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CN111505670A - Multipath detection and suppression method and system using dual antennas - Google Patents

Multipath detection and suppression method and system using dual antennas Download PDF

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Publication number
CN111505670A
CN111505670A CN202010373758.5A CN202010373758A CN111505670A CN 111505670 A CN111505670 A CN 111505670A CN 202010373758 A CN202010373758 A CN 202010373758A CN 111505670 A CN111505670 A CN 111505670A
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carrier phase
value
multipath
calculating
baseline vector
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陈佳佳
何智力
袁洪
刘杨斌
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Suzhou Xiangtian Chunyu Technology Co ltd
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Suzhou Xiangtian Chunyu Technology 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
    • G01S19/13—Receivers
    • G01S19/22—Multipath-related issues

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Abstract

The invention relates to a multipath detection and inhibition method and a system using double antennas, which comprises the steps of obtaining carrier phase and broadcast ephemeris of GNSS signals; calculating the error square sum according to the carrier phase, the known length of the antenna base line and the broadcast ephemeris; comparing the error square sum with a threshold value, judging whether the numerical value of the error square sum is larger than the threshold value, if so, determining that at least one multipath signal exists in the currently received satellite signal, otherwise, determining that the multipath signal does not exist currently; calculating a carrier phase error estimation value caused by a multipath signal, and calculating the carrier phase estimation value according to the carrier phase and the carrier phase error estimation value; the antenna is positioned. The invention can realize the purpose of multi-path inhibition, reduce the cost and realize real-time detection and calculation.

Description

Multipath detection and suppression method and system using dual antennas
Technical Field
The invention relates to the technical field of satellite measurement and control, in particular to a multipath detection and suppression method and system using double antennas.
Background
Navigation plays a very critical role throughout the development of human civilization, and its fundamental task is to clarify the location information of a carrier and guide the carrier from the current location to a destination according to a specified time and route. With the rapid improvement of the positioning precision of a global navigation satellite system (GNSS for short), the subjects of aviation, transportation, mapping, disaster monitoring and the like put higher requirements on high-precision positioning. The carrier phase ranging accuracy is higher than the code phase ranging accuracy, so the carrier phase ranging is usually adopted in the high-precision positioning and navigation scenarios. However, errors caused by satellite clock errors, satellite ephemeris errors, ionospheric delays, tropospheric delays and multipath effects can have a serious impact on the positioning accuracy. Multipath effects generally refer to the fact that the receiver not only receives the direct navigation signal, but also is interfered by various indirect signals, which are referred to as multipath signals. Since systematic errors can be eliminated based on the principle of difference or modeling, while multipath errors are usually time-varying and vary with the user's environment, they are usually difficult to suppress based on the difference technique, and have become the most important errors affecting high-precision positioning.
Current multipath detection and mitigation techniques are generally classified into three types: the design of navigation signals, antenna technology and data post-processing technology. The navigation signal design needs to change the existing navigation signal structure, and the implementation difficulty is quite huge. Antenna technologies are generally classified into two types, one is a right-hand circularly polarized antenna, a chocking antenna, and the like, which essentially prevent multipath signals from entering the antenna, thereby suppressing the multipath signals. However, this technique requires redesigning the receiving antenna and cannot fully utilize the existing low-cost antenna; another antenna technology is to use an antenna array, which can extract more information about satellite signals and reduce the influence of multipath signals well in subsequent processing, but the antenna array usually needs more than four antennas, which is relatively large in size and cost.
Data post-processing techniques typically do not require adjustments to the architecture of the receiver. The technology utilizes the frequency and the period characteristics of multipath, and processed information mainly comprises pseudo range, carrier phase and the like received by a receiver. The current research on the data post-processing technology is very sufficient and is widely used in engineering, but the technology has obvious defects, the technology needs to carry out long-time data observation, cannot carry out real-time processing, and has very limited application conditions.
Disclosure of Invention
Therefore, the technical problem to be solved by the present invention is to overcome the problems of the prior art that real-time processing cannot be performed and the application conditions are limited, thereby providing a method and a system for multi-path detection and suppression using dual antennas, which can perform real-time processing and have small limitation on the application conditions.
