A combined positioning method for low-earth orbit satellite opportunity signals and MEMS-INS

Abstract

The present invention proposes a combined positioning method for low-orbit satellite opportunity signals and MEMS-INS. By extracting Doppler observation information of multiple low-orbit satellite constellation opportunity signals, and then through the extended Kalman filter algorithm, an effective combination of multiple low-orbit satellites and MEMS-INS is achieved. At the same time, the information weights of each sensor are obtained. The information weights are calculated from the forward data of each sensor through time series analysis. After calculating the weights of the filter according to the information weights, the ratio of the extended Kalman filter can be adjusted according to the state of the sensor and the validity of the navigation information, so as to suppress the divergence of MEMS-INS errors and reduce the influence of insufficient prior knowledge of parameters. It has good performance in terms of dispersion, real-time performance, accuracy, reliability and fault tolerance, and realizes the improvement of positioning performance.

Description

Technical Field

[0001] The present invention relates to the technical field of combined positioning, and specifically to a combined positioning method for low-earth orbit satellite opportunistic signals and MEMS-INS. Background Art

[0002] With the increasing demand for location services, the global navigation satellite system (GNSS) has developed rapidly and is the main means of outdoor positioning. However, its disadvantages have gradually emerged. Currently, the mainstream combined navigation and positioning uses the GNSS / INS combined navigation and positioning method. However, the GNSS signal has low power and is easily affected by various unintentional or intentional interferences, resulting in reduced system performance or even failure. Therefore, replacing the GNSS signal with an opportunistic signal and using the opportunistic signal for outdoor scene positioning to get rid of the dependence on GNSS and improve the positioning and navigation accuracy in complex scenarios has become a new research hotspot for complex scene positioning.

[0003] Opportunistic signals are mainly divided into terrestrial-based opportunistic signals and space-based opportunistic signals: Terrestrial-based opportunistic signals mainly include radiation signals such as mobile communication networks, local wireless networks, and digital televisions, which are mainly concentrated in urban densely populated areas, and it is difficult to achieve navigation and positioning in areas with sparse population such as islands, mountains, and deserts. Space-based opportunistic signals have advantages such as a wide coverage range and a wide frequency band range compared with terrestrial-based opportunistic signals.

[0004] Low-earth orbit (LEO) satellites are a typical source of space-based opportunistic signals. The LEO constellation is mainly a global coverage mobile communication satellite system. Currently, well-operated in orbit are LEO constellations such as Iridium, Orbcomm, and Globalstar. Space Exploration Technologies Corporation of the United States plans to launch a Starlink system with a total of tens of thousands of satellites (more than 2,000 have been launched currently), and China is also planning to develop a large LEO constellation system, which provides rich radiation sources for future LEO opportunistic signal positioning. However, using a single LEO constellation for positioning has problems such as insufficient visibility and poor constellation configuration, and it is impossible to independently achieve high-precision dynamic positioning. Multi-LEO constellation positioning also has the disadvantage of insufficient accuracy.

[0005] At present, there are also studies on combining multi-source opportunistic signals of LEO constellation satellites with INS inertial navigation data for integrated positioning and navigation. For example, the Chinese patent application "High-precision navigation method based on the integration of multi-source opportunistic signals of LEO constellation satellites" with the publication number CN118857279A. This method obtains the position information and velocity information of the user through inertial navigation, and then calculates the calculated value of the Doppler frequency of the downlink opportunistic signal of the low-earth orbit satellite and the calculated value of the unit direction vector of the low-earth orbit satellite; uses the difference between the Doppler frequency, the calculated value of the unit direction vector of the low-earth orbit satellite and the observed value as the navigation observation quantity; finally, based on the Kalman filter, realizes the prediction and update of high-precision user navigation information. Since this method uses the position information and velocity information of the user obtained by inertial navigation as the reference value to calculate the Doppler frequency of the downlink opportunistic signal of the low-earth orbit satellite and the unit direction vector of the low-earth orbit satellite, it has high requirements for the accuracy of inertial navigation. For positioning carriers equipped with only low-precision and low-cost inertial navigation devices, this method cannot achieve the purpose of accurate positioning and navigation. Summary of the Invention

[0006] In view of the problems existing in the prior art and considering the usage cost in engineering practice, the applicant proposes a combined positioning method for low-earth orbit satellite opportunistic signals and a low-precision microelectromechanical inertial navigation system (MEMS-INS), which can improve the positioning accuracy of positioning carriers equipped with only medium and low-precision and low-cost inertial navigation devices.

