CN115407379A - Ambiguity resolution method based on pseudo satellite and UWB fusion positioning system - Google Patents

Ambiguity resolution method based on pseudo satellite and UWB fusion positioning system Download PDF

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CN115407379A
CN115407379A CN202211039075.1A CN202211039075A CN115407379A CN 115407379 A CN115407379 A CN 115407379A CN 202211039075 A CN202211039075 A CN 202211039075A CN 115407379 A CN115407379 A CN 115407379A
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pseudolite
receiver
uwb
difference
ambiguity
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王庆
刘昊
许九靖
张波
吴新祺
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Southeast University
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Southeast University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position
    • G01S19/43—Determining position using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
    • G01S19/44—Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
    • 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
    • G01S19/396—Determining accuracy or reliability of position or pseudorange measurements
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position
    • G01S19/45—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement
    • G01S19/46—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement the supplementary measurement being of a radio-wave signal type

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  • 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 an ambiguity resolution method based on a pseudo satellite and a UWB fusion positioning system, which is characterized in that when a carrier phase observation equation of a pseudo satellite is used for resolving a floating solution of ambiguity and a covariance matrix of the ambiguity, the floating solution of a UWB distance measurement result and the covariance matrix of the UWB distance measurement result are added, so that the floating solution of the pseudo satellite and the UWB fusion positioning system and the covariance matrix of the pseudo satellite and the UWB fusion positioning system are obtained, and then the system floating solution and the covariance matrix are used for fixing the ambiguity by using LAMBDA. The method solves the problem of fixed carrier phase integer ambiguity of the pseudo-satellite and UWB integrated positioning system, and enables the positioning result of the pseudo-satellite and UWB integrated positioning system to be more stable and reliable.

Description

Ambiguity resolution method based on pseudo satellite and UWB fusion positioning system
Technical Field
The invention relates to an ambiguity resolution method based on a pseudo satellite and UWB fusion positioning system, belonging to the technical field of radio navigation positioning.
Background
The resolution of the integer ambiguity is a critical issue in high precision positioning. LAMBDA (Least-square AMBiguity correlation Adjustment) search speed is high, and the method is a widely applied integer AMBiguity resolution method. However, LAMBDA is generally only used for one ambiguity fixing problem of the positioning system. For a fusion positioning system based on a pseudolite and a UWB, the conventional common LAMBDA aiming at a single system cannot be used for fixing the ambiguity.
Disclosure of Invention
The invention provides an ambiguity resolution method based on a pseudo satellite and UWB fusion positioning system, which is characterized in that a covariance matrix of the fusion positioning system based on the pseudo satellite and the UWB is provided, then the covariance matrix of the fusion positioning system is utilized to resolve the ambiguity of the whole circle, and the problem that the LAMBDA can not fix the ambiguity of the fusion positioning system based on the pseudo satellite and the UWB is solved.
The method for solving the problems is realized by the following technical scheme:
step 1, UWB ranging value acquisition and positioning: according to the TOF positioning method, quickly obtaining distance measurement values between the user receiver and each base station, namely UWB distance measurement values, recording the distance measurement values as UWB distance measurement results d, and further calculating to obtain UWB positioning results;
step 2, acquiring and positioning a pseudolite carrier phase observed value: the pseudolite carrier phase observation value is the phase difference between a pseudolite carrier signal received by the receiver and a reference pseudolite carrier signal generated by a receiver oscillator, and then a carrier phase observation equation of the pseudolite is constructed by using the pseudolite carrier phase observation value to solve to obtain a positioning result of the pseudolite;
step 3, initializing a positioning algorithm: the pseudo range of the pseudo satellite is the measured distance between the pseudo satellite and a receiver, the measured distance contains error factors and is not the real geometric distance of the satellite, so the pseudo range is called as pseudo range, different pseudo satellite carrier phase observation equations are obtained by observing through different receivers, the pseudo satellite carrier phase single difference observation equation is obtained by subtracting, the pseudo range is initialized by the UWB positioning result obtained in the step 1, the pseudo range of the pseudo satellite is replaced by the UWB ranging result d and is substituted into the pseudo satellite carrier phase single difference observation equation, and the carrier phase integer ambiguity is enabled to obtain an initial value;
and 4, resolving and checking the integer ambiguity.
Further, the specific method of step 1 is:
the UWB based on the TOF positioning single-side two-way ranging method is that a UWB base station actively transmits data, simultaneously records a transmission time stamp, and a receiver records a receiving time stamp after receiving the data; delayed by T reply Then, the receiver sends data and simultaneously records a sending time stamp, and the base station receives the data and simultaneously records a receiving time stamp; obtaining a base station time difference T round Sum receiver time difference T reply ；
The transmission time T of the signal between the exciter and the receiver prop Comprises the following steps:
Figure BDA0003820227350000021
the ranging result d of the UWB is:
d＝T prop c
where c is the speed of light.
