CN110727005B - Integer ambiguity determination method of positioning base station system - Google Patents

Integer ambiguity determination method of positioning base station system Download PDF

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CN110727005B
CN110727005B CN201810775354.1A CN201810775354A CN110727005B CN 110727005 B CN110727005 B CN 110727005B CN 201810775354 A CN201810775354 A CN 201810775354A CN 110727005 B CN110727005 B CN 110727005B
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integer ambiguity
positioning base
receiver
base station
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CN110727005A (en
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姚铮
王腾飞
陆明泉
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Tsinghua 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
    • G01S19/43Determining position using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
    • G01S19/44Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method

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Abstract

The application provides a method for determining integer ambiguity of a positioning base station system, which comprises the following steps: and receiving signals sent by the positioning base station, obtaining carrier phase observed quantity from the received signals, and directly constructing a linear observation model related to the integer ambiguity by using the carrier phase observed quantity to determine the integer ambiguity. By the integer ambiguity determination method, the linear observation model of the integer ambiguity can be established without relying on providing the initial position, the initial distance and/or the initial integer ambiguity by means of code phase measurement or other means such as measurement in advance, so that the integer ambiguity can be reliably determined.

Description

Integer ambiguity determination method of positioning base station system
Technical Field
The application relates to the determination of integer ambiguity in carrier phase measurements of a positioning base station system.
Background
As in the satellite positioning system, the carrier phase measurement positioning technology can also be used in the positioning base station system to achieve precise positioning. Also, in carrier phase measurement positioning of a positioning base station system, how to reliably determine the integer ambiguity is critical.
In the carrier phase measurement positioning of the positioning base station system, the prior method for determining the integer ambiguity in the satellite positioning system is usually adopted, that is, the initial position, the initial distance, and/or the initial integer ambiguity are provided by means of code phase measurement or other means of measurement in advance, and the integer ambiguity is solved iteratively. The existing method depends heavily on the initial solutions, and once the initial solutions are unreliable (which is also very likely to happen), the obtained integer ambiguity error can be too large, and even the iteration can not be converged, so that the integer ambiguity can not be determined.
Disclosure of Invention
According to the present application, there is provided a method for determining integer ambiguity of a positioning base station system, the method comprising: and receiving signals sent by the positioning base station, obtaining carrier phase observed quantity from the received signals, and directly constructing a linear observation model related to the integer ambiguity by using the carrier phase observed quantity to determine the integer ambiguity.
According to the integer ambiguity determination method of the positioning base station system, the linear observation model of the integer ambiguity can be established without relying on providing the initial position, the initial distance and/or the initial integer ambiguity by means of code phase measurement or other means in advance, so that the integer ambiguity can be reliably determined.
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Fig. 1 shows a flowchart of an integer ambiguity determination method of a positioning base station system according to an embodiment of the present application.
Fig. 2 shows a flowchart of a method for integer ambiguity determination of a positioning base station system according to an embodiment of the present application.
Fig. 3 shows a flowchart of a method for integer ambiguity determination of a positioning base station system according to an embodiment of the present application.
Fig. 4 shows a horizontal positioning trajectory diagram for positioning by using the integer ambiguity determination method of the positioning base station system according to the embodiment of the present application.
Fig. 5 shows a partial enlarged view of the horizontal positioning trace map of fig. 4.
Detailed Description
The method for determining the integer ambiguity of the positioning base station disclosed in the present application is explained in detail with reference to the accompanying drawings. For the sake of simplicity, the same or similar reference numerals are used for the same or similar devices in the description of the embodiments of the present application.
The positioning base stations in this application may be, for example, pseudolites, terrestrial-based positioning base stations, and/or wireless beacons. A positioning base station system comprises a plurality of positioning base stations with known positions, and a receiver can determine the position by receiving and processing signals transmitted by the positioning base stations, i.e. perform positioning of the receiver. In addition, carrier phase measurement positioning can be performed based on carrier phase observations obtained from the signals, thereby enabling fine positioning of the receiver.
According to one embodiment of the application, the integer ambiguity determination method of the positioning base station system comprises the following steps: and receiving signals sent by the positioning base station, obtaining carrier phase observed quantity from the received signals, and directly constructing a linear observation model related to the integer ambiguity by using the carrier phase observed quantity to determine the integer ambiguity. Fig. 1 shows a flowchart of the integer ambiguity determination method of the positioning base station system according to the embodiment, as shown in the figure: in S110, receiving a signal sent by a positioning base station; in S120, a carrier phase observation is obtained from the received signal; in S130, a linear observation model about the integer ambiguity is constructed by directly utilizing the carrier phase observation quantity; in S140, the integer ambiguity is determined.
