CN115877431A - Array antenna non-whole-cycle fuzzy strategy based low-operand direction-finding device and method - Google Patents
Array antenna non-whole-cycle fuzzy strategy based low-operand direction-finding device and method Download PDFInfo
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Abstract
The invention discloses a low-computation direction-finding device and a low-computation direction-finding method based on an array antenna non-integer fuzzy strategy, wherein the device comprises a PCB (printed Circuit Board), a receiving antenna module, a GNSS receiver module, a communication transmission unit and an STM32 signal processing unit, wherein a CPU (Central processing Unit) is integrated on the STM32 signal processing unit, and a storage unit, a gyroscope and a DMA (direct memory access) controller are connected with the CPU, and direction-finding information is transmitted to a display module in real time and accurately by connection.
Description
Technical Field
The invention belongs to the technical field of satellite navigation positioning, and particularly relates to a low-operand direction-finding device and method based on an array antenna non-integer fuzzy strategy.
Background
With the continuous perfection of satellite navigation systems and the increasing complexity of traffic roads, people have higher and higher requirements on the precision, power consumption, operability and the like of navigation terminals. The single GNSS system is used for positioning, the positioning result in certain areas is poor, two or more satellite navigation systems are combined together, and the navigation advantages of each navigation system are combined, so that the quality of positioning service can be improved, and the accuracy and the stability of positioning equipment can be improved.
Most of the calculation work of the GPS receiver is completed by a bulky receiver at the beginning, and after 20 th century, the receiver gradually adopts a small-sized processor and an integrated circuit to complete all the calculation work. Early analog signal processing schemes are gradually eliminated, the size of a receiver is gradually reduced, the application of an integrated circuit is increased along with the development of science and technology, and the current GPS receiver realizes the purpose of completing calculation work by using a high-speed microprocessor.
The navigation technology is developed along with the economic, military and political development requirements of human beings, and along with the improvement of the requirements, new requirements are continuously provided for the navigation positioning technology. In the navigation process, positioning is firstly needed, namely coordinate position information of the carrier is determined, and in order to enable the carrier to complete a preset navigation task, the real-time position information of the carrier is required to be known besides the positions of a guidance target point and a starting point.
The Beidou north-seeking theory is based on a carrier phase interference principle, real course angle resolving is achieved by utilizing millimeter-scale precision and carrier phase measurement values, but the carrier waves are periodic and the problem of cycle ambiguity exists.
Therefore, it is necessary to design a low computation direction-finding device and method based on an array antenna without a whole-cycle fuzzy strategy to solve the above technical problems.
Disclosure of Invention
In view of this, the invention provides a low computation amount direction-finding device and method based on an array antenna without a whole-cycle fuzzy strategy, the device has the advantages of simple system structure, high integration level, low equipment cost, high precision and wide popularization value, and the method has the advantages of small computation amount, high real-time performance and capability of realizing true course angle solution.
In order to achieve the purpose, the technical scheme of the invention is realized as follows:
low operation based on array antenna does not have whole week fuzzy strategy measures to device, and the device includes PCB board, receiving antenna module, GNSS receiver module, communication transmission unit and STM32 signal processing unit, the last integration of STM32 signal processing unit has CPU, memory cell, gyroscope and the DMA controller that links to each other with CPU, receiving antenna module, GNSS receiver module all contain five, and in five receiving antenna modules were connected to five GNSS receiver modules respectively, five GNSS receiver modules all linked to each other with STM32 signal processing unit's CPU, and one side of PCB board is equipped with communication transmission unit outward, is connected with CPU, will survey to information transmission to display module.
Furthermore, the receiving antenna module adopts five antennas to simultaneously receive multimode signals, is integrated on a PCB in parallel, is used for receiving satellite navigation signals from BDS, GPS and GLONASS systems, and is compatible with three frequency points of GPS/L1, GLONASS/L1 and BDS/B3.
Furthermore, the GNSS receiving antenna module utilizes satellite ephemeris information and Doppler frequency shift to resolve receiver triaxial navigation information in real time, various parameter settings are carried out through a serial port, parameters are stored in an internal FLASH and connected to the STM32 signal processing unit, and an internal CPU resolves direction-finding information of the module according to a communication protocol.
