CN116819580A - Inertial-assisted dual-antenna GNSS marine vessel attitude determination method - Google Patents
Inertial-assisted dual-antenna GNSS marine vessel attitude determination method Download PDFInfo
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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
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
- G01S19/43—Determining position using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
- G01S19/44—Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
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- G—PHYSICS
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
- G01S19/45—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement
- G01S19/47—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement the supplementary measurement being an inertial measurement, e.g. tightly coupled inertial
Abstract
The application designs an inertial-assisted dual-antenna GNSS marine vessel attitude determination method, which comprises the steps of firstly, providing a baseline length constraint model based on IMU assistance, and using high-precision priori position information output by the IMU to assist in constructing the baseline length constraint model by utilizing the characteristics of short time and high precision of the IMU, thereby enhancing the constraint effect of the model on ambiguity resolution; secondly, an observation value comprehensive weight determining method based on Helmert variance component estimation is provided, the weight between the provided base line length constraint model based on IMU assistance and GNSS satellite observation values is comprehensively determined through posterior variance by using Helmert variance component estimation, and therefore existing observation information can be fully utilized, and accurate estimation of ambiguity parameters is achieved.
Description
Technical Field
The application relates to a ship attitude determination method, in particular to an inertial-assisted dual-antenna GNSS marine ship attitude determination method.
Background
Because the ocean environment is complex and changeable, the precise navigation in the navigation process of the ship is very serious challenged. For a ship sailing in the ocean, high-precision navigation is not only required to acquire positioning information, but also necessary to accurately acquire attitude information of the ship. Typically, attitude information of a vessel may be obtained by inertial sensors, magnetic sensors, and the like. Among the many sensors, given the nature of natural complementarity of the global satellite navigation system (GNSS) and Inertial Measurement Unit (IMU), and the fact that IMU can provide continuous, stable, comprehensive attitude information, it is common to integrate both of them into a GNSS/IMU integrated navigation system to provide accurate, reliable carrier attitude information. However, in conventional GNSS/IMU integrated navigation systems, the accuracy of the pose measurement is mainly dependent on the accuracy of the gyroscopes in the IMU. Therefore, in the conventional integrated navigation system, the improvement of the attitude measurement accuracy generally requires the use of a relatively high-cost IMU, but this will certainly increase the cost of using the equipment, thereby limiting the popularization and application on a large scale.
In recent years, with the continuous development of satellite navigation technology, carrier attitude determination technology based on GNSS is considered as one of the most economical and effective attitude measurement methods. GNSS, one of the basic sensors for navigation, can provide continuous and high-precision navigation positioning information for users in an open environment. Attitude determination has recently received widespread attention from both domestic and foreign students as an important branch in the field of GNSS high-precision measurement. The attitude determination technology based on GNSS generally adopts double antennas or multiple antennas to carry out attitude calculation in an ultra-short baseline mode, and the main principle is that the coordinates of a baseline vector formed by two or more GNSS antennas are precisely measured through a GNSS real-time dynamic difference (RTK) technology, and then the attitude angle of a carrier can be calculated by utilizing the conversion relation of the baseline vector in different coordinate systems. The attitude determination technology based on the GNSS has the advantages of low cost, high precision, no accumulated error and the like, but the method is compared with the fixed rate of the whole-cycle ambiguity depending on the carrier phase of the GNSS, and the carrier attitude information with high precision can be obtained only by rapidly and accurately calculating the whole-cycle ambiguity. However, since GNSS signals are extremely subject to sea surface reflection in a marine observation environment, severe Multipath Interference (MI) and non line of sight reception (NLOS) are generated, resulting in a generally low ambiguity fixing rate of least squares ambiguity-resolved adjustment (LAMBDA), which negatively affects the accuracy and reliability of the ship attitude solution.
Many scholars have conducted a great deal of research with respect to the above problems. Among them, how to use external observation information to improve the fixing rate of GNSS integer ambiguity has been a hot spot of research. Since the baseline length formed by two GNSS antennas mounted on a vehicle is constant and can be accurately measured in advance, this baseline length constraint can be introduced to assist the GNSS ambiguity resolution process. Monikes et al propose to use the baseline length information to test candidate ambiguities searched by the LAMBDA algorithm and then select the optimal ambiguity fix solution from them. However, the known baseline length information is used only for ambiguity verification in this method and not directly into the process of participating in parameter estimation, and thus its performance may not be optimal. In addition, the baseline length constraint may also be used to assist the LAMBDA algorithm in searching for a fixed solution for integer ambiguity. Based on this, teunissen et al propose a constrained least squares ambiguity-resolved (C-LAMBDA) algorithm for dual-antenna GNSS attitude determination and then extend it to the case of multi-antenna attitude determination. However, the method introduces nonlinear constraint in the objective function of the ambiguity search, so that the search space of the ambiguity is no longer a standard ellipsoid, thereby increasing the calculation cost of the algorithm. Gong et al subsequently proposed an improved algorithm to replace the non-ellipsoidal search space with a progressively larger ellipsoid that fits the search process of the standard LAMBDA algorithm. However, the algorithm is high in calculation cost and still needs to be further researched. The other thinking is to linearize the base line length constraint model and add it into the GNSS integer ambiguity estimation model, thereby improving the integer ambiguity floating solution accuracy, and then use the standard LAMBDA algorithm to obtain the fixed solution of ambiguity. However, since the approximate baseline vector coordinates of the method in the linearization process are usually calculated by the GNSS pseudo-range observation values, and the accuracy of the pseudo-range observation values is poor, the method may introduce more errors in the ambiguity estimation process, thereby affecting the fixed rate of the whole-cycle ambiguity.