In order to solve the above technical problem, a multipath detection and suppression method using dual antennas of the present invention includes: step S1: acquiring a carrier phase and a broadcast ephemeris of a GNSS signal; step S2: calculating the error square sum according to the carrier phase, the known length of the antenna base line and the broadcast ephemeris; step S3: comparing the error square sum with a threshold value, judging whether the numerical value of the error square sum is larger than the threshold value, if so, determining that at least one multipath signal exists in the currently received satellite signal, and entering a step S4, otherwise, determining that the multipath signal does not exist currently, and entering a step S5; step S4: calculating a carrier phase error estimation value caused by a multipath signal, and calculating the carrier phase estimation value according to the carrier phase and the carrier phase error estimation value; step S5: the antenna is positioned.
In one embodiment of the present invention, the method for calculating the sum of the squares of the errors according to the carrier phase, the known base length, and the broadcast ephemeris is: and calculating a baseline vector estimation value according to the carrier phase and the broadcast ephemeris, calculating a baseline vector observation value and an antenna baseline length, and calculating a sum of squares of errors according to the baseline vector estimation value.
In one embodiment of the present invention, the method of calculating the baseline vector observations is: assuming that the number of the current observable satellites is N, selecting the satellite signal with the highest elevation angle as a reference satellite; carrier phase double-difference observation matrix
Figure BDA0002479349610000021
Wherein
Figure BDA0002479349610000022
Is (N)× 1) matrix representing a carrier phase double difference observation matrix, H is an (N × 3) matrix representing the direction cosine difference between the satellite and the reference satellite and calculated from the broadcast ephemeris, NrBAIs (N × 1) matrix, is zero mean Gaussian white noise and is recorded as
Figure BDA0002479349610000031
The observed value DeltaX of the baseline vector can be obtained by calculation by using a least square methodBA，
Figure BDA0002479349610000032
Wherein A ═ HTH)-1H。
In an embodiment of the present invention, a method for calculating a baseline vector estimation value according to the baseline vector observation value and the antenna baseline length comprises: singular Value Decomposition (SVD) of the matrix H:
Figure BDA0002479349610000033
wherein in the Chinese formula
Figure BDA0002479349610000034
Is the positive singular value, λ, of the matrix HiIs a characteristic value of H, D ═ diag (σ)1,σ2,σ3) Is a diagonal matrix, and σ1≥σ2≥σ3>0，μi、viColumn vectors of orthogonal matrices U and V, respectively; Δ XBAThe variances of (d) are respectively noted as:
Figure BDA0002479349610000035
Figure BDA0002479349610000036
ΔXBAis marked as
Figure BDA0002479349610000037
bBA＝[bx,by,bz]TIs the true value of the baseline vector, σX＝[σx,σy,σz]T(ii) a Using observed values Δ XBAAnd are knownEstimating the truth value by the length d of the base line to construct an iterative equation bn'+1＝bn'+XnWherein b'nAnd b'n+1B for the n-th and n + 1-th iteration, respectivelyBAThe value of the estimated value is,Xnis the residual of the nth estimate, the base length d can be expressed as
Figure BDA0002479349610000038
Linear expansion of base length d using first order Taylor's formula
Figure BDA0002479349610000039
Calculating by using a least square method again to obtain residual error of each iterationXnInitial value of iteration is observed value delta X of baseline vectorBAAnd iteratively calculated convergence value is recorded as b'BAViewed as the true value b of the baseline vectorBAAn estimate of (d).
In one embodiment of the invention, the method of calculating the sum of the squares of errors from the baseline vector estimates is: from b'BAFor Δ XBAThe result of normalization was designated as Δ X'BA：ΔX'BA＝(ΔXBA-b'BA)/σXWherein Δ X'BA＝[Δx'BA,Δy'BA,Δz'BA]T,b'BA＝[b ' x,b'y,b ' z]T(ii) a Using the sum of squared errors statistic to determine the quality of the baseline vector estimate, defining a sum of squared errors value Q as:
Figure BDA00024793496100000310
in one embodiment of the invention, the threshold value is determined based on a false alarm rate.
