Low-orbit satellite opportunistic signal and MEMS-INS combined positioning methodTechnical Field
The invention relates to the technical field of combined positioning, in particular to a low-orbit satellite opportunistic signal and MEMS-INS combined positioning method.
Background
With the increasing demand for location services, global satellite navigation systems (GNSS) have been rapidly developed as a main means of outdoor positioning, but their drawbacks are gradually exposed. At present, the combined navigation positioning method of GNSS/INS is used in the mainstream combined navigation positioning, but the GNSS signal power is low, and the GNSS signal is easy to be interfered by various kinds of accidents or intention, so that the system performance is reduced or even fails. Therefore, the GNSS signals are replaced by the opportunistic signals, the opportunistic signals are utilized for positioning in the outdoor scene, the dependence on GNSS is eliminated, and the positioning navigation precision in the complex scene is improved, so that a new research hotspot for positioning the complex scene is formed.
The signals of opportunity are mainly divided into land-based signals of opportunity and space-based signals of opportunity, wherein the land-based signals of opportunity mainly comprise mobile communication networks, local wireless networks, digital televisions and other radiation signals, the signals of opportunity are mainly concentrated in urban densely populated areas, navigation and positioning are difficult to achieve in areas such as islands, mountains and deserts where people are rare, and the signals of opportunity of the space-based signals have the advantages of wide coverage range, wide frequency band range and the like compared with the signals of opportunity of the land-based signals of opportunity.
Low-Orbit Satellites (LEOs) are a typical source of space-based signal-of-opportunity radiation. LEO constellations mainly cover mobile communication satellite systems, and currently, there are LEO constellations such as Iridium (Iridium), orbital communication satellites (Orbcomm), and global satellites (Globalstar) which are well-operated in orbit. The space exploration technique company in the United states plans to emit a star chain (Starlink) system with the total number of satellites being up to tens of thousands (more than 2000 are currently emitted), and China also plans to develop an LEO giant star seat system, so that a rich radiation source is provided for positioning LEO opportunity signals in the future. However, with single LEO constellation positioning, the problems of insufficient visibility, poor constellation configuration and the like exist, high-precision dynamic positioning cannot be independently realized, and multi-LEO constellation positioning also has the defect of insufficient precision.
At present, combined positioning navigation is carried out by combining LEO constellation satellite multisource opportunistic signals with INS inertial navigation data, for example, china patent application No. CN118857279A discloses a high-precision navigation method based on LEO constellation satellite multisource opportunistic signal fusion, the method obtains position information and speed information of a user through inertial navigation, further calculates a low-orbit satellite downlink opportunistic signal Doppler frequency calculated value and a low-orbit satellite direction unit vector calculated value, takes the difference between the Doppler frequency calculated value and the low-orbit satellite direction unit vector calculated value and an observed value as navigation observed value, and finally realizes high-precision user navigation information prediction and update based on Kalman filtering. The method takes the user position information and the speed information acquired by inertial navigation as reference values to calculate the Doppler frequency of the downlink opportunistic signal of the low-orbit satellite and the direction unit vector of the low-orbit satellite, so that the method has higher requirements on the inertial navigation precision, and can not realize the accurate positioning navigation purpose for the positioning carrier only provided with low-precision low-cost inertial navigation equipment.
Disclosure of Invention
Aiming at the problems existing in the prior art and based on the use cost in engineering practice, the applicant provides a combined positioning method of a low-orbit satellite opportunistic signal and a low-precision micro-electromechanical inertial navigation system (MEMS-INS), which can improve the positioning precision of a positioning carrier only provided with middle-low-precision low-cost inertial navigation equipment.
