A multi-source fusion positioning method and system for the lunar south pole that integrates lunar orbit satellites, inertial navigation, and wireless communications

Abstract

The present invention provides a multi-source fusion positioning method and system for the lunar South Pole that integrates lunar orbit satellites, inertial navigation, and wireless communications. The method comprises constructing a multi-source fusion positioning measurement model using lunar orbit satellite pseudorange measurements and wireless communication time difference of arrival (TDOA) measurements, and calculating position information using the least squares method; using the system error of the INS system as the error state, and the difference between the position calculated by the INS system and the least squares method as the measurement error state; constructing a loosely coupled model based on the error state Kalman filter (ESKF) to calculate the error state and correct the INS's calculated position, and updating the current INS internal information to obtain the accurate position of the lunar rover. The present invention effectively solves the problems of limited coverage and low positioning accuracy caused by the insufficient number of lunar orbit satellites; reduces the impact of INS error accumulation on positioning accuracy, and ultimately obtains the precise position of the lunar rover; and significantly improves the overall positioning accuracy and reliability of the system.

Description

Technical Field

[0001] The present invention relates to the field of lunar positioning technology, and in particular to a multi-source fusion positioning method and system for the lunar south pole that integrates lunar orbit satellites, inertial navigation, and wireless communications. Background Art

[0002] The Moon's South Pole has long been a key area for lunar exploration due to its unique geographical location, its permanent sunlight, and the potential for abundant water ice reserves. However, the South Pole presents an extremely complex environment, with a steep and varied terrain dotted with craters and ridges. These factors pose significant challenges to the precise positioning of lunar rovers.

[0003] Traditional technologies primarily rely on ground-based measurement for lunar positioning. However, these methods require robust ground infrastructure, and their coverage is limited by the Earth's rotation and the distribution of ground stations, making real-time and continuous positioning difficult. Furthermore, the signal transmission distance from Earth to the Moon is long and can be affected by factors such as ionospheric interference and solar activity, reducing positioning accuracy.

[0004] With the continuous advancement of lunar exploration activities, multi-source fusion positioning technology has gradually been applied to lunar exploration missions. This technology utilizes information from multiple sources, including lunar-orbiting satellites, vision, lidar, inertial navigation systems (INS), ground beacons, and Earth-Moon radio communications, combined with the unique topographical and astronomical features of the lunar surface, to achieve high-precision integrated positioning. By integrating the advantages of different positioning sources, multi-source fusion positioning technology can improve positioning accuracy and reliability. In particular, the fusion positioning method of satellites and inertial navigation systems (INS) has been proven on Earth to significantly improve positioning accuracy and reliability. However, the unique lunar environment poses new challenges to existing positioning technologies.

[0005] First of all, the current number of lunar-orbit satellites is limited and insufficient to build a complete navigation and positioning system. As a result, the existing positioning methods that rely on lunar-orbit satellites are difficult to solve and have low positioning accuracy, making it impossible to provide the lunar rover with continuous, reliable, full-time high-precision positioning services.

[0006] Secondly, the complex environment at the lunar South Pole, with deep craters and ridges, can easily obstruct satellite signals. Furthermore, the lunar surface's microgravity and weak magnetic field can interfere with signals. These factors limit the effectiveness of existing positioning methods that rely on a single lunar orbiter or INS, making them ineffective in meeting the precise navigation needs of lunar rovers. Summary of the Invention

[0007] In response to the shortcomings of the existing technology, the present invention provides a multi-source fusion positioning method and system for the lunar South Pole that integrates lunar orbit satellites, inertial navigation and wireless communications. The present invention can effectively solve the problems of limited coverage and low positioning accuracy caused by the insufficient number of lunar orbit satellites, as well as the impact of error accumulation on positioning accuracy.

[0008] The technical solution of the present invention is: a multi-source fusion positioning method for the lunar south pole that integrates lunar orbit satellites, inertial navigation and wireless communication, comprising the following steps:

[0009] S1) Build a multi-source fusion positioning measurement model using lunar orbit satellite pseudo-range measurement values ​​and wireless communication arrival time difference TDOA measurement values, and calculate the position information using the least squares method;

[0010] S2), taking the system error of the INS system as the error state, and taking the difference between the position solved by the INS system and the position solved by the least square method as the measurement error state;

[0011] S3) Build a loosely coupled model based on the error state Kalman filter (ESKF) to solve the error state and correct the INS's solved position, and update the current INS internal information to obtain the accurate position of the lunar rover.

[0012] Preferably, in step S1), constructing a multi-source fusion positioning measurement model specifically includes the following steps:

[0013] S11), constructing a lunar orbit satellite pseudo-range single point positioning model; obtaining the coordinates of the lunar rover receiver through the lunar orbit satellite pseudo-range single point positioning model; its expression is:

[0014]

[0015] Where, ρ i,t represents the corrected pseudo-range measurement between the ith lunar orbiter and the lunar rover receiver; represents the geometric distance between the i-th lunar orbit satellite and the lunar rover receiver at time t; δt=c×Δt r,t ; c represents the speed of light; Δt r,t represents the lunar rover receiver clock error; Other noise in the measurement process;

[0016] S12) Establish a wireless communication TDOA positioning model, and calculate the coordinates of the lunar rover receiver through the wireless communication TDOA positioning model; the expression is:

[0017]

[0018] Where Δd m1,t represents the distance difference between the primary base station 1 and the mth base station at time t; represents the geometric distance between the mth base station and the lunar rover receiver; represents the geometric distance between the main base station 1 and the lunar rover receiver; ε m1,trepresents other noise measured during the communication between the mth base station and the main base station 1.

