A low-orbit satellite Doppler positioning method and device

Abstract

The present invention discloses a low-orbit satellite Doppler positioning method and device, belonging to the field of satellite navigation and positioning technology. The method disclosed in the present invention mainly includes: obtaining the Doppler observation quantity and satellite ephemeris information of the satellite; constructing a damping term according to the satellite ephemeris information; estimating the initial state according to the satellite ephemeris information and the Doppler observation quantity in combination with the damping term; performing forward weighted filtering according to the initial state to calculate the precise positioning and speed determination result. The present invention can quickly perform Doppler positioning when the initial position is unknown by constructing a damping term to limit the divergence of the algorithm; and performing weighted filtering using the satellite speed and the line-of-sight angle to reduce the filter convergence time and ensure the positioning and speed determination performance of the device in a dynamic environment.

Description

Technical Field

[0001] The present invention belongs to the technical field of satellite navigation and positioning, and in particular relates to a low-orbit satellite Doppler positioning method and device. Background Art

[0002] Using low-orbit satellites for navigation enhancement or independent navigation services is one of the key technologies for building a more integrated and ubiquitous integrated PNT (Positing Navigating Timing) system. Using the large number of low-orbit communication satellites or low-orbit navigation satellites for Doppler positioning can effectively supplement the positioning and navigation needs in GNSS denial situations. In terms of satellite Doppler positioning algorithms, iterative least squares and extended Kalman filter (EKF) are often used in the state estimation problem of navigation systems. However, for low-orbit satellite Doppler positioning, its observation equation is highly nonlinear and geometrically manifested as a complex surface. High nonlinearity usually causes ill-posed problems in the equation solution process. The latest research has found that low-orbit satellite Doppler positioning is sensitive to the prior initial position. When using the iterative least squares method, when the initial position error is greater than 200km, there is a solution failure and the solution result cannot be output in real time. When using the EKF method, the larger the prior initial position difference, the larger the low-orbit satellite Doppler speed error. Therefore, for the low-orbit satellite Doppler positioning system, the existing methods need to be improved to meet the positioning needs in the case of GNSS denial and unknown a priori initial position. Summary of the invention

[0003] In view of the above technical problems, the present invention proposes a low-orbit satellite Doppler positioning solution.

[0004] The first aspect of the present invention discloses a low-orbit satellite Doppler positioning method, the method comprising:

[0005] Step S1, according to the visible satellites of the carrier to be positioned, obtain the satellite ephemeris information of the visible satellites at the same time and the Doppler observation value corresponding to the satellite frequency point;

[0006] Step S2, using the satellite ephemeris information in combination with the iterative matrix eigenvalue to calculate the damping term;

[0007] Step S3, based on the satellite ephemeris information and the Doppler observation quantity, combined with the damping term, determining the position, velocity and clock drift of the carrier to be positioned as an initial state vector;

[0008] Step S4: According to the initial state vector, the Doppler observation quantity is weighted filtered using the line-of-sight angle between the visible satellite and the carrier to be positioned and the visible satellite velocity contained in the satellite ephemeris information to calculate the precise positioning and constant speed result of the carrier to be positioned.

[0009] According to the method of the first aspect of the present invention:

[0010] The satellite ephemeris information refers to a protocol file used to calculate the position coordinates and three-dimensional velocity of visible satellites in the Earth-centered Earth-fixed coordinate system;

[0011] The visible satellite indicators refer to low-orbit communication satellites or low-orbit navigation satellites with consistent frequencies.

[0012] According to the method of the first aspect of the present invention, in step S1:

[0013] Obtained according to the visible satellites of the carrier to be positioned time The satellite ephemeris information of the visible satellites and the Doppler observations corresponding to the satellite frequency points;

[0014] Wherein, when the carrier to be positioned is in a stationary state, ≥4; when the carrier to be positioned is in motion, ≥7.