In addition, in the attitude determination technology based on GNSS, the accuracy between different observation information is different, so a reasonable random model needs to be introduced to determine the weight of each observation value in the process of least square parameter estimation. At present, the baseline length constraint model mostly adopts an empirical random model to participate in the whole-cycle ambiguity resolving process, which can cause a certain negative influence on the accuracy of parameter estimation, thereby limiting the full play of the model constraint effect.
In summary, the drawbacks of the prior art are as follows:
the base line length constraint is used as important external observation information in the dual-antenna GNSS attitude determination technology, and the constraint effect of the model can influence the fixed rate of GNSS integer ambiguity. The existing baseline length constraint model is generally constructed by adopting GNSS pseudo-range observation values, and the precision of the pseudo-range observation values is insufficient, so that the constraint effect of the model is generally limited. In particular, when the pseudorange observations themselves contain large errors, the model can even in turn reduce the accuracy of the ambiguity parameter estimation, thereby affecting the accuracy and reliability of the pose solution. In addition, the existing baseline length constraint model adopts an empirical random model to carry out parameter estimation, and the problems that an error source is complex and the random model is difficult to accurately determine exist, so that the constraint effect of the model cannot be fully exerted.
Disclosure of Invention
The application aims to: the application aims to solve the technical problem of providing an inertial-assisted dual-antenna GNSS marine vessel attitude determination method aiming at the defects of the prior art.
In order to solve the technical problems, the application discloses an inertial-assisted dual-antenna GNSS marine vessel attitude determination method, which comprises the following steps:
step 1, constructing a dual-antenna GNSS attitude determination model, which specifically comprises the following steps:
step 1-1, constructing a GNSS single-difference pseudo-range and carrier phase observation model, which comprises the following steps:
；
in the formula ,for a single difference operator, a and B represent the slave antenna and the master antenna, respectively; /> and />Respectively single-difference pseudo-range and carrier phase observation values; />Is a single difference in geometric distance between the satellite and the receiver; />Is the speed of light;a single difference value that is the receiver clock difference; />Is the wavelength of the carrier wave; />Is single difference ambiguity; /> and />Single differences representing ionospheric and convective errors, respectively; /> and />Single difference values of pseudo range and carrier phase measurement noise are respectively represented;
regarding the line-of-sight vector between the same satellite and two antennas as parallel, the following is obtained:
；
in the formula ,the coordinates of the baseline vector in a geocentric fixed coordinate system, namely an e-system; />Is a unit line-of-sight vector from the antenna to the satellite;
the method is carried into a GNSS single-difference pseudo-range and carrier phase observation model, and the method comprises the following steps of:
；
step 1-2, constructing a GNSS double-difference pseudo-range and carrier phase observation model, which comprises the following steps:
assuming that a satellite corresponding to the maximum height angle is used as a reference satellite, and the observation values of the other satellites and the observation values of the reference satellite are differentiated to obtain a GNSS double-difference pseudo-range and carrier phase observation model as follows:
；
in the formula ,representing a double difference operator; />A number indicating the other satellites than the reference satellite; />Is a unit matrix;
step 1-3, according to a GNSS double-difference pseudo-range and carrier phase observation model, calculating a baseline vector coordinate, wherein the method specifically comprises the following steps:
carrying out least square solution on the GNSS double-difference pseudo-range and the carrier phase observation model to obtain a coordinate initial value and a floating point ambiguity solution result of the baseline vector, and searching to obtain a fixed solution of the ambiguity by using an LAMBDA algorithm so as to calculate and obtain the final baseline vector coordinate;
step 1-4, converting coordinates of a baseline vector, and determining a preliminary attitude of the ship, wherein the preliminary attitude is specifically as follows:
step 1-4-1, converting coordinates of a baseline vector, specifically including:
converting the final baseline vector coordinates calculated in the steps 1-3 from an e-system to an east-north-day coordinate system, namely an n-system, specifically as follows:
；
in the formula ,coordinates in the n-series for the baseline vector; />The rotation matrix from e-series to n-series is represented as follows:
；
in the formula , and />Latitude and longitude of the ship position respectively;
step 1-4-2, determining the preliminary attitude of the ship, which specifically comprises the following steps:
assume that the baseline vector coordinates calculated in step 1-4-1 areThe initial attitude of the ship, namely the pitch angle and the course angle of the ship based on GNSS are as follows:
；
in the formula ,is the pitch angle of the ship, < > is>Is the course angle of the ship.
