Moon south-pole multi-source fusion positioning method and system integrating lunar orbit satellite, inertial navigation and wireless communication

Abstract

The invention provides a lunar south pole multi-source fusion positioning method and system fusing a lunar orbit satellite, inertial navigation and wireless communication, and the method comprises the steps: building a multi-source fusion positioning measurement model through employing a lunar orbit satellite pseudo-range measurement value and a wireless communication time difference of arrival (TDOA) measurement value, and solving the position information through a least square method; the system error of the INS system is used as an error state, and the difference value between the INS system and the resolving position of the least square method is used as a measurement error state; and constructing a loose coupling model based on ESKF (Error State Kalman Filter) to calculate the error state and correct the calculation position of the INS, and updating the current INS internal information to obtain the accurate position of the lunar probe vehicle. According to the invention, the problems of limited coverage range and low positioning precision caused by insufficient lunar orbit satellites are effectively solved; the influence of INS error accumulation on the positioning accuracy is reduced, and finally the accurate position of the lunar probe vehicle is obtained; and the overall positioning precision and reliability of the system are obviously improved.

Description

Technical Field

[0001] The present invention relates to the technical field of lunar positioning, 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 communication. Background Art

[0002] Due to its special geographical location, the lunar south pole has permanently illuminated areas and may contain large amounts of water ice resources, and has always been the core area of lunar exploration. However, the environment of the lunar south pole is extremely complex, with steep and variable terrain, and is covered with craters and ridges. These factors pose great challenges to the precise positioning of lunar rovers.

[0003] Traditional technologies mainly achieve lunar positioning through ground-based measurement positioning methods. However, ground-based measurement positioning methods require powerful ground infrastructure support, and the coverage range is limited by the rotation of the earth and the distribution of ground stations, making it difficult to achieve real-time and continuous positioning. In addition, the signal transmission distance from the earth to the moon is relatively long, and it may be affected by factors such as ionospheric interference and solar activity, thereby reducing the positioning accuracy.

[0004] With the continuous advancement of lunar exploration activities, multi-source fusion positioning technologies have gradually been applied to lunar exploration missions. By using multi-source information from lunar orbit satellites, vision, lidar, INS, ground beacons, earth-moon radio communication, etc., combined with the unique terrain and astronomical features on the lunar surface, high-precision integrated positioning is achieved. Multi-source fusion positioning technologies can improve positioning accuracy and reliability by integrating the advantages of different positioning sources. 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 special environment of the moon 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, resulting in difficult solution and low positioning accuracy of existing positioning methods that rely on lunar orbit satellites, and thus unable to provide continuous and reliable full-time high-precision positioning services for lunar rovers.

[0006] Secondly, the environment of the lunar south pole is complex, and there are terrains such as deep pits and ridges that are likely to block satellite signals. In addition, factors such as microgravity and weak magnetic fields on the lunar surface will also interfere with signals. These effects limit the effectiveness of existing positioning methods that rely on a single lunar orbit satellite or INS, and it is difficult to meet the precise navigation requirements of lunar rovers. Summary of the Invention

[0007] Aiming at the deficiencies 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 communication. The present invention can effectively solve the problems of limited coverage range and low positioning accuracy caused by insufficient number of lunar orbit satellites, as well as the influence of error accumulation on positioning accuracy.

[0008] The technical solution of the present invention is as follows: 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:

[0009] S1), Use the pseudo-range measurement value of the lunar orbit satellite and the time difference of arrival TDOA measurement value of wireless communication to construct a multi-source fusion positioning measurement model, and calculate the position information by the least squares method;

[0010] S2), Take the system error of the INS system as the error state, and take the difference between the calculated position of the INS system and the calculated position of the least squares method as the measured error state;

[0011] S3), Construct a loose coupling model based on the error state Kalman filter ESKF to calculate the error state and correct the calculated position of the INS, and update the current internal information of the INS to obtain the accurate position of the lunar rover.