[0015] According to the method of the first aspect of the present invention, in step S2:

[0016] At the initial moment, construct the Doppler observation equation:

[0017] in, The nominal carrier frequency of the satellite signal; is the speed of light in vacuum; For the Doppler observations from satellites; is the state vector of the carrier to be located; For the The three-dimensional position vector of the satellite, , Corresponding to , , Position vector in direction; For the The three-dimensional velocity vector of the satellite, , Corresponding to , , The velocity vector in the direction; for The observation noise of the satellites; , , To select the matrix, the expressions are:

[0018]

[0019]

[0020]

[0021] The state vector of the carrier to be located Expressed as , are respectively the three-dimensional position coordinates and the three-dimensional velocity coordinates of the carrier to be positioned in the Earth-centered Earth-fixed coordinate system, , , Corresponding to , , direction; is the clock drift of the carrier to be positioned; the iteration matrix is ​​a 7×7 symmetric square matrix, and the calculation formula is:

[0022]

[0023] in, Indicates The iteration matrix in iterations; Indicates The Jacobian matrix of the observation equation in the iteration is of size ×7, the expression is:

[0024]

[0025] in, For the The state quantity of the carrier to be positioned calculated in the iteration;

[0026] The calculation formula of the damping term is:

[0027]

[0028] in, For the The damping term in the iteration, I is the 7×7 identity matrix; is the iteration matrix The maximum eigenvalue of is the iteration matrix The minimum eigenvalue of ; is the condition number coefficient, and the calculation formula is:

[0029] .

[0030] According to the method of the first aspect of the present invention, in step S3:

[0031] Construct the linearized system of Doppler observation equations:

[0032]

[0033] in, For the Linearized Doppler observations of satellites; For the Satellite No. The Doppler observation in the iterative calculation is For the The Doppler measurements of the satellites are The state quantity of the carrier to be located in the iterative calculation The partial derivative at is calculated as:

[0034]

[0035] in:

[0036]

[0037] in, For the The position coordinates of the carrier to be positioned in the iteration calculation, , Corresponding to , , Position coordinates in direction, For the The three-dimensional velocity of the carrier to be positioned in the iterative calculation, , Corresponding to , , Speed ​​in direction; For the The clock drift of the carrier to be positioned in the iteration calculation; is the direction cosine, , is the velocity cosine, ;

[0038] Calculate the The Jacobian matrix of the observation equation in the iteration , and calculate the iteration matrix ; According to the iteration matrix And the condition number coefficient C calculates the damping term; according to the The state quantity of the carrier to be located in the iterative calculation , calculate the first +1 state quantity of the carrier to be located in the iterative calculation :

[0039]

[0040] in, is the Doppler observation matrix, is the calculated state matrix; judge whether the solution state residual value is less than the initial set iteration termination condition ; If yes, then output the solution result ; If not, continue iterating; the state residual value is calculated as follows: ; Iteration termination condition <0.0001.

[0041] According to the method of the first aspect of the present invention, in step S4:

[0042] The initial state vector is the solution result , the weighted filter is an extended Kalman filter, and its state equation is:

[0043]

[0044] in, For the The predicted state vector of the carrier to be located at the time instant; For the -1 The estimated state vector of the carrier to be located at time; is the state transfer matrix, the matrix size is 7×7; is the process noise; When -1=0, ; The observation equation of the extended Kalman filter Doppler observation equation; The observation weight matrix of the extended Kalman filter at time t is:

[0045]

[0046] in, , For the The line-of-sight angle of the satellites, For the The number of satellites observed at any given moment; The calculation formula is:

[0047]

[0048] in, For the -1 time, the position coordinates of the carrier to be located are estimated by the extended Kalman filter, and the initial state vector is combined with the extended Kalman filter. , Doppler observations, satellite ephemeris information, observation weight matrix , present the first The estimated state vector of the carrier to be located at time , including information on the precise position, precise three-dimensional velocity and precise clock drift of the carrier to be positioned.

[0049] According to the method of the first aspect of the present invention, the carrier to be positioned is a low-orbit satellite receiver or an observation station.

[0050] A second aspect of the present invention discloses a low-orbit satellite Doppler positioning device, the device comprising a processing module, the processing module being configured to execute:

[0051] Step S1, according to the visible satellites of the carrier to be positioned, obtain the satellite ephemeris information of the visible satellites at the same time and the Doppler observation value corresponding to the satellite frequency point;

[0052] Step S2, using the satellite ephemeris information in combination with the iterative matrix eigenvalue to calculate the damping term;

[0053] Step S3, based on the satellite ephemeris information and the Doppler observation quantity, combined with the damping term, determining the position, velocity and clock drift of the carrier to be positioned as an initial state vector;

[0054] Step S4: According to the initial state vector, the Doppler observation quantity is weighted filtered using the line-of-sight angle between the visible satellite and the carrier to be positioned and the visible satellite velocity contained in the satellite ephemeris information to calculate the precise positioning and constant speed result of the carrier to be positioned.

[0055] The third aspect of the present invention discloses an electronic device. The electronic device includes a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, the low-orbit satellite Doppler positioning method described in the first aspect of the present disclosure is implemented.