Step 2, constructing a baseline length constraint ambiguity resolution model based on IMU assistance, which specifically comprises the following steps:
step 2-1, constructing a baseline length constraint model, which specifically comprises the following steps:
；
in the formula ,is the norm of the vector; />The length of the baseline vector is measured in advance; the final baseline vector coordinates are +.>When, the above formula is expressed as:
。
step 2-2, constructing an ambiguity resolution model with additional baseline length constraint, which specifically comprises the following steps:
linearizing at the approximate solution of the base line length constraint model, assuming that the approximate solution coordinates of the base line vector arePerforming taylor expansion on the above formula and taking a term to obtain:
；
order theFor the coefficient matrix of the base line vector coordinates to be estimated, the a priori distance information is considered simultaneously>Error of measurement error of (2) and error of higher order term neglected in linearization process +.>The above transform is:
；
adding the above model into the GNSS double-difference pseudo-range and carrier phase observation model constructed in the step 1-2, and obtaining an ambiguity resolution model with additional base line length constraint as follows:
。
step 2-3, calculating an approximate solution based on the IMU-assisted baseline vectorThe method specifically comprises the following steps:
obtaining the coordinates of the baseline vector in the system by vector addition calculationThe method comprises the following steps:
；
wherein C is the geometric center of the inertial measurement unit IMU; and />Vectors from IMU geometric center C to antenna a and B phase center, respectively, +.> and />The calculation method comprises the following steps:
；
in the formula ,、/> and />The coordinates of the geometrical centers C of the antenna A, the antenna B and the IMU in an n system are respectively shown; wherein (1)>Derived from the IMU mechanical programming output, +.>Is derived from the GNSS pseudo-range single-point location, +.>The coordinates of (2) are calculated as follows:
；
wherein ,the vector from the geometrical center C of the IMU to the phase center of the antenna A in the carrier coordinate system, namely the b system, is obtained by accurate measurement in advance; />For the rotation matrix from b-series to n-series, the calculation method is as follows:
；
in the formula ,is the roll angle of the ship; />The IMU mechanical arrangement output at the current moment is obtained;
to be calculated to obtainRe-substituting into calculation->In (2) obtaining an approximate solution of the baseline vector based on IMU aided calculation>。
Step 2-4, approximating solution of the baseline vector based on IMU auxiliary calculationAnd (3) substituting the model into the ambiguity resolution model with the additional baseline length constraint in the step (2-2) to obtain the ambiguity resolution model based on the IMU auxiliary baseline length constraint.
And 3, determining the comprehensive weight of the observed value based on the Helmert variance component estimation, wherein the method specifically comprises the following steps of:
assuming that all the observed values are mutually independent, linearizing the ambiguity resolution model based on the IMU auxiliary baseline length constraint obtained in the step 2-4 to obtain a system error equation as follows:
；
in the formula ,is an observation residual vector; />For the parameter vector to be estimated, includingCoordinates of the baseline vector and integer ambiguity parameters; />Designing a matrix for coefficients of parameters to be estimated; />Is an observation vector;
according to the calculation process of the ambiguity resolution model based on IMU auxiliary baseline length constraint, the observed value vectorThe sources of observation information in (a) are classified into 2 classes, including: GNSS and built base line length constraint model based on IMU assistance; correspondingly, the error types of all the observed values are also classified into 2 types, and all the observed values corresponding to each information source are respectively 1 group, and then the system error equation is expressed as follows:
；
in the formula , and />Respectively representing an observation value weight matrix corresponding to the GNSS and the constructed base line length constraint model based on IMU assistance, wherein the initial weight ratio between the GNSS and the constructed base line length constraint model is 1:1; within the GNSS system, the pseudo-ranges and carrier phase observations of different satellites are weighted using an altitude-based random model as follows:
；
in the formula ,is the variance of the observed value; />Is the altitude of the satellite; /> and />Constant terms related to observed noise, respectively; the weight ratio between the GNSS pseudo-range and the carrier phase observations is set to 1:100;
then, carrying out least square adjustment processing on the system error equation, and calculating to obtain a correction corresponding to the GNSS and the base line length constraint model based on IMU assistance and />；
Then, according to the Helmert variance component estimation rigorous formula, calculating a unit weight variance factor between the GNSS and the base line length constraint model based on IMU assistance；
Then, based on the new unit weight variance factor obtained by the calculationUse of the unit weight variance estimate therein +.> and />Reassigning a weight matrix between the GNSS and the base line length constraint model based on IMU assistance:
；
in the subscript and />Respectively representing the calculation results of the previous time and the current time; />Is constant with->Replacement;
repeating the iterative process until the unit weight variance factors between the GNSS and the base line length constraint model based on IMU assistance are equal, namelyOr the following termination condition is satisfied:
；
and stopping iteration and outputting the weight matrix corresponding to each moment.
Said parameters and />The pseudorange observations are set to 0.3m for GNSS and 0.003m for GNSS carrier phase observations.
The unit weight variance factor between the calculated GNSS and the base line length constraint model based on IMU assistanceThe specific method comprises the following steps:
；
in the formula, each variable calculation method is as follows:
；
in the formula , and />The number of observations of the ambiguity resolution model based on the GNSS and IMU assisted baseline length constraints, respectively.
And 4, constructing a double-antenna GNSS and IMU loose coupling scheme to obtain optimal estimation of ship attitude information, namely finishing inertial-assisted double-antenna GNSS marine ship attitude determination.