According to this method, a linear observation model regarding the integer ambiguity can be constructed directly using the obtained carrier-phase observations, instead of having to first obtain initial values of the position, distance, and/or integer ambiguity by means such as code ranging, and then construct an approximately linear observation model regarding the integer ambiguity by performing expansion around the initial values using a linear expansion method (e.g., taylor expansion) to solve for the integer ambiguity, as in the method of the related art. Thus, the method of the application can avoid the problems that the error of solving the integer ambiguity is too large and the integer ambiguity cannot be determined due to the unreliable initial value (possibly occurring), thereby reliably determining the integer ambiguity. After the linear observation model about the integer ambiguity is constructed by the method, the integer ambiguity can be solved, and thus the positioning is realized.
According to one embodiment of the application, in the integer ambiguity determination method of the positioning base station system, a multi-difference square observation quantity is determined based on the square of a carrier phase observation quantity, and a linear observation model is constructed based on the multi-difference square observation quantity. Fig. 2 is a flowchart of the integer ambiguity determination method of the positioning base station system according to the embodiment, as shown in the figure: in S210, receiving a signal sent by a positioning base station; in S220, obtaining a carrier phase observation from the received signal; determining a multi-difference squared observation based on a square of the carrier-phase observations in S230; in S240, a linear observation model is constructed based on the multi-difference squared observation; in S250, the integer ambiguity is determined.
The multi-difference squared observations are obtained by differentiating the squares of the carrier-phase observations a number of times between different positioning base stations and between different locations of the receiver. After the multi-difference squared observations are obtained, a linear observation model for integer ambiguity can be constructed based on the multi-difference squared observations.
According to the method, in the process of constructing the linear observation model, the carrier phase observation quantity can be directly utilized to construct the linear observation model related to the integer ambiguity, so that the integer ambiguity can be determined, the code phase observation quantity or other initial observation quantity is not needed, the initial position, the initial distance and/or the initial integer ambiguity are not needed, the initial rough integer ambiguity estimation value is not needed to be introduced, the linear model related to the integer ambiguity is directly and simply constructed by adopting a linear expansion method and other means, and the integer ambiguity is further reliably determined.
Hereinafter, the integer ambiguity determination method according to the embodiment of the present application will be described in more detail by analyzing a carrier phase observation model of the positioning base station system.
In a positioning base station system, the carrier phase observation of the ith positioning base station can be expressed as:
Figure BDA0001731268240000031
wherein,
Figure BDA0001731268240000032
a carrier phase observation representing the receiver's position at the kth epoch for locating base station i, i =1,2, …, L, K =1,2, …, K;
sia position vector representing the known i-th positioning base station;
ukindicates the position of the receiver in the k-th epoch, where k indicates the sequence number of each position of the receiver, and u may also be saidkRepresents the kth position of the receiver;
λ represents the wavelength of the carrier;
Nirepresents the integer ambiguity of the ith positioning base station, and the signal loss lock and cycle slip do not occur in the movement process of the receiver and are constant quantity;
fcrepresents a frequency of a carrier wave;
δtia clock difference indicating a clock of the ith positioning base station;
δtkrepresents the clock difference of the clock of the receiver at the k-th position;
Figure BDA0001731268240000041
indicating errors with respect to the ith positioning base station and the kth position of the receiver including observation noise, multipath errors, etc.
In the carrier phase observation model of equation (1), the presence of | | si-ukIisuch a non-linear term, the model is therefore non-linear and hence difficult to solve for the whole-cycle ambiguity therein. In the prior art, the initial position, initial distance, and/or initial integer ambiguity obtained by code measurement or other means are used to expand the non-linear observation model, and based on this, the integer ambiguity is solved and determined by iteration. As described above, for example, when the initial value is unreliable due to terrestrial multipath, the error of the calculated integer ambiguity may become too large, and the iteration may not converge, so that the integer ambiguity cannot be determined.