[0056] The fourth aspect of the present invention discloses a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the low-orbit satellite Doppler positioning method described in the first aspect of the present disclosure is implemented.

[0057] The beneficial technical effects brought about by the present invention include: (1) Through the damping term construction scheme of the present invention, the divergence of the positioning algorithm can be limited when the initial error is too large. (2) Through the iterative estimation of the initial state quantity of the carrier to be positioned scheme of the present invention, the initial position and speed of the carrier to be positioned can be quickly estimated. (3) Through the satellite speed and line of sight weighted and forward filtered positioning solution scheme of the present invention, the state vector can converge quickly, and can simultaneously estimate the position coordinates, three-dimensional velocity and clock drift of the carrier to be positioned. (4) Through the method of the present invention, the applicability and positioning performance of the satellite Doppler positioning system can be significantly improved. (5) Through the method of the present invention, it can be widely used in low-orbit satellite receivers and measurement stations. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0059] Figure 1 The flowchart of the Doppler positioning method for low-orbit satellites;

[0060] Figure 2 Observation sky map for typical low-orbit satellite scenarios;

[0061] Figure 3a A schematic diagram of the loss of the solution process when the initial state of the carrier to be positioned is determined by using the present invention;

[0062] Figure 3b A schematic diagram of the loss of the solution process when the initial state of the carrier to be positioned is determined by the iterative least square method;

[0063] Figure 4 It is a trajectory comparison diagram of the present invention and the grid method when the initial value is unknown;

[0064] Figure 5 It is a trajectory comparison diagram of the weighting scheme of the present invention and the traditional weighting scheme;

[0065] Figure 6a and Figure 6b The comparison diagrams of positioning errors of the weighted scheme of the present invention and the traditional weighted scheme are respectively;

[0066] Figure 7a and Figure 7b They are respectively a comparison diagram of the constant speed error of the weighted scheme of the present invention and the traditional weighted scheme. DETAILED DESCRIPTION

[0067] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0068] The present invention relates to a method and device for positioning and speed determination using Doppler observations from a low-orbit communication satellite or a low-orbit navigation satellite under the background of building a low-orbit satellite backup navigation system. The method and device are suitable for Doppler positioning and speed determination under GNSS (Global Navigation Satellite System) denial, unknown a priori initial position and dynamic carrier conditions.

[0069] The first aspect of the present invention discloses a low-orbit satellite Doppler positioning method, the method comprising (such as Figure 1 shown):

[0070] Step S1, according to the visible satellites of the carrier to be positioned, obtain the satellite ephemeris information of the visible satellites at the same time and the Doppler observation value corresponding to the satellite frequency point;

[0071] Step S2, using the satellite ephemeris information in combination with the iterative matrix eigenvalue to calculate the damping term;

[0072] Step S3, based on the satellite ephemeris information and the Doppler observation quantity, combined with the damping term, determining the position, velocity and clock drift of the carrier to be positioned as an initial state vector;

[0073] Step S4: According to the initial state vector, the Doppler observation quantity is weighted filtered using the line-of-sight angle between the visible satellite and the carrier to be positioned and the visible satellite velocity contained in the satellite ephemeris information to calculate the precise positioning and constant speed result of the carrier to be positioned.

[0074] According to the method of the first aspect of the present invention:

[0075] The satellite ephemeris information refers to a protocol file used to calculate the position coordinates and three-dimensional velocity of visible satellites in the Earth-centered Earth-fixed coordinate system;

[0076] The visible satellite indicators refer to low-orbit communication satellites or low-orbit navigation satellites with consistent frequencies.

[0077] According to the method of the first aspect of the present invention, in step S1:

[0078] Obtaining the visible satellites of the carrier to be positioned time The satellite ephemeris information of the visible satellites and the Doppler observations corresponding to the satellite frequency points;

[0079] Wherein, when the carrier to be positioned is in a stationary state, ≥4; when the carrier to be positioned is in motion, ≥7.