[0019] Preferably, in step S11), constructing a lunar orbit satellite pseudo-range single point positioning model specifically includes the following steps:

[0020] S111) Let the coordinates of each lunar orbit satellite at time t be (i=1,2,…,N)}, the lunar rover receiver coordinates are (x t ,y t ,z t ); For the i-th lunar orbit satellite, its pseudorange measurement value is:

[0021]

[0022] Where, ρ oi represents the pseudorange measurement value between the i-th lunar orbit satellite and the lunar rover receiver; represents the geometric distance between the i-th lunar orbit satellite and the lunar rover receiver; c represents the speed of light; Δt r,t represents the lunar rover receiver clock error; represents the clock error of the i-th lunar orbit satellite; I n is the ionospheric error of the nth lunar orbit satellite; O n is the tropospheric error of the nth satellite; represents other noise in the measurement process;

[0023] S112) Let δt = c × Δt r,t , and correct the pseudo-range measurement value to obtain the corrected pseudo-range measurement value ρ i,t ,Right now:

[0024]

[0025] S113) According to formula (2), when the number of visible satellites is N, the expression of the lunar orbit satellite pseudo-range single point positioning model is obtained as follows:

[0026]

[0027] Where, ρ i,t represents the corrected pseudo-range measurement between the ith lunar orbiter and the lunar rover receiver; represents the geometric distance between the i-th lunar orbit satellite and the lunar rover receiver at time t; δt=c×Δt r,t ; c represents the speed of light; Δt r,t represents the lunar rover receiver clock error; Other noise in the measurement process.

[0028] Preferably, in step S12), a wireless communication TDOA positioning model is established, specifically by the following steps:

[0029] S121) Assume that the coordinates of the wireless communication signal base station at time t are For any two base stations h and k, the time difference Δt between the lunar rover receiver and the two base stations after the signal is transmitted hk,t for:

[0030] Δt hk,t =t h,t -t k,t ; (4)

[0031] Where, t h,t , t k,t are the times when the signal transmitted by the lunar rover receiver reaches base stations h and k respectively;

[0032] S122), the time difference Δt hk,t Convert to distance difference Δd hk,t ,Right now:

[0033] Δd hk,t =c·Δt hk,t ; (5)

[0034] Where c represents the speed of light;

[0035] S123), assuming that the base stations are time synchronized, the distance difference Δd is calculated based on the geometric relationship. hk,t Expressed as:

[0036]

[0037] Where, represents the geometric distance between the hth base station and the lunar rover receiver; represents the geometric distance between the kth base station and the lunar rover receiver; ε hk,t represents other noise in the measurement process;

[0038] S124) Assume that the main reference base station is base station 1, and when the number of base stations is M, establish the wireless communication TDOA positioning model as follows:

[0039]

[0040] Where Δd m1,t represents the distance difference between the primary base station 1 and the mth base station at time t; represents the geometric distance between the mth base station and the lunar rover receiver; represents the geometric distance between the main base station 1 and the lunar rover receiver; ε m1,t represents other noise measured during the communication between the mth base station and the main base station 1.

[0041] Preferably, in step S1), calculating the position information of the lunar rover by the least squares method specifically includes the following steps:

[0042] S1-1) Convert the lunar orbit satellite pseudo-range single point positioning model and the wireless communication TDOA positioning model to the lunar center-moon fixed coordinate system, and then combine the measurement equations of the two to construct a joint positioning measurement equation group:

[0043]

[0044] S1-2) Use the least squares method to solve the joint positioning measurement equation group of formula (8) and calculate the position of the lunar rover As the final joint positioning result.

[0045] Preferably, in step S2), at time t, the system error of the INS system includes the attitude error φ t , velocity error δv t 、Position error δr t ; Their expressions are:

[0046] φ t =[φ E,t φ N,t φ U,t ] T ;

[0047] δv t =[δv E,t δv N,t δv U,t ] T ;

[0048] δr t =[δl t δλ t δh t ] T ;

[0049] Where, φ E,t φ N,t φ U,t Respectively represent the attitude errors in the east, north, and sky directions in the “East-North-Sky” (ENU) coordinate system; δv E,t δv N,t δv U,t Respectively represent the velocity errors in the east, north and sky directions in the ENU coordinate system; δl t , δλ t ,δh t They represent the latitude, longitude and altitude position errors respectively; T represents the transposition operation; δ represents the corresponding error.

[0050] Preferably, in step S2), the position coordinates calculated by the least squares method are first converted to the ENU coordinate system where the INS system is located, and then converted into the form of latitude, longitude and altitude, that is:

[0051]

[0052] Where, The position of the lunar rover calculated by the least squares method; represent the latitude, longitude, and altitude of the lunar rover position calculated by the least squares method;

[0053] Then, the difference between the position calculated by the INS system and the position calculated by the least square method is used as the measurement error state z t ,Right now:

[0054]

[0055] Where, The position of the lunar rover calculated by the INS system, The position of the lunar rover calculated by the least squares method.

[0056] Preferably, in step S3), the system error of the INS system is used as the error state to construct the ESKF state equation for fusion INS positioning:

[0057] x t =Fx t-1 +w t ; (9)

[0058] Where x t represents the error state; F represents the state transfer matrix of the system; w t represents the process noise vector of the system.