Further, the specific method of step 2 is:
let the initial phase of the pseudolite carrier signal received by the receiver be
Figure BDA0003820227350000022
The initial phase of the reference pseudolite carrier signal generated by the receiver oscillator is
Figure BDA0003820227350000023
The carrier signal transmission time is
Figure BDA0003820227350000024
The carrier signal having a frequency f and the receiver clock difference being δ t r The pseudolite clock error being δ t s ，
The phase of the pseudolite carrier signal received by the receiver at time t
Figure BDA0003820227350000025
Is that
Figure BDA0003820227350000026
Phase of reference pseudolite carrier signal generated by receiver oscillator at time t
Figure BDA0003820227350000027
Is that
Figure BDA0003820227350000028
The difference between them, i.e. carrier phase observations of pseudolites
Figure BDA0003820227350000029
Is that
Figure BDA00038202273500000210
In the formula
Figure BDA00038202273500000211
In order to obtain the whole-cycle ambiguity,
Figure BDA00038202273500000212
observing an error term for the carrier phase;
for the wavelength lambda, knowing that c = lambda · f, substituting the formula into the above equation to construct the pseudolite carrier phase observation equation
Figure BDA00038202273500000213
In the formula
Figure BDA00038202273500000214
Is the geometric distance of the pseudolite from the receiver,
Figure BDA00038202273500000215
is the tropospheric induced phase difference.
Further, the specific method of step 3 is:
if two receivers i and j simultaneously observe the same pseudolite p, the carrier phase observation equation for the receiver i to observe the pseudolite p is as follows:
Figure BDA00038202273500000216
in the formula
Figure BDA00038202273500000217
Is the carrier phase observation of the pseudolite p observed by the receiver i,
Figure BDA00038202273500000218
is the geometric distance, deltat, of the receiver i from the pseudolite p i Is the clock difference, δ t, of the receiver i p Is the clock error of the pseudolite p,
Figure BDA00038202273500000219
is the troposphere induced phase difference when the receiver i observes the pseudolite p,
Figure BDA00038202273500000220
is the initial phase of the pseudolite carrier signal received by the receiver,
Figure BDA00038202273500000221
is the initial phase of the reference pseudolite p-carrier signal generated by the receiver oscillator,
Figure BDA00038202273500000222
is the integer ambiguity, e, of the receiver i observing the pseudolite p i Is the carrier phase observation error term of receiver i;
the carrier phase observation equation observed by receiver j pseudolite p is:
Figure BDA0003820227350000031
in the formula
Figure BDA0003820227350000032
Is the carrier phase observation that receiver j observes pseudolite p,
Figure BDA0003820227350000033
is the geometric distance, deltat, of the receiver j from the pseudolite p j Is the clock difference of the receiver j,
Figure BDA0003820227350000034
is the tropospheric induced phase difference when the receiver j observes the pseudolite p,
Figure BDA0003820227350000035
is the integer ambiguity, e, of the receiver j observing the pseudolite p j Is the carrier phase observation error term for receiver j;
and the two receivers i and j simultaneously observe the carrier phase observation equation of the same pseudolite p to make difference to obtain a pseudolite carrier phase single difference observation equation:
Figure BDA0003820227350000036
in the formula
Figure BDA0003820227350000037
The difference between the observed carrier phase values of two receivers i and j in the same epoch for the same pseudolite p,
Figure BDA0003820227350000038
the difference between the geometric distances of two receivers i, j to the same pseudolite p in the same epoch,
Figure BDA0003820227350000039
delta Tp is the difference in phase difference caused by the troposphere when two receivers epsilon, j observe pseudolite p for a single difference integer ambiguity,Δ e is the difference between the observation error terms when the two receivers i, j observe the pseudolite p.