Further, the antenna of the receiving antenna module is a ceramic antenna.
Further, the GNSS receiver module is a module with L1 raw carrier phase output.
Further, the STM32 signal processing unit utilizes a multi-channel serial port to perform high-speed acquisition on data received by the GNSS receiver module;
and the STM32 signal processing unit realizes serial port data transmission by using a DMA controller.
The invention also provides a low-operation direction measurement method based on the array antenna non-whole-cycle fuzzy strategy, which utilizes the direction measurement device to carry out measurement and specifically comprises the following steps:
step 1, setting a short base line on a carrier to simultaneously observe two satellites s1 and s2, and then the double-difference carrier phase observation equation is as follows:
wherein,
for the observed value of double-difference carrier phase, the distance between the antennas in the direction-finding device is very short, and the apparent vector from all the antenna receiving centers on the same epoch carrier to the same satellite is set to be the same and is recorded as s 12 And b is a baseline vector; epsilon is single-baseline double-difference carrier phase observation noise under the condition of observing two satellites;
y i ＝Sb i +v
D(y i )＝Q yi (2)
wherein, S represents a GNSS view vector,
(i =1,2,3,4, j =1, \8230;, n), wherein v is n +1 co-view satellites, and in the case of selecting the satellite with the highest elevation angle as the reference satellite, the single-baseline double-difference carrier phase observation noise is observed, and D (-) is a dispersion operator, assuming the vector y of the observed quantity j Affected by Gaussian distribution errors, which are represented by a variance-covariance (v-c) matrix Q vi Described, the different baselines are assumed to be the same;
Y＝SRB B +V
D(vec(Y))＝Q Y ,R T R＝I (3)
wherein, B B Expressed as the corresponding vector of B in the carrier coordinate system, RB B R isAttitude rotation matrix, satisfy R T R = I, V is n +1 co-view satellites, and when a satellite with the highest elevation angle is selected as a reference satellite, the noise is observed by a multi-baseline double-difference carrier phase, a vec operator is introduced to define a V-c matrix of an observable object, and the dispersion of a vector vec (Y) is a V-c matrix Q Y To characterize;
step 4, introducing a vector operator vec, and vectorizing the formula (3) to obtain:
vec(Y)＝vec(SRB B )+vec(V) (4)
wherein, the symbol
Representing a tensor product;
and 6, improving the precision by using the redundancy and the least square, namely solving:
the precision is improved by solving a least square problem called constraint with quadratic identity;
compared with the prior art, the low-operand direction-finding device and method based on the array antenna without the whole-cycle fuzzy strategy have the following advantages:
1. the method has the advantages that multi-system fusion positioning is adopted, so that the normal work of a satellite receiver can be guaranteed under the condition that a satellite mode has a problem, the stability of satellite signals is guaranteed, the requirements of multi-system compatibility and high-precision measurement at present are met, a single board integrates a GNSS array antenna and an inertial unit, the inertial unit measures the three-axis attitude angle (or angular rate) and the acceleration of an object by adopting a gyroscope and an accelerometer, the requirements of multi-system compatibility and low-cost north seeking and orientation at present are met, and the influence of a magnetic field, latitude and speed is avoided;
2. the method adopts a unique five-antenna configuration, starts from a carrier phase interference equation, takes an ultra-short baseline as a research object, deduces the condition without ambiguity, designs a Beidou carrier phase interference north-seeking algorithm without integer ambiguity, improves the precision by utilizing redundancy and least square, has small operand and high real-time performance, can realize true course angle solution, and can still normally solve in some occasions with serious shielding;
3. the built-in gyroscope can provide high-speed output for smooth course, and can also ensure stable output in long-term flight when GNSS signals are lost;
4. the DMA controller is adopted to open a channel for directly transmitting data for RAM and I/O equipment, so that the CPU efficiency is greatly improved.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate an embodiment of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 is a schematic diagram of a low-k direction measurement device based on an array antenna non-integer ambiguity strategy;
FIG. 2 is a flow chart of a low computation vector device operation based on an array antenna integer ambiguity free strategy;
FIG. 3 is a direction-finding flow of a low-computation direction-finding method based on an array antenna non-whole-cycle fuzzy strategy;
description of the reference numerals
1-a PCB board; 2-a receive antenna module; a 3-GNSS receiver module; 4-a communication transmission unit; 5-STM32 signal processing unit; 6-CPU; 7-a storage unit; 8-a gyroscope; 9-DMA controller.