[0059] Preferably, in step S3), the error state vector x(t) of the system is expressed as:

[0060]

[0061] Where, δr t Indicates position error; δv t Indicates speed error; φ t represents the attitude error; ε t =[ε gx,t ε gy,t ε gz,t ] T Indicates the gyroscope drift error; Indicates the accelerometer bias error; ε gx,t , ε gy,t, ε gz,t Represents the gyroscope drift error in the x, y, and z directions respectively; They represent the accelerometer bias errors in the x, y, and z directions, respectively; T represents the transpose operation; and δ represents the corresponding error.

[0062] Preferably, in step S3), the ESKF measurement equation is obtained by subtracting the position calculated by the INS system from the position calculated by the least square method:

[0063]

[0064] Where z(t) represents the measurement error state; The lunar rover position calculated by the INS system,

[0065] is the position of the lunar rover calculated by the least squares method; H represents the measurement matrix of the system, v t represents the measurement noise vector of the system.

[0066] Preferably, in step S3), the loosely coupled model based on the error state Kalman filter ESKF is constructed, and its system equation is:

[0067]

[0068] Where: x t 、x t-1 Represent the error states at time t and t-1 respectively; F t represents the state transfer matrix of the system at time t; w t represents the process noise of the system at time t; z t Represents the measurement error state of the system at time t; H t represents the measurement matrix of the system at time t, v t represents the measurement noise of the system at time t.

[0069] Preferably, in step S3), the error state is solved using a loosely coupled model based on an error state Kalman filter (ESKF), including prediction and update stages; wherein:

[0070] Prediction stage:

[0071]

[0072]

[0073] in, is the posterior error state estimate at time t-1; F t represents the state transfer matrix of the system at time t; is the prior error state estimate at time t; P t-1 is the posterior error state estimate covariance matrix at time t-1; P t,t-1 is the prior error state estimate covariance matrix at time t, Q t represents the process noise covariance matrix; T represents the transpose operation;

[0074] Update phase:

[0075]

[0076]

[0077] P t =(IK t H t )P t,t-1 ; (16)

[0078] Where K t represents the Kalman gain at time t; H t represents the measurement matrix of the system at time t; R t represents the measurement noise covariance matrix; z t represents the measurement error state of the system at time t; represents the posterior error state estimate at time t; I represents the identity matrix.

[0079] Finally, the error state calculated by ESKF is obtained Using the position error in the error state Correct the INS's calculated position, then update the current INS internal information. The final corrected INS calculated position is used as the lunar rover's position:

[0080]

[0081] Where; represents the corrected lunar rover position; The lunar rover position solved by the INS system; It is the position error in the error state solved by ESKF.

[0082] The present invention also provides a lunar south pole multi-source fusion positioning system integrating lunar orbit satellites, inertial navigation and wireless communications, comprising:

[0083] A data acquisition module for receiving signals from a real lunar scene;

[0084] The multi-source fusion positioning measurement module is used to calculate the position of the lunar rover receiver based on the lunar orbit satellite pseudo-range single-point positioning model and the wireless communication TDOA positioning model;

[0085] The first solution module is used to solve the position of the lunar rover from the multi-source fusion positioning measurement module according to the least squares method.

[0086] The second solution module is used to calculate the lunar rover position using INS And the position of the lunar rover calculated by the first solution module The error state is calculated by difference calculation, and the error state at the current moment is obtained based on ESKF solution.

[0087] Correction module, used to adjust the error state Position error in The lunar rover position calculated by INS Make corrections.

[0088] Preferably, the data acquisition module includes a lunar orbit satellite signal receiver and a wireless communication signal receiver; the lunar orbit satellite signal receiver is used to receive signals from N lunar orbit satellites, which contain the position data of the lunar orbit satellites. and the calculated pseudorange measurement (ρ 1,t ,ρ 2,t ,…,ρ N,t );

[0089] The wireless communication signal receiver is used to receive signals from M base stations, including base station location data. and TDOA measurement values ​​(Δt 21,t ,Δt 31,t ,…,Δt M1,t ), the distance difference measurement value (Δd 21,t ,Δd 31,t ,…,Δd M1,t ).

[0090] Preferably, the expression of the lunar orbit satellite pseudorange single point positioning model is:

[0091]

[0092] Where, ρ i,t represents the corrected pseudorange measurement value between the ith lunar orbit satellite and the lunar rover receiver; represents the geometric distance between the i-th lunar orbit satellite and the lunar rover receiver at time t; δt=c×Δt r,t ; c represents the speed of light; Δt r,t represents the lunar rover receiver clock error; Other noise in the measurement process;

[0093] The wireless communication TDOA positioning model is expressed as:

[0094]

[0095] Where Δd m1,t represents the distance difference between the primary base station 1 and the mth base station at time t; represents the geometric distance between the mth base station and the lunar rover receiver; represents the geometric distance between the main base station 1 and the lunar rover receiver; ε m1,t represents other noise measured during the communication between the mth base station and the main base station 1.

[0096] Preferably, the second solution module first converts the position coordinates calculated by the least squares method into the ENU coordinate system where the INS system is located, and converts it into the form of latitude, longitude and altitude, that is:

[0097]

[0098] Where, The position of the lunar rover calculated by the least squares method; represent the latitude, longitude, and altitude of the lunar rover position calculated by the least squares method;

[0099] Then, the difference between the position calculated by the INS system and the position calculated by the least square method is used as the measurement error state z t ,Right now:

[0100]

[0101] Where, The position of the lunar rover calculated by the INS system, The position of the lunar rover calculated by the least squares method.