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

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

[0014]

[0015] In the formula, ρ i,t represents the pseudo-range measurement value of the i-th lunar orbit satellite corrected with 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 clock error of the lunar rover receiver; Other noises 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; its expression is:

[0017]

[0018] In the formula, Δd m1,t represents the distance difference from the main base station 1 to the m-th base station at time t; represents the geometric distance between the m-th base station and the lunar rover receiver; represents the geometric distance between the main base station 1 and the lunar rover receiver; ε m1,tIt represents other noises measured during the communication between the m-th base station and the main base station 1.

[0019] Preferably, in step S11), a lunar orbiting satellite pseudorange single-point positioning model is constructed, which specifically includes the following steps:

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

[0021]

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

[0023] S112), Let δt = c × Δt r,t , and correct the pseudorange measurement value to obtain the corrected pseudorange measurement value ρ i,t , that is:

[0024]

[0025] S113), According to formula (2), when the number of visible satellites is N, the expression of the lunar orbiting satellite pseudorange single-point positioning model is:

[0026]

[0027] In the formula, ρ i,t represents the corrected pseudorange measurement value between the i-th lunar orbiting satellite and the lunar rover receiver; represents the geometric distance between the i-th lunar orbiting 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 clock error of the lunar rover receiver; Other noises during the measurement process.

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

[0029] S121) Let the coordinates of the wireless communication signal base station at time t be For any two base stations h and k, the time difference Δt between the lunar rover receiver transmitting a signal and the signal reaching the two base stations is hk,t as follows:

[0030] Δt hk,t = t h,t - t k,t ; (4)

[0031] In the formula, t h,t and t k,t are respectively the times when the lunar rover receiver transmits a signal and the signal reaches base stations h and k;

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

[0033] Δd hk,t = c·Δt hk,t ; (5)

[0034] In the formula, c represents the speed of light;

[0035] S123) Assuming time synchronization between base stations, according to the geometric relationship, express the distance difference Δd hk,t as:

[0036]

[0037] In the formula, represents the geometric distance between the h-th base station and the lunar rover receiver; represents the geometric distance between the k-th base station and the lunar rover receiver; ε hk,t represents other noises in the measurement process;

[0038] S124) Let the main reference base station be base station 1. When the number of base stations is M, establish a wireless communication TDOA positioning model as:

[0039]

[0040] In the formula, Δd m1,t represents the distance difference between the main base station 1 and the m-th base station at time t; represents the geometric distance between the m-th 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 noises measured during the communication between the m-th base station and the main base station 1.

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

[0042] S1-1), Convert the pseudo-range single-point positioning model of the lunar orbit satellite and the wireless communication TDOA positioning model to the lunar-centered lunar-fixed coordinate system, and then jointly construct a combined positioning measurement equation set with the measurement equations of both:

[0043]

[0044] S1-2), Use the least squares method to solve the combined positioning measurement equation set of formula (8) and take the calculated position of the lunar rover as the final combined positioning result.

[0045] Preferably, in step S2), at time t, the system errors of the INS system include the attitude error φ t , the velocity error δv t , and the position error δr t ; their expressions are respectively:

[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] In the formula, 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-Up" (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 respectively represent the latitude, longitude, and altitude position errors; T represents the transpose operation; δ represents the corresponding error.

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

[0051]

[0052] In the formula, is the position of the lunar rover calculated by the least squares method; respectively represent the latitude, longitude, and altitude of the position of the lunar rover 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 squares method is used as the measurement error state z t , that is:

[0054]

[0055] In the formula, is the position of the lunar rover calculated by the INS system, is the position of the lunar rover calculated by the least squares method.

[0056] Preferably, in step S3), according to the system error of the INS system as the error state, an ESKF state equation for fusing INS positioning is constructed:

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

[0058] In the formula, x t represents the error state; F represents the system state transition matrix; w t represents the system process noise vector.