[0080] According to the method of the first aspect of the present invention, in step S2:

[0081] At the initial moment, construct the Doppler observation equation:

[0082]

[0083] in, The nominal carrier frequency of the satellite signal; is the speed of light in vacuum; For the Doppler observations from satellites; is the state vector of the carrier to be located; For the The three-dimensional position vector of the satellite, , Corresponding to , , Position vector in direction; For the The three-dimensional velocity vector of the satellite, , Corresponding to , , The velocity vector in the direction; for The observation noise of the satellites; , , To select the matrix, the expressions are:

[0084]

[0085]

[0086]

[0087] The state vector of the carrier to be located Expressed as , are respectively the three-dimensional position coordinates and the three-dimensional velocity coordinates of the carrier to be positioned in the Earth-centered Earth-fixed coordinate system, , , Corresponding to , , direction; is the clock drift of the carrier to be positioned; the iteration matrix is ​​a 7×7 symmetric square matrix, and the calculation formula is:

[0088]

[0089] in, Indicates The iteration matrix in iterations; Indicates The Jacobian matrix of the observation equation in the iteration is of size ×7, the expression is:

[0090]

[0091]

[0092] in, Indicates The iteration matrix in iterations; Indicates The Jacobian matrix of the observation equation in the iteration is of size ×7, the expression is:

[0093]

[0094] in, For the The state quantity of the carrier to be positioned calculated in the iteration;

[0095] The calculation formula of the damping term is:

[0096]

[0097] in, For the The damping term in the iteration, I is the 7×7 identity matrix; is the iteration matrix The maximum eigenvalue of is the iteration matrix The minimum eigenvalue of ; is the condition number coefficient, and the calculation formula is:

[0098] .

[0099] According to the method of the first aspect of the present invention, in step S3:

[0100] Construct the linearized system of Doppler observation equations:

[0101]

[0102] in, For the Linearized Doppler observations of satellites; For the Satellite No. The Doppler observation in the iterative calculation is For the The Doppler measurements of the satellites are The state quantity of the carrier to be located in the iterative calculation The partial derivative at is calculated as follows:

[0103]

[0104] in:

[0105]

[0106]

[0107] in, For the The position coordinates of the carrier to be positioned in the iteration calculation, , Corresponding to , , Position coordinates in direction, For the The three-dimensional velocity of the carrier to be positioned in the iterative calculation, , Corresponding to , , Speed ​​in direction; For the The clock drift of the carrier to be positioned in the iteration calculation; is the direction cosine, , is the velocity cosine, ;

[0108] Calculate the The Jacobian matrix of the observation equation in the iteration , and calculate the iteration matrix ; According to the iteration matrix And the condition number coefficient C calculates the damping term; according to the The state quantity of the carrier to be located in the iterative calculation , calculate the first +1 state quantity of the carrier to be located in the iterative calculation :

[0109]

[0110] in, is the Doppler observation matrix, The state matrix calculated by the model; determine whether the solution state residual value is less than the initial set iteration termination condition ; If yes, then output the solution result ; If not, continue iterating; the state residual value is calculated as follows: ; Iteration termination condition <0.0001.

[0111] According to the method of the first aspect of the present invention, in step S4:

[0112] The initial state vector is the solution result , the weighted filter is an extended Kalman filter, and its state equation is:

[0113]

[0114] in, For the The predicted state vector of the carrier to be located at the time instant; For the -1 The estimated state vector of the carrier to be located at time; is the state transfer matrix, the matrix size is 7×7; is the process noise; When -1=0, ; The observation equation of the extended Kalman filter Doppler observation equation; The observation weight matrix of the extended Kalman filter at time t is:

[0115]

[0116] in, , For the The line-of-sight angle of the satellites, For the The number of satellites observed at any given moment; The calculation formula is:

[0117]

[0118] in, For the -1 time, the position coordinates of the carrier to be located are estimated by the extended Kalman filter, and the initial state vector is combined with the extended Kalman filter. , Doppler observations, satellite ephemeris information, observation weight matrix , present the first The estimated state vector of the carrier to be located at time , including information on the precise position, precise three-dimensional velocity and precise clock drift of the carrier to be positioned.

[0119] According to the method of the first aspect of the present invention, the carrier to be positioned is a low-orbit satellite receiver or an observation station.

[0120] First embodiment (satellite Doppler positioning method applicable to the case where the initial position is unknown)

[0121] The first step is to obtain the Doppler observations and satellite ephemeris information of n low-orbit satellites;

[0122] As a more preferred embodiment, the ephemeris information of n satellites at time k and the Doppler observation amount corresponding to the satellite frequency are obtained according to the satellites visible to the carrier to be positioned. If the carrier to be positioned is stationary, n is greater than or equal to 4; if the carrier to be positioned is in motion, n is greater than or equal to 7. The ephemeris information is a protocol file that can calculate the position coordinates and three-dimensional velocity of the satellite in the Earth-centered Earth-fixed coordinate system. The satellite is a low-orbit communication satellite or a low-orbit navigation satellite with a consistent nominal frequency.

[0123] The ephemeris information and Doppler observations of n satellites in corresponding motion states are extracted as input data for subsequent processing steps.