Detailed Description
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
In the description of the present invention, it is to be understood that the terms "central," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like are used in the orientations and positional relationships indicated in the drawings, which are based on the orientations and positional relationships indicated in the drawings, and are used for convenience in describing the present invention and for simplicity in description, but do not indicate or imply that the device or element so referred to must have a particular orientation, be constructed in a particular orientation, and be operated, and thus should not be construed as limiting the present invention. Furthermore, the terms "first", "second", etc. are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first," "second," etc. may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless otherwise specified.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meaning of the above terms in the present invention can be understood by those of ordinary skill in the art through specific situations.
The present invention will be described in detail below with reference to the embodiments with reference to the attached drawings.
Fig. 1 is a structural diagram of a low computation direction-finding device based on an array antenna integer ambiguity strategy, which includes a PCB board 1, a receiving antenna module 2, a GNSS receiver module 3, a communication transmission unit 4, an STM32 signal processing unit 5, a CPU6 integrated on the STM32 signal processing unit 5, a storage unit 7, a gyroscope 8 and a DMA controller 9 connected with the CPU6, wherein five receiving antenna modules 2 are respectively connected to five GNSS receiver modules 3, five GNSS receiver modules 3 are all connected with the CPU6 of the STM32 signal processing unit 5, a communication transmission unit 4 is arranged outside one side of the PCB board 1 and connected with the CPU6, and finally, direction-finding information is accurately transmitted to a display module in real time.
Specifically, the PCB board adopts a modular design mode and is respectively a receiving antenna module, a GNSS receiving antenna module and an STM32 signal processing unit.
Specifically, the receiving antenna module comprehensively considers the stability of received signals and the size of the device, adopts five antennas to simultaneously receive multimode signals, is integrated on a PCB in parallel, is used for receiving satellite navigation signals from BDS, GPS and GLONASS systems, is compatible with three frequency points of GPS/L1, GLONASS/L1 and BDS/B3, and can receive a large number of satellites, and has wide application range, high output positioning precision and good reliability.
Specifically, the GNSS receiving antenna module utilizes satellite ephemeris information and Doppler frequency shift to resolve navigation information such as the position, the speed and the like of the receiver in the three axial directions in real time, various parameter settings are carried out through a serial port, parameters are stored in an internal FLASH, the GNSS receiving antenna module is convenient to use and is conveniently connected to an STM32 signal processing unit, and an internal processor analyzes direction-finding information of the module according to a communication protocol.
Specifically, STM32 signal processing unit has designed clock configuration program, serial port communication program and the storage program among the signal processing program respectively, realizes the processing of signal through STM32 singlechip configuration receiver module, realizes the communication between the serial ports with the idle interrupt of serial port plus DMA's mode, and storage program design part has added the SD card, makes the module miniaturization, and whole processing unit will solve the program and transplant to C language platform, handles with STM 32.
The code efficiency is high by calculating the measuring and calculating information through converting the frequency and demodulating the signal, the number of configured peripheral interfaces is large, the integration level is high, the function is strong, the cost performance is high, the real-time performance is good, all the adopted key chips are low-power-consumption chips based on simplified instructions, and the price is relatively low.
In one embodiment of the invention, the PCB is integrally designed by SMT, the integration level is high, and the assembly time is saved.
In one embodiment of the invention, the antenna in the receiving antenna module is a ceramic antenna.
In one embodiment of the invention, the GNSS receiver module is a module with L1 raw carrier phase output.
In an embodiment of the invention, the storage unit adopts an SD card with high-density storage capacity mainly used for storing user debugging data, when the power is off, the parameters are stored in the storage medium, and the last set parameter value is read from the memory after the power is on again, so that the data is not lost after the power is off.
In one embodiment of the invention, the gyroscope is highly compact, lightweight, and fully self-contained, using an adaptive reduced-order kalman filter to reduce errors affecting such sensors.
In an embodiment of the invention, the receiving antenna module adopts the existing high-gain double-feed point measurement type antenna, so that the cost advantage and the phase center performance are considered, and the measurement precision is ensured.