[0007] The technical solution of the present invention is as follows:

[0008] A combined positioning method for low-earth orbit satellite opportunistic signals and MEMS-INS includes the following steps:

[0009] Step 1: Obtain the data of each sensor of the integrated positioning system;

[0010] The integrated positioning system includes a low-precision microelectromechanical inertial navigation system MEMS-INS, a first LEO constellation, and a second LEO constellation;

[0011] Step 2: Establish the error equation of the MEMS-INS sensor as:

[0012]

[0013] Where: is the system error of the MEMS-INS sensor system predicted by using at the moment; is the system error of the MEMS-INS sensor system at the moment, is the system error prediction matrix of the MEMS-INS sensor system from the moment to the moment; is the process noise vector;

[0014] Step 3: Establish the combined positioning module extended Kalman filter system model:

[0015] Establish the prediction model for the first combined positioning module composed of the first LEO constellation and MEMS-INS as:

[0016]

[0017] Establish the prediction model for the second combined positioning module composed of the second LEO constellation and MEMS-INS as:

[0018]

[0019] where is the system error of the first combined positioning module predicted using at time , is the system error of the first combined positioning module at time , is the system error of the second combined positioning module predicted using at time , is the system error of the second combined positioning module at time ; is the prediction matrix of the first combined positioning module from time to time , is the prediction matrix of the second combined positioning module from time to time ;

[0020] Step 4: Establish the combined positioning module extended Kalman filter observation model:

[0021] For a certain combined positioning module, its extended Kalman filter observation model is:

[0022]

[0023] where , is the Doppler bias obtained through the LEO constellation in this combined positioning module, c is the speed of light, is the carrier frequency of the LEO constellation in this combined positioning module; is the Doppler positioning observation matrix of this combined positioning module, is the state deviation vector of the LEO constellation user receiver in this combined positioning module, is the pseudorange measurement noise vector, is the derivative of the pseudorange measurement noise vector;

[0024] Step 5: Based on the extended Kalman filter system model of the combined positioning module established in Step 3 and the extended Kalman filter observation model of the combined positioning module established in Step 4, obtain the state of the positioning carrier at time 、 and the posterior covariance matrix , ;

[0025] The process formula of the extended Kalman filter algorithm is as follows:

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] where is the fused state of the positioning carrier at time obtained by feedback in Step 6 , is the state of the positioning carrier predicted using at time , is the fused state of the positioning carrier at time obtained by feedback in Step 6 , is the state of the positioning carrier predicted using at time ; is the state covariance matrix of the i-th combined positioning module at time obtained by feedback in Step 6 is the noise covariance matrix of the i-th combined positioning module at time is the prior state covariance matrix of the i-th combined positioning module at time is the Kalman gain of the i-th combined positioning module at time is the Doppler positioning observation matrix of the i-th combined positioning module at time is the transposed matrix of is the observation noise covariance matrix of the i-th combined positioning module at time is the positioning carrier state obtained by the first combined positioning module at time is the positioning carrier state obtained by the second combined positioning module at time is the actual measurement value of the i-th combined positioning module at time is the posterior covariance matrix of the state of the i-th combined positioning module at time is the identity matrix;

[0034] Step 6: Based on the , and obtained in Step 5, according to the fusion formula

[0035]

[0036] calculate to obtain the fused state of the positioning carrier at time

[0037]

[0038] and feedback, where

[0039]

[0040] calculate to obtain the state covariance matrix of the i-th combined positioning module at time and feedback, where

[0041]

[0042] where is the information weight of the MEMS-INS sensor, is the information weight of the first LEO constellation antenna, is the information weight of the second LEO constellation antenna; for each sensor, the autoregressive prediction error of the sensor is used as the information weight;

[0043] When the difference between the obtained and is less than the preset threshold , it is considered that the current and are the optimal state estimates of the positioning carrier and the optimal state covariance .

[0044] Furthermore, the first LEO constellation adopts the Iridium constellation, and the second LEO constellation adopts the Orbcomm constellation.

[0045] Furthermore, the MEMS-INS sensor is used as the main sensor, and the antennas of the first LEO constellation and the second LEO constellation are used as sub-sensors; the velocity, position, and attitude of the positioning carrier in the north-east-down coordinate system are obtained through the MEMS-INS sensor, and the position in the north-east-down coordinate system is converted into longitude, latitude, and altitude. At the same time, the Doppler observables of the positioning carrier are obtained through the antennas of the first LEO constellation and the second LEO constellation;

[0046] The MEMS-INS filter is used as the main filter to update the velocity, position, and attitude data obtained by the MEMS-INS sensor. The filters of the first LEO constellation and the second LEO constellation are used as sub-filters to assist in updating the velocity, position, and attitude data obtained by the MEMS-INS sensor.

[0047] Furthermore, the system error of the MEMS-INS sensor at a specific moment is not considered The expression is:

[0048] δ x INS = [ δϕ n δϕ e δϕ d δ v n δ v e δ v d δ L b δλ b δ h b ] T

[0049] where , , are the attitude errors in the north, east, and down directions of the positioning carrier in the north-east-down coordinate system, respectively, , , are the velocity errors in the north, east, and down directions of the positioning carrier in the north-east-down coordinate system, respectively, , and are the errors in longitude, latitude, and altitude of the positioning carrier in the longitude-latitude-altitude coordinate system, respectively.