The construction of the double-antenna GNSS and IMU loose coupling scheme, namely the double-antenna GNSS and IMU loose coupling filtering fusion, specifically comprises the following steps:
step 4-1, constructing a system state vector based on an extended Kalman filter EKFThe following are provided:
；
in the formula , and />Respectively the three-dimensional position and speed errors of the ship in the n series; />Is the attitude misalignment angle of the ship; /> and />Zero offset and scale factor error of the accelerometer in the IMU; /> and />Zero offset and scale factor error of gyroscopes in the IMU respectively;
in step 4-2, the system state equation is constructed as follows:
；
in the formula ,is a system state transition matrix; />Is a noise matrix;
extended Kalman filter EKF measurement vectorThe three-dimensional position and posture information of the ship, which are output by the GNSS, and the three-dimensional position and posture information of the ship, which are mechanically arranged and output by the IMU, are obtained by differentiating:
；
in the formula , and />Respectively representing the three-dimensional positions of the ship output by the GNSS and the IMU; />Andrepresenting pitch angles output by the GNSS and IMU, respectively; /> and />Representing GNSS and I respectivelyHeading angle output by MU;
step 4-3, constructing a measurement equation based on an extended Kalman filter EKF, as follows:
；
in the formula ,to design a matrix; />Measuring a noise matrix;
and 4-4, setting a filtered initial value, starting filtering iteration, obtaining the optimal estimation of the ship attitude information at the current moment, and outputting the optimal estimation.
The beneficial effects are that:
the application utilizes the characteristic of high precision of the IMU in a short time, and uses the high precision position information output by the IMU mechanical arrangement to assist in constructing a base line length constraint model, thereby improving the constraint effect of the model on ambiguity resolution. Meanwhile, the post-test variance of each observation information is calculated by using a Helmert variance component estimation method, and a random model among all observation values is determined, so that the precision of GNSS ambiguity parameter estimation is further improved, and important guarantee is provided for the attitude calculation of the ship.
Drawings
The foregoing and/or other advantages of the application will become more apparent from the following detailed description of the application when taken in conjunction with the accompanying drawings and detailed description.
FIG. 1 is a flow chart of a method for inertial aided dual antenna GNSS marine vessel attitude determination.
FIG. 2 is a schematic diagram of a dual antenna GNSS baseline measurement.
FIG. 3 is a schematic diagram of the relationship between the attitude angle of the carrier in the system and the baseline vector.
Fig. 4 is an error chart of experimental results of a conventional baseline length-constrained dual-antenna GNSS/IMU combined attitude determination algorithm and an embodiment of the present application.
Detailed Description
An inertial-aided dual-antenna GNSS marine vessel attitude determination method, as shown in fig. 1, includes:
step 1, constructing a dual-antenna GNSS attitude determination model;
step 2, constructing a baseline length constraint ambiguity resolution model based on IMU assistance;
step 3, comprehensively determining weights based on the observed values of the Helmert variance component estimation;
and 4, performing loose combination filtering fusion on the dual-antenna GNSS/IMU.
The specific scheme is as follows:
1. dual antenna GNSS attitude determination model construction
The GNSS single-difference pseudorange and carrier-phase observation model may be expressed as follows:
；
in the formula , a and B respectively represent a slave antenna and a master antenna; /> and />Respectively single-difference pseudo-range and carrier phase observation values; />Is a single difference in geometric distance between the satellite and the receiver; />Is the speed of light;a single difference value that is the receiver clock difference; />Is the wavelength of the carrier wave; />Is single difference ambiguity; /> and />Single differences representing ionospheric and convective errors, respectively; /> and />Representing the single difference in pseudorange and carrier phase measurement noise, respectively.
Since the distance between the two antennas is much smaller than the distance between the antennas and the satellite, the line-of-sight vectors between the same satellite and the two antennas can be approximately considered to be parallel, as shown in fig. 2, which can be derived:
；
in the formula ,coordinates of the baseline vector in a geocentric earth fixed coordinate system (ECEF, abbreviated as e-system); />Is the unit line of sight vector from the antenna to the satellite.
The method is carried into a GNSS single difference observation model and can be obtained:
；
assuming that the satellite corresponding to the maximum height angle is used as a reference satellite, and the observation values of the other satellites are differentiated from the observation values of the reference satellite, the GNSS double-difference observation model can be obtained as follows:
；
in the formula ,representing a double difference operator; />A number indicating the other satellites than the reference satellite; />Is an identity matrix. And carrying out least square solution on the above formula to obtain the initial value of the coordinates of the base line vector and the floating ambiguity resolution result. Based on this, the LAMBDA algorithm is usually reused to search for a fixed solution of ambiguity. Once the ambiguity fixing is successful, accurate baseline vector coordinates can be calculated. (ref. Zhang Shubi, liu Xin, song Bing, etc. BDS single frequency single epoch modified Parlambda algorithm with constraints J]University of mineral school report, 2017,46 (01): 201-208.)
Then, the calculated baseline vector coordinates are converted from the e-system into an "east-north-day" coordinate system (n-system for short):
；
in the formula ,coordinates in the n-series for the baseline vector; />For a rotation matrix from e-series to n-series, it can be expressed as follows:
；
in the formula , and />The latitude and longitude of the ship's location, respectively.
As shown in fig. 3, assume that the calculated baseline vector coordinates areThe GNSS based vessel pitch angle and heading angle can be calculated as follows:
；
in the formula ,is the pitch angle of the ship, < > is>Is the course angle of the ship.
2. Baseline length constraint ambiguity resolution model construction based on IMU assistance
From the above description, it is known that the length of the virtual baseline formed between two GNSS antennas installed on a ship is kept unchanged, and thus the baseline length constraint model can be expressed as follows:
；
in the formula ,is the norm of the vector; />For the length of the baseline vector measured in advance.