The technical scheme of the invention is as follows:
A low-orbit satellite opportunistic signal and MEMS-INS combined positioning method comprises the following steps:
step 1, acquiring data of each sensor of a combined positioning system;
the combined positioning system comprises a low-precision micro-electromechanical inertial navigation system MEMS-INS, a first LEO constellation and a second LEO constellation;
step 2, establishing an error equation of the MEMS-INS sensor as follows:
Wherein: to utilizePredictedA MEMS-INS sensor system error at the moment; Is thatMEMS-INS sensor systematic errors at the moment,Is the slaveFrom moment to momentA MEMS-INS sensor system error prediction matrix at moment; is a process noise vector;
Step 3, establishing a combined positioning module extended Kalman filtering system model:
The method comprises the steps of establishing a prediction model of a first combined positioning module consisting of a first LEO constellation and an MEMS-INS as follows:
The method comprises the steps of establishing a prediction model of a second combined positioning module consisting of a second LEO constellation and an MEMS-INS as follows:
Wherein the method comprises the steps ofTo utilizePredictedThe systematic errors of the first combined positioning module of the moments,Is thatThe systematic errors of the first combined positioning module of the moments,To utilizePredictedThe systematic errors of the second combined positioning module of the moments,Is thatA system error of the second combined positioning module at the moment; Is the slaveFrom moment to momentThe first combined positioning module predicts the matrix at time,Is the slaveFrom moment to momentA second combined positioning module predicts a matrix at the moment;
step 4, establishing a combined positioning module extended Kalman filtering observation model:
for a certain combined positioning module, the extended Kalman filtering observation model is as follows:
Wherein the method comprises the steps of,For the doppler bias amount obtained by the LEO constellation in the combined positioning module, c is the speed of light,Carrier frequencies for LEO constellations in the combined positioning module; for the doppler positioning observation matrix of the combined positioning module,For the LEO constellation user receiver state bias vector in the combined positioning module,For the pseudorange measurement of the noise vector,Derivatives of noise vectors for pseudo-range measurements;
Step 5, based on the combined positioning module extended Kalman filtering system model established in the step 3 and the combined positioning module extended Kalman filtering observation model established in the step4, obtaining the combined positioning module extended Kalman filtering observation model through an extended Kalman filtering algorithmTime of day positioning of carrier status、Posterior covariance matrix,;
The flow formula of the extended Kalman filtering algorithm is as follows:
Wherein the method comprises the steps ofIs obtained by feedback in step6Time positioning carrier fusion state,To utilizePredictedThe carrier state is positioned at the moment,Is obtained by feedback in step6Time positioning carrier fusion state,To utilizePredictedPositioning the carrier state at any time; Is obtained by feedback in step6A time i-th combined positioning module state covariance matrix,Is thatThe time i-th combined positioning module noise covariance matrix,Is thatA state priori covariance matrix of a ith combined positioning module at moment; Is thatThe kalman gain of the instant i-th combined positioning module,Is thatThe Doppler positioning observation matrix of the ith combined positioning module at the moment,Is thatIs used to determine the transposed matrix of (a),Is thatAn observation noise covariance matrix of the ith combined positioning module at the moment; Is thatThe positioning carrier state obtained by the first combined positioning module at the moment,Is thatThe positioning carrier state obtained by the second combined positioning module at the moment,Is thatThe actual measured value of the ith combined positioning module at the moment; Is thatMoment i is the combined positioning module state posterior covariance matrix,Is a unit matrix;
Step 6 based on the step 5、AndAccording to the fusion formula
Calculated to obtainTime-of-day positioning carrier fusion stateAnd feed back, wherein
And according to the formula
Calculated to obtainState covariance matrix of instant i-th combined positioning moduleAnd feed back, whereinTo obtain the filter weight by a variable ratio adaptive method:
Wherein the method comprises the steps ofIs the information weight of the MEMS-INS sensor,For the information weights of the first LEO constellation antenna,For each sensor, adopting the autoregressive prediction error of the sensor as the information weight;
when obtainedAnd (3) withThe difference is smaller than a preset threshold valueAt this time, it is considered thatAndOptimal state estimation for positioning a carrierAnd optimal state covariance。
Further, the first LEO constellation adopts an Iridium constellation, and the second LEO constellation adopts an Orbcomm constellation.
Further, the MEMS-INS sensor is used as a main sensor, the first LEO constellation antenna and the second LEO constellation antenna are used as sub sensors, the speed, the position and the gesture of the positioning carrier under the north east coordinate system are obtained through the MEMS-INS sensor, the position under the north east coordinate system is converted into longitude, latitude and altitude, and meanwhile Doppler observed quantity of the positioning carrier is obtained through the first LEO constellation antenna and the second LEO constellation antenna;
The MEMS-INS filter is used as a main filter for updating the speed, position and gesture data acquired by the MEMS-INS sensor, and the first LEO constellation filter and the second LEO constellation filter are used as sub-filters for assisting in updating the speed, position and gesture data acquired by the MEMS-INS sensor.
