Low-orbit satellite opportunity signal and MEMS-INS combined positioning method

Abstract

The invention provides a low earth orbit satellite opportunity signal and MEMS-INS combined positioning method, which comprises the following steps: extracting Doppler observation information of multiple low earth orbit satellite constellation opportunity signals, then realizing effective combination of multiple low earth orbit satellites and MEMS-INS through an extended Kalman filtering algorithm, and simultaneously obtaining information weights of all sensors; the information weight is calculated from forward data of each sensor through time sequence analysis, and after the weight of the filter is calculated according to the information weight, the proportion of the extended Kalman filtering can be adjusted according to the state of the sensor and the effectiveness of navigation information, so that divergence of MEMS-INS errors is inhibited, and the reliability of the MEMS-INS system is improved. Meanwhile, the influence of insufficient parameter priori knowledge is reduced, good performance is achieved in the aspects of dispersity, real-time performance, precision, reliability, fault tolerance and the like, and the positioning performance is improved.

Description

Technical Field

[0001] The present invention relates to the field of combined positioning technology, and in particular to a low-orbit satellite opportunity signal and MEMS-INS combined positioning method. Background Art

[0002] With the growing demand for location services, the global satellite navigation system (GNSS) has developed rapidly and is the main means of outdoor positioning. However, its shortcomings are gradually exposed. At present, the mainstream combined navigation positioning uses the combined navigation positioning method of GNSS / INS, but the GNSS signal power is low and is easily affected by various unintentional or intentional interferences, which reduces the system performance or even makes it fail. Therefore, replacing GNSS signals with opportunity signals, using opportunity signals for positioning in outdoor scenes, getting rid of dependence on GNSS, and improving the accuracy of positioning and navigation in complex scenes have become a new research hotspot for complex scene positioning.

[0003] Opportunity signals are mainly divided into land-based opportunity signals and space-based opportunity signals: land-based opportunity signals mainly include radiation signals such as mobile communication networks, local wireless networks, digital television, etc., which are mainly concentrated in densely populated urban areas. It is difficult to achieve navigation and positioning in sparsely populated areas such as islands, mountainous areas and deserts; compared with land-based opportunity signals, space-based opportunity signals have the advantages of wide coverage and wide frequency band.

[0004] Low Earth Orbit (LEO) satellites are a typical source of space-based opportunity signal radiation. LEO constellations are mainly global mobile communication satellite systems. Currently, LEO constellations such as Iridium, Orbcomm and Globalstar are operating well in orbit. The US Space Exploration Technology Company plans to launch a Starlink system with a total number of tens of thousands of satellites (currently more than 2,000 have been launched). my country is also planning to develop a LEO giant constellation system, which will provide a rich source of radiation for future LEO opportunity signal positioning. However, positioning using a single LEO constellation 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 the fusion of multi-source opportunity signals of LEO constellation satellites with INS inertial navigation data for combined positioning and navigation. For example, the Chinese patent application with publication number CN118857279A, "High-precision navigation method based on fusion of multi-source opportunity signals of LEO constellation satellites", obtains the user's position information and speed information through inertial navigation, and then calculates the Doppler frequency calculation value of the downlink opportunity signal of the low-orbit satellite and the calculated value of the direction unit vector of the low-orbit satellite; the difference between the calculated value and the observed value of the Doppler frequency and the direction unit vector of the low-orbit satellite is used as the navigation observation; finally, the high-precision user navigation information prediction and update is achieved based on Kalman filtering. Since this method uses the user position information and speed information obtained by inertial navigation as the reference value to calculate the Doppler frequency of the downlink opportunity signal of the low-orbit satellite and the direction unit vector of the low-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 equipment, this method cannot achieve accurate positioning and navigation purposes. Summary of the invention

[0006] In response to the problems existing in the existing technology and based on the cost considerations in actual engineering applications, the applicant proposed a positioning method that combines low-orbit satellite opportunity signals with a low-precision micro-electromechanical inertial navigation system (MEMS-INS), which can improve the positioning accuracy of positioning carriers equipped with only medium- and low-precision, low-cost inertial navigation equipment.

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

[0008] A low-orbit satellite opportunity signal and MEMS-INS combined positioning method, comprising the following steps:

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

[0010] The combined positioning system includes a low-precision micro-electromechanical 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:

[0012]

[0013] 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;

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

[0015] The prediction model of the first combined positioning module consisting of the first LEO constellation and MEMS-INS is established as:

[0016]

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

[0018]

[0019] 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;

[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] 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;

[0024] 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 , ;

[0025] The extended Kalman filter algorithm flow formula is:

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] 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;

[0034] Step 6: Based on the results from step 5 , as well as , according to the fusion formula

[0035]

[0036] Calculated Positioning carrier fusion status at the moment And feedback, including

[0037]

[0038] And according to the formula

[0039]

[0040] 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:

[0041]

[0042] 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;

[0043] 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 .