The above formula can be expressed as follows:
；
from the above equation, the baseline length constraint model is a nonlinear model that needs to be linearized at its approximate solution. Assuming a base lineThe approximate solution coordinates of the quantity arePerforming taylor expansion on the above formula, taking a primary term, and ignoring the influence of a high-order term, thereby obtaining the following components:
；
order theTaking into account both the measurement error of the a priori distance information and the error of the higher order term ignored during linearization>The above equation may be transformed into:
；
adding the above to the equation of GNSS ambiguity resolution, the ambiguity resolution model with additional baseline length constraint can be obtained as follows:
；
from the above derivation, it can be seen that the baseline vector approximates the solutionHas a large influence on the constraint effect of the model. If->Lower precision of (2), then->The constraint effect of the model is also reduced due to the larger size. If the calculation is performed by adopting the traditional method based on the pseudo-range observation value, the accuracy limitation of the pseudo-range is limited, and the calculation cannot be ensuredIs used for solving the problem of the accuracy of the calculation. Aiming at the problems, the application provides a baseline vector approximate solution construction method based on IMU assistance, which is as follows.
From the vector addition, it is possible to:
；
wherein C is the geometrical center of the IMU; and />The vector from IMU geometric center C to antenna a and B phase center, respectively. /> and />The following can be calculated:
；
in the formula , 、 /> and />The coordinates of the antenna a, antenna B and IMU geometric center C in the system, respectively. Wherein (1)>The output can be mechanically programmed by the IMU. />May be obtained from a GNSS pseudorange single point location. Considering that the pseudo-range observation value is easy to be interfered by the external observation environment, the method leads to largerIs a function of the error of (a). Thus, in the present application +.>The coordinates of (c) can be calculated as follows:
；
wherein , the vector from the geometrical center C of the IMU to the phase center of the antenna A in a carrier coordinate system (called b system for short) can be accurately measured in advance; />For a rotation matrix from b-series to n-series, the following can be calculated:
；/>
in the formula , is the roll angle of the ship; since the IMU has a high precision in a short time, the +.>Can be obtained by the mechanical arrangement output of the IMU at the current moment. Calculated +.>Is carried back into the equation of the approximate solution calculation of the baseline vector, and the approximate solution of the baseline vector based on the IMU auxiliary calculation can be obtained>. And then substituting the model into the base line length constraint model to obtain the base line length constraint ambiguity resolution model based on IMU assistance, thereby enhancing the fixed rate of the GNSS ambiguity.
In a traditional baseline length constraint model, GNSS pseudo-range observation values are generally adopted to construct an approximate solution of a baseline vector. But the constraint effect of the model is limited due to the limited accuracy of GNSS pseudorange observations.
Aiming at the problems, the application innovates a construction method of the baseline vector approximate solution in the baseline vector constraint model, utilizes the characteristics of short time and high precision of the IMU, provides a construction method of the baseline length constraint model based on IMU assistance, utilizes high precision priori position information output by IMU mechanical arrangement to assist in constructing the approximate solution of the baseline vector in the baseline length constraint model, and adds the baseline length constraint model based on IMU assistance to a GNSS double difference observation model for joint solution, thereby improving the precision of ambiguity parameter estimation.
3. Observations comprehensive weight determination based on Helmert variance component estimation
In the process of gesture calculation, the observation information for estimating the ambiguity parameters mainly comes from GNSS and a constructed base line length constraint model based on IMU assistance. In the actual calculation process, the accuracy of each observation information is different, and the accuracy of parameter estimation may be reduced by using a traditional empirical random model. Therefore, the application provides an observation value comprehensive weight determining method based on Helmert variance component estimation, which comprises the following specific steps:
firstly, assuming that all observed values are mutually independent, carrying out linearization treatment on an ambiguity resolution model based on IMU auxiliary base line length constraint to obtain a system error equation as follows:
；
in the formula ,is an observation residual matrix; />For the parameter matrix to be estimated, including the coordinates of the baseline vector and the whole circumferenceA ambiguity parameter; />Designing a matrix for coefficients of parameters to be estimated; />Is an observation vector.
The error types of all observations are also correspondingly classified into 2 classes (observation vectorsThe observations are derived from GNSS (pseudorange, carrier phase observations) and the established IMU assistance-based baseline length constraint model. Thus, the two types of systems herein refer to both GNSS and IMU assistance-based baseline length constraint models that are constructed. Note that, here, the IMU-assistance-based baseline length constraint model is an information source independent of GNSS, and the "IMU-assistance-based baseline length constraint ambiguity resolution model" includes both GNSS and IMU-assistance-based baseline length constraint information. ) All the observed values corresponding to each information source are respectively 1 group. The above formula can be expressed as follows:
；/>
in the formula , and />The weight matrixes respectively represent GNSS and a baseline length constraint model based on IMU assistance, and the initial weight ratio between the GNSS and the baseline length constraint model is 1:1. Considering that the precision of the GNSS observations also varies, the pseudo-ranges and carrier phase observations of different satellites are weighted by a random model based on altitude angles as follows:
；
in the formula , Is the variance of the observed value; />Is the altitude of the satellite; /> and />Are constant terms related to observed noise, typically set to 0.3m and 0.003m for pseudorange and carrier phase observations, respectively (where the two parameters correspond to the parameters +.in the altitude-based random model described above, respectively)> and />I.e. for GNSS pseudo-range observations, parameter +.> and />Typically set to 0.3 and get the weight of each pseudorange observation; whereas for GNSS carrier phase observations, the parameter +.> and />Typically set to 0.003 and a weight for each carrier phase observation is obtained. It should be noted that the weights determined here are weights that are internal to each of the GNSS pseudorange and carrier phase observations. ). Further, the weight ratio between the pseudo-range and carrier phase observations is set to 1:100 (the weight is set as the weight between the GNSS pseudo-range and carrier phase observations. Mainly because the GNSS pseudo-range observations are subject to large errors due to external interference, and the GNSS carrier phaseThe accuracy of the bit observations is much higher than that of the pseudo-range observations, so the overall weight of the pseudo-range observations is reduced by this step of weight setting, thereby reducing the impact of low-quality pseudo-range observations on the navigation solution).