In an embodiment of the present invention, the method for determining the threshold value according to the false alarm rate includes: at a certain false alarm rate PfaLower setting of a suitable threshold value
Figure BDA00024793496100000311
Wherein
Figure BDA00024793496100000312
Is x2(3) Δ X 'if there is at least one multipath signal in the currently received satellite signal'BAN (0,1), then the Q statistic should obey a chi-square distribution with a degree of freedom of 3, noted as χ2(3) If there are multipath signals, the Q index should obey a non-central chi-squared distribution with a degree of freedom of 3 and a parameter of γ, denoted as χ2(3,γ)，
Figure BDA00024793496100000313
In one embodiment of the present invention, a method for calculating an estimated value of a carrier phase error caused by a multipath signal comprises: if the carrier phase error estimate
Figure BDA00024793496100000314
Baseline vector observations containing multipath signals
Figure BDA0002479349610000041
Then
Figure BDA0002479349610000042
Wherein the carrier phase double difference observation matrix
Figure BDA0002479349610000043
Is marked as
Figure BDA0002479349610000044
Figure BDA0002479349610000045
Is a matrix of (N × 1) and is a baseline vector observation of carrier phase multipath error containing multipath signals
Figure BDA0002479349610000046
In one embodiment of the invention, when at least one multipath signal exists in the currently received satellite signal, the prompt message of 'multipath exists' is output; otherwise, outputting the prompt information of 'no multipath'.
The present invention also provides a multipath detection and mitigation system using dual antennas, comprising: the acquisition module is used for acquiring a carrier phase and a broadcast ephemeris of a mixed signal in the GNSS system; the first calculation module is used for calculating the error square sum according to the carrier phase, the known antenna base length and the broadcast ephemeris; the judging module is used for comparing the error square sum with a threshold value, judging whether the numerical value of the error square sum is larger than the threshold value, if so, considering that at least one multipath signal exists in the currently received satellite signal, and entering the second calculating module, otherwise, considering that the multipath signal does not exist currently, and directly entering the positioning module; the second calculation module is used for calculating a carrier phase error estimation value caused by a multipath signal and calculating the carrier phase estimation value according to the carrier phase and the carrier phase error estimation value; and the positioning module is used for positioning the antenna.
Compared with the prior art, the technical scheme of the invention has the following advantages:
the multipath detection and suppression method and system using the double antennas acquire the carrier phase and the broadcast ephemeris of the GNSS signal, thereby being beneficial to calculating the error square sum; calculating the sum of squares of errors according to the carrier phase, the known length of the antenna base line and the broadcast ephemeris, and being beneficial to judging whether the test is satisfied; comparing the error square sum with a threshold value, judging whether the numerical value of the error square sum is larger than the threshold value, if so, considering that at least one multipath signal exists in the currently received satellite signal, and needing to suppress the multipath signal, otherwise, considering that the multipath signal does not exist currently; calculating a carrier phase error estimation value caused by a multipath signal, and calculating the carrier phase estimation value according to the carrier phase and the carrier phase error estimation value, thereby achieving the purpose of multipath signal suppression; the antenna is positioned, so that the positioning precision is effectively improved, in addition, the detection system and the size can be effectively reduced, the cost is reduced, and the real-time detection and the calculation are realized.
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In order that the present disclosure may be more readily and clearly understood, reference is now made to the following detailed description of the embodiments of the present disclosure taken in conjunction with the accompanying drawings, in which
Fig. 1 is a flow chart of a multipath detection and mitigation method using dual antennas of the present invention.