By the integer ambiguity determination method, carrier phase observed quantity can be directly utilized, multi-difference square observed quantity is determined based on the square of the carrier phase observed quantity, and a linear observation model related to integer ambiguity is constructed based on the multi-difference square observed quantity without the aid of an initial value which is possibly unreliable and an approximate linear expansion method.
According to one embodiment of the application, in the case that two-way ranging (two-way ranging) is available in the positioning base station system, a two-way ranging double-difference square observed quantity can be obtained according to a carrier phase observed quantity subjected to two-way ranging, and a linear observation model about integer ambiguity can be constructed.
In this embodiment, the carrier-phase observations are obtained via two-way ranging, and the multi-difference squared observations may comprise two-way ranging double-difference squared observations, which may be obtained by differentiating the squares of the carrier-phase observations between two different locations of the receiver and between two different positioning base stations.
By using two-way ranging between the receiver of the positioning base station system and the positioning base station, the following carrier phase observations can be obtained at the receiver:
Figure BDA0001731268240000051
and the following carrier phase observed quantities can be obtained at the ith positioning base station end:
Figure BDA0001731268240000052
wherein,
Figure BDA0001731268240000053
representing a carrier phase observation at a kth position for an ith positioning base station and receiver observed at a receiver end (r);
Figure BDA0001731268240000054
representing a carrier phase observation at a kth position for an ith positioning base station and receiver observed at a positioning base station end(s);
Nr,iand Ns,iRespectively representing the integer ambiguity of the carrier phase observation value for the ith positioning base station observed at the receiver end (r) and the positioning base station end(s);
Figure BDA0001731268240000055
represents the clock difference of the clock of the receiver at the k-th position;
Figure BDA0001731268240000056
and
Figure BDA0001731268240000057
errors included in carrier phase observations observed at the receiver side and the positioning base station side, respectively, are represented, including observation noise, multipath errors, and the like.
Then, the two-way ranging carrier-phase observation can be expressed as:
Figure BDA0001731268240000058
wherein,
Figure BDA0001731268240000059
representing a two-way ranging carrier-phase observation,
Figure BDA00017312682400000510
Zirepresenting the integer ambiguity over two-way ranging,
Zi=Nr,i+Ns,i; (6)
Figure BDA00017312682400000511
error representing the observed amount of carrier phase over two-way ranging,
Figure BDA00017312682400000512
according to the formula (4), the clock difference of the clock of the positioning base station and the clock difference of the clock of the receiver are eliminated in the bidirectional ranging carrier phase observed quantity model, so that the subsequently constructed linear model does not contain the clock differences, the solved integer ambiguity is not influenced by the clock differences, and the integer solution of the integer ambiguity can be directly obtained theoretically.
After obtaining the two-way-ranged carrier-phase observations, two-way-ranged double-difference-squared observations may be obtained by differentiating the squares of the two-way-ranged carrier-phase observations between two different locations of the receiver and between two different positioning base stations, and constructing a linear observation model for integer ambiguity based on the two-way-ranged double-difference-squared observations.
According to one embodiment of the application, a linear observation model about integer ambiguity can be constructed based on two-way ranging double difference square observations as follows:
Figure BDA0001731268240000061
wherein,
Figure BDA0001731268240000062
representing a two-way ranging double-difference squared observation,
Figure BDA0001731268240000063
Figure BDA0001731268240000064
carrier phase observations obtained by two-way ranging
Figure BDA0001731268240000065
In the middle, the superscripts i and j represent the serial numbers of the positioning base stations, and the subscripts k and m represent the position serial numbers of the receivers;
Zi、Zjrepresenting the integer ambiguity measured in both directions,
Zi=Nr,i+Ns,i
q (u) represents a displacement parameter determined by the variation of the receiver position u,
Figure BDA0001731268240000066
wherein s isi、sjIndicating the known position vectors, u, of the ith and jth positioning base stationsk、umA k, m position vector representing the receiver; w represents an error term including observation noise, multipath error, and the like.
In the linear observation model of the formula (8), i and j represent the serial numbers of the positioning base stations, which can be used for representing the ith and jth positioning base stations; the k and m denote the position numbers of the receiver, and may be used to denote the kth and mth positions of the receiver, and from the viewpoint of the receiver observing the carrier phase, the k and m may be considered to denote the observation numbers of the carrier phase observed quantities.