[0102] Preferably, the second solving module constructs the ESKF state equation for fusion INS positioning based on the system error of the INS system as the error state:

[0103] x t =Fx t-1 +w t ; (9)

[0104] Where x t represents the error state; F represents the state transfer matrix of the system; w t represents the process noise vector of the system.

[0105] The ESKF measurement equation is obtained by subtracting the position calculated by the INS system from the position calculated by the least square method:

[0106]

[0107] Where z(t) represents the measurement error state; The lunar rover position calculated by the INS system, is the position of the lunar rover calculated by the least squares method; H represents the measurement matrix of the system, v t represents the measurement noise vector of the system.

[0108] Then the loosely coupled model based on the error state Kalman filter ESKF is constructed, and its system equation is:

[0109]

[0110] Where: x t 、x t-1 Represent the error states at time t and t-1 respectively; F t represents the state transfer matrix of the system at time t; w t represents the process noise of the system at time t; z t Represents the measurement error state of the system at time t; H t represents the measurement matrix of the system at time t, v t represents the measurement noise of the system at time t.

[0111] Finally, the error state is solved using a loosely coupled model based on the error state Kalman filter (ESKF), including prediction and update stages.

[0112] Prediction stage:

[0113]

[0114]

[0115] in, is the posterior error state estimate at time t-1; F t represents the state transfer matrix of the system at time t; is the prior error state estimate at time t; P t-1 is the posterior error state estimate covariance matrix at time t-1; p t,t-1 is the prior error state estimate covariance matrix at time t, Q t represents the process noise covariance matrix; T represents the transpose operation;

[0116] Update phase:

[0117]

[0118]

[0119] p t =(IK t H t )P t,t-1 ; (16)

[0120] Where K t represents the Kalman gain at time t; H t represents the measurement matrix of the system at time t; R t represents the measurement noise covariance matrix; z t Represents the measurement error state of the system at time t; represents the posterior error state estimate at time t; I represents the identity matrix.

[0121] As an example, the correction module uses the error state calculated by ESKF Position error in Correct the INS's calculated position, then update the current INS internal information. The final corrected INS calculated position is used as the lunar rover's position:

[0122]

[0123] Where; represents the corrected lunar rover position; The lunar rover position solved by the INS system; It is the position error in the error state solved by ESKF.

[0124] The beneficial effects of the present invention are:

[0125] 1. The present invention effectively solves the problems of limited coverage and low positioning accuracy caused by the insufficient number of lunar orbit satellites by combining lunar orbit satellite positioning and wireless communication positioning;

[0126] 2. This invention further integrates the joint positioning results of lunar orbit satellites and wireless communications with the INS positioning results, uses the Error State Kalman Filter (ESKF) to correct the INS's calculated position, and then updates the current INS internal information, thereby effectively reducing the impact of INS error accumulation on positioning accuracy and ultimately obtaining the precise position of the lunar rover; significantly improving the overall positioning accuracy and reliability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0127] Figure 1 Schematic diagram of the framework of the method of the present invention. DETAILED DESCRIPTION

[0128] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings:

[0129] Example 1

[0130] like Figure 1 As shown, the present invention provides a multi-source fusion positioning method for the lunar south pole that integrates lunar orbit satellites, inertial navigation and wireless communication, including the following steps:

[0131] S1) Data collection

[0132] The lunar rover is equipped with a lunar orbit satellite signal receiver and a wireless communication signal receiver to receive signals from the real lunar scene, thereby obtaining positioning data. Assume that the position coordinates of the lunar rover at time t are r t =(x t ,y t ,z t ) T The lunar orbit satellite signal receiver can receive signals from N lunar orbit satellites, which contain the position data of the lunar orbit satellites. and the calculated pseudorange measurement (ρ 1,t ,ρ 2,t ,…,ρ N,t ).

[0133] The wireless communication signal receiver can receive signals from M base stations, including base station location data. and TDOA measurement values ​​(Δt 21,t ,Δt 31,t ,…,Δt M1,t ).

[0134] S2) Build a multi-source fusion positioning measurement model using lunar orbit satellite pseudo-range measurement values ​​and wireless communication arrival time difference TDOA measurement values, and calculate the position information using the least squares method;

[0135] The construction of a multi-source fusion positioning measurement model specifically includes the following steps:

[0136] S21) constructing a lunar orbit satellite pseudo-range single point positioning model; obtaining the coordinates of the lunar rover receiver through the lunar orbit satellite pseudo-range single point positioning model; specifically comprising the following steps:

[0137] S211) Let the coordinates of each lunar orbit satellite at time t be ,(i=1,2,…,N)}, the lunar rover receiver coordinates are (x t ,y t ,z t ); For the i-th lunar orbit satellite, its pseudorange measurement value is:

[0138]

[0139] Where, ρ oi represents the pseudorange measurement value between the i-th lunar orbit satellite and the lunar rover receiver; represents the geometric distance between the i-th lunar orbit satellite and the lunar rover receiver; c represents the speed of light; Δt r,t represents the lunar rover receiver clock error; represents the clock error of the i-th lunar orbit satellite; I n is the ionospheric error of the nth lunar orbit satellite; O n is the tropospheric error of the nth satellite; represents other noise in the measurement process;

[0140] S212) Let δt = c × Δt r,t , and correct the pseudo-range measurement value to obtain the corrected pseudo-range measurement value ρ i,t ,Right now:

[0141]

[0142] S213) According to formula (2), when the number of visible satellites is N, the expression of the lunar orbit satellite pseudo-range single point positioning model is obtained as follows:

[0143]

[0144] Where, ρ i,t represents the corrected pseudo-range measurement between the ith lunar orbiter and the lunar rover receiver; represents the geometric distance between the i-th lunar orbit satellite and the lunar rover receiver at time t; δt=c×Δt r,t ; c represents the speed of light; Δt r,t represents the lunar rover receiver clock error; Other noise in the measurement process.