Further, the MEMS-INS sensor system error at specific moment is not consideredThe expression is:
Wherein the method comprises the steps of、、The positioning carrier is respectively positioned in the north direction, the east direction and the ground direction under the north east coordinate system,、、Sequentially respectively positioning the carrier at the north direction, the east direction and the ground direction of the north east coordinate system,、AndThe errors of longitude, latitude and altitude of the positioning carrier under the longitude and latitude high coordinate system are respectively shown in sequence.
Further, fromFrom moment to momentTime MEMS-INS sensor system error prediction matrixThe expression is:
Wherein the method comprises the steps ofAn identity matrix of 9 rows and 9 columns, T being the sampling interval,、、、AndIs an intermediate matrix, and the expression is
Wherein: Representation pairPerforming anti-symmetric transformation to obtain an anti-symmetric matrix; A zero matrix of 3 rows and 3 columns; the rotation angular rate of a navigation coordinate system relative to an inertial coordinate system for positioning the carrier; acceleration vectors in a navigation coordinate system for positioning the carrier; Is the rotation angular velocity of the earth; the rotation angle rate of the navigation coordinate system relative to the geocentric fixed coordinate system is L is the latitude of the position of the positioning carrier; AndThe radius of curvature of the meridian and the radius of curvature of the mortise ring at the position of the positioning carrier are respectively arranged in sequence; In order to locate the eastern speed of the carrier,In order to locate the carrier north speed,To position the carrier the ground speed, h is the height.
Further, the system error of the first combined positioning module is not considered in the specific momentSystematic error of second combined positioning module,Is thatIs used to determine the transposed matrix of (a),For the frequency offset error of the first LEO constellation system and the user receiver,For the frequency offset error of the second LEO constellation system with the user receiver,Is thatIs used to determine the transposed matrix of (a),Is thatIs a transposed matrix of (a).
Further, the method comprises the steps of,Is the slaveFrom moment to momentThe first combined positioning module predicts the matrix at the moment:
Is the slaveFrom moment to momentThe second combined positioning module predicts the matrix at the moment:
Wherein the method comprises the steps ofIs the slaveFrom moment to momentThe first LEO constellation signal-of-opportunity error prediction matrix at time instant,Is the slaveFrom moment to momentThe second LEO constellation opportunity signal error prediction matrix at time instant.
Further, it is considered in the prediction process thatThe satellite frequency difference of the first LEO constellation and the second LEO constellation is the same as the k moment。
Further, user receiver state bias vectorWherein、、The components of the user receiver position error along the X, Y, Z three axes in the geocentric fixed coordinate system are respectively arranged in sequence,Clock-up for the user receiver.
Further, doppler positioning observation matrix
In the middle ofFor the components of the unit observation vector of the mth satellite of the LEO constellation in the combined positioning module at the user receiver along the X, Y, Z three axes in the geocentric fixed coordinate system,Is thatIs a transposed matrix of (a); The transformation matrix is from a northeast day coordinate system to a geocentric earth fixed coordinate system; a velocity vector for the mth satellite relative to the positioning carrier; For locating the geometric distance of the carrier from the mth satellite; Representation fetchIs the first 2 columns of (c).
The beneficial effects are that:
According to the combined positioning method of the low-orbit satellite opportunistic signals and the MEMS-INS, doppler observation information of a plurality of low-orbit satellite constellation opportunistic signals is extracted, then effective combination of a plurality of low-orbit satellites and the MEMS-INS is achieved through an extended Kalman filtering algorithm, meanwhile, information weights of all sensors are obtained, the information weights are obtained through calculation from forward data of all the sensors through time sequence analysis, after the weights of the filters are calculated according to the information weights, the proportion of the extended Kalman filtering can be adjusted according to the states of the sensors and the effectiveness of navigation information, so that divergence of MEMS-INS errors is restrained, meanwhile, influence of insufficient prior knowledge of parameters is reduced, good performance is achieved in the aspects of dispersity, instantaneity, accuracy, reliability, fault tolerance and the like, and improvement of positioning performance is achieved.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
The foregoing and/or additional aspects and advantages of the invention will become apparent and may be better understood from the following description of embodiments taken in conjunction with the accompanying drawings in which:
Fig. 1 is a flow chart of the method of the present invention.
