CN113640834A - Method for improving satellite double-difference pseudo range positioning accuracy - Google Patents

Method for improving satellite double-difference pseudo range positioning accuracy Download PDF

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Publication number
CN113640834A
CN113640834A CN202111200387.1A CN202111200387A CN113640834A CN 113640834 A CN113640834 A CN 113640834A CN 202111200387 A CN202111200387 A CN 202111200387A CN 113640834 A CN113640834 A CN 113640834A
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difference
double
satellite
receiver
pseudorange
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Inventor
曲春凯
周胜洪
陈晓智
王雪松
王翀
张玉国
姜陶然
高航
林治浩
曹睿
李振
刘海龙
侯现钦
刘智勇
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QINGDAO JARI AUTOMATION CO Ltd
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QINGDAO JARI AUTOMATION CO Ltd
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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
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/03—Cooperating elements; Interaction or communication between different cooperating elements or between cooperating elements and receivers
    • G01S19/07—Cooperating elements; Interaction or communication between different cooperating elements or between cooperating elements and receivers providing data for correcting measured positioning data, e.g. DGPS [differential GPS] or ionosphere corrections
    • G01S19/072—Ionosphere corrections
    • 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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems

Abstract

The invention discloses a method for improving satellite double-difference pseudorange positioning accuracy, which comprises the following steps: establishing a pseudo-range observation equation, establishing a single-difference pseudo-range observation equation, establishing a double-difference pseudo-range observation equation, calculating double-difference pseudo-range measurement values, calculating double-difference pseudo-range measurement value residual errors, performing zero-phase Kaiser window filtering on the residual errors, and solving a baseline vector by using the filtered double-difference pseudo-range measurement values. The method utilizes the double-difference pseudorange measurement value to eliminate the satellite clock error, the atmospheric time delay and the receiver clock error, and utilizes the zero-phase Kaiser window to filter and suppress the thermal noise, thereby improving the double-difference pseudorange positioning accuracy. The zero-phase Kaiser window filter can flexibly set filter parameters including the cut-off frequency of the filter, the pitch number of the filter and the attenuation of the filter, can effectively filter noise components, and can not introduce phase errors.

Description

Method for improving satellite double-difference pseudo range positioning accuracy
Technical Field
The invention relates to the field of communication satellite navigation and testing, in particular to a method for improving satellite double-difference pseudorange positioning accuracy.
Background
During differential positioning, there are three types of errors in the pseudorange measurements. The first is satellite-related errors, such as satellite clock error, ephemeris error. The second is propagation-related delay errors that are difficult to correct by the model, such as ionospheric delay, tropospheric delay. The third is the error inherent to various devices, such as thermal noise of satellite transmitters and receivers, etc. The first error can be completely eliminated by differential positioning, the second error can be eliminated by most of the differential positioning, the second error is mainly determined by the positions of a user receiver and a base station, and the third error is difficult to eliminate by the differential positioning and can only be weakened by a filtering noise reduction technology.
Noise is a random signal whose spectrum is spread over the radio frequency range and is one of the main factors affecting the performance of various types of receivers. The noise may be classified into thermal noise, shot noise, and flicker noise. Thermal noise is white noise that is very common in electronic devices and is also a noise component that the present technique considers to cancel. Thermal noise in satellite communication equipment originates mainly from the receiver and the satellite transmitter.
Double-differenced pseudorange location algorithms may remove most of the error but have no effect on thermal noise. The double-difference pseudo range observation quantity containing thermal noise can influence the precision of differential positioning, and simple filtering can introduce phase errors and can also influence the precision of differential positioning.
