covariance matrix of this filter result is calculated:
Qk.k=(I-KkAk)Qk,k-1 (4-5)
Wherein, Qk,kIt is the error covariance matrix of this filter result, I is unit matrix.
CN201710977413.9A 2017-10-17 2017-10-17 GNSS high-precision locating methods based on mobile intelligent terminal Pending CN107807373A (en)

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