Then, the adjustment processing is carried out on the observation equation, and the correction of the observation value of each system is calculated and /> 。
Next, according to the Helmert variance component estimation rigorous formula, calculating a GNSS and a unit weight variance factor of the proposed base line length constraint model based on IMU assistanceThe following are provided:
；
where the variables can be calculated as follows:
；
in the formula , and />The number of observations of each of the GNSS and the proposed IMU assistance-based baseline length constraint model is represented, respectively.
And then, carrying out assignment on a weight matrix between the GNSS and the proposed base line length constraint model based on IMU assistance again according to the new unit weight variance factor obtained by the calculation:
；/>
in the subscript and />Respectively representing the calculation results of the previous time and the current time; />Is constant and can be usually used>Instead of.
Repeating the iterative process until the unit weight variance factors between the GNSS and the base line length constraint model based on IMU assistance are equal, namely. Or stopping iteration when the following termination condition is met, and outputting a weight matrix corresponding to each system at the moment.
；
4. Double-antenna GNSS/IMU loose coupling filtering fusion
Based on the extended Kalman filter EKF, the application constructs a double-antenna GNSS/IMU loose coupling scheme, and carries out filtering fusion on navigation information output by the GNSS and the IMU, thereby obtaining and outputting optimal estimation of ship attitude information.
The system state vector of the extended kalman filter EKF can be constructed as follows:
；
in the formula , and />Three-dimensional position and speed errors of the vessels in the n-series respectively； />Is the attitude misalignment angle of the ship; /> and />Zero offset and scale factor error of the accelerometer in the IMU; /> and />Zero offset and scale factor error of gyroscopes in the IMU respectively; and 21-dimensional state variable information.
The system state equation may be constructed as follows:
；
in the formula , is a system state transition matrix; />Is a noise matrix.
The measurement vector of the extended Kalman filter EKF is obtained by differentiating the ship three-dimensional position and attitude information output by the GNSS and the corresponding information output by the IMU mechanical arrangement:
；
in the formula , and />Respectively representing the three-dimensional positions of the ship output by the GNSS and the IMU; />Andrepresenting pitch angles output by the GNSS and IMU, respectively; /> and />The heading angles of the GNSS and IMU outputs are represented, respectively.
The filtered metrology equation can be constructed as follows:
；
in the formula ,to design a matrix; />To measure the noise matrix. After the initial value of the filtering is given, the filtering iteration can be started, so that the optimal estimation of the ship attitude information at the current moment is obtained and output.
Examples:
fig. 4 is a diagram showing experimental error results of a conventional dual-antenna GNSS/IMU integrated navigation and attitude determination method and an embodiment of the present application. From the figure, in the experimental process, the results of the embodiment of the application are superior to the combined attitude determination method of the traditional baseline length constraint in the resolving precision of the roll angle, the pitch angle and the course angle.
In a specific implementation, the present application provides a computer storage medium and a corresponding data processing unit, where the computer storage medium is capable of storing a computer program, where the computer program when executed by the data processing unit may perform some or all of the steps of the inertial assisted dual antenna GNSS marine vessel attitude determination method provided by the present application. The storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM), a random-access memory (random access memory, RAM), or the like.
It will be apparent to those skilled in the art that the technical solutions in the embodiments of the present application may be implemented by means of a computer program and its corresponding general hardware platform. Based on such understanding, the technical solutions in the embodiments of the present application may be embodied essentially or in the form of a computer program, i.e. a software product, which may be stored in a storage medium, and include several instructions to cause a device (which may be a personal computer, a server, a single-chip microcomputer, MUU or a network device, etc.) including a data processing unit to perform the methods described in the embodiments or some parts of the embodiments of the present application.
The application provides an inertial-assisted dual-antenna GNSS marine vessel attitude determination method, and a method for realizing the technical scheme, and the method are a plurality of methods, and the above description is only a preferred embodiment of the application, and it should be noted that a plurality of improvements and modifications can be made by those skilled in the art without departing from the principle of the application, and the improvements and modifications are also considered as the protection scope of the application. The components not explicitly described in this embodiment can be implemented by using the prior art.
Claims (10)
1. An inertial-aided dual-antenna GNSS marine vessel attitude determination method, comprising:
step 1, constructing a dual-antenna GNSS attitude determination model;
step 2, constructing a baseline length constraint ambiguity resolution model based on IMU assistance;
step 3, comprehensively determining weights based on the observed values of the Helmert variance component estimation;
and 4, constructing a double-antenna GNSS and IMU loose coupling scheme to obtain optimal estimation of ship attitude information, namely finishing inertial-assisted double-antenna GNSS marine ship attitude determination.