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

[0060]

[0061] In the formula, δr t represents the position error; δv t represents the velocity error; φ t represents the attitude error; ε t = [ε gx,t ε gy,t ε gz,t T represents the gyroscope drift error; represents the accelerometer zero bias error; ε gx,t 、ε gy,t ​, ε gz,t respectively represent the gyroscope drift errors in the x, y, and z directions; respectively represent the accelerometer bias errors in the x, y, and z directions; T represents the transpose operation; δ represents the corresponding error.

[0062] Preferably, in step S3), the ESKF measurement equation is obtained by taking the difference between the calculated position of the INS system and the calculated position of the least squares method:

[0063]

[0064] In the formula; z(t) represents the measurement error state; is the position of the lunar rover 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 loose coupling model based on the error state Kalman filter ESKF is constructed, and its system equation is:

[0067]

[0068] In the formula; x t , x t-1 respectively represent the error states at times t and t - 1; F t represents the state transition 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 loose coupling model based on the error state Kalman filter ESKF is used to calculate the error state, including the prediction and update phases; where:

[0070] Prediction phase:

[0071]

[0072]

[0073] Among them, is the posterior error state estimate at time t - 1; F t represents the state transition 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 =(I - K t H t )P t,t-1 ; (16)

[0078] In the formula, 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 calculated position of the INS, and then update the internal information of the current INS. Finally, the corrected calculated position of the INS is used as the position of the lunar rover:

[0080]

[0081] In the formula; represents the corrected position of the lunar rover; is the position of the lunar rover calculated by the INS system; is the position error in the error state calculated 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 communication, including:

[0083] A data acquisition module for receiving signals in the real lunar scene;

[0084] A multi-source fusion positioning measurement module for calculating the position of the lunar rover receiver according to the lunar orbit satellite pseudorange single-point positioning model and the wireless communication TDOA positioning model;

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

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

[0087] The correction module is used to correct the position of the lunar rover calculated by INS according to the position error in the error state for the position of the lunar rover calculated by INS for correction

[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, including the position data of the lunar orbit satellites and the calculated pseudorange measurement values (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 position data and TDOA measurement values (Δt 21,t , Δt 31,t , …, Δt M1,t ), and calculate the range difference measurement values (Δd 21,t , Δd 31,t , …, Δd M1,t ) according to the TDOA measurement values

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

[0091]

[0092] In the formula, ρ i,t represents the pseudorange measurement value of the i-th corrected 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 clock error of the lunar rover receiver; other noises in the measurement process;

[0093] The expression obtained from the described wireless communication TDOA positioning model is as follows:

[0094]

[0095] In the formula, Δd m1,t represents the distance difference from the master base station 1 to the m-th base station at time t; represents the geometric distance between the m-th base station and the lunar rover receiver; represents the geometric distance between the master base station 1 and the lunar rover receiver; ε m1,t represents other noises measured during the communication between the m-th base station and the master base station 1.

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

[0097]

[0098] In the formula, is the position of the lunar rover calculated by the least squares method; respectively represent the latitude, longitude, and altitude of the position of the lunar rover 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 squares method is used as the measurement error state z t , that is:

[0100]

[0101] In the formula, is the position of the lunar rover calculated by the INS system, is the position of the lunar rover calculated by the least squares method.

[0102] Preferably, the second calculation module constructs an ESKF state equation for fusing 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] In the formula, x t represents the error state; F represents the state transition matrix of the system; w t represents the process noise vector of the system.

[0105] And an ESKF measurement equation is obtained by taking the difference between the position calculated by the INS system and the position calculated by the least squares method:

[0106]

[0107] where; \(z(t)\) represents the measurement error state; is 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.

[0108] Then, a loose coupling model based on the error state Kalman filter (ESKF) is constructed, and its system equation is:

[0109]

[0110] where; \(x\) t and \(x\) t-1 represent the error states at times \(t\) and \(t - 1\) respectively; \(F\) t represents the state transition 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 loose coupling model based on the error state Kalman filter (ESKF) is used to calculate the error state, including the prediction and update phases; where:

[0112] Prediction phase:

[0113]

[0114]

[0115] where, is the posterior error state estimate at time \(t - 1\); \(F\) t represents the state transition 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 = (I - K t H t )P t,t-1 ; (16)

[0120] Wherein, 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 estimated value of the posterior error state at time t; I represents the identity matrix.