In summary, it is necessary to design a method for improving the double-differenced pseudorange positioning accuracy of a satellite to solve the problem of poor thermal noise cancellation effect in the prior art.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a method for improving the satellite double-difference pseudorange positioning accuracy, which can flexibly set filter parameters including the cutoff frequency of a filter, the number of filter nodes and the attenuation of the filter, can effectively filter noise components and does not introduce a phase error.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for improving satellite double-differenced pseudorange positioning accuracy, comprising the steps of:
s1, establishing a pseudo-range observation equation:
Figure DEST_PATH_IMAGE001
wherein the content of the first and second substances,
Figure 756375DEST_PATH_IMAGE002
: pseudorange measurements from satellite i to base station receiver r, in units: rice;
Figure 876777DEST_PATH_IMAGE003
: pseudorange calculation for satellite i to base station receiver r, in units: rice;
c: speed of light, unit: m/s;
Figure 125356DEST_PATH_IMAGE004
: clock error of base station receiver r, unit: second;
Figure 989407DEST_PATH_IMAGE005
: clock error of satellite i, unit: second;
Figure 527748DEST_PATH_IMAGE006
: ionospheric delay from satellite i to base station receiver r, unit: rice;
Figure 819052DEST_PATH_IMAGE007
: tropospheric delay from satellite i to base station receiver r, unit: rice;
Figure 351664DEST_PATH_IMAGE009
: pseudorange measurement noise from satellite i to base station receiver r, in units: rice;
s2, establishing a single difference observation equation:
Figure 19406DEST_PATH_IMAGE010
wherein the content of the first and second substances,
Figure 891547DEST_PATH_IMAGE011
: single differenced pseudorange measurements for satellite i by base station receiver r and user receiver u, in units: rice;
Figure 603020DEST_PATH_IMAGE012
: pseudorange measurements from satellite i to user receiver uBit: rice;
Figure 622928DEST_PATH_IMAGE013
: the unit of the difference between the single difference pseudo range calculation value of the base station receiver r to the satellite i and the single difference pseudo range calculation value of the user receiver u to the satellite i is: rice;
Figure 828782DEST_PATH_IMAGE014
: the difference between the clock difference of the base station receiver r and the clock difference of the user receiver u, unit: second;
Figure 821009DEST_PATH_IMAGE015
: difference between pseudorange measurement noise from satellite i to base receiver r and pseudorange measurement noise from satellite i to user receiver u, in units: rice;
s3, establishing a double-difference pseudorange observation equation:
Figure 454115DEST_PATH_IMAGE016
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE017
: double difference pseudorange measurements for satellites i and j by base station receiver r and user receiver u, in units: rice;
Figure 882691DEST_PATH_IMAGE018
: single differenced pseudorange measurements for satellite j by base station receiver r and user receiver u, in units: rice;
Figure 423394DEST_PATH_IMAGE019
：
Figure 535707DEST_PATH_IMAGE013
and
Figure 74135DEST_PATH_IMAGE020
a difference of (d);
Figure 521166DEST_PATH_IMAGE020
the unit of the difference between the single difference pseudo range calculation value of the base station receiver r to the satellite j and the single difference pseudo range calculation value of the user receiver u to the satellite i is: rice;
Figure 68822DEST_PATH_IMAGE021
：
Figure 832379DEST_PATH_IMAGE015
and
Figure 72867DEST_PATH_IMAGE022
the difference value of (a) to (b),
Figure 226768DEST_PATH_IMAGE022
the difference between the pseudorange measurement noise from satellite j to the base receiver r and the pseudorange measurement noise from satellite j to the user receiver u is given by: rice;
Figure 827383DEST_PATH_IMAGE006
: a unit vector of a base station receiver r to the observation direction of a satellite i;
Figure 648708DEST_PATH_IMAGE023
: a unit vector of a base station receiver r to a satellite j observation direction;
Figure 856835DEST_PATH_IMAGE024
for baseline vectors from user receiver u to base receiver r
Figure 763612DEST_PATH_IMAGE025
；
S4, calculating the residual error of the double-difference pseudorange measurement value:
Figure 653070DEST_PATH_IMAGE026
Figure DEST_PATH_IMAGE027
: a double-difference pseudo range fitting value is obtained by performing high-order fitting on a double-difference pseudo range measured value;
s5, designing a Kaiser window low-pass filter:
the low pass filter designed using the Kaiser window as the window function is:
Figure 47011DEST_PATH_IMAGE028
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE029
is the impulse response of an ideal digital low-pass filter;
Figure 894882DEST_PATH_IMAGE030
is a Kaiser window function;
s6, performing zero-phase filtering on the residual error given in the S4 to obtain a filtered double-difference pseudorange measurement value:
Figure 288954DEST_PATH_IMAGE031
wherein the content of the first and second substances,
Figure 965792DEST_PATH_IMAGE032
: filtering the double difference pseudorange measurement;
Figure 496130DEST_PATH_IMAGE033
: filtering out the double-difference pseudorange measurement residual errors after noise filtering;
s7, constructing a double-difference observation equation set by using the filtered double-difference pseudo-range measured values and solving a baseline vector
Figure 46060DEST_PATH_IMAGE034
。
In some embodiments of the invention, the impulse response of the ideal digital low-pass filter
Figure 927429DEST_PATH_IMAGE029
The following formula is satisfied:
Figure 424269DEST_PATH_IMAGE035
wherein the content of the first and second substances,
Figure 58381DEST_PATH_IMAGE036
is the normalized cut-off frequency of the filter,
Figure 716896DEST_PATH_IMAGE037
is the filter window length.