[0145] S22) establishing a wireless communication TDOA positioning model, and calculating the coordinates of the lunar rover receiver using the wireless communication TDOA positioning model; specifically, the following steps:

[0146] S221) Assume that the coordinates of the wireless communication signal base station at time t are (h=1,2,…,M)}; For any two base stations h and k, the time difference Δt between the lunar rover receiver and the two base stations after the signal is transmitted hk,t for:

[0147]

[0148] Where, t h,t , t k,t are the times when the signal transmitted by the lunar rover receiver reaches base stations h and k respectively;

[0149] S222), the time difference Δt hk,t Convert to distance difference Δdhk,t ,Right now:

[0150]

[0151] Where c represents the speed of light;

[0152] S223), assuming that the base stations are time synchronized, the distance difference Δd is calculated based on the geometric relationship. hk,t Expressed as:

[0153]

[0154] Where, represents the geometric distance between the hth base station and the lunar rover receiver; represents the geometric distance between the kth base station and the lunar rover receiver; ε hk,t represents other noise in the measurement process;

[0155] S224) Assume that the main reference base station is base station 1, and when the number of base stations is M, establish the wireless communication TDOA positioning model as follows:

[0156]

[0157] Where Δd m1,t represents the distance difference between the primary base station 1 and the mth base station at time t; represents the geometric distance between the mth base station and the lunar rover receiver; represents the geometric distance between the main base station 1 and the lunar rover receiver; ε m1,t represents other noise measured during the communication between the mth base station and the main base station 1.

[0158] The position information is calculated using the least squares method, which specifically includes the following steps:

[0159] S2-1) Convert the lunar orbit satellite pseudo-range single point positioning model and the wireless communication TDOA positioning model to the lunar center-moon fixed coordinate system, and then combine the measurement equations of the two to construct a joint positioning measurement equation group:

[0160]

[0161] S2-2) Use the least squares method to solve the joint positioning measurement equations of formula (8) and calculate the position of the lunar rover As the final joint positioning result.

[0162] S3), taking the system error of the INS system as the error state, and taking the difference between the position solved by the INS system and the position solved by the least square method as the measurement error state;

[0163] In this embodiment, at time t, the system error of the INS system includes the attitude error φ t , velocity error δv t 、Position error δr t ; Their expressions are:

[0164] φ t =[φ E,t φ N,t φ U,t ] T ;

[0165] δv t =[δv E,t δv N,t δv U,t ] T ;

[0166] δr t =[δl t δλ t δh t ] T ;

[0167] Where, φ E,t φ N,t φ U,t Respectively represent the attitude errors in the east, north, and sky directions in the “East-North-Sky” (ENU) coordinate system; δv E,t δv N,t δv U,t Respectively represent the velocity errors in the east, north and sky directions in the ENU coordinate system; δl t , δλ t ,δh t Represent the latitude, longitude and altitude position errors respectively; T represents the transposition operation; δ represents the corresponding error. First, the position coordinates calculated by the least squares method are converted to the ENU coordinate system where the INS system is located, and then converted into the latitude, longitude and altitude form, that is:

[0168]

[0169] Where, The position of the lunar rover calculated by the least squares method; They represent the latitude, longitude, and altitude of the lunar rover position calculated by the least squares method;

[0170] Then, the difference between the position calculated by the INS system and the position calculated by the least square method is used as the measurement error state z t ,Right now:

[0171]

[0172] Where, The position of the lunar rover calculated by the INS system, The position of the lunar rover calculated by the least squares method.

[0173] S4) Build a loosely coupled model based on the error state Kalman filter (ESKF) to solve the error state and correct the INS's solved position, and update the current INS internal information to obtain the accurate position of the lunar rover.

[0174] First, the ESKF state equation for INS fusion positioning is constructed based on the system error of the INS system as the error state:

[0175] x t =Fx t-1 +w t ; (9)

[0176] Where x t represents the error state; F represents the state transfer matrix of the system; w t represents the process noise vector of the system.

[0177] Among them, the ESKF error state vector x of the system t The expression is:

[0178]

[0179] Where, δr t Indicates position error; δv t Indicates speed error; φ t represents the attitude error; ε t =[ε gx,t ε gy,t ε gz,t ] T Indicates the gyroscope drift error; Indicates the accelerometer bias error; ε gx,t , ε gy,t , ε gz,t Represents the gyroscope drift error in the x, y, and z directions respectively; They represent the accelerometer bias errors in the x, y, and z directions, respectively; T represents the transpose operation; and δ represents the corresponding error.

[0180] Then, the ESKF measurement equation is obtained by subtracting the position calculated by the INS system from the position calculated by the least square method:

[0181]

[0182] Where z(t) represents the measurement error state; The position of the lunar rover calculated by the INS system, is the position of the lunar rover calculated by the least squares method; H represents the measurement matrix of the system, v t represents the measurement noise vector of the system.

[0183] Finally, the loosely coupled model based on the error state Kalman filter ESKF is constructed, and its system equation is:

[0184]

[0185] Where: x t 、x t-1 Represent the error states at time t and t-1 respectively; F t represents the state transfer matrix of the system at time t; w t represents the process noise of the system at time t; z t Represents the measurement error state of the system at time t; H t represents the measurement matrix of the system at time t, v t represents the measurement noise of the system at time t.