The invention selects the high-stability constant-temperature crystal oscillator as the local clock, realizes high-precision time service, and simultaneously ensures the accuracy, reliability and stability of the satellite receiving synchronous system.
The invention adopts multi-system fusion positioning, can ensure that a satellite receiver can work normally under the condition that one satellite mode has problems, ensures the stability of receiving satellite signals, and meets the requirements of multi-system compatibility and high-precision measurement at present. The multi-system satellite signals can reduce reflection and gravitation in the universe, so that a lower geometric factor value is obtained, error influence is improved, and deviation of positioning accuracy is reduced.
The invention can be applied to static scenes and can also be oriented to the direction-finding device and method of dynamic scenes, adopt the instant true north resolving technology design based on array antenna, support BDS, GPS and QZSS satellite navigation signal reception of the system, can meet the carrier north-seeking, directional demand under the complicated environment, is not influenced by magnetic field, latitude, speed.
Fig. 2 is a flowchart of the low computation measurement vector apparatus based on the array antenna non-integer ambiguity strategy:
the receiving antenna module collects satellite signals through a ceramic antenna, adopts an eight-arm coupling and four-feed-point feed technology, supports the L1 frequency band satellite navigation signal receiving of the second generation Beidou, GPS, GLONASS and GALILEO systems, is internally provided with a low noise amplifier, adopts a two-stage filter, has good out-of-band suppression and strong anti-interference capability, and ensures normal work in severe electromagnetic environment. Satellite navigation signals of 5 paths of BDS and GPS are received at the same time and reach a receiving end through different paths, multi-path fading can be effectively resisted, the fluctuation of the signal-to-noise ratio of the receiving end is reduced, then the signals received on five antennas are combined, the maximization of the signal interference-to-noise ratio is realized, diversity gain and array gain can be obtained, and the direction finding stability of the device is obviously enhanced.
After the satellite signals are collected by the receiving antenna, the azimuth angle is obtained by internal calculation of the GNSS receiver module, and the module optimizes precision and availability by measurement and single satellite time service, works with low periodicity, minimizes power consumption, integrates monitoring and alarming, and maximizes reliability, so the invention has the characteristics of high precision and high reliability.
The downward inclination angle of the base station antenna is measured through internal calculation of the GNSS receiver module and a gyroscope on the STM32 signal processing unit, and an inclination angle sensor is arranged in the gyroscope to acquire accurate pitching and rolling data and assist in providing quick start and course recapture. Therefore, the method can output very accurate and stable angular speed and heading angle, and improves the accuracy in direction finding under dynamic conditions.
STM32 signal processing module adopts modularization programming, the high-speed signal that is received by GNSS receiver module of gathering of multichannel serial ports, through the processing of DMA controller, open up a direct transfer data's passageway for RAM and I/O equipment, adopt DMA mode control PWM pulse quantity, through DMA from memory to timer transmission data, the every pulse of sending of timer, through DMA to the register transfer of timer enable signal, produce DMA interrupt after sending the pulse of memory specified quantity. In the interrupt processing, the DMA sends an enable signal to the timer enable register, so that the PWN pulse is stopped, each pulse of the timer is prevented from entering the interrupt, the system time is saved, and the response rate of the system is improved. Because the DMA transmission mode does not need to transmit data through the CPU, the current program does not need to be interrupted, the I/O and the host computer work in parallel, and the program and the transmission work in parallel, thereby greatly improving the efficiency of the CPU. Therefore, the invention has high transmission speed and good real-time property.
The communication transmission unit can be a WiFi module or a Bluetooth module, and is transmitted to a computer terminal, or connected to a mobile phone, or connected to a required transmission terminal through the unit, so that the device has a wide application range and is suitable for wide popularization.