In some embodiments of the invention, the Kaiser window function
Figure 882298DEST_PATH_IMAGE030
The following formula is satisfied:
Figure 917250DEST_PATH_IMAGE038
wherein the content of the first and second substances,
Figure 687760DEST_PATH_IMAGE039
a first type of modified zero order Bessel function;
Figure 518442DEST_PATH_IMAGE040
is an adjustable parameter.
In some embodiments of the present invention, the zero-phase filtering in step S6 is performed by using an FRR method.
In some embodiments of the present invention, the time-domain description filtered by the FRR method may be expressed as:
Figure DEST_PATH_IMAGE041
Figure 639982DEST_PATH_IMAGE042
Figure 478625DEST_PATH_IMAGE043
Figure 838062DEST_PATH_IMAGE044
wherein, N is the sequence length,
Figure DEST_PATH_IMAGE045
；
Figure 556488DEST_PATH_IMAGE046
representing input sequences, i.e. double-differenced pseudorange measurement residuals
Figure 634166DEST_PATH_IMAGE047
；
Figure 73237DEST_PATH_IMAGE048
Representing the result after filtering or sequence inversion,
Figure DEST_PATH_IMAGE049
for double-differenced pseudorange measurement residuals after filtering noise, i.e.
Figure 5290DEST_PATH_IMAGE032
。
In some embodiments of the present invention, the step of constructing the double-difference observation equation set in step S7 is:
if the base station receiver r and the user receiver u have pseudo-range measurements for M satellites, then M-1 mutually independent double-differenced pseudo-range observation equations may form a matrix equation as follows:
Figure 442088DEST_PATH_IMAGE050
=
Figure DEST_PATH_IMAGE051
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE053
the remaining residual is.
In some embodiments of the invention, the baseline vector
Figure 741482DEST_PATH_IMAGE034
The solution is performed by the least square method.
Compared with the prior art, the technical scheme of the invention has the following technical effects:
the method utilizes the double-difference pseudorange measurement value to eliminate the satellite clock error, the atmospheric time delay and the receiver clock error, and utilizes the zero-phase Kaiser window to filter and suppress the thermal noise, thereby improving the double-difference pseudorange positioning accuracy. The zero-phase Kaiser window filter can flexibly set filter parameters including the cut-off frequency of the filter, the pitch number of the filter and the attenuation of the filter, can effectively filter noise components, and can not introduce phase errors.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a diagram illustrating calculation of the double-differenced pseudorange measurements.
Fig. 2 is a diagram showing the actual amplitude characteristic of the low-pass filter.
FIG. 3 is a schematic view of the shape of the Kaiser window for different values of α.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it should be noted that the terms "mounted," "connected," and "connected" are to be construed broadly and may be, for example, fixedly connected, detachably connected, or integrally connected unless otherwise explicitly stated or limited. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art. In the foregoing description of embodiments, the particular features, structures, materials, or characteristics may be combined in any suitable manner in any one or more embodiments or examples.
In the process of propagation, Beidou satellite signals are affected by factors such as an ionosphere, a troposphere, a broadcast ephemeris error, a satellite clock error, tides and a relativistic effect, so that the positioning accuracy errors are larger, but the errors are closely related to 2 geographically adjacent Beidou receivers, so that most of the errors can be cancelled out by establishing a differential equation to obtain a relatively accurate baseline azimuth solution, but the cost is that the double-difference pseudorange measurement value noise is increased. The invention can effectively eliminate the noise of the double-difference pseudo-range measured value by a zero-phase Kaiser window filtering mode.