[0186] In this embodiment, a loosely coupled model based on an error state Kalman filter (ESKF) is used to solve the error state, including prediction and update stages; wherein:

[0187] Prediction stage:

[0188]

[0189]

[0190] in, is the posterior error state estimate at time t-1; F t represents the state transfer matrix of the system at time t; is the prior error state estimate at time t; P t-1 is the posterior error state estimate covariance matrix at time t-1; P t,t-1 is the prior error state estimate covariance matrix at time t, Q t represents the process noise covariance matrix; T represents the transpose operation;

[0191] Update phase:

[0192]

[0193]

[0194] P t =(IK t H t )P t,t-1 ; (16)

[0195] Where K t represents the Kalman gain at time t; H t represents the measurement matrix of the system at time t; R t represents the measurement noise covariance matrix; z t Represents the measurement error state of the system at time t; represents the posterior error state estimate at time t; I represents the identity matrix.

[0196] Finally, the error state calculated by ESKF is obtained Using the position error in the error state Correct the INS's calculated position, then update the current INS internal information. The final corrected INS calculated position is used as the lunar rover's position:

[0197]

[0198] Where; represents the corrected lunar rover position; The lunar rover position solved by the INS system; It is the position error in the error state solved by ESKF.

[0199] Example 2

[0200] like Figure 1 As shown, this embodiment provides a lunar South Pole multi-source fusion positioning system that integrates lunar orbit satellites, inertial navigation, and wireless communications, including:

[0201] A data acquisition module for receiving signals from a real lunar scene;

[0202] In this embodiment, the data acquisition module includes a lunar orbit satellite signal receiver and a wireless communication signal receiver; the lunar orbit satellite signal receiver is used to receive signals from N lunar orbit satellites, which contain the position data of the lunar orbit satellites. and the calculated pseudorange measurements (with 1,t ,match 2,t ,…,match N,t );

[0203] The wireless communication signal receiver is used to receive signals from M base stations, including base station location data. and TDOA measurement values ​​(Δt 21,t ,Δt 31,t ,…,Δt M1,t ), the distance difference measurement value (Δd 21,t ,Δd 31,t ,…,Δd M1,t ).

[0204] The multi-source fusion positioning measurement module is used to calculate the position of the lunar rover receiver based on the lunar orbit satellite pseudo-range single-point positioning model and the wireless communication TDOA positioning model;

[0205] In this embodiment, the expression of the lunar orbit satellite pseudorange single point positioning model is:

[0206]

[0207] Where, ρ i,t represents the corrected pseudorange measurement value between the ith lunar orbit satellite and the lunar rover receiver; represents the geometric distance between the i-th lunar orbit satellite and the lunar rover receiver at time t; δt=c×Δt r,t ; c represents the speed of light; Δt r,t represents the lunar rover receiver clock error; Other noise in the measurement process;

[0208] The wireless communication TDOA positioning model is expressed as:

[0209]

[0210] Where Δd m1,t represents the distance difference between the primary base station 1 and the mth base station at time t; represents the geometric distance between the mth base station and the lunar rover receiver; represents the geometric distance between the main base station 1 and the lunar rover receiver; ε m1,t represents other noise measured during the communication between the mth base station and the main base station 1.

[0211] The first solution module is used to solve the position of the lunar rover from the multi-source fusion positioning measurement module according to the least squares method.

[0212] The second solution module is used to calculate the lunar rover position using INS And the position of the lunar rover calculated by the first solution module The error state is calculated by difference calculation, and the error state at the current moment is obtained based on ESKF solution.

[0213] The second solution module first converts the position coordinates calculated by the least squares method into the ENU coordinate system where the INS system is located, and then converts it into the form of latitude, longitude and altitude, that is:

[0214]

[0215] Where, The position of the lunar rover calculated by the least squares method; represent the latitude, longitude, and altitude of the lunar rover position calculated by the least squares method;

[0216] Then, the difference between the position calculated by the INS system and the position calculated by the least square method is used as the measurement error state z t ,Right now:

[0217]

[0218] Where, The position of the lunar rover calculated by the INS system, The position of the lunar rover calculated by the least squares method.

[0219] The second solution module constructs the ESKF state equation for fusion INS positioning based on the system error of the INS system as the error state:

[0220] x t =Fx t-1 +w t ; (9)

[0221] Where x t represents the error state; F represents the state transfer matrix of the system; w t represents the process noise vector of the system.

[0222] The ESKF measurement equation is obtained by subtracting the position calculated by the INS system from the position calculated by the least square method:

[0223]

[0224] Where z(t) represents the measurement error state; The position of the lunar rover calculated by the INS system,

[0225] is the position of the lunar rover calculated by the least squares method; H represents the measurement matrix of the system, v t represents the measurement noise vector of the system.

[0226] Then the loosely coupled model based on the error state Kalman filter ESKF is constructed, and its system equation is:

[0227]

[0228] Where: x t 、x t-1 Represent the error states at time t and t-1 respectively; F t represents the state transfer matrix of the system at time t; w trepresents the process noise of the system at time t; z t Represents the measurement error state of the system at time t; H t represents the measurement matrix of the system at time t, v t represents the measurement noise of the system at time t.

[0229] Finally, the error state is solved using a loosely coupled model based on the error state Kalman filter (ESKF), including prediction and update stages.