[0050] Furthermore, the prediction matrix of the MEMS-INS sensor system error from time to time The expression is:

[0051] ϕ INS ( k + 1 , k ) = I + T ⋅ [ -[ ω iN N Λ ] F 12 N F 13 N -[ f N Λ ] − [( 2 × ω iE N + ω EN N ) Λ ] F 23 N 0 3 , 3 F 32 N F 33 N ]

[0052] where is a 9×9 identity matrix, and T is the sampling interval , , , and is the intermediate matrix, and the expression is

[0053] F 12 N = [ 0 -1 / （ R 2 + h ) 0 1 / ( R 1 + h ) 0 0 0 tan L / （ R 2 + h ) 0 ]

[0054] F 13 N = [ ω iE N sin L 0 v e / （ R 2 + h ) 2 0 0 - v n / （ R 2 + h ) 2 ω iE N cos L + v e (sec L ) 2 / （ R 2 + h ) 0 − v e tan L / （ R 2 + h ) 2 ]

[0055] F 23 N = [ ( v e ) 2 (sec L ) 2 / （ R 2 + h ) − 2 ∗ ω iE N v e cos L 0 ( v e ) 2 (tan L ) 2 / （ R 2 + h ) 2 − v n v d / （ R 2 + h ) 2 v n v e (sec L ) 2 / （ R 1 + h ) + 2 ∗ ω iE N v n cos L 0 -( v n v e tan L + v e v d ) / （ R 1 + h ) 2 2 ∗ ω iE N v e sin L 0 ( v e ) 2 / （ R 2 + h ) 2 + ( v n ) 2 / （ R 1 + h ) 2 ]

[0056] F 32 N = [ 1 / （ R 1 + h ） 0 0 0 sec L / （ R 2 + h ） 0 0 0 − 1 ]

[0057] F 33 N = [ 0 0 v n / ( R 1 + h ) 2 v e ⋅ tan L sec L / ( R 2 + h ) 0 − v e sec L / ( R 2 + h ) 2 0 0 0 ]

[0058] In the formula: [ • Λ ] represents the skew-symmetric matrix obtained by performing a skew-symmetric transformation on ; is a 3×3 zero matrix; is the angular rate of rotation of the navigation coordinate system of the positioning carrier relative to the inertial coordinate system; is the acceleration vector of the positioning carrier in the navigation coordinate system; is the angular velocity of the Earth's rotation; is the angular rate of rotation of the navigation coordinate system relative to the Earth-centered Earth-fixed coordinate system; L is the latitude of the location of the positioning carrier; and are the radius of curvature of the meridian and the radius of curvature of the prime vertical at the location of the positioning carrier, respectively; is the eastward velocity of the positioning carrier, is the northward velocity of the positioning carrier, is the downward velocity of the positioning carrier, and h is the altitude.

[0059] Furthermore, without considering the specific moment, the system error δ x IRI = [ δ x INS T δ t f 1 T ] T of the first combined positioning module, and the system error δ x ORB = [ δ x INS T δ t f 2 T ] T of the second combined positioning module, is the transpose matrix of is the frequency difference error between the first LEO constellation system and the user receiver, is the frequency difference error between the second LEO constellation system and the user receiver, is the transpose matrix of is The transposed matrix.

[0060] Furthermore, From moment to moment, the first combined positioning module prediction matrix:

[0061] ϕ 1 ( k + 1 , k ) = [ ϕ INS ( k + 1 , k ) 0 8 , 1 0 1 , 8 ϕ IRI ( k + 1 , k ) ]

[0062] From moment to moment, the second combined positioning module prediction matrix:

[0063] ϕ 2 ( k + 1 , k ) = [ ϕ INS ( k + 1 , k ) 0 8 , 1 0 1 , 8 ϕ ORB ( k + 1 , k ) ]

[0064] Where From moment to moment, the first LEO constellation opportunity signal error prediction matrix, From moment to moment, the second LEO constellation opportunity signal error prediction matrix.

[0065] Furthermore, during the prediction process, it is considered that at moment, the satellite frequency difference of the first LEO constellation and the second LEO constellation is the same as that at moment k, then .

[0066] Furthermore, the user receiver state deviation vector δ x p = [ δ p X δ p Y δ p Z δ t ru ] , where , , are successively the components of the user receiver position error on the X, Y, and Z axes in the Earth-Centered Earth-Fixed coordinate system, is the user receiver clock error.

[0067] Furthermore, the Doppler positioning observation matrix

[0068]

[0069] In the formula e m = [ e m X e m Y e m Z ] T are the components of the unit observation vector of the m-th satellite of the LEO constellation in the combined positioning module at the user receiver on the X, Y, and Z axes in the Earth-Centered Earth-Fixed coordinate system, is 's transposed matrix; is the conversion matrix from the Northeast-East-Down coordinate system to the Earth-Centered Earth-Fixed coordinate system; is the velocity vector of the m-th satellite relative to the positioning vehicle; is the geometric distance between the positioning vehicle and the m-th satellite; denotes taking the first 2 columns of.