Detailed Description
The following detailed description of embodiments of the invention is exemplary and intended to be illustrative of the invention and not to be construed as limiting the invention.
The embodiment provides a low-orbit satellite opportunistic signal and MEMS-INS combined positioning method, which realizes the combined positioning function of the low-orbit satellite opportunistic signal and the MEMS-INS through an AR-FKF (autoregressive-federal Kalman filtering) algorithm. The principle is that Doppler observation information of the multi-low orbit satellite opportunistic signals is extracted, then effective combination of the multi-low orbit satellite and the MEMS-INS is realized through an FKF algorithm, meanwhile, the information weight of each sensor is obtained, the information weight can be obtained by calculating forward data of a navigation sensor through time sequence analysis, after the weight of a filter is calculated according to the information weight, the proportion of the FKF can be adjusted according to the state of the sensor and the effectiveness of the navigation information, so that divergence of MEMS-INS errors is restrained, meanwhile, influence of insufficient priori knowledge of parameters is reduced, good performance is achieved in the aspects of dispersity, instantaneity, accuracy, reliability, fault tolerance and the like, and improvement of positioning performance is realized.
The method specifically comprises the following steps:
step 1, acquiring data of each sensor of a combined positioning system;
The combined positioning system adopted by the embodiment comprises a low-precision MEMS-INS, a first LEO constellation and a second LEO constellation, wherein the Iridium constellation and the Orbcomm constellation are complementary in layout design, so that the first LEO constellation adopts the Iridium constellation and the second LEO constellation adopts the Orbcomm constellation in the embodiment.
The method comprises the steps of taking an MEMS-INS sensor as a main sensor, taking an Iridium antenna and an Orbcomm antenna as sub sensors, obtaining the speed, the position and the gesture of a target (positioning carrier) to be positioned under a North east coordinate system through the MEMS-INS sensor, converting the position under the North east coordinate system into longitude, latitude and altitude, and obtaining Doppler observed quantity of the positioning carrier through the Iridium antenna and the Orbcomm antenna;
The method comprises the steps of taking the MEMS-INS filter as a main filter for updating speed, position and gesture data acquired by the MEMS-INS sensor, taking the Iridium filter and the Orbcomm filter as sub-filters for assisting in updating the speed, position and gesture data acquired by the MEMS-INS.
And 2, the error of the MEMS-INS comprises speed errors, position errors and attitude errors of three channels besides inertial element errors. Thus, the error equation of the MEMS-INS sensor is established as follows:
(1)
Wherein: to utilizePredictedA MEMS-INS sensor system error at the moment; Is thatThe MEMS-INS sensor system errors at the moment comprise position errors, speed errors and attitude errors; Is the slaveFrom moment to momentA MEMS-INS sensor system error prediction matrix at moment; is a process noise vector;
Error of MEMS-INS sensor system without consideration of specific momentThe expression is:
Wherein the method comprises the steps of、、The positioning carrier is respectively positioned in the north direction, the east direction and the ground direction under the north east coordinate system,、、Sequentially respectively positioning the carrier at the north direction, the east direction and the ground direction of the north east coordinate system,、AndErrors of longitude, latitude and altitude of the positioning carrier under a longitude and latitude high coordinate system are sequentially respectively shown;
From the slaveFrom moment to momentTime MEMS-INS sensor system error prediction matrixThe expression is:
(2)
Wherein the method comprises the steps ofAn identity matrix of 9 rows and 9 columns, T being the sampling interval,、、、AndIs an intermediate matrix, and the expression is
(3)
(4)
(5)
(6)
(7)
Wherein: Representation pairPerforming anti-symmetric transformation to obtain an anti-symmetric matrix; A zero matrix of 3 rows and 3 columns; the rotation angular rate of a navigation coordinate system relative to an inertial coordinate system for positioning the carrier; acceleration vectors in a navigation coordinate system for positioning the carrier; Is the rotation angular velocity of the earth; the rotation angle rate of the navigation coordinate system relative to the geocentric fixed coordinate system is L is the latitude of the position of the positioning carrier; AndThe radius of curvature of the meridian and the radius of curvature of the mortise ring at the position of the positioning carrier are respectively arranged in sequence; In order to locate the eastern speed of the carrier,In order to locate the carrier north speed,To position the carrier the ground speed, h is the height.