As shown in fig. 3, a direction finding process of the low-computation direction-finding method based on the array antenna without the whole-cycle fuzzy strategy is shown:
the GNSS positioning usually adopts two observation values of pseudo-range and carrier phase, and because the positioning accuracy by utilizing the carrier phase is usually higher by one order of magnitude difference than the pseudo-range positioning to centimeter level, the carrier phase positioning is one of the important methods for realizing high-precision positioning and attitude measurement at present. However, the precise positioning of the phase observation value can be realized only under the condition that the whole-cycle ambiguity is correctly fixed in the carrier phase positioning, the array antenna-based low-operand direction finding without the whole-cycle ambiguity strategy starts from a carrier phase interference equation, an ultra-short baseline is taken as a research object, a Beidou carrier phase interference north-seeking algorithm without the whole-cycle ambiguity is designed, a Crohn's product-tolerant structure equation without the ambiguity of five antennas is constructed by the method, the precision is improved by utilizing the redundancy and the least square, and the low-operand method comprises the following seven steps:
step 1, assuming that a short base line on a carrier simultaneously observes two satellites s1 and s2, a double-difference carrier phase observation equation is as follows:
wherein
For double-difference carrier phase observed values, the distance between the antennas in the device is very short, and the apparent vector from all the antenna receiving centers on the same epoch carrier to the same satellite can be assumed to be the same and is marked as s 12 And b is a baseline vector; epsilon is single-baseline double-difference carrier phase observation noise under the condition of observing two satellites;
in the step 1, a carrier phase double-difference observation equation, namely a single-difference equation between two antennas of each base line in four base lines and a single-difference equation between a satellite k and a reference satellite 1, is adopted to reduce error items such as an ionospheric error, a tropospheric error, a satellite clock error, a receiver clock error and observation noise.
y i ＝Sb i +v
D(y i )＝Q yi (2)
wherein, S represents a GNSS view vector,
(i =1,2,3,4, j =1, \8230;, n), v is n +1 co-view satellites and the highest elevation angle is selectedWhen the satellite is used as a reference satellite, the single-baseline double-difference carrier phase observation noise is observed, D (-) is a dispersion operator, and a vector y of an assumed observation quantity j Affected by Gaussian distribution errors, which are represented by a variance-covariance (v-c) matrix Q vi Described, the different baselines are assumed to be the same;
Y＝SRB B +V
D(vec(Y))＝Q Y ,Z∈Z 4×n ,R T R＝I (3)
wherein, B B Expressed as the corresponding vector of B in the carrier coordinate system, RB B = B, R is attitude rotation matrix satisfying R T R = I, V is n +1 co-view satellites, and when a satellite with the highest elevation angle is selected as a reference satellite, the noise is observed by a multi-baseline double-difference carrier phase, a vec operator is introduced to define a V-c matrix of an observable object, and the dispersion of a vector vec (Y) is a V-c matrix Q Y To characterize;
step 4, introducing a vector operator vec, and vectorizing the formula (3) to obtain:
vec(Y)＝vec(SRB B )+vec(V) (4)
and 5, converting the formula (4) into a structure of the Krokask product, wherein the structure is as follows:
wherein, the symbol
Representing the tensor product.
And 6, improving the precision by using the redundancy and the least square, namely solving:
accuracy is improved by solving a problem called least squares with quadratic identity constraints.
And 7, obtaining a high-precision baseline solution vector b, and further obtaining a course angle and a pitch angle, wherein the baseline vector is the expression of a vector formed by two antenna phase centers in a local geographic coordinate system, and comprises three components, namely an east component, a north component and a sky component, which are respectively marked as b e ,b n ,b u And then the course angle and the pitch angle of the carrier are respectively recorded as:
therefore, the purpose of low-operation direction measurement result based on the array antenna non-whole-cycle fuzzy strategy is achieved.
Although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that various changes, modifications, equivalents, improvements and the like can be made therein without departing from the spirit and principles of the invention.
Claims (7)
1. The low operation direction measuring device based on array antenna non-whole cycle fuzzy strategy is characterized in that: the device includes PCB board, receiving antenna module, GNSS receiver module, communication transmission unit and STM32 signal processing unit, the integration has CPU on the STM32 signal processing unit, memory cell, gyroscope and the DMA controller that link to each other with CPU, receiving antenna module, GNSS receiver module all contain five, and in five receiving antenna modules were connected to five GNSS receiver modules respectively, five GNSS receiver modules all linked to each other with STM32 signal processing unit's CPU, and one side of PCB board is equipped with communication transmission unit outward, is connected with CPU, will look for direction information transmission to display module.