[0070] Advantageous effects:

[0071] The combined positioning method of low-earth orbit satellite opportunity signals and MEMS-INS proposed by the present invention extracts Doppler observation information of multiple low-earth orbit satellite constellation opportunity signals, and then realizes the effective combination of multiple low-earth orbit satellites and MEMS-INS through the extended Kalman filtering algorithm. At the same time, the information weights of each sensor are obtained. The information weights are calculated from the forward data of each sensor through time series analysis. After calculating the weights of the filter according to the information weights, the ratio of the extended Kalman filter can be adjusted according to the state of the sensor and the effectiveness of the navigation information, so as to suppress the divergence of MEMS-INS errors and reduce the influence of insufficient prior knowledge of parameters. It has good performance in terms of dispersion, real-time performance, accuracy, reliability and fault tolerance, and realizes the improvement of positioning performance.

[0072] The additional aspects and advantages of the present invention will be partially given in the following description, partially will become obvious from the following description, or will be understood through the practice of the present invention. Description of the drawings

[0073] The above and / or additional aspects and advantages of the present invention will become obvious and easy to understand from the description of the embodiments in conjunction with the following drawings, where:

[0074] Figure 1 is the flowchart of the method of the present invention. Detailed implementation manners

[0075] The embodiments of the present invention will be described in detail below. The embodiments are exemplary and are intended to explain the present invention and should not be construed as a limitation to the present invention.

[0076] This embodiment proposes a combined positioning method for low-earth orbit satellite opportunity signals and MEMS-INS. Through the AR-FKF (Autoregressive-Federated Kalman Filter) algorithm, the combined positioning function of low-earth orbit satellite opportunity signals and MEMS-INS is realized. The principle is to extract the Doppler observation information of multiple low-earth orbit satellite opportunity signals, and then through the FKF algorithm, an effective combination of multiple low-earth orbit satellites and MEMS-INS is achieved. At the same time, the information weights of each sensor are obtained. The information weights can be calculated from the forward data of the navigation sensor through time series analysis. After calculating the weights of the filter according to the information weights, the ratio of FKF can be adjusted according to the state of the sensor and the validity of the navigation information, so as to suppress the divergence of MEMS-INS errors and reduce the influence of insufficient prior knowledge of parameters. It has good performance in terms of dispersion, real-time performance, accuracy, reliability, and fault tolerance, and realizes the improvement of positioning performance.

[0077] Specifically, it includes the following steps:

[0078] Step 1: Obtain the data of each sensor in the combined positioning system;

[0079] The combined positioning system adopted in this embodiment includes a low-precision microelectromechanical inertial navigation system MEMS-INS, a first LEO constellation, and a second LEO constellation; since the Iridium constellation and the Orbcomm constellation are complementary in layout design, in this embodiment, the first LEO constellation adopts the Iridium constellation, and the second LEO constellation adopts the Orbcomm constellation.

[0080] Among them, the MEMS-INS sensor is the main sensor, and the Iridium antenna and the Orbcomm antenna are the sub-sensors. The velocity, position, and attitude of the target to be positioned (positioning carrier) in the north-east-down coordinate system are obtained through the MEMS-INS sensor, and the position in the north-east-down coordinate system is converted into longitude, latitude, and altitude. At the same time, the Doppler observables of the positioning carrier are obtained through the Iridium antenna and the Orbcomm antenna;

[0081] The MEMS-INS filter is used as the main filter to update the velocity, position, and attitude data obtained by the MEMS-INS sensor. The Iridium filter and the Orbcomm filter are used as sub-filters to assist in updating the velocity, position, and attitude data obtained by the MEMS-INS.

[0082] Step 2: In addition to the inertial element errors, the errors of MEMS-INS also include velocity errors, position errors, and attitude errors in three channels. Therefore, the error equation of the MEMS-INS sensor is established as:

[0083] (1)

[0084] Wherein: is the MEMS-INS sensor system error predicted at predicted time; is the MEMS-INS sensor system error at time, including position error, velocity error and attitude error; is from time to time MEMS-INS sensor system error prediction matrix; is the process noise vector;

[0085] Without considering the MEMS-INS sensor system error at a specific time The expression is:

[0086] δ x INS = [ δϕ n δϕ e δϕ d δ v n δ v e δ v d δ L b δλ b δ h b ] T

[0087] Wherein , , are respectively the attitude errors of the positioning carrier in the north, east and down directions in the north-east-down coordinate system, , , are respectively the velocity errors of the positioning carrier in the north, east and down directions in the north-east-down coordinate system, , and are respectively the errors of the longitude, latitude and altitude of the positioning carrier in the longitude-latitude-altitude coordinate system;

[0088] From time to time MEMS-INS sensor system error prediction matrix The expression is:

[0089] ϕ INS ( k + 1 , k ) = I + T ⋅ [ -[ ω iN N Λ ] F 12 N F 13 N -[ f N Λ ] − [( 2 × ω iE N + ω EN N ) Λ ] F 23 N 0 3 , 3 F 32 N F 33 N ] (2)