Further, step 4 specifically includes:
step 4.1: calculating a floating point solution based on a pseudo satellite and UWB fusion positioning system and a corresponding covariance matrix:
variance σ of UWB observation data 2 The calculation is as follows:
Figure BDA00038202273500000310
in the formula, x i The ith observation for a set of UWB observation sample samples,
Figure BDA00038202273500000311
is the sample mean value, and n is the number of UWB observation data in the sample;
constructing covariance matrix Q of observation data dd Comprises the following steps:
Figure BDA00038202273500000312
in the formula (I), the compound is shown in the specification,
Figure BDA00038202273500000313
the variances of n groups of different UWB observation data sample samples are respectively;
and (3) linearizing the carrier phase single difference observation equation to obtain:
y＝Aa+Bb+e
in the formula, y is a single difference observation vector; a is the wavelength with algebraic sign after linearization, and the sign is negative, so A = -lambda; a is a single-difference ambiguity parameter; b is a cosine value from the approximate position of the receiver to each direction of the pseudolite; b is a receiver coordinate parameter; e is a measurement noise vector;
the observation data of the pseudolite and the UWB are independent, so that a floating point solution based on the pseudolite and the UWB fusion positioning system is obtained according to the least square, and the corresponding covariance matrix is as follows;
Figure BDA00038202273500000314
in the formula
Figure BDA00038202273500000315
For a single-difference ambiguity floating-point solution,
Figure BDA00038202273500000316
for the floating-point solution of the receiver coordinates,
Figure BDA00038202273500000317
a solution is floated for the UWB ranging result,
Figure BDA00038202273500000318
is composed of
Figure BDA0003820227350000041
The covariance matrix of (a) is obtained,
Figure BDA0003820227350000042
is composed of
Figure BDA0003820227350000043
And
Figure BDA0003820227350000044
the covariance matrix of (a) is obtained,
Figure BDA0003820227350000045
is composed of
Figure BDA0003820227350000046
And
Figure BDA0003820227350000047
the covariance matrix of (a) is obtained,
Figure BDA0003820227350000048
is composed of
Figure BDA0003820227350000049
The covariance matrix of (a) is obtained,
Figure BDA00038202273500000410
is composed of
Figure BDA00038202273500000411
A covariance matrix of (2);
step 4.2: using the floating-point solution and its covariance matrix, compute its integer solution:
using Z-transform, the ambiguities are re-parameterized to improve the accuracy of the ambiguity vector elements while reducing the correlation between ambiguities, the original single-differenced ambiguities are converted into a new set of ambiguities:
Figure BDA00038202273500000412
in the formula (I), the compound is shown in the specification,
Figure BDA00038202273500000413
for new ambiguities after Z transformation, Z T A transformation matrix that is a Z transformation;
at this point, the corresponding covariance matrix is converted to:
Figure BDA00038202273500000414
Figure BDA00038202273500000415
Figure BDA00038202273500000416
in the formula (I), the compound is shown in the specification,
Figure BDA00038202273500000417
is new after Z transformation
Figure BDA00038202273500000418
The covariance matrix of (a) is obtained,
Figure BDA00038202273500000419
is new after Z transformation
Figure BDA00038202273500000420
And
Figure BDA00038202273500000421
the covariance matrix of (a) is obtained,
Figure BDA00038202273500000422
is new after Z transformation
Figure BDA00038202273500000423
And
Figure BDA00038202273500000424
the covariance matrix of (a) is obtained,
after conversion, the floating point solution and its covariance matrix become:
Figure BDA00038202273500000425
then using floating point solution
Figure BDA00038202273500000426
Computing corresponding integer solutions
Figure BDA00038202273500000427
Figure BDA00038202273500000428
Where S is an integer mapping from an n-dimensional real space to an n-dimensional integer space;
then, inverse Z transformation is carried out to solve the integer solution of the original single-difference ambiguity:
Figure BDA00038202273500000429
in the formula (I), the compound is shown in the specification,
Figure BDA00038202273500000430
is an integer solution of the original single-differenced ambiguity, Z -T A transformation matrix that is an inverse Z-transform;
step 4.3: performing Ratio test:
the function value of the combination of all ambiguities is
Figure BDA00038202273500000431
Wherein z is a true ambiguity vector;
checking a Ratio of the next smallest F (z) value to the smallest F (z) value,
Figure BDA00038202273500000432
if the Ratio is larger than the threshold value, the result is a fixed solution after passing the test; otherwise, the result of the ambiguity floating solution is brought back to the covariance matrix to compensate the covariance matrix according to the failure of the detection;
step 4.4: and substituting the acquired integer ambiguity into a carrier phase observation equation to obtain a coordinate value of the user receiver.
Compared with the prior art, the invention has the following advantages and beneficial effects:
in the ambiguity resolution method based on the pseudo satellite and UWB fusion positioning system, the covariance matrix comprises the covariance matrix of the ambiguity parameters and the receiver coordinate parameters in the pseudo satellite carrier phase observation equation and the covariance matrix of UWB observation data. The fusion covariance matrix considers pseudo satellite carrier phase positioning parameters and pseudo range parameters obtained by UWB ranging, and therefore the fusion covariance matrix can be used for ambiguity fixing based on a pseudo satellite and UWB fusion positioning system.
Drawings
FIG. 1 is an overall flow chart of the ambiguity resolution method based on the pseudolite and UWB fusion positioning system of the invention.
FIG. 2 is a diagram of the steps of the ambiguity resolution method based on the pseudo satellite and UWB integrated positioning system of the present invention.