Detailed Description
Example one
As shown in fig. 1, the present embodiment provides a multipath detection and suppression method using dual antennas, including the following steps, step S1: acquiring a carrier phase and a broadcast ephemeris of a GNSS signal; step S2: calculating the error square sum according to the carrier phase, the known length of the antenna base line and the broadcast ephemeris; step S3: comparing the error square sum with a threshold value, judging whether the numerical value of the error square sum is larger than the threshold value, if so, determining that at least one multipath signal exists in the currently received satellite signal, and entering a step S4, otherwise, determining that the multipath signal does not exist currently, and entering a step S5; step S4: calculating a carrier phase error estimation value caused by a multipath signal, and calculating the carrier phase estimation value according to the carrier phase and the carrier phase error estimation value; step S5: the antenna is positioned.
In the multi-path detection and suppression method using dual antennas according to this embodiment, in step S1, the carrier phase and the broadcast ephemeris of the GNSS signal are obtained, so as to facilitate calculation of the error sum of squares; in step S2, the sum of squares of errors is calculated according to the carrier phase, the known length of the antenna base and the broadcast ephemeris, which is beneficial to determining whether the test is satisfied; in the step S3, comparing the sum of squared errors with a threshold, and determining whether the value of the sum of squared errors is greater than the threshold, if so, determining that at least one multipath signal exists in the currently received satellite signal, and then needing to suppress the multipath signal, and entering step S4, otherwise, determining that the multipath signal does not exist currently, and entering step S5; in step S4, a carrier phase error estimation value caused by a multipath signal is calculated, and the carrier phase estimation value is calculated according to the carrier phase and the carrier phase error estimation value, so as to achieve the purpose of multipath signal suppression; in the step S5, the antenna is positioned, so that the positioning accuracy is effectively improved, in addition, the detection system and the volume can be effectively reduced, the cost is reduced, and real-time detection and calculation are realized.
In step S1, the method for obtaining the carrier phase and the broadcast ephemeris of the GNSS signal includes: the baseline vector observations are advantageously obtained using a receiver to obtain carrier phase and broadcast ephemeris data of the GNSS signals.
The method for calculating the sum of squares of errors according to the carrier phase, the known length of the antenna base line, and the broadcast ephemeris in step S2 includes: and calculating a baseline vector observation value according to the carrier phase and the broadcast ephemeris, calculating a baseline vector estimation value according to the baseline vector observation value and the antenna baseline length, and calculating a sum of squares of errors according to the baseline vector estimation value. After the baseline vector observed value is obtained through calculation, a baseline vector estimated value is obtained through iterative calculation by utilizing the known baseline length, which is described in detail by combining a formula as follows:
the method for calculating the baseline vector observed value comprises the following steps: assuming that the number of the current observable satellites is N, selecting the satellite signal with the highest elevation angle as a reference satellite; carrier phase double-difference observation matrix
Figure BDA0002479349610000061
Wherein
Figure BDA0002479349610000062
Is a (N × 1) matrix representing a carrier phase double difference observation matrix, H is a (N × 3) matrix representing the direction cosine difference between the satellite and the reference satellite and calculated from the broadcast ephemeris, NrBAIs (N × 1) matrix, is zero mean Gaussian white noise and is recorded as
Figure BDA0002479349610000063
The observed value DeltaX of the baseline vector can be obtained by calculation by using a least square methodBA，
Figure BDA0002479349610000064
Wherein A ═ HTH)-1H。
The method for calculating the baseline vector estimation value according to the baseline vector observation value and the antenna baseline length comprises the following steps: singular Value Decomposition (SVD) of the matrix H:
Figure BDA0002479349610000065
wherein in the Chinese formula
Figure BDA0002479349610000066
Is the positive singular value, λ, of the matrix HiIs a characteristic value of H, D ═ diag (σ)1,σ2,σ3) Is a diagonal matrix, and σ1≥σ2≥σ3>0，μi、viColumn vectors of orthogonal matrices U and V, respectively; Δ XBAThe variances of (d) are respectively noted as:
Figure BDA0002479349610000067
ΔXBAis marked as
Figure BDA0002479349610000068
bBA＝[bx,by,bz]TIs the true value of the baseline vector, σX＝[σx,σy,σz]T(ii) a Using observed values Δ XBAEstimating the truth value with the known base length d to construct an iterative equation bn'+1＝bn'+XnWherein b'nAnd b'n+1B for the n-th and n + 1-th iteration, respectivelyBAThe value of the estimated value is,Xnis the residual of the nth estimate, the base length d can be expressed as
Figure BDA0002479349610000069
Linear expansion of base length d using first order Taylor's formula
Figure BDA00024793496100000610
Calculating by using a least square method again to obtain residual error of each iterationXnInitial value of iteration is observed value delta X of baseline vectorBAAnd iteratively calculated convergence value is recorded as b'BAViewed as the true value b of the baseline vectorBAAn estimate of (d).