[0090] Wherein is a 9×9 identity matrix, T is the sampling interval, , , , and are intermediate matrices, and the expression is

[0091] F 12 N = [ 0 -1 / （ R 2 + h ) 0 1 / ( R 1 + h ) 0 0 0 tan L / （ R 2 + h ) 0 ] (3)

[0092] F 13 N = [ ω iE N sin L 0 v e / （ R 2 + h ) 2 0 0 - v n / （ R 2 + h ) 2 ω iE N cos L + v e (sec L ) 2 / （ R 2 + h ) 0 − v e tan L / （ R 2 + h ) 2 ] (4)

[0093] F 23 N = [ ( v e ) 2 (sec L ) 2 / （ R 2 + h ) − 2 ∗ ω iE N v e cos L 0 ( v e ) 2 (tan L ) 2 / （ R 2 + h ) 2 − v n v d / （ R 2 + h ) 2 v n v e (sec L ) 2 / （ R 1 + h ) + 2 ∗ ω iE N v n cos L 0 -( v n v e tan L + v e v d ) / （ R 1 + h ) 2 2 ∗ ω iE N v e sin L 0 ( v e ) 2 / （ R 2 + h ) 2 + ( v n ) 2 / （ R 1 + h ) 2 ] (5)

[0094] F 32 N = [ 1 / （ R 1 + h ） 0 0 0 sec L / （ R 2 + h ） 0 0 0 − 1 ] (6)

[0095] F 33 N = [ 0 0 v n / ( R 1 + h ) 2 v e ⋅ tan L sec L / ( R 2 + h ) 0 − v e sec L / ( R 2 + h ) 2 0 0 0 ] (7)

[0096] In the formula: [ • Λ ] represents the skew-symmetric matrix obtained by performing a skew-symmetric transformation on ; is a 3×3 zero matrix; is the angular rate of rotation of the navigation coordinate system of the positioning carrier relative to the inertial coordinate system; is the acceleration vector of the positioning carrier in the navigation coordinate system; is the angular velocity of the Earth's rotation; is the angular rate of rotation of the navigation coordinate system relative to the Earth-centered Earth-fixed coordinate system; L is the latitude of the location of the positioning carrier; and are respectively the radius of curvature of the meridian and the radius of curvature of the prime vertical at the location of the positioning carrier; is the eastward velocity of the positioning carrier, is the northward velocity of the positioning carrier, is the vertical velocity of the positioning carrier, and h is the altitude.

[0097] Step 3: Establish the extended Kalman filter system model of the integrated positioning module:

[0098] Establish the prediction model of the first integrated positioning module composed of the Iridium constellation and MEMS-INS as:

[0099] (8)

[0100] Establish the prediction model of the second integrated positioning module composed of the Orbcomm constellation and MEMS-INS as:

[0101] (9)

[0102] Where is the system error of the first integrated positioning module predicted using at the moment of , is the system error of the first integrated positioning module at the moment of is the system error of the first integrated positioning module predicted using at the moment of The systematic error of the second combined positioning module at a moment is the systematic error of the second combined positioning module at a moment;

[0103] Without considering a specific moment, the systematic error of the first combined positioning module δ x IRI = [ δ x INS T δ t f 1 T ] T , the systematic error of the second combined positioning module δ x ORB = [ δ x INS T δ t f 2 T ] T , is the transpose matrix of, is the frequency difference error between the Iridium constellation system and the user receiver, is the frequency difference error between the Orbcomm constellation system and the user receiver, is the transpose matrix of; is the transpose matrix of;

[0104] is from moment to moment, the prediction matrix of the first combined positioning module:

[0105] ϕ 1 ( k + 1 , k ) = [ ϕ INS ( k + 1 , k ) 0 8 , 1 0 1 , 8 ϕ IRI ( k + 1 , k ) ] (10)

[0106] is from moment to moment, the prediction matrix of the second combined positioning module:

[0107] ϕ 2 ( k + 1 , k ) = [ ϕ INS ( k + 1 , k ) 0 8 , 1 0 1 , 8 ϕ ORB ( k + 1 , k ) ] (11)

[0108] Wherein is from moment to moment, the prediction matrix of the Iridium constellation opportunity signal error, is from moment to moment, the prediction matrix of the Orbcomm constellation opportunity signal error; In the prediction process of the present invention, it is considered that at moment, the satellite frequency differences of the Iridium constellation and the Orbcomm constellation are the same as those at moment k, then and are:

[0109] (12)

[0110] In the formula is 1.

[0111] Step 4: Establish the observation model of the combined positioning module extended Kalman filter:

[0112] The system observation update process is a process of updating the current predicted state quantity according to the observation model to obtain the optimal estimate of the state quantity. The specific derivation process of the observation model of the low-earth orbit satellite opportunity signal and the MEMS-INS combined positioning system is as follows.