[0121] Preferably, the correction module uses the position error in the error state calculated by ESKF to correct the calculated position of INS, then update the internal information of the current INS, and finally use the corrected calculated position of INS as the position of the lunar rover:

[0122]

[0123] Wherein; represents the position of the corrected lunar rover; is the position of the lunar rover calculated by the INS system; is the position error in the error state calculated by ESKF.

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

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

[0126] 2. The present invention further fuses the combined positioning results of lunar orbit satellites and wireless communication with the INS positioning result, and uses the error state Kalman filter (ESKF) to correct the calculated position of INS, and then updates the internal information of the current INS, thereby effectively reducing the influence of INS error accumulation on positioning accuracy, and finally obtaining the accurate position of the lunar rover; significantly improving the overall positioning accuracy and reliability of the system. Brief Description of the Drawings

[0127] Figure 1 is a schematic framework diagram of the method of the present invention. Detailed Embodiments

[0128] The following further describes the detailed embodiments of the present invention with reference to the drawings:

[0129] Embodiment 1

[0130] As Figure 1 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 acquisition

[0132] The signals in the real lunar scenario are received through the lunar orbit satellite signal receiver and the wireless communication signal receiver installed on the lunar exploration vehicle, so as to obtain positioning data. Let the position coordinates of the lunar exploration vehicle at time t be r t =(x t , y t , z t ). T ; The lunar orbit satellite signal receiver can receive the signals from N lunar orbit satellites, including the position data of the lunar orbit satellites and the calculated pseudorange measurement values (ρ 1,t , ρ 2,t , …, ρ N,t ).

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

[0134] S2), Construct a multi-source fusion positioning measurement model using the lunar orbit satellite pseudorange measurement values and the wireless communication time difference of arrival TDOA measurement values, and solve the position information through the least squares method;

[0135] Among them, constructing a multi-source fusion positioning measurement model specifically includes the following steps:

[0136] S21), Construct a lunar orbit satellite pseudorange single-point positioning model; obtain the coordinates of the lunar exploration vehicle receiver through the lunar orbit satellite pseudorange single-point positioning model; specifically include the following steps:

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

[0138]

[0139] In the formula, ρ oi represents the pseudorange measurement value between the i-th lunar orbit satellite and the lunar exploration vehicle receiver; represents the geometric distance between the \(i\)-th lunar orbiting satellite and the receiver of the lunar rover; \(c\) represents the speed of light; \(\Delta t\) r,t represents the clock error of the receiver of the lunar rover; represents the clock error of the \(i\)-th lunar orbiting satellite; \(I\) n is the ionospheric error of the \(n\)-th lunar orbiting satellite; \(O\) n is the tropospheric error of the \(n\)-th satellite; represents other noises in the measurement process;

[0140] S212), Let \(\delta t = c\times\Delta t\) r,t , and correct the pseudorange measurement value to obtain the corrected pseudorange measurement value \(\rho\) i,t , that is:

[0141]

[0142] S213), According to Equation (2), when the number of visible satellites is \(N\), the expression of the pseudorange single-point positioning model of the lunar orbiting satellite is:

[0143]

[0144] In the formula, \(\rho\) i,t represents the corrected pseudorange measurement value between the \(i\)-th lunar orbiting satellite and the receiver of the lunar rover; represents the geometric distance between the \(i\)-th lunar orbiting satellite and the receiver of the lunar rover at time \(t\); \(\delta t = c\times\Delta t\) r,t ; \(c\) represents the speed of light; \(\Delta t\) r,t represents the clock error of the receiver of the lunar rover; other noises in the measurement process.