The above equation (9) indicates that the square of the bidirectional-ranging carrier phase observed quantity of the receiver at the kth position is differentiated between two positioning base stations (i-th and j-th positioning base stations, respectively), the square of the bidirectional-ranging carrier phase observed quantity of the receiver at the mth position is differentiated between the two positioning base stations, and then the two differential results are differentiated to obtain the bidirectional-ranging double-difference squared observed quantity. It can be seen that, the square of the carrier phase observed quantity of the receiver for the ith positioning base station may be differentiated between two different positions (the kth position and the mth position, respectively) of the receiver, the square of the carrier phase observed quantity of the receiver for the jth positioning base station may be differentiated between the two different positions of the receiver, and then the two difference results may be further differentiated to obtain the two-way ranging double-difference square observed quantity, where the process may be represented as:
Figure BDA0001731268240000071
that is, the order of the differences does not affect the results of the bi-directional ranging double difference squared observations, as long as the squares of the carrier phase observations are differentiated between two different locations of the receiver and between two different positioning base stations.
As can be seen from equation (10), the displacement parameter q (u) is linear with respect to the unknown term u therein, and equation (8) is linear with respect to the integer ambiguity. Therefore, as described above, with the method according to the present application, it is possible to construct a linear observation model for integer ambiguity, which does not contain a nonlinear term as the prior art must face, directly using carrier-phase observations.
As described above, according to the integer ambiguity determination method according to the embodiment of the present application, a linear observation model regarding integer ambiguity can be constructed based on a two-way ranging carrier phase observed quantity.
Further, as described above, since the unknown terms such as the clock difference of the positioning base station clock and the clock difference of the receiver clock are eliminated after the two-way ranging, the integer solution of the integer ambiguity can be theoretically solved based on the linear observation model in equation (8) with respect to the integer ambiguity.
In general, for example, when there is no bidirectional ranging in the positioning base station system, the integer ambiguity determination method according to the embodiment of the present application can also construct a linear observation model for integer ambiguity based on the multi-difference square observation amount by directly using the carrier phase observation amount. This is described in detail below.
In the carrier phase observation model of equation (1), the clock difference of the clock of the positioning base station can be regarded as constant; the clock difference of the clock of the receiver can be represented by the following model:
Figure BDA0001731268240000072
wherein,
Figure BDA0001731268240000073
represents the clock difference of the clock of the receiver at the initial position, namely the initial value of the clock difference of the clock of the receiver;
alpha represents the frequency deviation of the receiver clock relative to the positioning base station clock and can be estimated by methods such as static observation and the like;
ηtkrepresenting the error term of the clock model.
Thus, formula (12) can be substituted for formula (1),
Figure BDA0001731268240000081
after the finishing of the formula (13), can be obtained,
Figure BDA0001731268240000082
wherein,
Figure BDA0001731268240000083
Figure BDA0001731268240000084
since two-way ranging is not performed, the carrier phase observation model of equation (14) includes the clock difference of the clock of the positioning base station and the clock difference of the clock of the receiver, and these two clock differences will affect the subsequent solution of the integer ambiguity.
As described above, the clock difference δ t of the clock of the receiver can be obtainedkAnd performing static observation, and then estimating the frequency deviation alpha of the receiver clock relative to the positioning base station clock according to the observation result, in this case, a linear observation model about the integer ambiguity can be constructed by the integer ambiguity determination method according to the embodiment of the application. According to this embodiment, the multi-difference squared observations may comprise double-difference squared observations obtained by differentiating the squares of the carrier-phase observations between two different locations of the receiver and between two different positioning base stations. That is, in the case where the frequency deviation of the receiver clock with respect to the positioning base station clock can be estimated, it is possible to base on dualThe difference-squared observations are used to construct a linear observation model for integer ambiguities.
According to one embodiment of the present application, a linear observation model for integer ambiguity can be constructed based on a double difference squared observation as follows:
Figure BDA0001731268240000085
wherein,
Figure BDA0001731268240000086
representing a double-difference-squared observation,
Figure BDA0001731268240000087
Figure BDA0001731268240000091
observed quantity of carrier phase
Figure BDA0001731268240000092
In the middle, the superscripts i and j represent the serial numbers of the positioning base stations, and the subscripts k and m represent the position serial numbers of the receivers;
zi、zjrepresenting an integer ambiguity, i.e., an integer ambiguity for the carrier phase observations of the ith and jth positioning base stations;
α represents a frequency deviation of a receiver clock with respect to a base station clock;
r (alpha, u) represents a displacement parameter determined by the frequency deviation alpha of the receiver clock relative to the base station clock and the variation of the receiver position u,
Figure BDA0001731268240000093
wherein,
Figure BDA0001731268240000094
si、sjindicating the known position vectors, u, of the ith and jth positioning base stationsk、umA k, m position vector representing the receiver;
n represents an error term including observation noise, multipath error, and the like.