The method specifically comprises the following steps:
a method for improving satellite double-differenced pseudorange positioning accuracy, comprising the steps of:
s1, establishing a pseudo-range observation equation:
Figure 171195DEST_PATH_IMAGE001
wherein the content of the first and second substances,
Figure 239645DEST_PATH_IMAGE054
: pseudorange measurements from satellite i to base station receiver r, in units: rice;
Figure 847344DEST_PATH_IMAGE003
: pseudorange calculation for satellite i to base station receiver r, in units: rice;
c: speed of light, unit: m/s;
Figure DEST_PATH_IMAGE055
: clock error of base station receiver r, unit: second;
Figure 165193DEST_PATH_IMAGE056
: clock error of satellite i, unit: second;
Figure 133018DEST_PATH_IMAGE006
: ionospheric delay from satellite i to base station receiver r, unit: rice;
Figure 587133DEST_PATH_IMAGE057
: tropospheric delay from satellite i to base station receiver r, unit: rice;
Figure 100154DEST_PATH_IMAGE059
: pseudorange measurement noise from satellite i to base station receiver r, in units: rice;
s2, establishing a single difference observation equation:
single differencing is the first difference between the receivers to the same satellite measurement, and single differencing pseudo-range measurements of the base receiver r and the user receiver u to the satellite i
Figure 639720DEST_PATH_IMAGE060
The definition and observation equation of (a) is as follows:
Figure 958706DEST_PATH_IMAGE061
wherein the content of the first and second substances,
Figure 516595DEST_PATH_IMAGE060
: single differenced pseudorange measurements for satellite i by base station receiver r and user receiver u, in units: rice;
Figure 466096DEST_PATH_IMAGE062
: pseudorange measurements from satellite i to user receiver u, in units: rice;
Figure 961800DEST_PATH_IMAGE063
: the unit of the difference between the single difference pseudo range calculation value of the base station receiver r to the satellite i and the single difference pseudo range calculation value of the user receiver u to the satellite i is: rice;
Figure 287739DEST_PATH_IMAGE064
: the difference between the clock difference of the base station receiver r and the clock difference of the user receiver u, unit: second;
Figure 700134DEST_PATH_IMAGE065
: difference between pseudorange measurement noise from satellite i to base receiver r and pseudorange measurement noise from satellite i to user receiver u, in units: rice;
s3, establishing a double-difference pseudorange observation equation:
the double difference is the difference between the single differences of two different satellites, i.e. the difference is obtained between the stations and between the satellites. Double differenced pseudorange measurements to satellites i and j by base receiver r and user receiver u
Figure 617275DEST_PATH_IMAGE066
The definition and observation equation of (1) are:
Figure 131433DEST_PATH_IMAGE067
wherein the content of the first and second substances,
Figure 729904DEST_PATH_IMAGE066
: double difference pseudorange measurements for satellites i and j by base station receiver r and user receiver u, in units: rice;
Figure 747539DEST_PATH_IMAGE068
: single differenced pseudorange measurements for satellite j by base station receiver r and user receiver u, in units: rice;
Figure 553690DEST_PATH_IMAGE069
：
Figure 289565DEST_PATH_IMAGE063
and
Figure 957306DEST_PATH_IMAGE070
a difference of (d);
Figure 626185DEST_PATH_IMAGE070
the unit of the difference between the single difference pseudo range calculation value of the base station receiver r to the satellite j and the single difference pseudo range calculation value of the user receiver u to the satellite i is: rice;
Figure 353970DEST_PATH_IMAGE071
：
Figure 832268DEST_PATH_IMAGE065
and
Figure 38121DEST_PATH_IMAGE072
the difference value of (a) to (b),
Figure 764769DEST_PATH_IMAGE072
the difference between the pseudorange measurement noise from satellite j to the base receiver r and the pseudorange measurement noise from satellite j to the user receiver u is given by: rice and its production process；
Figure 663454DEST_PATH_IMAGE006
: a unit vector of a base station receiver r to the observation direction of a satellite i;
Figure 905080DEST_PATH_IMAGE073
: a unit vector of a base station receiver r to a satellite j observation direction;
Figure 163892DEST_PATH_IMAGE034
for baseline vectors from user receiver u to base receiver r
Figure 276204DEST_PATH_IMAGE074
；
Fig. 1 is a schematic diagram of double-difference pseudorange measurement values, in which a user receiver u and a base station receiver r observe a satellite i and a satellite j respectively, and the pseudoranges thereof are used to form double-difference pseudorange observations.
Figure 814633DEST_PATH_IMAGE075
Where is the baseline vector of user receiver u to base receiver r,
Figure 12396DEST_PATH_IMAGE054
is the pseudorange measurement from satellite i to receiver r,
Figure 809320DEST_PATH_IMAGE006
is a unit vector of the direction of observation of satellite i by the base station receiver,
Figure 776139DEST_PATH_IMAGE076
the pseudoranges are computed for the base receiver r and the user receiver u for satellite i.