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

[0045] Further, the MEMS-INS sensor is used as a 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-east earth coordinate system are obtained by the MEMS-INS sensor, and the position in the north-east earth coordinate system is converted into longitude, latitude and altitude, and the Doppler observation quantity of the positioning carrier is obtained by the first LEO constellation antenna and the second LEO constellation antenna;

[0046] 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.

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

[0048] d x INS = [ df n df e df d d v n d v e d v d d L b dl b d h b ] T

[0049] 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.

[0050] Further, from Time has come The MEMS-INS sensor system error prediction matrix at time The expression is:

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

[0052] 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

[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 = [ oh iE N sin L 0 v e / （ R 2 + h ) 2 0 0 - v n / （ R 2 + h ) 2 oh 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 ∗ oh 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 ∗ oh iE N v n cos L 0 -( v n v e tan L + v e v d ) / （ R 1 + h ) 2 2 ∗ oh 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 seconds L / （ R 2 + h ） 0 0 0 − 1 ]

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

[0058] Where: [ • L ] Express The antisymmetric matrix obtained by 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.

[0059] Furthermore, without considering the specific time, the system error of the first combined positioning module d x IRI = [ d x INS T d t f 1 T ] T , the second combined positioning module system error d x ORB = [ d x INS T d t f 2 T ] T , 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 .

[0060] Furthermore, For Time has come The prediction matrix of the first combined positioning module at time:

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

[0062] For Time has come The prediction matrix of the second combined positioning module at time:

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

[0064] 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

[0065] Furthermore, in the prediction process, 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 .

[0066] Furthermore, the user receiver state deviation vector d x p = [ d p X d p Y d p Z d t ru ] ,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.

[0067] Furthermore, the Doppler positioning observation matrix

[0068]

[0069] In the formula e m = [ e m X e m Y e m Z ] T 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.

[0070] Beneficial effects:

[0071] The low-orbit satellite opportunity signal and MEMS-INS combined positioning method proposed in the present invention extracts Doppler observation information of opportunity signals of multiple low-orbit satellite constellations, and then realizes the effective combination of multiple low-orbit satellites and MEMS-INS through an extended Kalman filter algorithm, and obtains the information weight of each sensor at the same time. The information weight is calculated from the forward data of each sensor through time series analysis. After the weight of the filter is calculated according to the information weight, the proportion of the extended Kalman filter can be adjusted according to the state of the sensor and the validity of the navigation information, thereby suppressing the divergence of MEMS-INS errors and reducing the influence of insufficient prior knowledge of parameters. It has good performance in terms of dispersion, real-time, accuracy, reliability and fault tolerance, and realizes the improvement of positioning performance.

[0072] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0074] Figure 1 It is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0075] Embodiments of the present invention are described in detail below. The embodiments are exemplary and intended to be used to explain the present invention, but should not be construed as limiting the present invention.

[0076] This embodiment proposes a combined positioning method of low-orbit satellite opportunity signals and MEMS-INS, and uses the AR-FKF (autoregressive-federated Kalman filter) algorithm to achieve the combined positioning function of low-orbit satellite opportunity signals and MEMS-INS. The principle is to extract the Doppler observation information of multiple low-orbit satellite opportunity signals, and then use the FKF algorithm to achieve the effective combination of multiple low-orbit satellites and MEMS-INS, and at the same time obtain the information weight of each sensor. The weight of the information can be calculated from the forward data of the navigation sensor through time series analysis. After calculating the weight of the filter according to the weight of the information, the proportion of FKF can be adjusted according to the state of the sensor and the effectiveness of the navigation information, thereby suppressing the divergence of MEMS-INS errors and reducing the influence of insufficient prior knowledge of parameters. It has good performance in terms of dispersion, real-time, accuracy, reliability and fault tolerance, and achieves improved positioning performance.

[0077] The specific steps include:

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

[0079] The combined positioning system adopted in this embodiment includes a low-precision micro-electromechanical 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] The MEMS-INS sensor is the main sensor, and the Iridium antenna and the Orbcomm antenna are sub-sensors. The MEMS-INS sensor is used to obtain the speed, position and attitude of the target to be located (positioning carrier) in the north-east coordinate system, and the position in the north-east coordinate system is converted into longitude, latitude and altitude. At the same time, the Doppler observation of the positioning carrier is obtained through the Iridium antenna and the Orbcomm antenna.