FIG. 3 is a schematic diagram of a single-side two-way ranging method of UWB positioning according to TOF based on a pseudolite and UWB fusion positioning system.
FIG. 4 shows the specific steps of the integer ambiguity resolution and verification based on the pseudo-satellite and UWB integrated positioning system of the present invention.
FIG. 5 shows a positioning track after the ambiguity resolution method based on the pseudo satellite and UWB fusion positioning system is applied.
Detailed Description
The technical solutions provided by the present invention will be described in detail below with reference to specific examples, and it should be understood that the following specific embodiments are only illustrative of the present invention and are not intended to limit the scope of the present invention.
As shown in fig. 2, an ambiguity resolution method based on a pseudolite and UWB fusion positioning system of the present embodiment includes the following steps:
step 1: UWB ranging value acquisition and positioning;
step 2: acquiring and positioning a carrier phase value of a pseudolite;
and step 3: initializing a positioning algorithm;
and 4, step 4: and (4) resolving and checking the integer ambiguity.
Further, in the step 1, the UWB ranging value acquisition is to acquire the distance measurement value between the user receiver and each base station quickly according to the TOF positioning method, and further operation is performed to obtain the UWB positioning result.
As shown in fig. 3, in the UWB, according to the single-sided two-way ranging method of TOF positioning, a UWB base station actively transmits data, and records a transmission time stamp, and a receiver records a reception time stamp after receiving the transmission time stamp; delayed by T reply And then, the receiver sends data and simultaneously records the sending time stamp, and the base station receives the data and simultaneously records the receiving time stamp. So that the base station time difference T can be obtained round Sum receiver time difference T reply 。
The transmission time T of the signal between the exciter and the receiver prop Comprises the following steps:
Figure BDA0003820227350000061
the UWB ranging result is noted as d, i.e
d＝T prop c
Where c is the speed of light.
Further, in step 2, the pseudolite carrier phase observation value is the phase difference between the pseudolite carrier signal received by the receiver and the reference pseudolite carrier signal generated by the receiver oscillator, and then the carrier phase observation equation of the pseudolite is constructed by using the pseudolite carrier phase observation value, so that the positioning result of the pseudolite can be obtained by solving.
Setting the initial phase of the pseudolite carrier signal received by the receiver to be
Figure BDA0003820227350000062
The initial phase of the reference pseudolite carrier signal generated by the receiver oscillator is
Figure BDA0003820227350000063
The carrier signal transmission time is
Figure BDA0003820227350000064
The carrier signal having a frequency f and the receiver clock difference being δ t r The pseudolite clock error being δ t s 。
Then the phase of the pseudolite carrier signal received by the receiver at time t is
Figure BDA0003820227350000065
the phase of the reference pseudolite carrier signal generated by the receiver oscillator at time t is
Figure BDA0003820227350000066
The difference between them, i.e. the carrier phase observation of the pseudolite is
Figure BDA0003820227350000067
In the formula
Figure BDA0003820227350000068
In order to obtain the whole-cycle ambiguity,
Figure BDA0003820227350000069
error terms are observed for the carrier phase.
For a wavelength λ, knowing c = λ · f, substituting the above equation can construct a pseudolite carrier phase observation equation as
Figure BDA00038202273500000610
In the formula
Figure BDA00038202273500000611
Is the geometric distance of the pseudolite from the receiver,
Figure BDA00038202273500000612
is the tropospheric induced phase difference.
Further, the pseudoranges for the pseudolites in step 3 are the measured ranges between the pseudolites and the receiver, and are not true satellite-to-satellite geometries because the measured ranges contain error factors, and are therefore referred to as "pseudoranges". Observing by different receivers to obtain different pseudolite carrier phase observation equations, subtracting to obtain a pseudolite carrier phase single difference observation equation, initializing the pseudolite carrier phase single difference observation equation by the UWB positioning result obtained in the step 1, replacing the pseudo range of the pseudolite with a UWB ranging result d and substituting the pseudo range into the pseudolite carrier phase single difference observation equation so as to obtain an initial value of the carrier phase integer ambiguity, and then gradually resolving the integer ambiguity in the step 4.
If two receivers i and j simultaneously observe the same pseudolite p, the carrier phase observation equation for the receiver i to observe the pseudolite p is as follows:
Figure BDA00038202273500000613
in the formula
Figure BDA00038202273500000614
Is the carrier phase observation that receiver i observes pseudolite p,
Figure BDA00038202273500000615
is the geometric distance, deltat, of the receiver i from the pseudolite p i Is the clock difference, δ t, of the receiver i p Is the clock error of the pseudolite p,
Figure BDA00038202273500000616
is the tropospheric induced phase difference when the receiver i observes the pseudolite p,
Figure BDA0003820227350000071
is the initial phase of the pseudolite carrier signal received by the receiver,
Figure BDA0003820227350000072
is the initial phase of the reference pseudolite p-carrier signal generated by the receiver oscillator,
Figure BDA0003820227350000073
is the integer ambiguity, e, of the receiver i observing the pseudolite p i Is the carrier phase observation error term for the receiver epsilon.