S4, calculating the residual error of the double-difference pseudorange measurement value:
performing high-order fitting on the double-difference pseudo range measured value to obtain a double-difference pseudo range fitted value
Figure 547786DEST_PATH_IMAGE027
And with double differenced pseudorange measurements
Figure 232845DEST_PATH_IMAGE066
And (3) carrying out difference to obtain a double-difference pseudorange measurement value residual error:
Figure 584192DEST_PATH_IMAGE026
s5, designing a Kaiser window low-pass filter:
the low pass filter designed using the Kaiser window as the window function is:
Figure 389206DEST_PATH_IMAGE028
wherein the content of the first and second substances,
Figure 800595DEST_PATH_IMAGE029
is the impulse response of an ideal digital low-pass filter;
Figure 504109DEST_PATH_IMAGE030
is a Kaiser window function;
with respect to filters, transfer functions of filters
Figure 393568DEST_PATH_IMAGE077
Can be expressed in polar coordinates as:
Figure 334979DEST_PATH_IMAGE078
in the formula (I), the compound is shown in the specification,
Figure 635379DEST_PATH_IMAGE079
、
Figure 29451DEST_PATH_IMAGE080
referred to as the amplitude response and the phase response of the filter, respectively, expressed as:
Figure 722601DEST_PATH_IMAGE081
Figure 315256DEST_PATH_IMAGE082
where Re () is the real part of the function, Im () is the imaginary part of the function, j is the imaginary unit, and ω is the digital frequency.
According to the amplitude response of the filter, the filter can be divided into four types of filters, namely a low-pass filter, a high-pass filter, a pass band filter and a stop band filter, when the filter is actually designed, the filter is allowed to have certain deviation from an ideal state in the pass band and the stop band filter according to actual filtering requirements, and a transition band is allowed between the pass band and the stop band filter. Taking a low-pass filter as an example, the actual amplitude-frequency characteristic of the filter is shown in fig. 2. The abscissa is angular frequency and the ordinate is amplitude.
Figure 68449DEST_PATH_IMAGE083
、
Figure 933505DEST_PATH_IMAGE084
Referred to as passband ripple and stopband ripple, respectively;
Figure 164767DEST_PATH_IMAGE085
、
Figure 815191DEST_PATH_IMAGE086
referred to as passband cutoff frequency and stopband cutoff frequency, respectively;
Figure 536022DEST_PATH_IMAGE087
referred to as the transition zone. The frequency components in the stop band are regarded as harmful components, the amplitude of the frequency components after filtering is obviously suppressed, the frequency components in the pass band are regarded as useful components, and the amplitude of the frequency components after filtering is not influenced, so that the aim of filtering the harmful components is fulfilled.
When designing a filter, the amplitude characteristics are generally determined by the attenuation given to the pass band and stop band, and the attenuation a (ω) is generally determined by the magnitude square function or modulo square function reflecting the power gain
Figure DEST_PATH_IMAGE088
To define, namely:
Figure 357216DEST_PATH_IMAGE089
so pass band attenuation
Figure 392169DEST_PATH_IMAGE090
And stopband attenuation
Figure 897099DEST_PATH_IMAGE091
Can be expressed as:
Figure DEST_PATH_IMAGE092
Figure 257673DEST_PATH_IMAGE093
the invention needs a low-pass filter to filter out the high-frequency thermal noise in the original signal, and improves the signal-to-noise ratio of the signal, so as to improve the double-difference positioning resolving precision. Considering that the FIR digital filter can have strict linear phase and can adopt fast Fourier transform when realizing filtering, the invention designs a low-pass FIR digital filter by using a window function method. The Kaiser window has adjustability.
The Kaiser window function
Figure 362902DEST_PATH_IMAGE030
The following formula is satisfied:
Figure 670386DEST_PATH_IMAGE038
wherein the content of the first and second substances,
Figure 295402DEST_PATH_IMAGE039
a first type of modified zero order Bessel function;
Figure DEST_PATH_IMAGE094
the following number of stages can be used for calculation:
Figure 826878DEST_PATH_IMAGE095
Figure 147964DEST_PATH_IMAGE040
is a tunable parameter, and is related to the main lobe width and the side lobe attenuation. In general terms, the amount of the solvent to be used,
Figure 790298DEST_PATH_IMAGE040
the larger the transition band, the wider the stop band, and the greater the attenuation.
FIG. 3 is the shape of a Kaiser window; if the stopband minimum attenuation is expressed as
Figure 269820DEST_PATH_IMAGE096
Then, then
Figure 441039DEST_PATH_IMAGE040
The following empirical formula may be used for the determination of (c):
Figure 255280DEST_PATH_IMAGE097
if the filter passband and stopband ripple are equal, i.e.