[0145] S22), Establish a wireless communication TDOA positioning model, and calculate the coordinates of the receiver of the lunar rover through the wireless communication TDOA positioning model; the specific steps are as follows:

[0146] S221), Assume that the coordinates of the wireless communication signal base station at time \(t\) are \(\{(h = 1,2,\cdots,M)\}\); for any two base stations \(h\) and \(k\), the time difference \(\Delta t\) between the signals transmitted by the receiver of the lunar rover and reaching the two base stations is hk,t as follows:

[0147]

[0148] In the formula, \(t\) h,t , \(t\) k,t are the times when the signals transmitted by the receiver of the lunar rover reach the base stations \(h\) and \(k\) respectively;

[0149] S222), Convert the time difference \(\Delta t\) hk,t to the distance difference \(\Delta d\)hk,t , that is:

[0150]

[0151] In the formula, c represents the speed of light;

[0152] S223), assuming time synchronization between base stations, according to geometric relationships, express the distance difference Δd hk,t as:

[0153]

[0154] In the formula, represents the geometric distance between the h-th base station and the lunar rover receiver; represents the geometric distance between the k-th base station and the lunar rover receiver; ε hk,t represents other noises in the measurement process;

[0155] S224), set the main reference base station as base station 1. When the number of base stations is M, establish a wireless communication TDOA positioning model as:

[0156]

[0157] In the formula, Δd m1,t represents the distance difference from the main base station 1 to the m-th base station at time t; represents the geometric distance between the m-th 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 noises measured during the communication between the m-th base station and the main base station 1.

[0158] Calculate the position information through the least squares method, which specifically includes the following steps:

[0159] S2-1), convert the lunar orbiting satellite pseudorange single-point positioning model and the wireless communication TDOA positioning model to the lunar-centered lunar-fixed coordinate system, and then jointly construct a combined positioning measurement equation set from the measurement equations of both:

[0160]

[0161] S2-2), use the least squares method to solve the combined positioning measurement equation set of formula (8) and take the calculated position of the lunar rover as the final combined positioning result.

[0162] S3), regard the systematic error of the INS system as the error state, and take the difference between the calculated position of the INS system and the calculated position of the least squares method as the measurement error state;

[0163] In this embodiment, at time t, the systematic errors of the INS system include attitude error φ t , velocity error δv t , and position error δr t ; their expressions are respectively:

[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] In the formula, φ E,t φ N,t φ U,t respectively represent the attitude errors in the east, north, and up directions in the "east - north - up" (ENU) coordinate system; δv E,t δv N,t δv U,t respectively represent the velocity errors in the east, north, and up directions in the ENU coordinate system; δl t , δλ t , δh t respectively represent the latitude, longitude, and altitude position errors; T represents the transpose operation; δ represents the corresponding error. First, convert the position coordinates calculated by the least - squares method to the ENU coordinate system where the INS system is located and convert them into the form of latitude, longitude, and altitude, that is:

[0168]

[0169] In the formula, is the position of the lunar rover calculated by the least - squares method; respectively represent the latitude, longitude, and altitude of the position of the lunar rover calculated by the least - squares method;

[0170] Then, take the difference between the position calculated by the INS system and the position calculated by the least - squares method as the measurement error state z t , that is:

[0171]

[0172] In the formula,​​​ The position of the lunar rover solved by the INS system is the position of the lunar rover solved by the least squares method.

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

[0174] First, construct the ESKF state equation that fuses INS positioning with the system error of the INS system as the error state:

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

[0176] In the formula, x t represents the error state; F represents the system state transition matrix; w t represents the system process noise vector.

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

[0178]

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

[0180] Then, use the difference between the solved position of the INS system and the solved position of the least squares method to obtain the ESKF measurement equation as:

[0181]

[0182] In the formula; z(t) represents the measured error state; is the position of the lunar rover solved 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, and v t represents the measurement noise vector of the system.

[0183] Finally, the system equation of the loosely coupled model based on the error state Kalman filter (ESKF) is:

[0184]

[0185] where; x t , x t-1 represent the error states at times t and t-1 respectively; F t represents the state transition 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, and v t represents the measurement noise of the system at time t.