The above equation (18) indicates that the square of the carrier phase observed quantity at the kth position of the receiver is differentiated between two positioning base stations (i-th and j-th positioning base stations, respectively), the square of the carrier phase observed quantity at the mth position of the receiver is differentiated between the two positioning base stations, and then the two differential results are differentiated to obtain the double-difference square observed quantity. It can be seen that, the square of the carrier phase observed quantity of the receiver for the ith positioning base station may be differentiated between two different positions (the kth position and the mth position, respectively) of the receiver, the square of the carrier phase observed quantity of the receiver for the jth positioning base station may be differentiated between the two different positions of the receiver, and then the two difference results may be differentiated to obtain a double-difference square observed quantity, where the process may be represented as:
Figure BDA0001731268240000095
again, this indicates that the order of differentiation has no effect on the results of the double difference squared observations, as long as the square of the carrier phase observations is differentiated between two different locations of the receiver and between two different positioning base stations.
As can be seen from equation (19), the displacement parameter R (α, u) is linear with respect to the unknown term u therein, and since the frequency deviation α of the receiver clock from the base station clock is known by estimation, the observation model of equation (17) is linear with respect to the integer ambiguity therein. By the method according to this embodiment it is thus possible to construct a linear observation model with respect to the whole-cycle ambiguity directly from the carrier-phase observations, which linear observation model also does not contain non-linear terms as has to be faced in the prior art.
Furthermore, as can be seen from equation (15), the integer ambiguity includes clock difference of the clock, so the integer ambiguity obtained by the linear model constructed by the embodiment is a floating solution, for example, an integer solution can be obtained by the LAMDA algorithm based on the floating solution. As will be explained later.
The above describes how the clock difference deltat can be measured by the clock of the receiverkWhen the frequency deviation α is estimated by performing static observation, the integer ambiguity determination method according to the embodiment of the present application can construct a linear observation model regarding the integer ambiguity by directly using the carrier phase observation amount. For the more general case, i.e. without clock difference deltat passing through the clock to the receiverkIn the case where the frequency deviation α is estimated by performing static observation, that is, in the case where the frequency deviation α is unknown, a linear observation model regarding the integer ambiguity can be constructed by the integer ambiguity determination method according to the embodiment of the present application. According to this embodiment, according to one embodiment of the present application, the multi-difference squared observations may further comprise tri-difference squared observations obtained by differentiating a square of the carrier-phase observations between three different locations of the receiver and between two different positioning base stations. That is, in a more general case where the frequency deviation α remains unknown, a linear observation model with respect to the integer ambiguity can be constructed based on the three-difference squared observation quantity.
According to one embodiment of the present application, a linear observation model for integer ambiguity can be constructed based on the tri-difference squared observation as follows:
Figure BDA0001731268240000101
wherein,
Figure BDA0001731268240000102
representing the three-difference squared observations,
Figure BDA0001731268240000103
Figure BDA0001731268240000104
Figure BDA0001731268240000105
Figure BDA0001731268240000106
observed quantity of carrier phase
Figure BDA0001731268240000111
In the middle, the superscripts i and j represent the serial numbers of the positioning base stations, and the subscripts k, m and p represent the position serial numbers of the receivers;
zi、zjrepresenting an integer ambiguity, i.e., an integer ambiguity for the carrier phase observations of the ith and jth positioning base stations;
p (alpha, u) represents a shift parameter determined by the frequency deviation alpha of the receiver clock relative to the base station clock and the variation of the receiver position u,
Figure BDA0001731268240000112
wherein,
Figure BDA0001731268240000113
si、sjindicating the known position vectors, u, of the ith and jth positioning base stationsk、um、upA kth, mth, pth position vector representing the receiver;
e represents an error term including observation noise, multipath error, etc.