Step 3, establishing a combined positioning module extended Kalman filtering system model:
The method comprises the following steps of establishing a prediction model of a first combined positioning module consisting of an Iridium constellation and an MEMS-INS:
(8)
The method comprises the steps of establishing a prediction model of a second combined positioning module consisting of an Orbcomm constellation and an MEMS-INS as follows:
(9)
Wherein the method comprises the steps ofTo utilizePredictedThe systematic errors of the first combined positioning module of the moments,Is thatThe systematic errors of the first combined positioning module of the moments,To utilizePredictedThe systematic errors of the second combined positioning module of the moments,Is thatA system error of the second combined positioning module at the moment;
Without considering the specific time, the system error of the first combined positioning moduleSystematic error of second combined positioning module,Is thatIs used to determine the transposed matrix of (a),As the frequency offset error of the Iridium constellation system and the user receiver,For the frequency offset error of the Orbcomm constellation system and the user receiver,Is thatIs used to determine the transposed matrix of (a),Is thatIs a transposed matrix of (a);
Is the slaveFrom moment to momentThe first combined positioning module predicts the matrix at the moment:
(10)
Is the slaveFrom moment to momentThe second combined positioning module predicts the matrix at the moment:
(11)
Wherein the method comprises the steps ofIs the slaveFrom moment to momentThe Iridium constellation signal-of-opportunity error prediction matrix for the time instant,Is the slaveFrom moment to momentThe invention considers the error prediction matrix of the opportunistic signal of the Orbcomm constellation at the moment in the prediction processThe satellite frequency difference of the Iridium constellation and the Orbcomm constellation at the moment is the same as the moment k, thenAndThe method comprises the following steps:
(12)
In the middle of1.
Step 4, establishing a combined positioning module extended Kalman filtering observation model:
the system observation updating process is a process for updating the current prediction state quantity according to the observation model to obtain the state quantity optimal estimation. The specific deduction process of the observation model of the low orbit satellite opportunistic signal and MEMS-INS combined positioning system is as follows.
For each combined positioning module, establishing a pseudo-range positioning linear navigation state update equation as follows:
(13)
In the middle ofWhereinFor a priori pseudorange measurement bias, z is the measured pseudorange vector,Is a predicted pseudorange vector; Measuring noise vectors for pseudo-ranges; for a user receiver state deviation vector,Wherein、、The components of the user receiver position error along the X, Y, Z three axes in the geocentric fixed coordinate system are respectively arranged in sequence,The method comprises the steps of providing a user receiver clock error, and providing a Jacobian matrix for pseudo-range positioning in a northeast day coordinate system, wherein the Jacobian matrix has the following expression:
(14)
In the middle ofA component of X, Y, Z triaxial in the geocentric-geodetic fixed coordinate system for a unit observation vector of the mth satellite at the user receiver; the expression form of the transformation matrix from the northeast coordinate system to the geocentric earth fixed coordinate system is as follows:
(15)
In the middle ofLongitude for the location of the positioning carrier;
deriving formula (13):
(16)
In the middle ofExpanding equation (14) and ignoring the user receiver altitude channel to obtain a Doppler positioning observation matrix as follows:
(17)
Wherein: Is thatIs a transposed matrix of (a); a velocity vector for the mth satellite relative to the positioning carrier; For locating the geometric distance of the carrier from the mth satellite; Representation fetchThe extended Kalman filtering observation model of the combined positioning module is obtained as follows:
(18)
Wherein: WhereinC is the light velocity, which is the Doppler shift amount obtained by the Iridium constellation or the Orbcomm constellation; the carrier frequency is either the Iridium constellation or the Orbcomm constellation.