[0230] Prediction stage:

[0231]

[0232]

[0233] in, is the posterior error state estimate at time t-1; F t represents the state transfer matrix of the system at time t; is the prior error state estimate at time t; P t-1 is the posterior error state estimate covariance matrix at time t-1; p t,t-1 is the prior error state estimate covariance matrix at time t, Q t represents the process noise covariance matrix; T represents the transpose operation;

[0234] Update phase:

[0235]

[0236]

[0237] P t =(IK t H t )P t,t-1 ; (16)

[0238] Where K t represents the Kalman gain at time t; H t represents the measurement matrix of the system at time t; R t represents the measurement noise covariance matrix; z t represents the measurement error state of the system at time t; represents the posterior error state estimate at time t; I represents the identity matrix.

[0239] Correction module, used to adjust the error state The lunar rover position calculated by INS The correction module uses the error state calculated by ESKF Position error in Correct the INS's calculated position, then update the current INS internal information. The final corrected INS calculated position is used as the lunar rover's position:

[0240]

[0241] Where; represents the corrected lunar rover position; The lunar rover position solved by the INS system; It is the position error in the error state solved by ESKF.

[0242] As a preferred embodiment of the present invention, the system further includes an inertial measurement unit, which includes a gyroscope and an accelerometer. The drift error ε of the gyroscope is calculated by the inertial measurement unit. t =[ε gx,t ε gy,t ε gz,t ] T and the accelerometer bias error

[0243] The above embodiments and descriptions are only for explaining the principles and best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention may be subject to various changes and improvements, which shall fall within the scope of the invention to be protected.

Claims

1. A multi-source fusion positioning method for the lunar south pole that integrates lunar orbit satellites, inertial navigation and wireless communications, characterized in that: The steps include: S1) Build a multi-source fusion positioning measurement model using lunar orbit satellite pseudo-range measurement values ​​and wireless communication arrival time difference TDOA measurement values, and calculate the position information using the least squares method; specifically, the following steps: S11), constructing a lunar orbit satellite pseudo-range single point positioning model; obtaining the coordinates of the lunar rover receiver through the lunar orbit satellite pseudo-range single point positioning model; Its expression is: Where, ρ i,t represents the corrected pseudo-range measurement between the ith lunar orbiter and the lunar rover receiver; represents the geometric distance between the i-th lunar orbit satellite and the lunar rover receiver at time t; δt=c×Δt r,t ; c represents the speed of light; Δt r,t represents the lunar rover receiver clock error; Other noise in the measurement process; S12), establishing a wireless communication TDOA positioning model, and calculating the coordinates of the lunar rover receiver through the wireless communication TDOA positioning model; Its expression is: Where Δd m1,t represents the distance difference between the primary base station 1 and the mth base station at time t; represents the geometric distance between the mth base station and the lunar rover receiver; represents the geometric distance between the main base station 1 and the lunar rover receiver; ε m1,t represents other noise measured during the communication between the mth base station and the main base station 1; S2), taking the system error of the INS system as the error state, and taking the difference between the position solved by the INS system and the position solved by the least square method as the measurement error state; S3) Build a loosely coupled model based on the error state Kalman filter (ESKF) to solve the error state and correct the INS's solved position, and update the current INS internal information to obtain the accurate position of the lunar rover.

2. The multi-source fusion positioning method for the lunar south pole that integrates lunar orbit satellites, inertial navigation, and wireless communications according to claim 1 is characterized in that: In step S2), at time t, the system error of the INS system includes the attitude error φ t , velocity error δv t 、Position error δr t ; Their expressions are: f t =[φ E,t f N,t f U,t ] T ; δv t =[δv E,t δv N,t δv U,t ] T ; δr t =[δl t dl t dh t ] T ; Where, φ E,t φ N,t φ U,t Respectively represent the attitude errors in the east, north, and sky directions in the "east-north-sky" ENU coordinate system; δv E,t δv N,t δv U,t Respectively represent the velocity errors in the east, north and sky directions in the ENU coordinate system; δl t , δλ t ,δh t Represent the latitude, longitude and altitude position errors respectively; T represents the transposition operation; δ represents the corresponding error; Finally, the error state vector x of the INS system is obtained. t The expression is: Where, δr t Indicates position error; δv t Indicates speed error; φ t represents the attitude error; ε t =[ε gx,t ε gy,t ε gz,t ] T Indicates the gyroscope drift error; Indicates the accelerometer bias error; ε gx,t , ε gy,t , ε gz,t Represents the gyroscope drift error in the x, y, and z directions respectively; They represent the accelerometer bias errors in the x, y, and z directions, respectively; T represents the transpose operation; and δ represents the corresponding error.

3. The multi-source fusion positioning method for the lunar south pole that integrates lunar orbit satellites, inertial navigation, and wireless communications according to claim 2 is characterized in that: In step S2), the position coordinates calculated by the least squares method are first converted to the ENU coordinate system where the INS system is located, and then converted into the form of latitude, longitude and altitude, that is: Where, The position of the lunar rover calculated by the least squares method; They represent the latitude, longitude, and altitude of the lunar rover position calculated by the least squares method; Then, the difference between the position calculated by the INS system and the position calculated by the least square method is used as the measurement error state z t ,Right now: Where, The lunar rover position calculated by the INS system, The position of the lunar rover calculated by the least squares method.

4. The multi-source fusion positioning method for the lunar south pole that integrates lunar orbit satellites, inertial navigation, and wireless communications according to claim 3 is characterized in that: In step S3), the ESKF state equation for fusion INS positioning is constructed based on the system error of the INS system as the error state: x t =Fx t-1 +w t ; (9) Where x t represents the error state; F represents the state transfer matrix of the system; w t represents the process noise vector of the system.