The carrier phase observation equation observed by receiver j pseudolite p is:
Figure BDA0003820227350000074
in the formula
Figure BDA0003820227350000075
Is the carrier phase observation of the pseudolite p observed by receiver j,
Figure BDA0003820227350000076
is the geometric distance, δ t, of the receiver j from the pseudolite p j Is the clock difference of the receiver j,
Figure BDA0003820227350000077
is the tropospheric induced phase difference when the receiver j observes the pseudolite p,
Figure BDA0003820227350000078
is the integer ambiguity, e, of the receiver j observing the pseudolite p j Is the carrier phase observation error term for receiver j.
Two receivers i and j simultaneously observe the carrier phase observation equation of the same pseudolite p to make difference, so that a pseudolite carrier phase single-difference observation equation can be obtained:
Figure BDA0003820227350000079
in the formula
Figure BDA00038202273500000710
The difference between the observed carrier phase values of two receivers i and j in the same epoch for the same pseudolite p,
Figure BDA00038202273500000711
the difference between the geometric distances of two receivers i, j to the same pseudolite p in the same epoch,
Figure BDA00038202273500000712
for single-difference integer ambiguity, Δ Tp is the difference between the phase differences caused by the troposphere when two receivers i, j observe pseudolite p, and Δ e is the difference between the observation error terms when two receivers i, j observe pseudolite p.
As shown in fig. 4, the integer ambiguity resolution and inspection in step 4 specifically comprises the following steps:
firstly, calculating a floating point solution based on a pseudo satellite and UWB fusion positioning system and a corresponding covariance matrix:
the variance of the UWB observations is calculated as follows:
Figure BDA00038202273500000713
in the formula, x i The ith observation for a set of UWB observation sample samples,
Figure BDA00038202273500000714
is the sample mean, and n is the number of UWB observations in the sample.
The covariance matrix of the observation data is constructed as follows:
Figure BDA00038202273500000715
in the formula (I), the compound is shown in the specification,
Figure BDA00038202273500000716
the variance of each of the n different sets of UWB observation data sample samples.
The carrier phase single difference observation equation is linearized to obtain:
y＝Aa+Bb+e
in the formula, y is a single difference observation vector; a is the wavelength with algebraic sign after linearization, and the sign is negative, so A = -lambda; a is a single difference ambiguity parameter; b is a cosine value from the approximate position of the receiver to each direction of the pseudolite; b is a receiver coordinate parameter; e is the measurement noise vector.
The observation data of the pseudo satellite and the UWB are independent, so that a floating point solution based on the pseudo satellite and the UWB fusion positioning system is obtained according to the least square, and the corresponding covariance matrix is shown as follows;
Figure BDA0003820227350000081
in the formula
Figure BDA0003820227350000082
For a single-difference ambiguity floating-point solution,
Figure BDA0003820227350000083
for the floating-point solution of the receiver coordinates,
Figure BDA0003820227350000084
for the UWB ranging result floating point solution,
Figure BDA0003820227350000085
is composed of
Figure BDA0003820227350000086
The covariance matrix of (a) is obtained,
Figure BDA0003820227350000087
is composed of
Figure BDA0003820227350000088
And
Figure BDA0003820227350000089
the covariance matrix of (a) is obtained,
Figure BDA00038202273500000810
is composed of
Figure BDA00038202273500000811
And
Figure BDA00038202273500000812
the covariance matrix of (a) is obtained,
Figure BDA00038202273500000813
is composed of
Figure BDA00038202273500000814
The covariance matrix of (a) is obtained,
Figure BDA00038202273500000815
is composed of
Figure BDA00038202273500000816
Covariance matrix of (2).
Then, using the floating solution and its covariance matrix, its integer solution is computed:
the ambiguities are re-parameterized using a Z-transform to improve the accuracy of the ambiguity vector elements while reducing the correlation between ambiguities. The original single-differenced ambiguities are converted into a new set of ambiguities:
Figure BDA00038202273500000817
in the formula (I), the compound is shown in the specification,
Figure BDA00038202273500000818
and ZT is a transformation matrix of Z transformation, wherein the new ambiguity is the new ambiguity after Z transformation.