2. The inertial aided dual-antenna GNSS marine vessel attitude determination method of claim 1, wherein said constructing a dual-antenna GNSS attitude determination model in step 1 specifically comprises:
step 1-1, constructing a GNSS single-difference pseudo-range and carrier phase observation model, which comprises the following steps:
；
in the formula ,for a single difference operator, a and B represent the slave antenna and the master antenna, respectively; /> and />Respectively single-difference pseudo-range and carrier phase observation values; />Is a single difference in geometric distance between the satellite and the receiver; />Is the speed of light; />A single difference value that is the receiver clock difference; />Is the wavelength of the carrier wave; />Is single difference ambiguity; /> and />Single differences representing ionospheric and convective errors, respectively; /> and />Single difference values of pseudo range and carrier phase measurement noise are respectively represented;
regarding the line-of-sight vector between the same satellite and two antennas as parallel, the following is obtained:
；
in the formula ,the coordinates of the baseline vector in a geocentric fixed coordinate system, namely an e-system; />Is a unit line-of-sight vector from the antenna to the satellite;
the method is carried into a GNSS single-difference pseudo-range and carrier phase observation model, and the method comprises the following steps of:
；
step 1-2, constructing a GNSS double-difference pseudo-range and carrier phase observation model, which comprises the following steps:
assuming that a satellite corresponding to the maximum height angle is used as a reference satellite, and the observation values of the other satellites and the observation values of the reference satellite are differentiated to obtain a GNSS double-difference pseudo-range and carrier phase observation model as follows:
；
in the formula ,representing a double difference operator; />A number indicating the other satellites than the reference satellite; />Is a unit matrix;
step 1-3, according to a GNSS double-difference pseudo-range and carrier phase observation model, calculating a baseline vector coordinate, wherein the method specifically comprises the following steps:
carrying out least square solution on the GNSS double-difference pseudo-range and the carrier phase observation model to obtain a coordinate initial value and a floating point ambiguity solution result of the baseline vector, and searching to obtain a fixed solution of the ambiguity by using an LAMBDA algorithm so as to calculate and obtain the final baseline vector coordinate;
step 1-4, converting coordinates of a baseline vector, and determining a preliminary attitude of the ship, wherein the preliminary attitude is specifically as follows:
step 1-4-1, converting coordinates of a baseline vector, specifically including:
converting the final baseline vector coordinates calculated in the steps 1-3 from an e-system to an east-north-day coordinate system, namely an n-system, specifically as follows:
；
in the formula ,coordinates in the n-series for the baseline vector; />The rotation matrix from e-series to n-series is represented as follows:
；
in the formula , and />Latitude and longitude of the ship position respectively;
step 1-4-2, determining the preliminary attitude of the ship, which specifically comprises the following steps:
assume that the baseline vector coordinates calculated in step 1-4-1 areThe initial attitude of the ship, namely the pitch angle and the course angle of the ship based on GNSS are as follows:
；
in the formula ,is the pitch angle of the ship, < > is>Is the course angle of the ship.
3. The inertial aided dual-antenna GNSS marine vessel attitude determination method of claim 2, wherein said constructing an IMU-aided based baseline length constraint ambiguity resolution model in step 2 specifically comprises:
step 2-1, constructing a base line length constraint model;
step 2-2, constructing an ambiguity resolution model with additional base line length constraint;
step 2-3, calculating an approximate solution based on the IMU-assisted baseline vector；
Step 2-4, approximating solution of the baseline vector based on IMU auxiliary calculationAnd (3) substituting the model into the ambiguity resolution model with the additional baseline length constraint in the step (2-2) to obtain the ambiguity resolution model based on the IMU auxiliary baseline length constraint.
4. The inertial aided dual-antenna GNSS marine vessel attitude determination method of claim 3, wherein said constructing a baseline length constraint model in step 2-1 is specifically described as follows:
；
in the formula ,is the norm of the vector; />The length of the baseline vector is measured in advance; final baseline vector coordinates areWhen, the above formula is expressed as:
。
5. the inertial aided dual-antenna GNSS marine vessel attitude determination method of claim 4, wherein said constructing an additional baseline length constraint ambiguity resolution model in step 2-2 specifically comprises:
linearizing at the approximate solution of the base line length constraint model, assuming that the approximate solution coordinates of the base line vector arePerforming taylor expansion on the above formula and taking a term to obtain:
；
order theFor the coefficient matrix of the base line vector coordinates to be estimated, the a priori distance information is considered simultaneously>And the measurement error of the upper order term ignored in the linearization process, the above equation is transformed into:
；
adding the above model into the GNSS double-difference pseudo-range and carrier phase observation model constructed in the step 1-2, and obtaining an ambiguity resolution model with additional base line length constraint as follows:
。
6. the inertial aided dual antenna GNSS marine vessel attitude determination method of claim 5, wherein said calculating in step 2-3 is based on an approximate solution of IMU aided baseline vectorsThe method specifically comprises the following steps:
obtaining the coordinates of the baseline vector in the system by vector addition calculationThe method comprises the following steps:
；
wherein C is the geometric center of the inertial measurement unit IMU; and />Vectors from IMU geometric center C to antenna a and B phase center, respectively, +.> and />The calculation method comprises the following steps:
；