[0186] In this embodiment, the error state is solved using the loosely coupled model based on the error state Kalman filter (ESKF), including the prediction and update phases; where:

[0187] Prediction phase:

[0188]

[0189]

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

[0191] Update phase:

[0192]

[0193]

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

[0195] In the formula, 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 estimated value of the posterior error state 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 calculated position of the INS, and then update the internal information of the current INS. Finally, the corrected calculated position of the INS is used as the position of the lunar rover:

[0197]

[0198] In the formula; represents the position of the corrected lunar rover; is the position of the lunar rover calculated by the INS system; is the position error in the error state calculated by ESKF.

[0199] Embodiment 2

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

[0201] A data acquisition module for receiving signals in a real lunar scenario;

[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, including the position data of the lunar orbit satellites and the calculated pseudorange measurement values (p 1,t , p 2,t , …, p N,t );

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

[0204] A multi-source fusion positioning measurement module is used to calculate the position of the lunar rover receiver according to 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 pseudo-range single-point positioning model is:

[0206]

[0207] In the formula, ρ i,t represents the measured pseudo-range value between the corrected 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 at time t; δt = c × Δt r,t ; c represents the speed of light; Δt r,t represents the clock error of the lunar rover receiver; Other noises during the measurement process;

[0208] The expression of the wireless communication TDOA positioning model is:

[0209]

[0210] In the formula, Δd m1,t represents the distance difference between the master base station 1 and the m-th base station at time t; represents the geometric distance between the m-th base station and the lunar rover receiver; represents the geometric distance between the master base station 1 and the lunar rover receiver; ε m1,t represents other noises measured during the communication between the m-th base station and the master base station 1.

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

[0212] The second calculation module is used to calculate the position of the lunar rover obtained by INS and make a difference calculation with the position of the lunar rover calculated by the first calculation module to measure the error state and calculate the error state at the current moment based on ESKF

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

[0214]

[0215] In the formula, is the position of the lunar rover calculated by the least squares method; respectively represent the latitude, longitude and altitude of the position of the lunar rover 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 squares method is used as the measurement error state z t , that is:

[0217]

[0218] In the formula, is the position of the lunar rover calculated by the INS system, is the position of the lunar rover calculated by the least squares method.

[0219] The second calculation module constructs an ESKF state equation for fusing 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] In the formula, x t represents the error state; F represents the state transition matrix of the system; w t represents the process noise vector of the system.

[0222] And the ESKF measurement equation is obtained by taking the difference between the position calculated by the INS system and the position calculated by the least squares method:

[0223]

[0224] In the formula; z(t) represents the measurement error state; is 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, a loosely coupled model based on the error state Kalman filter ESKF is constructed, and its system equation is:

[0227]

[0228] In the formula; x t , x t-1 respectively represent the error states at times t and t-1; F t represents the state transition 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, a loose coupling model based on the Error State Kalman Filter (ESKF) is used to calculate the error state, including the prediction and update phases; where:

[0230] Prediction phase:

[0231]

[0232]

[0233] Where, is the posterior error state estimate at time t - 1; F t Represents the state transition 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 =(I - K t H t )P t,t-1 ; (16)

[0238] In the formula, 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 correct the position of the lunar rover calculated by the INS according to the error state The correction module uses the position error in the error state calculated by the ESKF of the lunar rover Correct the calculated position of the INS, and then update the internal information of the current INS. Finally, the corrected calculated position of the INS is used as the position of the lunar rover:

[0240]

[0241] In the formula; Represents the position of the corrected lunar rover; Is the position of the lunar rover calculated by the INS system; Is the position error in the error state calculated by the ESKF.