Figure 170146DEST_PATH_IMAGE098
Then the number of filter sections N can be determined by:
Figure 769755DEST_PATH_IMAGE099
the most basic parameter of the Kaiser low-pass filter is the cut-off frequency
Figure 174191DEST_PATH_IMAGE100
Filter number N and Kaiser window parameter alpha. But in the actual design of the filter,the Kaiser window parameter alpha is not intuitive enough and filter attenuation is usually chosen
Figure 226461DEST_PATH_IMAGE101
，
Figure 194286DEST_PATH_IMAGE101
And α can be converted by a formula.
And the double-difference pseudo-range measurement value is filtered by using a zero-phase Kaiser window low-pass filter and then subjected to double-difference positioning calculation, so that the settlement precision of the baseline vector from the user receiver to the base station receiver can be greatly improved.
Impulse response of the ideal digital low-pass filter
Figure 648401DEST_PATH_IMAGE029
The following formula is satisfied:
Figure 161422DEST_PATH_IMAGE035
wherein the content of the first and second substances,
Figure 700988DEST_PATH_IMAGE036
is the normalized cut-off frequency of the filter,
Figure 472503DEST_PATH_IMAGE037
is the filter window length.
S6, performing zero-phase filtering on the residual error given in the S4 to obtain a filtered double-difference pseudorange measurement value:
Figure 577863DEST_PATH_IMAGE031
wherein the content of the first and second substances,
Figure 527364DEST_PATH_IMAGE032
: filtering the double difference pseudorange measurement;
Figure 23068DEST_PATH_IMAGE033
: filtering out the double-difference pseudorange measurement residual errors after noise filtering;
regarding zero phase filtering, after a signal passes through a filter system, the amplitude of each frequency component of the signal is multiplied by the mode of the amplitude response of the system, so that the effect of changing the energy of different frequency components of the signal is achieved, and the effect of filtering noise is achieved. The filter system adds a phase to the original signal phase while changing the amplitude-frequency property of the signal, which is called the phase shift of the system. If such a change in phase is not desired, it can cause phase distortion and affect data quality.
When double difference pseudo-range measurement data are filtered, the phase is not expected to change, and the zero-phase filter has the characteristic of a zero-phase system, so that accurate zero-phase distortion signals can be obtained. The FRR method can be adopted for realizing the zero-phase filtering, firstly, the input sequence is filtered in sequence (forward filter), then, the obtained result is reversed and then passes through a filter (reverse filter), and then, the obtained result is reversed and output (reverse output), and the output sequence with accurate zero-phase distortion is obtained.
The time-domain description of the FRR method filtering can be expressed as:
Figure 349007DEST_PATH_IMAGE041
Figure 308872DEST_PATH_IMAGE102
Figure 678543DEST_PATH_IMAGE103
Figure 192701DEST_PATH_IMAGE104
wherein, N is the sequence length,
Figure 791172DEST_PATH_IMAGE045
；
Figure 808807DEST_PATH_IMAGE046
representing input sequences, i.e. double-differenced pseudorange measurement residuals
Figure 162428DEST_PATH_IMAGE047
；
Figure 147570DEST_PATH_IMAGE048
Representing the result after filtering or sequence inversion,
Figure 284153DEST_PATH_IMAGE049
for double-differenced pseudorange measurement residuals after filtering noise, i.e.
Figure 421874DEST_PATH_IMAGE032
。
The frequency descriptions of FRR filtering are:
Figure 149658DEST_PATH_IMAGE105
Figure 903988DEST_PATH_IMAGE106
Figure 624688DEST_PATH_IMAGE107
Figure 351335DEST_PATH_IMAGE108
this gives:
Figure 984442DEST_PATH_IMAGE109
from the above equation, output
Figure 694909DEST_PATH_IMAGE110
And input
Figure 501191DEST_PATH_IMAGE111
There is no additional phase between, FRR achieves accurate zero phase distortion filtering. The invention adopts the method to carry out zero phase filtering, and in order to reduce the boundary effect problem which is encountered by digital filtering, the prolongation which is the same as the node number of the filter is respectively carried out in the head and tail directions of the data before the filtering. Let the original data be
Figure 597192DEST_PATH_IMAGE112
The data amount is N, the filter number is M, and the expanded data can be expressed as:
Figure 401200DEST_PATH_IMAGE113
s7, constructing a double-difference observation equation set by using the filtered double-difference pseudo-range measured values and solving a baseline vector
Figure 333384DEST_PATH_IMAGE034
：
The double-difference observation equation set is constructed by the following steps:
if the base station receiver r and the user receiver u have pseudo-range measurements for M satellites, then M-1 mutually independent double-differenced pseudo-range observation equations may form a matrix equation as follows:
Figure 943357DEST_PATH_IMAGE050
=
Figure 910176DEST_PATH_IMAGE051
in the formula (I), the compound is shown in the specification,
Figure 140212DEST_PATH_IMAGE053
the remaining residual is.