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

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

[0083] (1)

[0084] Where: To use Predicted MEMS-INS sensor system error at each moment; for The MEMS-INS sensor system error at each moment, including position error, velocity error and attitude error; For Time has come The MEMS-INS sensor system error prediction matrix at the moment; is the process noise vector;

[0085] The MEMS-INS sensor system error at a specific time is not considered The expression is:

[0086] d x INS = [ df n df e df d d v n d v e d v d d L b dl b d h b ] T

[0087] 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;

[0088] from Time has come The MEMS-INS sensor system error prediction matrix at time The expression is:

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

[0090] 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

[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 = [ oh iE N sin L 0 v e / （ R 2 + h ) 2 0 0 - v n / （ R 2 + h ) 2 oh 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 ∗ oh 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 ∗ oh iE N v n cos L 0 -( v n v e tan L + v e v d ) / （ R 1 + h ) 2 2 ∗ oh 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 seconds 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 seconds L / ( R 2 + h ) 0 − v e seconds L / ( R 2 + h ) 2 0 0 0 ] (7)

[0096] Where: [ • L ] Express The antisymmetric matrix obtained by 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.

[0097] Step 3: Establish the combined positioning module and extend the Kalman filter system model:

[0098] The prediction model of the first combined positioning module consisting of the Iridium constellation and MEMS-INS is established as follows:

[0099] (8)

[0100] The prediction model of the second combined positioning module composed of Orbcomm constellation and MEMS-INS is established as:

[0101] (9)

[0102] 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;

[0103] Without considering the specific time, the system error of the first combined positioning module d x IRI = [ d x INS T d t f 1 T ] T , the second combined positioning module system error d x ORB = [ d x INS T d t f 2 T ] T , for The transposed matrix of is the frequency difference between the Iridium constellation system and the user receiver, is the frequency difference between the Orbcomm constellation system and the user receiver, for The transposed matrix of for The transposed matrix of

[0104] For Time has come The prediction matrix of the first combined positioning module at time:

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

[0106] For Time has come The prediction matrix of the second combined positioning module at time:

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

[0108] in For Time has come The Iridium constellation opportunity signal error prediction matrix at time, For Time has come The Orbcomm constellation opportunity signal error prediction matrix at the moment; the present invention considers in the prediction process At time k, the satellite frequency difference of the Iridium constellation and the Orbcomm constellation is the same as that at time k, then and for:

[0109] (12)

[0110] In the formula is 1.

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

[0112] The system observation update process is the 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-orbit satellite opportunity signal and MEMS-INS combined positioning system is as follows.

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

[0114] (13)

[0115] In the formula ,in is the prior pseudorange measurement deviation, z is the measured pseudorange vector, is the predicted pseudorange vector; is the pseudorange measurement noise vector; is the user receiver state deviation vector, d x p = [ d p X d p Y d p Z d t ru ] ,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; A is the Jacobian matrix of pseudorange positioning in the northeast sky 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 is the X, Y, and Z components of the unit observation vector of the mth satellite at the user receiver in the Earth-centered Earth-fixed coordinate system; is the transformation matrix from the northeast celestial coordinate system to the earth-centered earth-fixed coordinate system, and its expression is:

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

[0119] In the formula The longitude of the location of the positioning carrier;

[0120] Derivation of formula (13) yields:

[0121] (16)

[0122] In the formula is the derivative of the pseudorange measurement noise vector; after expanding equation (14) and ignoring the user receiver height channel, the Doppler positioning observation matrix is ​​obtained as follows:

[0123] (17)

[0124] Where: for The transposed matrix of 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 two columns of the combined positioning module are:

[0125] (18)

[0126] Where: ,in is the Doppler deviation obtained through the Iridium constellation or the Orbcomm constellation, and c is the speed of light; It 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 extended Kalman filter algorithm Positioning carrier status at all times , and the posterior covariance matrix , , 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 extended Kalman filter algorithm flow formula is:

[0129] (19)

[0130] (20)

[0131] (twenty one)

[0132] (twenty two)

[0133] (twenty three)

[0134] (twenty four)

[0135] (25)

[0136] 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.

[0137] Step 6: Based on the results from step 5 , as well as , according to the fusion formula

[0138] (26)

[0139] Calculated Positioning carrier fusion status at the moment And feedback, including

[0140] (27)

[0141] And according to the formula

[0142] (28)

[0143] 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:

[0144] (29)

[0145] in 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.

[0146] Finally, when you get and The difference is less than the preset threshold , that is, at this time and The optimal state estimate for the positioning carrier and the optimal state covariance .

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

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

[0149] (30)

[0150] Where: N is the order, model error has a mean of zero and a variance of Gaussian white noise, is the i-th coefficient, and accordingly, an N-1 order autoregressive model can also be given.

[0151] Can give The autocorrelation function matrix for:

[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] set up is the estimate of the i-th coefficient in the N-order autoregressive model, and the minimum error power of the N-order autoregressive model ; According to the Levinson-Durbin recursive algorithm, the estimation of the coefficients of the N-order autoregressive model is:

[0154] (32)

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

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

[0157] The autoregressive prediction value of the sensor is obtained as

[0158] (34)

[0159] The autoregressive prediction error is Since the autoregressive model is a whole-area model built 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] Measured data show that the combined positioning method of 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 is to be understood that the above embodiments are exemplary and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and intent 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 the 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 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 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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