[0113] For each combined positioning module, establish the pseudo-range positioning linear navigation state update equation as:

[0114] (13)

[0115] In the formula , where is the prior pseudo-range measurement deviation, z is the measured pseudo-range vector, is the predicted pseudo-range vector; is the pseudo-range measurement noise vector; is the user receiver state deviation vector, δ x p = [ δ p X δ p Y δ p Z δ t ru ] , where , , are the components of the user receiver position error on the X, Y, and Z axes in the earth-centered earth-fixed coordinate system, is the user receiver clock error; A is the Jacobian matrix of pseudo-range positioning in the northeast-up coordinate system, and its expression is:

[0116] A = [ ( e 1 ) T 1 ( e 2 ) T 1 ⋮ ⋮ ( e m ) T 1 ] ⋅ C enu ecef = [ − e 1 X − e 1 Y − e 1 Z 1 − e 2 X − e 2 Y − e 2 Z 1 ⋮ ⋮ ⋮ ⋮ − e m X − e m Y − e m Z 1 ] ⋅ C enu ecef (14)

[0117] In the formula e m = [ e m X e m Y e m Z ] T are the components of the unit observation vector of the mth satellite at the user receiver on the X, Y, and Z axes in the earth-centered earth-fixed coordinate system; is the transformation matrix from the northeast-up coordinate system to the earth-centered earth-fixed coordinate system, and its expression form is:

[0118] C enu ecef = [ − sin L − cos L sin λ cos L cos λ cos L − sin λ sin L cos λ sin L 0 cos λ sin λ ] (15)

[0119] In the formula is the longitude of the location where the positioning carrier is located;

[0120] Derive formula (13) to get:

[0121] (16)

[0122] In the formula is the derivative of the pseudo-range measurement noise vector; After expanding formula (14) and ignoring the user receiver height channel, the Doppler positioning observation matrix is obtained as:

[0123] (17)

[0124] In the formula: is the transpose matrix of; the velocity vector of the m-th satellite relative to the positioning carrier; the geometric distance between the positioning carrier and the m-th satellite; denotes taking the first 2 columns of; Then the extended Kalman filter observation model of the combined positioning module is obtained as:

[0125] (18)

[0126] In the formula: , where is the Doppler deviation obtained through the Iridium constellation or the Orbcomm constellation, and c is the speed of light; is the carrier frequency of the Iridium constellation or the Orbcomm constellation.

[0127] Step 5: Based on the combined positioning module extended Kalman filter system model established in Step 3 and the combined positioning module extended Kalman filter observation model established in Step 4, set the initial system noise covariance matrix Q and the observation noise covariance matrix R, and obtain the positioning carrier state at time , and the posterior covariance matrix , , where i is both the combined positioning module number and the sub-filter number; the first sub-filter corresponds to the Iridium filter, and the second sub-filter corresponds to the Orbcomm filter.

[0128] The flow formula of the extended Kalman filter algorithm therein is:

[0129] (19)

[0130] (20)

[0131] (21)

[0132] (22)

[0133] (23)

[0134] (24)

[0135] (25)

[0136] Among them is obtained by feedback in step 6 Time to locate the carrier fusion state , is to use predicted Time to locate the carrier state, is obtained by feedback in step 6 Time to locate the carrier fusion state , is to use predicted Time to locate the carrier state; is obtained by feedback in step 6 Time covariance matrix of the state of the i-th combined positioning module, is Time noise covariance matrix of the i-th combined positioning module, is Time prior covariance matrix of the state of the i-th combined positioning module; is Time Kalman gain of the i-th combined positioning module, is Time Doppler positioning observation matrix of the i-th combined positioning module, is The transpose matrix of, is Time observation noise covariance matrix of the i-th combined positioning module; is Time positioning carrier state obtained by the first combined positioning module, is Time positioning carrier state obtained by the second combined positioning module, is Time actual measurement value of the i-th combined positioning module; is Time posterior covariance matrix of the state of the i-th combined positioning module, is the identity matrix.

[0137] Step 6: Based on the , and obtained in step 5, according to the fusion formula

[0138] (26)

[0139] Calculate to obtain Time positioning carrier fusion state and feedback, where

[0140] (27)

[0141] and according to the formula

[0142] (28)

[0143] calculate to obtain the state covariance matrix of the i-th combined positioning module at the moment and feedback, where is the filter weight obtained by the variable ratio adaptive method:

[0144] (29)

[0145] where is the information weight of the MEMS-INS sensor, is the information weight of the Iridium antenna, is the information weight of the Orbcomm antenna; correspondingly, represents the weight 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.

[0146] Finally, when the obtained and the difference is less than the preset threshold then it is considered that the current and are the optimal state estimates of the positioning carrier and the optimal state covariance .

[0147] For a certain sensor, the process of obtaining its autoregressive prediction error is as follows:

[0148] Assume that the output value of the sensor at time k The N-order autoregressive (AR) model is given by the following formula:

[0149] (30)

[0150] In the formula: N is the order, and the model error is Gaussian white noise with zero mean and variance ​is the i-th coefficient. Correspondingly, an autoregressive model of order N-1 can also be given.