Step 5, setting an initial system noise covariance matrix Q and an observed noise covariance matrix R based on the combined positioning module extended Kalman filtering system model established in the step 3 and the combined positioning module extended Kalman filtering observation model established in the step 4, and obtaining the combined positioning module extended Kalman filtering system model through an extended Kalman filtering algorithmTime of day positioning of carrier status、Posterior covariance matrix,I is the number of the combined positioning module and the number of the sub-filter, the 1 st sub-filter corresponds to the Iridium filter, and the 2 nd sub-filter corresponds to the Orbcomm filter.
The flow formula of the extended Kalman filtering algorithm is as follows:
(19)
(20)
(21)
(22)
(23)
(24)
(25)
Wherein the method comprises the steps ofIs obtained by feedback in step6Time positioning carrier fusion state,To utilizePredictedThe carrier state is positioned at the moment,Is obtained by feedback in step6Time positioning carrier fusion state,To utilizePredictedPositioning the carrier state at any time; Is obtained by feedback in step6A time i-th combined positioning module state covariance matrix,Is thatThe time i-th combined positioning module noise covariance matrix,Is thatA state priori covariance matrix of a ith combined positioning module at moment; Is thatThe kalman gain of the instant i-th combined positioning module,Is thatThe Doppler positioning observation matrix of the ith combined positioning module at the moment,Is thatIs used to determine the transposed matrix of (a),Is thatAn observation noise covariance matrix of the ith combined positioning module at the moment; Is thatThe positioning carrier state obtained by the first combined positioning module at the moment,Is thatThe positioning carrier state obtained by the second combined positioning module at the moment,Is thatThe actual measured value of the ith combined positioning module at the moment; Is thatMoment i is the combined positioning module state posterior covariance matrix,Is an identity matrix.
Step 6 based on the step 5、AndAccording to the fusion formula
(26)
Calculated to obtainTime-of-day positioning carrier fusion stateAnd feed back, wherein
(27)
And according to the formula
(28)
Calculated to obtainState covariance matrix of instant i-th combined positioning moduleAnd feed back, whereinTo obtain the filter weight by a variable ratio adaptive method:
(29)
Wherein the method comprises the steps ofIs the information weight of the MEMS-INS sensor,Is the information weight of the Iridium antenna,Information weight for an Orbcomm antenna, and corresponding,Representing the weights of the MEMS-INS filter,Is the weight of the Iridium filter,Is the weight of the Orbcomm filter. For the main sensor (MEMS-INS sensor) and the two sub-sensors (Iridium antenna and Orbcomm antenna), the autoregressive prediction error of the sensor is used as the information weight, respectively.
Finally, when obtainedAnd (3) withThe difference is smaller than a preset threshold valueAt this time, it is consideredAndOptimal state estimation for positioning a carrierAnd optimal state covariance。
For a certain sensor, the process of obtaining the autoregressive prediction error of the sensor is as follows:
setting the output value of the sensor at the moment kAn N-th order Autoregressive (AR) model of (2) is given by:
(30)
wherein N is the order, model errorZero mean and variance ofIs a white gaussian noise of (a) and (b),For the ith coefficient, a corresponding N-1 order autoregressive model may also be provided.
Can be givenIs an autocorrelation function matrix of (a)The method comprises the following steps:
(31)
Is provided withIs the estimation of the ith coefficient in the N-order autoregressive model, and the minimum error power of the N-order autoregressive modelAccording to the Levinson-Durbin recursive algorithm, the estimation of the N-order autoregressive model coefficients is as follows:
(32)
(33)
Wherein the method comprises the steps ofIs an estimate of the i-th coefficient in the N-1 th order autoregressive model.
Thereby obtaining the autoregressive predicted value of the sensor as
(34)
The autoregressive prediction error is. Since the autoregressive model is an integral model built in a stable space, the prediction error of the autoregressive model can describe the smoothness of the output of the sensor, so that the autoregressive prediction error of the sensor is used as the information weight, the smaller the prediction error is, the smoother the output of the sensor is, and the smaller the information weight is.
The practical measurement data show that the low orbit satellite opportunistic signal and MEMS-INS combined positioning method improves LEO opportunistic signal positioning accuracy, experimental verification positioning accuracy is superior to 150m, and the accuracy is improved by approximately 20% compared with the current research level accuracy.
Although embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the invention, and that variations, modifications, alternatives, and variations may be made in the above embodiments by those skilled in the art without departing from the spirit and principles of the invention.