At this point, the corresponding covariance matrix is converted to:
Figure BDA00038202273500000819
Figure BDA00038202273500000820
Figure BDA00038202273500000821
in the formula (I), the compound is shown in the specification,
Figure BDA00038202273500000822
is new after Z transformation
Figure BDA00038202273500000823
The covariance matrix of (a) is obtained,
Figure BDA00038202273500000824
is new after Z transformation
Figure BDA00038202273500000825
And
Figure BDA00038202273500000826
the covariance matrix of (a) is obtained,
Figure BDA00038202273500000827
is new after Z transformation
Figure BDA00038202273500000828
And
Figure BDA00038202273500000829
the covariance matrix of (a) is obtained,
after conversion, the floating point solution and its covariance matrix become:
Figure BDA00038202273500000830
then using floating point solution
Figure BDA00038202273500000831
Computing corresponding integer solutions
Figure BDA00038202273500000832
Figure BDA00038202273500000833
In the above equation, S is an integer mapping from an n-dimensional real number space to an n-dimensional integer space.
Then, inverse Z transformation is carried out to solve the integer solution of the original single-difference ambiguity:
Figure BDA00038202273500000834
in the formula (I), the compound is shown in the specification,
Figure BDA00038202273500000835
is an integer solution of the original single-differenced ambiguity, Z -T A transformation matrix that is an inverse Z-transform.
Next, a Ratio test is performed:
the function values for all combinations of ambiguities are:
Figure BDA00038202273500000836
where z is the true ambiguity vector.
Checking a Ratio of the next smallest F (z) value to the smallest F (z) value,
Figure BDA0003820227350000091
if the Ratio is greater than the threshold value, the result is a fixed solution after passing the test; otherwise, the result of the ambiguity floating solution is brought back to the covariance matrix to compensate the covariance matrix according to the failure of the test. Generally, if the Ratio is greater than 2 or 3, the group of ambiguities can be considered as the correct ambiguity, but in practical use, a Ratio value of greater than 2 or 3 does not indicate that the group of ambiguities is certainly correct, and in order to ensure the reliability of ambiguity search, only the same group of ambiguities which continuously satisfy the condition for a period of time can be considered as the correct ambiguity group.
And finally, substituting the acquired integer ambiguity into a carrier phase observation equation to obtain a coordinate value of the user receiver.
The ambiguity resolution process based on the pseudo satellite and the UWB fusion positioning system in the embodiment corresponds to the ambiguity resolution method based on the pseudo satellite and the UWB fusion positioning system.
The positioning track of the embodiment after the ambiguity resolution method based on the pseudo satellite and UWB fusion positioning system is applied is shown in FIG. 5.
The foregoing shows and describes the general principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are intended to further illustrate the principles of the invention, but that various changes and modifications may be made without departing from the spirit and scope of the invention, which is to be protected by the following claims. The scope of the invention is defined by the claims and their equivalents.

Claims (5)

1. An ambiguity resolution method based on a pseudolite and UWB fusion positioning system is characterized by comprising the following steps:
step 1, UWB ranging value acquisition and positioning: according to the TOF positioning method, quickly obtaining distance measurement values between the user receiver and each base station, namely UWB distance measurement values, recording the distance measurement values as UWB distance measurement results d, and further calculating to obtain UWB positioning results;
step 2, acquiring and positioning a pseudolite carrier phase observation value: the pseudolite carrier phase observation value is the phase difference between a pseudolite carrier signal received by the receiver and a reference pseudolite carrier signal generated by a receiver oscillator, and then a carrier phase observation equation of the pseudolite is constructed by using the pseudolite carrier phase observation value to solve to obtain a positioning result of the pseudolite;
step 3, initializing a positioning algorithm: the pseudo range of the pseudo satellite is the measured distance between the pseudo satellite and a receiver, the measured distance contains error factors and is not the real geometric distance of the satellite, so the pseudo range is called as pseudo range, different pseudo satellite carrier phase observation equations are obtained by observing through different receivers, the pseudo satellite carrier phase single difference observation equation is obtained by subtracting, the pseudo range is initialized by the UWB positioning result obtained in the step 1, the pseudo range of the pseudo satellite is replaced by the UWB ranging result d and is substituted into the pseudo satellite carrier phase single difference observation equation, and the carrier phase integer ambiguity is enabled to obtain an initial value;
and 4, resolving and checking the integer ambiguity.
2. The ambiguity resolution method based on the pseudolite and UWB fusion positioning system according to claim 1, characterized in that the specific method of step 1 is:
the UWB based on the TOF positioning single-side two-way ranging method is that a UWB base station actively transmits data, simultaneously records a transmission time stamp, and a receiver records a receiving time stamp after receiving the data; delayed by T reply Then, the receiver sends data and simultaneously records a sending time stamp, and the base station receives the data and simultaneously records a receiving time stamp; obtaining a base station time difference T round Sum receiver time difference T reply ；
The transmission time T of the signal between the battle and the receiver prop Comprises the following steps:
Figure FDA0003820227340000011
the ranging result d of the UWB is:
d＝T propc
where c is the speed of light.