[0151] An autocorrelation function matrix of can be given as: is:

[0152] R N + 1 = [ r ^ x ( 0 ) r ^ x ( 1 ) r ^ x ( 2 ) ⋯ r ^ x ( N ) r ^ x ( 1 ) r ^ x ( 0 ) r ^ x ( 2 ) ⋯ r ^ x ( N − 1 ) r ^ x ( 2 ) r ^ x ( 1 ) r ^ x ( 0 ) ⋯ r ^ x ( N − 2 ) ⋮ ⋮ ⋮ ⋮ ⋮ r ^ x ( N ) r ^ x ( N − 1 ) r ^ x ( N − 2 ) ⋯ r ^ x ( 0 ) ] (31)

[0153] Let be the estimate of the i-th coefficient in the autoregressive model of order N, and the minimum error power of the autoregressive model of order N ; According to the Levinson-Durbin recursion algorithm, the estimate of the coefficients of the autoregressive model of order N is:

[0154] (32)

[0155] q ^ N =− [ ∑ i = 1 N − 1 φ ^ N − 1 ( i ) r ^ x ( N − i ) + r ^ x ( N ) ] / ρ ^ N f (33)

[0156] where is the estimate of the i-th coefficient in the autoregressive model of order N-1.

[0157] Thus, the autoregressive prediction value of the sensor is

[0158] (34)

[0159] Then the autoregressive prediction error is . Since the autoregressive model is an integrated model in a stationary space, its prediction error can describe the smoothness of the sensor output. Therefore, the autoregressive prediction error of the sensor is used as the information weight. The smaller the prediction error, the smoother the sensor output and the smaller the information weight.

[0160] The measured data shows that the method for combining low-orbit satellite opportunity signals and MEMS-INS proposed in the present invention improves the positioning accuracy of LEO opportunity signals. Experimental verification shows that the positioning accuracy is better than 150 m, which is nearly 20% higher than the current research level.

[0161] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention without departing from the principles and purposes of the present invention.

Claims

1. A low-orbit satellite opportunity signal and MEMS-INS combined positioning method, characterized in that: The following steps are involved: Step 1: Obtain the data of each sensor of the combined positioning system; The combined positioning system includes a low-precision micro-electromechanical inertial navigation system MEMS-INS, a first LEO constellation and a second LEO constellation; Step 2: Establish the error equation of the MEMS-INS sensor: Where: To use Predicted MEMS-INS sensor system error at each moment; for The MEMS-INS sensor system error at the moment, For Time has come The MEMS-INS sensor system error prediction matrix at the moment; is the process noise vector; Step 3: Establish the combined positioning module and extend the Kalman filter system model: The prediction model of the first combined positioning module consisting of the first LEO constellation and MEMS-INS is established as: The prediction model of the second combined positioning module composed of the second LEO constellation and MEMS-INS is established as: in To use Predicted The system error of the first combined positioning module at time, for The system error of the first combined positioning module at time, To use Predicted The system error of the second combined positioning module at the moment, for System error of the second combined positioning module at the moment; For Time has come The first combined positioning module prediction matrix at time, For Time has come The second combined positioning module prediction matrix at the moment; Step 4: Establish the combined positioning module extended Kalman filter observation model: For a certain combined positioning module, its extended Kalman filter observation model is: in , is the Doppler deviation obtained by the LEO constellation in the combined positioning module, c is the speed of light, is the carrier frequency of the LEO constellation in the combined positioning module; is the Doppler positioning observation matrix of the combined positioning module, is the state deviation vector of the LEO constellation user receiver in the combined positioning module, is the pseudorange measurement noise vector, is the derivative of the pseudorange measurement noise vector; Step 5: Based on the combined positioning module extended Kalman filter system model established in step 3 and the combined positioning module extended Kalman filter observation model established in step 4, the extended Kalman filter algorithm is used to obtain Positioning carrier status at all times , and the posterior covariance matrix , ; The extended Kalman filter algorithm flow formula is: in is obtained through step 6 feedback Always locate carrier fusion status , To use Predicted Always locate the carrier status, is obtained through step 6 feedback Always locate carrier fusion status , To use Predicted Locate the carrier status at all times; is obtained through step 6 feedback The state covariance matrix of the i-th combined positioning module at time, for The noise covariance matrix of the i-th combined positioning module at time, for The prior covariance matrix of the state of the i-th combined positioning module at the moment; for The Kalman gain of the i-th combined positioning module at time, for The Doppler positioning observation matrix of the i-th combined positioning module at time, for The transposed matrix of for The observation noise covariance matrix of the i-th combined positioning module at time; for The positioning carrier state obtained by the first combined positioning module at the moment, for The positioning carrier state obtained by the second combined positioning module at the moment, for The actual measurement value of the i-th combined positioning module at the moment; for The posterior covariance matrix of the state of the i-th combined positioning module at time, is the identity matrix; Step 6: Based on the results from step 5 , as well as , according to the fusion formula Calculated Positioning carrier fusion status at the moment And feedback, including And according to the formula Calculated The state covariance matrix of the i-th combined positioning module at time And feedback, including To obtain the filter weights by variable scale adaptive method: in is the information weight of the MEMS-INS sensor, is the information weight of the first LEO constellation antenna, is the information weight of the second LEO constellation antenna; for each sensor, the autoregressive prediction error of the sensor is used as the information weight; When obtained and The difference is less than the preset threshold At this time, it is believed that and The optimal state estimate for the positioning carrier and the optimal state covariance .