in the formula ,、/> and />The coordinates of the geometrical centers C of the antenna A, the antenna B and the IMU in an n system are respectively shown; wherein,derived from the IMU mechanical programming output, +.>Is derived from the GNSS pseudo-range single-point location, +.>The coordinates of (2) are calculated as follows:
；
wherein ,the vector from the geometrical center C of the IMU to the phase center of the antenna A in the carrier coordinate system, namely the b system, is obtained by accurate measurement in advance; />For the rotation matrix from b-series to n-series, the calculation method is as follows:
；
in the formula ,is the roll angle of the ship; />The IMU mechanical arrangement output at the current moment is obtained;
to be calculated to obtainRe-substituting into calculation->In (2) obtaining an approximate solution of the baseline vector based on IMU aided calculation>。
7. The inertial aided dual-antenna GNSS marine vessel attitude determination method of claim 6, wherein said Helmert variance component estimation based observation comprehensive weight determination in step 3 specifically comprises:
assuming that all the observed values are mutually independent, linearizing the ambiguity resolution model based on the IMU auxiliary baseline length constraint obtained in the step 2-4 to obtain a system error equation as follows:
；
in the formula ,is an observation residual vector; />The method comprises the steps of taking a parameter vector to be estimated, wherein the parameter vector comprises coordinates of a baseline vector and integer ambiguity parameters; />Designing a matrix for coefficients of parameters to be estimated; />Is an observation vector;
according to the calculation process of the ambiguity resolution model based on IMU auxiliary baseline length constraint, the observed value vectorThe sources of observation information in (a) are classified into 2 classes, including: GNSS and built base line length constraint model based on IMU assistance; correspondingly, the error types of all the observed values are also classified into 2 types, and all the observed values corresponding to each information source are respectively 1 group, and then the system error equation is expressed as follows:
；
in the formula , and />Respectively representing an observation value weight matrix corresponding to the GNSS and the constructed base line length constraint model based on IMU assistance, wherein the initial weight ratio between the GNSS and the constructed base line length constraint model is 1:1; within the GNSS system, the pseudo-ranges and carrier phase observations of different satellites are weighted using an altitude-based random model as follows:
；
in the formula ,is the variance of the observed value; />Is the altitude of the satellite; /> and />Constant terms related to observed noise, respectively; the weight ratio between the GNSS pseudo-range and the carrier phase observations is set to 1:100;
then, carrying out least square adjustment processing on the system error equation, and calculating to obtain a correction corresponding to the GNSS and the base line length constraint model based on IMU assistance and />；
Then, according to the Helmert variance component estimation rigorous formula, calculating a unit weight variance factor between the GNSS and the base line length constraint model based on IMU assistance；
Then, based on the new unit weight variance factor obtained by the calculationUse of the unit weight variance estimate therein +.> and />Reassigning a weight matrix between the GNSS and the base line length constraint model based on IMU assistance:
；
in the subscript and />Respectively representing the calculation results of the previous time and the current time; />Is constant with->Replacement;
repeating the iterative process until the unit weight variance factors between the GNSS and the base line length constraint model based on IMU assistance are equal, namelyOr the following termination condition is satisfied:
；
and stopping iteration and outputting the weight matrix corresponding to each moment.
8. The inertial-assisted dual-antenna GNSS marine vessel attitude determination method of claim 7, wherein in step 4, a dual-antenna GNSS and IMU loose coupling scheme is constructed, that is, dual-antenna GNSS and IMU loose coupling filtering fusion is performed, specifically including:
step 4-1, constructing a system state vector based on an extended Kalman filter EKFThe following are provided:
；
in the formula , and />Respectively the three-dimensional position and speed errors of the ship in the n series; />Is the attitude misalignment angle of the ship; /> and />Zero offset and scale factor error of the accelerometer in the IMU; /> and />Zero offset and scale factor error of gyroscopes in the IMU respectively;
in step 4-2, the system state equation is constructed as follows:
；
in the formula ,is a system state transition matrix; />Is a noise matrix;
extended Kalman filter EKF measurement vectorThe three-dimensional position and posture information of the ship, which are output by the GNSS, and the three-dimensional position and posture information of the ship, which are mechanically arranged and output by the IMU, are obtained by differentiating:
；
in the formula , and />Respectively representing the three-dimensional positions of the ship output by the GNSS and the IMU; /> and />Representing pitch angles output by the GNSS and IMU, respectively; /> and />Respectively representHeading angles output by GNSS and IMU;
step 4-3, constructing a measurement equation based on an extended Kalman filter EKF, as follows:
；
in the formula ,to design a matrix; />Measuring a noise matrix;
and 4-4, setting a filtered initial value, starting filtering iteration, obtaining the optimal estimation of the ship attitude information at the current moment, and outputting the optimal estimation.
9. The inertial aided dual antenna GNSS marine vessel attitude determination method of claim 8, wherein said parameters of step 3 and />The pseudorange observations are set to 0.3m for GNSS and 0.003m for GNSS carrier phase observations.
10. The inertial aided dual antenna GNSS marine vessel attitude determination method of claim 9, wherein said calculating in step 3 a unit weight variance factor between GNSS and IMU aided based baseline length constraint modelThe specific method comprises the following steps:
；
in the formula, each variable calculation method is as follows:
；
in the formula , and />The number of observations of the ambiguity resolution model based on the GNSS and IMU assisted baseline length constraints, respectively.
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