3. The ambiguity resolution method based on the pseudolite and UWB fusion positioning system according to claim 1, characterized in that the specific method of step 2 is:
let the initial phase of the pseudolite carrier signal received by the receiver be
Figure FDA0003820227340000012
The initial phase of the reference pseudolite carrier signal generated by the receiver oscillator is
Figure FDA0003820227340000013
The carrier signal transmission time is
Figure FDA0003820227340000014
The carrier signal having a frequency f and the receiver clock difference being δ t r The pseudolite clock error being δ t s ，
The phase of the pseudolite carrier signal received by the receiver at time t
Figure FDA0003820227340000015
Is that
Figure FDA0003820227340000016
Phase of reference pseudolite carrier signal generated by receiver oscillator at time t
Figure FDA0003820227340000021
Is that
Figure FDA0003820227340000022
The difference between them, i.e. carrier phase observations of pseudolites
Figure FDA0003820227340000023
Is that
Figure FDA0003820227340000024
In the formula
Figure FDA0003820227340000025
In order to obtain the integer ambiguity of the image,
Figure FDA0003820227340000026
an error term is observed for the carrier phase;
for the wavelength lambda, knowing that c = lambda · f, substituting the formula into the above equation to construct the pseudolite carrier phase observation equation
Figure FDA0003820227340000027
In the formula
Figure FDA0003820227340000028
Is the geometric distance of the pseudolite from the receiver,
Figure FDA0003820227340000029
is the tropospheric induced phase difference.
4. The ambiguity resolution method based on the pseudolite and UWB fusion positioning system according to claim 1, characterized in that the specific method of step 3 is:
if two receivers i and j simultaneously observe the same pseudolite p, the carrier phase observation equation for the receiver i to observe the pseudolite p is as follows:
Figure FDA00038202273400000210
in the formula
Figure FDA00038202273400000211
Is the carrier phase observation that receiver i observes pseudolite p,
Figure FDA00038202273400000212
is the geometric distance, deltat, of the receiver i from the pseudolite p i Is the clock difference, δ t, of the receiver i p Is the clock error of the pseudolite p,
Figure FDA00038202273400000213
is the tropospheric induced phase difference when the receiver i observes the pseudolite p,
Figure FDA00038202273400000214
is the initial phase of the pseudolite carrier signal received by the receiver,
Figure FDA00038202273400000215
is the initial phase of the reference pseudolite p-carrier signal generated by the receiver oscillator,
Figure FDA00038202273400000216
is the integer ambiguity, e, of the receiver i observing the pseudolite p i Is the carrier phase observation error term of receiver i;
the carrier phase observation equation observed by receiver j pseudolite p is:
Figure FDA00038202273400000217
in the formula
Figure FDA00038202273400000218
Is the carrier phase observation of the pseudolite p observed by receiver j,
Figure FDA00038202273400000219
is the geometric distance, deltat, of the receiver j from the pseudolite p j Is the clock difference of the receiver j,
Figure FDA00038202273400000220
is the tropospheric induced phase difference when the receiver j observes the pseudolite p,
Figure FDA00038202273400000221
is the integer ambiguity, e, of the receiver j observing the pseudolite p j Is the carrier phase observation error term for receiver j;
and the two receivers i and j simultaneously observe the carrier phase observation equation of the same pseudolite p to make difference to obtain a pseudolite carrier phase single difference observation equation:
Figure FDA00038202273400000222
in the formula
Figure FDA00038202273400000223
For two receivers i, j of the same epoch to the same receiverThe difference between the carrier phase observations of pseudolite p,
Figure FDA00038202273400000224
the difference between the geometric distances of two receivers i, j to the same pseudolite p in the same epoch,
Figure FDA00038202273400000225
is single difference integer ambiguity, Δ T p The difference between the phase differences caused by the troposphere when the two receivers i, j observe the pseudolite p, and Δ e is the difference between the observation error terms when the two receivers i, j observe the pseudolite p.