2. According to claim 1, a low-orbit satellite opportunity signal and MEMS-INS combined positioning method is characterized by: The first LEO constellation uses the Iridium constellation, and the second LEO constellation uses the Orbcomm constellation.

3. A low-orbit satellite opportunity signal and MEMS-INS combined positioning method according to claim 1 or 2, characterized in that: The MEMS-INS sensor is used as the main sensor, and the first LEO constellation antenna and the second LEO constellation antenna are used as sub-sensors; The speed, position and attitude of the positioning carrier in the north-eastern coordinate system are obtained by the MEMS-INS sensor, and the position in the north-eastern coordinate system is converted into longitude, latitude and altitude. Meanwhile, the Doppler observation of the positioning carrier is obtained by the first LEO constellation antenna and the second LEO constellation antenna; The MEMS-INS filter is used as a main filter to update the speed, position and attitude data obtained by the MEMS-INS sensor, and the first LEO constellation filter and the second LEO constellation filter are used as sub-filters to assist in updating the speed, position and attitude data obtained by the MEMS-INS sensor.

4. According to claim 1, a low-orbit satellite opportunity signal and MEMS-INS combined positioning method is characterized by: The MEMS-INS sensor system error at a specific time is not considered The expression is: in , , They are the attitude errors of the positioning carrier in the north, east and ground directions in the north-east ground coordinate system, respectively. , , They are the velocity errors of the positioning carrier in the north, east and ground directions in the north-east ground coordinate system, respectively. , and They are respectively the errors of longitude, latitude and altitude of the positioning carrier in the longitude and latitude coordinate system.

5. According to claim 1, a low-orbit satellite opportunity signal and MEMS-INS combined positioning method is characterized by: from Time has come The MEMS-INS sensor system error prediction matrix at time The expression is: in is a 9-row 9-column identity matrix, T is the sampling interval, , , , as well as is the intermediate matrix, and the expression is Where: Express The antisymmetric matrix obtained by performing an antisymmetric transformation; is a zero matrix with 3 rows and 3 columns; The rotation angular rate of the navigation coordinate system of the positioning carrier relative to the inertial coordinate system; is the acceleration vector of the positioning carrier in the navigation coordinate system; is the angular velocity of the Earth's rotation; is the rotation angular rate of the navigation coordinate system relative to the Earth-fixed coordinate system; L is the latitude of the location of the positioning carrier; and They are respectively the meridian circle curvature radius and the meridian circle curvature radius at the location of the positioning carrier; To locate the eastward velocity of the carrier, To locate the north velocity of the carrier, is the ground velocity of the positioning carrier, and h is the height.

6. According to claim 4, a low-orbit satellite opportunity signal and MEMS-INS combined positioning method is characterized by: Without considering the specific time, the system error of the first combined positioning module , the second combined positioning module system error , for The transposed matrix of is the frequency difference error between the first LEO constellation system and the user receiver, is the frequency difference between the second LEO constellation system and the user receiver, for The transposed matrix of for The transposed matrix of .

7. According to claim 1, a low-orbit satellite opportunity signal and MEMS-INS combined positioning method is characterized by: For Time has come The prediction matrix of the first combined positioning module at time: For Time has come The prediction matrix of the second combined positioning module at time: in For Time has come The first LEO constellation opportunity signal error prediction matrix at time, For Time has come The second LEO constellation opportunity signal error prediction matrix at time t 8. According to claim 7, a low-orbit satellite opportunity signal and MEMS-INS combined positioning method is characterized by: In the prediction process, it is considered At time k, the satellite frequency difference between the first LEO constellation and the second LEO constellation is the same as at time k, then .

9. According to claim 1, a low-orbit satellite opportunity signal and MEMS-INS combined positioning method is characterized by: User receiver state deviation vector ,in , , They are respectively the components of the user receiver position error in the X, Y, and Z axes in the Earth-centered Earth-fixed coordinate system, is the user receiver clock error.

10. The method for combining low-orbit satellite opportunity signals and MEMS-INS positioning according to claim 1, characterized in that: Doppler positioning observation matrix In the formula is the X, Y, and Z components of the unit observation vector of the mth satellite of the LEO constellation in the combined positioning module at the user receiver in the Earth-centered Earth-fixed coordinate system, for The transposed matrix of is the transformation matrix from the northeast celestial coordinate system to the Earth-centered Earth-fixed coordinate system; is the velocity vector of the mth satellite relative to the positioning carrier; is the geometric distance between the positioning carrier and the mth satellite; Indicates taking The first 2 columns.

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