[0242] Preferably in this embodiment, the system further includes an inertial measurement unit. The inertial measurement unit includes a gyroscope and an accelerometer. The drift error ε of the gyroscope is calculated through the inertial measurement unit t =[ε gx,t ε gy,t ε gz,t T And the zero bias error of the accelerometer

[0243] The above embodiments and the descriptions in the specification only illustrate the principles and the best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed.​

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) Use the lunar orbit satellite pseudo-range measurement value and the wireless communication arrival time difference TDOA measurement value to build a multi-source fusion positioning measurement model, and calculate the position information by the least squares method; 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 error state Kalman filter (ESKF) to solve the error state and correct the solved position of INS, and update the current internal information of INS to obtain the accurate position of the lunar rover.

2. The multi-source fusion positioning method for the lunar south pole integrating lunar orbit satellite, inertial navigation and wireless communication according to claim 1 is characterized in that: In step S1), a multi-source fusion positioning measurement model is constructed, which specifically includes 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: In the formula, ρ i,t represents the corrected pseudo-range 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; δ t =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: In the formula, Δd m1,t represents the distance difference from the primary base station 1 to 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.

3. The multi-source fusion positioning method for the lunar south pole integrating lunar orbit satellite, inertial navigation and wireless communication 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 , speed error δv t 、Position error δr t ; Their expressions are: f t =[φ E,t f N,t f I,t ] T ; δv t =[δv E,t δv N,t δv U,t ] T ; δr t =[δl t dl t dh t ] T ; In the formula, 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 Respectively represent the latitude, longitude and altitude position errors; 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: In the formula, 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 Represent the gyroscope drift errors 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 transposition operation; and δ represents the corresponding error.

4. The multi-source fusion positioning method for the lunar south pole integrating lunar orbit satellite, inertial navigation and wireless communication according to claim 3 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: In the formula, 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 respectively; Then, the difference between the position calculated by the INS system and the position calculated by the least square method is taken as the measurement error state z t ,Right now: In the formula, The position of the lunar rover solved by the INS system, This is the lunar rover position calculated by the least squares method.

5. The multi-source fusion positioning method for the lunar south pole integrating lunar orbit satellite, inertial navigation and wireless communication according to claim 4 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) In the formula, 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.

6. The multi-source fusion positioning method for the lunar south pole integrating lunar orbit satellite, inertial navigation and wireless communication according to claim 5 is characterized in that: In step S3), the ESKF measurement equation is obtained by subtracting the position calculated by the INS system and the position calculated by the least square method: Where: z(t) represents the measurement error state; The position of the lunar rover solved 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.

7. The multi-source fusion positioning method for the lunar south pole integrating lunar orbit satellite, inertial navigation and wireless communication according to claim 6 is 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 Respectively represent the error state at time t and t-1; 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.

8. The multi-source fusion positioning method for the lunar south pole integrating lunar orbit satellite, inertial navigation and wireless communication according to claim 7 is characterized in that: 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: Prediction stage: in, is the a posteriori 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) In the formula, 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 solved position of INS, then update the current internal information of INS, and finally use the corrected solved position of INS as the position of lunar rover: 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.

9. 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 uses the method described in any one of claims 1 to 8 to achieve positioning, and the system includes: A data acquisition module, used to receive 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 use the lunar rover position calculated by INS And the position of the lunar rover calculated by the first solution module The error state is measured by differential calculation, and the error state at the current moment is obtained based on ESKF solution. Correction module, used to adjust the error state Position error in The lunar rover position calculated by INS Make corrections.

10. The multi-source fusion positioning system for the lunar south pole integrating lunar orbit satellite, inertial navigation and wireless communication according to claim 9 is characterized in that: The second solution module first converts the position coordinates calculated by the least squares method to the ENU coordinate system where the INS system is located, and converts it into the form of latitude, longitude and altitude, that is: In the formula, 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 respectively; 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: In the formula, The position of the lunar rover solved 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 of fusion INS positioning based on the system error of the INS system as the error state: x t =Fx t-1 +w t ; (9) In the formula, 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 calculated position of the INS system from the calculated position of the least square method: Where: z(t) represents the measurement error state; The position of the lunar rover solved 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 Respectively represent the error state at time t and t-1; 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 the prediction and update stages; Prediction stage: in, is the a posteriori 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) In the formula, 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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