Ignoring pseudorange measurement noise
Figure 559692DEST_PATH_IMAGE071
Given a sufficient number of double-differenced pseudorange measurementsUnder the condition (2), the receiver can theoretically solve the baseline vector from the above matrix equation
Figure 911039DEST_PATH_IMAGE034
(ii) a The baseline vector
Figure 529102DEST_PATH_IMAGE034
The solution is performed by the least square method.
But double differenced pseudorange measurement noise
Figure 674913DEST_PATH_IMAGE114
The existence of the pseudo-range can obviously influence the solution of the baseline vector, so that the invention effectively eliminates the influence of double-difference pseudo-range measurement noise through zero-phase kaiser window filtering.
In the foregoing description of embodiments, the particular features, structures, materials, or characteristics may be combined in any suitable manner in any one or more embodiments or examples.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (7)

1. A method for improving satellite double-differenced pseudorange positioning accuracy, comprising the steps of:
s1, establishing a pseudo-range observation equation:
Figure RE-708183DEST_PATH_IMAGE002
wherein the content of the first and second substances,
Figure RE-RE-DEST_PATH_IMAGE003
: satellite i to base stationPseudorange measurement for receiver r, unit: rice;
Figure RE-RE-DEST_PATH_IMAGE005
: pseudorange calculation for satellite i to base station receiver r, in units: rice;
c: speed of light, unit: m/s;
Figure RE-72300DEST_PATH_IMAGE006
: clock error of base station receiver r, unit: second;
Figure RE-RE-DEST_PATH_IMAGE007
: clock error of satellite i, unit: second;
Figure RE-245530DEST_PATH_IMAGE008
: ionospheric delay from satellite i to base station receiver r, unit: rice;
Figure RE-RE-DEST_PATH_IMAGE009
: tropospheric delay from satellite i to base station receiver r, unit: rice;
Figure RE-706598DEST_PATH_IMAGE010
: pseudorange measurement noise from satellite i to base station receiver r, in units: rice;
s2, establishing a single difference observation equation:
Figure RE-667601DEST_PATH_IMAGE012
wherein the content of the first and second substances,
Figure RE-RE-DEST_PATH_IMAGE013
: single differenced pseudorange measurements for satellite i by base station receiver r and user receiver u, in units: rice;
Figure RE-581330DEST_PATH_IMAGE014
: pseudorange measurements from satellite i to user receiver u, in units: rice;
Figure RE-RE-DEST_PATH_IMAGE015
: the unit of the difference between the single difference pseudo range calculation value of the base station receiver r to the satellite i and the single difference pseudo range calculation value of the user receiver u to the satellite i is: rice;
Figure RE-794137DEST_PATH_IMAGE016
: the difference between the clock difference of the base station receiver r and the clock difference of the user receiver u, unit: second;
Figure RE-RE-DEST_PATH_IMAGE017
: difference between pseudorange measurement noise from satellite i to base receiver r and pseudorange measurement noise from satellite i to user receiver u, in units: rice;
s3, establishing a double-difference pseudorange observation equation:
Figure RE-RE-DEST_PATH_IMAGE019
wherein the content of the first and second substances,
Figure RE-283281DEST_PATH_IMAGE020
: double difference pseudorange measurements for satellites i and j by base station receiver r and user receiver u, in units: rice;
Figure RE-RE-DEST_PATH_IMAGE021
: single differenced pseudorange measurements for satellite j by base station receiver r and user receiver u, in units: rice;
Figure RE-415185DEST_PATH_IMAGE022
：
Figure RE-550631DEST_PATH_IMAGE015
and
Figure RE-RE-DEST_PATH_IMAGE023
a difference of (d);
Figure RE-301549DEST_PATH_IMAGE023
the unit of the difference between the single difference pseudo range calculation value of the base station receiver r to the satellite j and the single difference pseudo range calculation value of the user receiver u to the satellite i is: rice;
Figure RE-330685DEST_PATH_IMAGE024
：
Figure RE-7392DEST_PATH_IMAGE017
and
Figure RE-RE-DEST_PATH_IMAGE025
the difference value of (a) to (b),
Figure RE-161293DEST_PATH_IMAGE025
the difference between the pseudorange measurement noise from satellite j to the base receiver r and the pseudorange measurement noise from satellite j to the user receiver u is given by: rice;