In the linear observation model of equation (21), i and j represent the serial numbers of the positioning base stations as described above, and can be used to represent the ith and jth positioning base stations; k, m, and p denote receiver position numbers, and may be used to denote the kth, mth, and pth positions of the receiver, and from the viewpoint of the receiver observing the carrier phase, it may be considered that k, m, and p denote the observation numbers of the carrier phase observed quantities.
The expression (22) shows that the square of the carrier phase observed quantity of the receiver at the kth position is differentiated between two positioning base stations (i-th and j-th positioning base stations respectively), then the square of the carrier phase observed quantity of the receiver at the mth position is differentiated between the two positioning base stations, and then the two differential results are differentiated to obtain a first result; then, the square of the carrier phase observed quantity of the receiver at the mth position is differentiated between two positioning base stations (i-th positioning base station and j-th positioning base station respectively), the square of the carrier phase observed quantity of the receiver at the p-th position is differentiated between the two positioning base stations, and then the two differential results are differentiated to obtain a second result; finally, the first result is divided by the sequence number difference of two different positions of the receiver related to the first result, and the second result is divided by the sequence number difference of two different positions of the receiver related to the second result, and then the two results are differentiated. It can be seen that three different positions of the receiver and two different positioning base stations are involved here. Similarly, the order of the differences has no effect on the results of the triple-difference squared observations, as long as the squares of the carrier-phase observations are differentiated between three different locations of the receiver and between two different positioning base stations.
As can be seen from equation (23), the displacement parameter P (α, u) is linear with respect to the unknown term α, u therein, and the observation model of equation (21) is linear with respect to the integer ambiguity therein. By the method according to this embodiment it is thus possible to construct a linear observation model with respect to the whole-cycle ambiguity directly from the carrier-phase observations, which linear observation model also does not contain non-linear terms as has to be faced in the prior art.
In addition, as can be seen from equation (15), the integer ambiguity includes clock difference of the clock, so that the integer ambiguity obtained by the linear model constructed by the embodiment is a floating solution, for example, an integer solution can be obtained by the LAMDA algorithm based on the floating solution. As will be explained later.
After a linear observation model about the integer ambiguity is constructed by the method according to the embodiment of the application, the linear observation model can be solved to obtain the integer ambiguity, so that the precise positioning is realized.
According to one embodiment of the application, a floating solution of the integer ambiguity is obtained through a least square method based on the constructed linear observation model, and an integer solution of the integer ambiguity is obtained according to the floating solution. Fig. 3 is a flowchart of the integer ambiguity determination method of the positioning base station system according to the embodiment, as shown in the figure: in S310, receiving a signal from a positioning base station; in S320, obtaining carrier phase observations from the received signal; in S330, determining a multi-difference squared observation based on a square of the carrier-phase observations; in S340, a linear observation model is constructed based on the multi-difference squared observation; in S350, a floating solution of integer ambiguity is obtained by a least square method based on the constructed linear observation model; in S360, an integer solution of integer ambiguity is obtained from the floating point solution.
According to an example of the present application, after obtaining a floating solution of integer ambiguity, an integer solution of integer ambiguity is obtained using the LAMDA algorithm based on the floating solution. Other schemes in the prior art may also be employed to obtain a floating solution for integer ambiguities and an integer solution for integer ambiguities based on the floating solution.
According to another embodiment of the present application, the floating solution of the integer ambiguity is obtained by the least square method based only on the constructed linear observation model, and the integer solution of the integer ambiguity is not obtained any more.
Fig. 4 shows a horizontal positioning trajectory diagram for positioning using the integer ambiguity determination method according to an embodiment of the present application. As shown in the figure, since the precision of positioning by the integer ambiguity determination method according to the embodiment of the present application is high, the horizontal trajectory obtained by positioning almost coincides with the real trajectory. In addition, according to the partial enlarged view shown in fig. 5, a plurality of horizontal positioning tracks obtained by a plurality of positioning are very close to the real track, which also can illustrate that a higher positioning accuracy can be obtained by performing positioning by using the integer ambiguity determination method according to the embodiment of the present application, in this example, the root mean square of the positioning error is 0.83 cm according to statistics.
Exemplary embodiments of the present application are described above with reference to the accompanying drawings. It will be appreciated by those skilled in the art that the above-described embodiments are merely exemplary for purposes of illustration and are not intended to be limiting, and that any modifications, equivalents, etc. that fall within the teachings of this application and the scope of the claims should be construed to be covered thereby.