The method for calculating the sum of the squares of errors from the baseline vector estimates is: from b'BAFor Δ XBAThe result of normalization was designated as Δ X'BA：ΔX'BA＝(ΔXBA-b'BA)/σXWherein Δ X'BA＝[Δx'BA,Δy'BA,Δz'BA]T,b'BA＝[b ' x,b'y,b ' z]T(ii) a Using the sum of squared errors statistic to determine the quality of the baseline vector estimate, defining a sum of squared errors value Q as:
Figure BDA0002479349610000071
in step S3, the threshold is determined according to the false alarm rate, and the threshold is calculated according to the Neyman-Pearson criterion under the condition that a certain false alarm rate is satisfied, so that the purpose of inspection is achieved and false alarm is prevented.
The method for determining the threshold value according to the false alarm rate comprises the following steps: at a certain false alarm rate PfaLower setting of a suitable threshold value Qth，
Figure BDA0002479349610000072
Wherein
Figure BDA0002479349610000073
Is x2(3) Δ X 'if there is at least one multipath signal in the currently received satellite signal'BAN (0,1), then the Q statistic should obey a chi-square distribution with a degree of freedom of 3, noted as χ2(3) If there are multipath signals, the Q index should obey a non-central chi-squared distribution with a degree of freedom of 3 and a parameter of γ, denoted as χ2(3,γ)，
Figure BDA0002479349610000074
In this embodiment, when the sum of squared errors statistic is compared with the threshold value, if the sum of squared errors statistic is smaller than or equal to the threshold value, the baseline vector estimation value is a valid approximation of the true value, the passing test condition is satisfied, it is considered that no multipath signal exists currently, and the prompt information of "no multipath" is output; if the error sum of squares statistic is greater than the threshold value, the test is not passed, at least one multipath signal exists in the currently received satellite signals, and prompt information of 'multipath exists' is output, which is needed at this moment.
In step S4, in order to improve the accuracy of the multipath error estimation value of the carrier phase, the method for calculating the multipath error estimation value of the carrier phase caused by the multipath signal includes: if the carrier phase error estimate
Figure BDA0002479349610000075
Baseline vector observations containing multipath signals
Figure BDA0002479349610000076
Then
Figure BDA0002479349610000077
Wherein the carrier phase double difference observation matrix
Figure BDA0002479349610000078
Is marked as
Figure BDA0002479349610000079
Figure BDA00024793496100000710
Is a matrix of (N × 1) and is a baseline vector observation of carrier phase multipath error containing multipath signals
Figure BDA00024793496100000711
Figure BDA00024793496100000712
The method for calculating the carrier phase estimation value according to the carrier phase and the carrier phase error estimation value comprises the following steps: and calculating the difference value of the carrier phase and the carrier phase error estimated value.
The multipath detection and suppression method provided by the invention only uses two existing commercial antennas, realizes the detection of multipath signals and effectively suppresses the multipath signals; and the invention combines the antenna array and the data post-processing technology, can effectively reduce the detection system, volume and cost, and realize real-time detection and calculation. Because two commercial low-cost GNSS antennas are used for constructing the short baseline vector, the volume is small, the real-time detection can be realized, the existence of the multipath signals can be detected without delay, and the multipath signals can be effectively inhibited.
In this embodiment, the length between the two antennas is used to iteratively correct the observed data to obtain an estimated value with higher accuracy, but the present invention is not limited to the use of two antennas. When one more antenna is added, the geometry information between the three antennas can be easily obtained in advance. On the basis of combining the antenna, the geometric shape and the length information, the precision of the carrier phase multipath error estimation value can be effectively improved, and the positioning precision is further improved.