5. The ambiguity resolution method based on the pseudolite and UWB fusion positioning system according to claim 1, wherein the step 4 specifically comprises:
step 4.1: calculating a floating point solution based on a pseudo satellite and UWB fusion positioning system and a corresponding covariance matrix:
variance σ of UWB observation data 2 The calculation is as follows:
Figure FDA0003820227340000031
in the formula, x i The ith observation for a set of UWB observation sample samples,
Figure FDA0003820227340000032
is the sample mean value, and n is the number of UWB observation data in the sample;
constructing covariance matrix Q of observation data dd Comprises the following steps:
Figure FDA0003820227340000033
in the formula (I), the compound is shown in the specification,
Figure FDA0003820227340000034
the variances of n groups of different UWB observation data sample samples are respectively;
and (3) linearizing the carrier phase single difference observation equation to obtain:
y＝Aa+Bb+e
in the formula, y is a single difference observation vector; a is the wavelength with algebraic sign after linearization, and the sign is negative, so A = -lambda; a is a single difference ambiguity parameter; b is a cosine value from the approximate position of the receiver to each direction of the pseudolite; b is a receiver coordinate parameter; e is a measurement noise vector;
the observation data of the pseudo satellite and the UWB are independent, so that a floating point solution based on the pseudo satellite and the UWB fusion positioning system is obtained according to the least square, and the corresponding covariance matrix is shown as follows;
Figure FDA0003820227340000035
in the formula
Figure FDA0003820227340000036
For a single-difference ambiguity floating-point solution,
Figure FDA0003820227340000037
for the floating-point solution of the coordinates of the receiver,
Figure FDA0003820227340000038
for the UWB ranging result floating point solution,
Figure FDA0003820227340000039
is composed of
Figure FDA00038202273400000310
The covariance matrix of (a) is obtained,
Figure FDA00038202273400000311
is composed of
Figure FDA00038202273400000312
And
Figure FDA00038202273400000313
the covariance matrix of (a) is obtained,
Figure FDA00038202273400000314
is composed of
Figure FDA00038202273400000315
And
Figure FDA00038202273400000316
the covariance matrix of (a) is obtained,
Figure FDA00038202273400000317
is composed of
Figure FDA00038202273400000318
The covariance matrix of (a) is obtained,
Figure FDA00038202273400000319
is composed of
Figure FDA00038202273400000320
A covariance matrix of (2);
and 4.2: using the floating point solution and its covariance matrix, compute its integer solution:
using Z-transform, the ambiguities are re-parameterized to improve the accuracy of the ambiguity vector elements while reducing the correlation between ambiguities, the original single-differenced ambiguities are converted into a new set of ambiguities:
Figure FDA00038202273400000321
in the formula (I), the compound is shown in the specification,
Figure FDA00038202273400000322
for new ambiguities after Z transformation, Z T Is a variation of ZChanging the matrix;
at this point, the corresponding covariance matrix is converted to:
Figure FDA00038202273400000323
Figure FDA00038202273400000324
Figure FDA00038202273400000325
in the formula (I), the compound is shown in the specification,
Figure FDA00038202273400000326
is new after Z transformation
Figure FDA00038202273400000327
The covariance matrix of (a) is obtained,
Figure FDA00038202273400000328
is new after Z transformation
Figure FDA00038202273400000329
And
Figure FDA00038202273400000330
the covariance matrix of (a) is obtained,
Figure FDA00038202273400000331
is new after Z transformation
Figure FDA0003820227340000041
And
Figure FDA0003820227340000042
covariance matrix of，
After conversion, the floating point solution and its covariance matrix become:
Figure FDA0003820227340000043
then using floating point solution
Figure FDA0003820227340000044
Computing corresponding integer solutions
Figure FDA0003820227340000045
Figure FDA0003820227340000046
Where S is an integer mapping from an n-dimensional real number space to an n-dimensional integer space;
then, inverse Z transformation is carried out to solve the integer solution of the original single-difference ambiguity:
Figure FDA0003820227340000047
in the formula (I), the compound is shown in the specification,
Figure FDA0003820227340000048
is an integer solution of the original single-differenced ambiguity, Z -T A transformation matrix that is an inverse Z-transform;
step 4.3: performing Ratio test:
the function value of the combination of all ambiguities is
Figure FDA0003820227340000049
Wherein z is a true ambiguity vector;
checking a Ratio of the next smallest F (z) value to the smallest F (z) value,
Figure FDA00038202273400000410
if the Ratio is greater than the threshold value, the result is a fixed solution after passing the test; otherwise, the result of the ambiguity floating solution is brought back to the covariance matrix to compensate the covariance matrix according to the failure of the detection;
step 4.4: and substituting the acquired integer ambiguity into a carrier phase observation equation to obtain a coordinate value of the user receiver.
CN202211039075.1A 2022-08-29 2022-08-29 Ambiguity resolution method based on pseudo satellite and UWB fusion positioning system Pending CN115407379A (en)

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CN116413658A (en) * 2023-02-27 2023-07-11 青岛柯锐思德电子科技有限公司 UWB and BLE combination-based low-power-consumption ranging method

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116413658A (en) * 2023-02-27 2023-07-11 青岛柯锐思德电子科技有限公司 UWB and BLE combination-based low-power-consumption ranging method
CN116413658B (en) * 2023-02-27 2023-12-05 青岛柯锐思德电子科技有限公司 UWB and BLE combination-based low-power-consumption ranging method

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