Claims (9)

1. The integer ambiguity determining method of the positioning base station system comprises the following steps: the method comprises the steps of receiving signals sent by a positioning base station, obtaining carrier phase observed quantities from the received signals, and directly utilizing the carrier phase observed quantities to construct a linear observation model related to integer ambiguity to determine the integer ambiguity, wherein the linear observation model is constructed based on multi-difference square observed quantities determined by squares of the carrier phase observed quantities.
2. The integer ambiguity determination method of claim 1, wherein the linear observation model is constructed directly using carrier observations and without code phase observations or initial observations.
3. The integer ambiguity determination method of claim 1, wherein,
the carrier phase observed quantity is obtained through bidirectional distance measurement; and
the multi-difference squared observations comprise two-way ranging double-difference squared observations obtained by differentiating squares of the two-way ranging obtained carrier-phase observations between two different locations of a receiver and between two different positioning base stations.
4. The integer ambiguity determination method of claim 3, wherein the linear observation model constructed based on the two-way ranging double-difference squared observation is:
Figure FDA0003303356380000011
wherein,
Figure FDA0003303356380000012
representing a two-way ranging double-difference squared observation;
Figure FDA0003303356380000013
carrier phase observations obtained by two-way ranging
Figure FDA0003303356380000014
In the middle, the superscripts i and j represent the serial numbers of the positioning base stations, and the subscripts k and m represent the position serial numbers of the receivers;
Zi、Zjrepresenting the integer ambiguity measured in both directions;
q (u) represents a displacement parameter determined by the variation of the receiver position u,
Figure FDA0003303356380000015
wherein s isi、sjIndicating the position vector, u, of the positioning base stationk、umA position vector representing the receiver, λ representing the carrier wavelength;
w represents an error term.
5. The integer ambiguity determination method of claim 1 wherein the multi-difference squared observations comprise double-difference squared observations obtained by differentiating a square of the carrier-phase observations between two different locations of a receiver and between two different positioning base stations.
6. The integer ambiguity determination method of claim 5, wherein the linear observation model constructed based on the double difference squared observation is:
Figure FDA0003303356380000021
wherein,
Figure FDA0003303356380000022
representing a double-difference-squared observation,
Figure FDA0003303356380000023
observed quantity of carrier phase
Figure FDA0003303356380000024
In the middle, the superscripts i and j represent the serial numbers of the positioning base stations, and the subscripts k and m represent the position serial numbers of the receivers;
zi、zjexpressing the integer ambiguity;
fcrepresents a carrier frequency;
α represents a frequency deviation of a receiver clock with respect to a base station clock;
r (alpha, u) represents a displacement parameter determined by the frequency deviation alpha of the receiver clock relative to the base station clock and the variation of the receiver position u,
Figure FDA0003303356380000025
where, λ represents the carrier wavelength,
Figure FDA0003303356380000026
si、sjindicating the position vector, u, of the positioning base stationk、umA position vector representing the receiver;
n represents an error term.
7. The integer ambiguity determination method of claim 1 wherein the multi-difference squared observations comprise tri-difference squared observations obtained by differentiating a square of the carrier-phase observations between three different locations of a receiver and between two different positioning base stations.
8. The integer ambiguity determination method of claim 7, wherein the linear observation model constructed based on the tri-difference squared observation is:
Figure FDA0003303356380000031
wherein,
Figure FDA0003303356380000032
representing a three-difference squared observation;
Figure FDA0003303356380000033
Figure FDA0003303356380000034
Figure FDA0003303356380000035
observed quantity of carrier phase
Figure FDA0003303356380000036
In the middle, the superscripts i and j represent the serial numbers of the positioning base stations, and the subscripts k, m and p represent the position serial numbers of the receivers;
zi、zjexpressing the integer ambiguity;
p (alpha, u) represents a shift parameter determined by the frequency deviation alpha of the receiver clock relative to the base station clock and the variation of the receiver position u,
Figure FDA0003303356380000037
wherein f iscRepresenting the carrier frequency, lambda represents the carrier wavelength,
Figure FDA0003303356380000038
si、sjindicating the position vector, u, of the positioning base stationk、um、upA position vector representing the receiver;
e denotes an error term.
9. The integer ambiguity determination method of any one of claims 3-8, wherein a floating solution of integer ambiguity is obtained by a least squares method based on the constructed linear observation model, from which an integer solution of integer ambiguity is obtained.
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