2. The array antenna integer cycle ambiguity-free low-k direction measurement device of claim 1, wherein: the receiving antenna module adopts five antennas to simultaneously receive multimode signals, is integrated on a PCB in parallel, is used for receiving satellite navigation signals from BDS, GPS and GLONASS systems, and is compatible with three frequency points of GPS/L1, GLONASS/L1 and BDS/B3.
3. The array antenna integer cycle ambiguity-free low-k direction measurement device of claim 1, wherein: the GNSS receiving antenna module utilizes satellite ephemeris information and Doppler frequency shift to resolve receiver triaxial navigation information in real time, various parameter settings are carried out through a serial port, parameters are stored in an internal FLASH and connected to an STM32 signal processing unit, and an internal CPU resolves direction-finding information of the module according to a communication protocol.
4. The array antenna integer cycle ambiguity-free low-k direction measurement device of claim 1, wherein: the antenna of the receiving antenna module is a ceramic antenna.
5. The array antenna integer cycle ambiguity-free low-k direction measurement device of claim 1, wherein: the GNSS receiver module is a module with L1 original carrier phase output.
6. The array antenna integer cycle ambiguity-free low-k direction measurement device of claim 1, wherein:
the STM32 signal processing unit utilizes a multi-channel serial port to carry out high-speed acquisition on data received by the GNSS receiver module;
and the STM32 signal processing unit realizes serial port data transmission by using a DMA controller.
7. A low-operation direction measurement method based on array antenna non-integer fuzzy strategy is characterized in that: the direction-finding device is used for measurement, and the method specifically comprises the following steps:
step 1, setting a short base line on a carrier to simultaneously observe two satellites s1 and s2, and then the double-difference carrier phase observation equation is as follows:
wherein,
for the observed value of double-difference carrier phase, the distance between the antennas in the direction-finding device is very short, and the apparent vector from all the antenna receiving centers on the same epoch carrier to the same satellite is set to be the same and is recorded as s 12 And b is a baseline vector; epsilon is single-baseline double-difference carrier phase observation noise under the condition of observing two satellites;
step 2, 5 receiving antenna modules are arranged on the direction finding device, the common view satellite number of the direction finding device is n +1, an antenna A is selected as a main antenna, four baselines of AB, AC, AD and AE are arranged in total, a satellite with the highest elevation angle is used as a reference satellite, and the symbol r represents that the observation equation of the baseline i is expressed as follows:
y i ＝Sb i +v
D(y i )＝Q yi (2)
wherein, S represents the GNSS view vector,
v is n +1 co-view satellites and under the condition that the satellite with the highest elevation angle is selected as a reference satellite, single-baseline double-difference carrier phase observation noise is generated, D (-) is a dispersion operator, and the vector y of the observed quantity is assumed j Affected by Gaussian distribution errors, which are represented by a variance-covariance (v-c) matrix Q vi Described, the different baselines are assumed to be the same; />
Step 3, combining the 4 baseline observed quantities on the carrier to obtain a multi-baseline observation equation:
Y＝SRB B +V
D(vec(Y))＝Q Y ,R T R＝I (3)
wherein, B B Expressed as the corresponding vector of B in the carrier coordinate system, RB B = B, R is attitude rotation matrix satisfying R T R = I, V is n +1 co-view satellites, and when a satellite with the highest elevation angle is selected as a reference satellite, the noise is observed by a multi-baseline double-difference carrier phase, a vec operator is introduced to define a V-c matrix of an observable object, and the dispersion of a vector vec (Y) is a V-c matrix Q Y To characterize;
step 4, introducing a vector operator vec, and vectorizing the formula (3) to obtain:
vec(Y)＝vec(SRB B )+vec(V) (4)
step 5, converting the formula (4) into the structure of the kronecker product, wherein the structure of the kronecker product is as follows:
wherein, the symbol
Representing a tensor product;
and 6, improving the precision by using the redundancy and the least square, namely solving:
the precision is improved by solving a least square problem called constraint with quadratic identity;
step 7, obtaining a high-precision baseline solution vector
Then obtaining course angle and pitch angle, the base line vector is the expression of the vector formed by two antenna phase centers in the local geographic coordinate system, and comprises three components, namely east component, north component and sky component, which are respectively marked as b e ,b n ,b u Course angle and pitch angle of the carrierRespectively recorded as:
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