Figure RE-574956DEST_PATH_IMAGE008
: a unit vector of a base station receiver r to the observation direction of a satellite i;
Figure RE-68386DEST_PATH_IMAGE026
: a unit vector of a base station receiver r to a satellite j observation direction;
Figure RE-RE-DEST_PATH_IMAGE027
for baseline vectors from user receiver u to base receiver r
Figure RE-RE-DEST_PATH_IMAGE029
；
S4, calculating the residual error of the double-difference pseudorange measurement value:
Figure RE-RE-DEST_PATH_IMAGE031
Figure RE-745355DEST_PATH_IMAGE032
: a double-difference pseudo range fitting value is obtained by performing high-order fitting on a double-difference pseudo range measured value;
s5, designing a Kaiser window low-pass filter:
the low pass filter designed using the Kaiser window as the window function is:
Figure RE-108857DEST_PATH_IMAGE034
wherein the content of the first and second substances,
Figure RE-RE-DEST_PATH_IMAGE035
is the impulse response of an ideal digital low-pass filter;
Figure RE-201578DEST_PATH_IMAGE036
is a Kaiser window function;
s6, performing zero-phase filtering on the residual error given in the S4 to obtain a filtered double-difference pseudorange measurement value:
Figure RE-939727DEST_PATH_IMAGE038
wherein the content of the first and second substances,
Figure RE-RE-DEST_PATH_IMAGE039
: filtering the double difference pseudorange measurement;
Figure RE-725280DEST_PATH_IMAGE040
: filtering out the double-difference pseudorange measurement residual errors after noise filtering;
s7, constructing a double-difference observation equation set by using the filtered double-difference pseudo-range measured values and solving a baseline vector
Figure RE-RE-DEST_PATH_IMAGE041
。
2. The method for improving satellite double-differenced pseudorange positioning accuracy of claim 1, wherein impulse response of ideal digital low pass filter
Figure RE-588194DEST_PATH_IMAGE035
The following formula is satisfied:
Figure RE-RE-DEST_PATH_IMAGE043
wherein the content of the first and second substances,
Figure RE-609240DEST_PATH_IMAGE044
is the normalized cut-off frequency of the filter,
Figure RE-RE-DEST_PATH_IMAGE045
is the filter window length.
3. The method of claim 1, wherein said Kaiser window function is a function of a single pseudorange to a single pseudorange
Figure RE-106955DEST_PATH_IMAGE036
The following formula is satisfied:
Figure RE-RE-DEST_PATH_IMAGE047
wherein the content of the first and second substances,
Figure RE-63409DEST_PATH_IMAGE048
a first type of modified zero order Bessel function;
Figure RE-882461DEST_PATH_IMAGE050
is an adjustable parameter.
4. The method of claim 1, wherein the zero-phase filtering in step S6 is performed by FRR method.
5. The method of claim 4, wherein the FRR-method-filtered time-domain description is represented by:
Figure RE-176039DEST_PATH_IMAGE052
Figure RE-888780DEST_PATH_IMAGE054
Figure RE-484978DEST_PATH_IMAGE056
Figure RE-915959DEST_PATH_IMAGE058
wherein, N is the sequence length,
Figure RE-RE-DEST_PATH_IMAGE059
；
Figure RE-655638DEST_PATH_IMAGE060
representing input sequences, i.e. double-differenced pseudorange measurement residuals
Figure RE-RE-DEST_PATH_IMAGE061
；
Figure RE-629410DEST_PATH_IMAGE062
Representing the result after filtering or sequence inversion,
Figure RE-RE-DEST_PATH_IMAGE063
for double-differenced pseudorange measurement residuals after filtering noise, i.e.
Figure RE-662089DEST_PATH_IMAGE039
。
6. The method of claim 1, wherein the constructing of the double-difference observation equation set in step S7 comprises:
if the base station receiver r and the user receiver u have pseudo-range measurements for M satellites, then M-1 mutually independent double-differenced pseudo-range observation equations may form a matrix equation as follows:
Figure RE-580366DEST_PATH_IMAGE064
=
Figure RE-356692DEST_PATH_IMAGE065
in the formula (I), the compound is shown in the specification,
Figure RE-DEST_PATH_IMAGE066
the remaining residual is.
7. The method of claim 1, wherein the baseline vector is used to improve accuracy of double-differenced pseudorange positioning
Figure RE-44025DEST_PATH_IMAGE041
The solution is performed by the least square method.
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