5. The multi-source fusion positioning method for the lunar south pole that integrates lunar orbit satellites, inertial navigation, and wireless communications according to claim 4 is characterized in that: In step S3), the ESKF measurement equation is obtained by subtracting the position calculated by the INS system from the position calculated by the least square method: Where z(t) represents the measurement error state; The position of the lunar rover calculated by the INS system, is the position of the lunar rover calculated by the least squares method; H represents the measurement matrix of the system, v t represents the measurement noise vector of the system.

6. The multi-source fusion positioning method for the lunar south pole that integrates lunar orbit satellites, inertial navigation, and wireless communications according to claim 5, characterized in that: In step S3), the loosely coupled model based on the error state Kalman filter ESKF is constructed, and its system equation is: Where: x t 、x t-1 Represent the error states at time t and t-1 respectively; F t represents the state transfer matrix of the system at time t; w t represents the process noise of the system at time t; z t Represents the measurement error state of the system at time t; H t represents the measurement matrix of the system at time t, v t represents the measurement noise of the system at time t.

7. The multi-source fusion positioning method for the lunar south pole integrating lunar orbit satellites, inertial navigation and wireless communication according to claim 6 is characterized in that: In step S3), the error state is solved using a loosely coupled model based on the error state Kalman filter (ESKF), including prediction and update stages; wherein: Prediction stage: in, is the posterior error state estimate at time t-1; F t represents the state transfer matrix of the system at time t; is the prior error state estimate at time t; P t-1 is the posterior error state estimate covariance matrix at time t-1; P t,t-1 is the prior error state estimate covariance matrix at time t, Q t represents the process noise covariance matrix; T represents the transpose operation; Update phase: P t =(I-K t H t )P t,t-1 ; (16) Where K t represents the Kalman gain at time t; H t represents the measurement matrix of the system at time t; R t represents the measurement noise covariance matrix; z t represents the measurement error state of the system at time t; represents the posterior error state estimate at time t; I represents the identity matrix; Finally, the error state calculated by ESKF is obtained Using the position error in the error state Correct the INS's calculated position, then update the current INS internal information. The final corrected INS calculated position is used as the lunar rover's position: Where; represents the corrected lunar rover position; The lunar rover position solved by the INS system; It is the position error in the error state solved by ESKF.

8. A multi-source fusion positioning system for the lunar South Pole that integrates lunar orbit satellites, inertial navigation, and wireless communications, characterized in that: The system implements positioning using the method according to any one of claims 1 to 7, and the system comprises: A data acquisition module for receiving signals from a real lunar scene; The multi-source fusion positioning measurement module is used to calculate the position of the lunar rover receiver based on the lunar orbit satellite pseudo-range single-point positioning model and the wireless communication TDOA positioning model; The first solution module is used to solve the position of the lunar rover from the multi-source fusion positioning measurement module according to the least squares method. The second solution module is used to calculate the lunar rover position using INS And the position of the lunar rover calculated by the first solution module Calculate the measurement error state by difference, and calculate the error state at the current moment based on ESKF solution Correction module, used to adjust the error state Position error in The lunar rover position calculated by INS Make corrections.

9. The multi-source fusion positioning system for the lunar south pole that integrates lunar orbit satellites, inertial navigation, and wireless communications according to claim 8, characterized in that: The second solution module first converts the position coordinates calculated by the least squares method into the ENU coordinate system where the INS system is located, and then converts it into the form of latitude, longitude and altitude, that is: Where, The position of the lunar rover calculated by the least squares method; represent the latitude, longitude, and altitude of the lunar rover position calculated by the least squares method; Then, the difference between the lunar rover position calculated by the INS system and the lunar rover position calculated by the least square method is used as the measurement error state z t ,Right now: Where, The position of the lunar rover calculated by the INS system, The position of the lunar rover calculated by the least squares method; The second solution module constructs the ESKF state equation for fusion INS positioning based on the system error of the INS system as the error state: x t =Fx t-1 +w t ; (9) Where x t represents the error state; F represents the state transfer matrix of the system; w t represents the process noise vector of the system; The ESKF measurement equation is obtained by subtracting the position calculated by the INS system from the position calculated by the least square method: Where z(t) represents the measurement error state; The lunar rover position calculated by the INS system, is the position of the lunar rover calculated by the least squares method; H represents the measurement matrix of the system, v t represents the measurement noise vector of the system; Then the loosely coupled model based on the error state Kalman filter ESKF is constructed, and its system equation is: Where: x t 、x t-1 Represent the error states at time t and t-1 respectively; F t represents the state transfer matrix of the system at time t; w t represents the process noise of the system at time t; z t Represents the measurement error state of the system at time t; H t represents the measurement matrix of the system at time t, v t represents the measurement noise of the system at time t; Finally, the error state is solved using a loosely coupled model based on the error state Kalman filter (ESKF), including prediction and update stages. Prediction stage: in, is the posterior error state estimate at time t-1; F t represents the state transfer matrix of the system at time t; is the prior error state estimate at time t; P t-1 is the posterior error state estimate covariance matrix at time t-1; P t,t-1 is the prior error state estimate covariance matrix at time t, Q t represents the process noise covariance matrix; T represents the transpose operation; Update phase: P t =(I-K t H t )P t,t-1 ; (16) Where K t represents the Kalman gain at time t; H t represents the measurement matrix of the system at time t; R t represents the measurement noise covariance matrix; z t Represents the measurement error state of the system at time t; represents the posterior error state estimate at time t; I represents the identity matrix.

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