In this embodiment, when positioning the antenna, since the multipath error usually has time-varying characteristics and changes with the environment of the user, it is only necessary to position the antenna containing the multipath signal.
Example two
Based on the same inventive concept, the present embodiment provides a multi-path detection and suppression system using dual antennas, and the principle of solving the problem is similar to the multi-path detection and suppression method using dual antennas, and repeated details are omitted.
The present embodiment provides a multipath detection and mitigation system using dual antennas, including:
the acquisition module is used for acquiring a carrier phase and a broadcast ephemeris of the GNSS signal;
the first calculation module is used for calculating the error square sum according to the carrier phase, the known antenna base length and the broadcast ephemeris;
the judging module is used for comparing the error square sum with a threshold value, judging whether the numerical value of the error square sum is larger than the threshold value, if so, considering that at least one multipath signal exists in the currently received satellite signal, and entering the second calculating module, otherwise, considering that the multipath signal does not exist currently, and directly entering the positioning module;
the second calculation module is used for calculating a carrier phase error estimation value caused by a multipath signal and calculating the carrier phase estimation value according to the carrier phase and the carrier phase error estimation value;
and the positioning module is used for positioning the antenna.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. And obvious variations or modifications therefrom are within the scope of the invention.

Claims (10)

1. A method for multipath detection and mitigation using dual antennas, comprising the steps of:
step S1: acquiring a carrier phase and a broadcast ephemeris of a GNSS signal;
step S2: calculating the error square sum according to the carrier phase, the known length of the antenna base line and the broadcast ephemeris;
step S3: comparing the error square sum with a threshold value, judging whether the numerical value of the error square sum is larger than the threshold value, if so, determining that at least one multipath signal exists in the currently received satellite signal, and entering a step S4, otherwise, determining that the multipath signal does not exist currently, and entering a step S5;
step S4: calculating a carrier phase error estimation value caused by a multipath signal, and calculating the carrier phase estimation value according to the carrier phase and the carrier phase error estimation value;
step S5: the antenna is positioned.
2. The multipath detection and mitigation method using dual antennas of claim 1, wherein: the method for calculating the error square sum according to the carrier phase, the known antenna base length and the broadcast ephemeris comprises the following steps: and calculating a baseline vector observation value according to the carrier phase and the broadcast ephemeris, calculating a baseline vector estimation value according to the baseline vector observation value and the antenna baseline length, and calculating a sum of squares of errors according to the baseline vector estimation value.
3. The multipath detection and mitigation method using dual antennas of claim 2, wherein: the method for calculating the baseline vector observed value comprises the following steps: assuming that the number of the current observable satellites is N, selecting the satellite signal with the highest elevation angle as a reference satellite; carrier phase double-difference observation matrix
Figure FDA0002479349600000011
Wherein
Figure FDA0002479349600000012
Is a (N × 1) matrix representing a carrier phase double difference observation matrix, H is a (N × 3) matrix representing the direction cosine difference between the satellite and the reference satellite and calculated from the broadcast ephemeris, NrBAIs (N × 1) matrix, is zero mean Gaussian white noise and is recorded as
Figure FDA0002479349600000013
The observed value DeltaX of the baseline vector can be obtained by calculation by using a least square methodBA，
Figure FDA0002479349600000014
Wherein A ═ HTH)-1H。
4. The method of multipath detection and mitigation using dual antennas of claim 3The method is characterized in that: the method for calculating the baseline vector estimation value according to the baseline vector observation value and the antenna baseline length comprises the following steps: singular Value Decomposition (SVD) of the matrix H:
Figure FDA0002479349600000021
wherein in the Chinese formula
Figure FDA0002479349600000022
Is the positive singular value, λ, of the matrix HiIs a characteristic value of H, D ═ diag (σ)1,σ2,σ3) Is a diagonal matrix, and σ1≥σ2≥σ3>0，μi、viColumn vectors of orthogonal matrices U and V, respectively; Δ XBAThe variances of (d) are respectively noted as:
Figure FDA0002479349600000023
ΔXBAis marked as
Figure FDA0002479349600000024
bBA＝[bx,by,bz]TIs the true value of the baseline vector, σX＝[σx,σy,σz]T(ii) a Using observed values Δ XBAAnd estimating a truth value with a known base line length d to construct an iterative equation b'n+1＝b′n+XnWherein b'nAnd b'n+1B for the n-th and n + 1-th iteration, respectivelyBAThe value of the estimated value is,Xnis the residual of the nth estimate, the base length d can be expressed as
Figure FDA0002479349600000025
Linear expansion of base length d using first order Taylor's formula
Figure FDA0002479349600000026
Calculating by using a least square method again to obtain residual error of each iterationXnInitial value of iteration is observed value delta X of baseline vectorBAAnd iteratively calculated convergence value is recorded as b'BAViewed as the true value b of the baseline vectorBAAn estimate of (d).
5. The multipath detection and mitigation method using dual antennas of claim 4, wherein: the method for calculating the sum of the squares of errors from the baseline vector estimates is: from b'BAFor Δ XBAThe result of normalization was designated as Δ X'BA：ΔX'BA＝(ΔXBA-b'BA)/σXWherein Δ X'BA＝[Δx'BA,Δy'BA,Δz'BA]T,b'BA＝[b′x,b'y,b′z]T(ii) a Using the sum of squared errors statistic to determine the quality of the baseline vector estimate, defining a sum of squared errors value Q as:
Figure FDA0002479349600000027
6. the multipath detection and mitigation method using dual antennas of claim 5, wherein: the threshold value is determined based on a false alarm rate.
7. The multipath detection and mitigation method using dual antennas of claim 6, wherein: the method for determining the threshold value according to the false alarm rate comprises the following steps: at a certain false alarm rate PfaLower setting of a suitable threshold value Qth，
Figure FDA0002479349600000028
Wherein
Figure FDA0002479349600000029
Is x2(3) Δ X 'if there is at least one multipath signal in the currently received satellite signal'BAN (0,1), then the Q statistic should obey a chi-square distribution with a degree of freedom of 3, noted as χ2(3) If there is a multipath signal, the Q index should beWhen the non-central chi-square distribution with the compliance degree of freedom of 3 and the parameter of gamma is recorded as chi2(3,γ)，
Figure FDA00024793496000000210
8. The multipath detection and mitigation method using dual antennas of claim 1, wherein: the method for calculating the carrier phase error estimated value caused by the multipath signal comprises the following steps: if the carrier phase error estimate
Figure FDA0002479349600000031
Baseline vector observations containing multipath signals
Figure FDA0002479349600000032
Then
Figure FDA0002479349600000033
Wherein the carrier phase double difference observation matrix
Figure FDA0002479349600000034
Is marked as
Figure FDA0002479349600000035
Figure FDA0002479349600000036
Is a matrix of (N × 1) and is a baseline vector observation of carrier phase multipath error containing multipath signals
Figure FDA0002479349600000037
Figure FDA0002479349600000038
9. The multipath detection and mitigation method using dual antennas of claim 1, wherein: when at least one multipath signal exists in the currently received satellite signal, outputting prompt information of 'having multipath'; otherwise, outputting the prompt information of 'no multipath'.
10. A multipath detection and mitigation system using dual antennas, comprising:
the acquisition module is used for acquiring a carrier phase and a broadcast ephemeris of the GNSS signal;
the first calculation module is used for calculating the error square sum according to the carrier phase, the known antenna base length and the broadcast ephemeris;
the judging module is used for comparing the error square sum with a threshold value, judging whether the numerical value of the error square sum is larger than the threshold value, if so, considering that at least one multipath signal exists in the currently received satellite signal, and entering the second calculating module, otherwise, considering that the multipath signal does not exist currently, and directly entering the positioning module;
the second calculation module is used for calculating a carrier phase error estimation value caused by a multipath signal and calculating the carrier phase estimation value according to the carrier phase and the carrier phase error estimation value;
and the positioning module is used for positioning the antenna.
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