[0124] The second step is to calculate the damping term based on the satellite ephemeris information and combined with the iterative matrix eigenvalue;

[0125] As a better implementation method, for solving the initial time, the following Doppler observation equation is constructed:

[0126]

[0127] in, is the nominal carrier frequency of the satellite signal, is the speed of light in vacuum; is the Doppler observation of the ith satellite; is the state vector of the carrier to be located; is the three-dimensional position vector of the i-th satellite; is the three-dimensional velocity vector of the i-th satellite; is the observation noise of the i satellite. , , To select the matrix, the calculation formula is as follows:

[0128]

[0129]

[0130]

[0131] The undetermined carrier state vector is specifically: ,in are the three-dimensional position and velocity coordinates of the carrier to be positioned in the Earth-centered Earth-fixed coordinate system, is the clock drift of the carrier to be located. The iteration matrix is ​​a 7×7 symmetric square matrix. The calculation formula is:

[0132]

[0133] in is the Jacobian matrix of the observation equation in the mth iteration. The matrix size is n×7 and its expression is as follows:

[0134]

[0135] in, is the state quantity of the carrier to be positioned calculated at the mth iteration. In particular, the state quantity of the carrier to be positioned calculated at the 0th iteration is [0,0,0,0,0,0,0], and no other prior initial position or velocity information is required.

[0136] The damping term is calculated as follows:

[0137]

[0138] in, is the damping term in the mth iteration, where I is a 7×7 identity matrix; is the iteration matrix The maximum eigenvalue of is the iteration matrix The minimum eigenvalue of ; Indicates modulo value operation; is the condition number coefficient, The calculation formula is as follows:

[0139]

[0140] Wherein, n is the number of satellites from which ephemeris information and Doppler observations can be obtained. The damping term is used as input data for subsequent iterative calculations.

[0141] The third step is to estimate the initial state based on the satellite ephemeris information, Doppler observations and the damping term.

[0142] As a more preferred implementation, a linearized set of equations of the Doppler observation equation is constructed, and the formula of the linearized set of equations is as follows:

[0143]

[0144] in, is the state quantity of the carrier to be located calculated in the mth iteration, is the Doppler observation of the i-th satellite; is the observation noise of the i-th satellite; is the partial derivative of the Doppler calculation formula of the ith satellite at the state quantity of the carrier to be positioned calculated in the mth iteration, and the calculation formula is as follows:

[0145]

[0146] in,

[0147]

[0148] in, is the position coordinate of the carrier to be positioned calculated in the mth iteration, is the three-dimensional velocity of the carrier to be positioned calculated at the mth iteration, The clock drift of the carrier to be located calculated for the mth iteration; is the direction cosine, Defined as the pseudo velocity cosine; represents the calculation of the vector's bi-norm, Represents the vector inner product.

[0149] Calculate the Jacobian matrix of the observation equation during the mth iteration , and calculate the iteration matrix According to the iteration matrix The condition number coefficient C is used to calculate the damping term. The state quantity of the carrier to be positioned calculated in the mth iteration is , calculate the m+1 state quantities of the carrier to be located The calculation formula is:

[0150] in, is the Doppler observation matrix, The state matrix calculated by the model; determine whether the solution state residual value is less than the initial set iteration termination condition If not, continue iterating; if yes, output the solution result , as the input data for the subsequent steps. The state residual value calculation formula is: ; The iteration termination condition <0.0001.

[0151] The fourth step is to calculate the precise positioning and speed determination results based on the initial state forward weighted filtering.

[0152] As a better implementation, the initial state vector is the solution result of step 3 The forward weighted filtering method is specifically an extended Kalman filter. The state equation of the extended Kalman filter is as follows:

[0153]

[0154] in is the predicted state vector of the carrier to be located at the kth moment; is the estimated state vector of the carrier to be located at the k-1th moment; A is a state transfer matrix of size 7×7; is the process noise. In particular, when k-1=0, The observation equation of the extended Kalman filter is the Doppler observation equation. The observation weight matrix of the extended Kalman filter at the kth moment is:

[0155]

[0156] in, is the angle between the velocity direction of the ith satellite and the line-of-sight direction, is the number of satellites that can be observed at the kth moment. The line-of-sight direction is the direction in which the satellite points to the carrier to be positioned. The calculation formula for the angle between the satellite velocity direction and the line-of-sight direction is as follows:

[0157]

[0158] in, It is the position coordinate of the carrier to be located estimated by Kalman filtering at time k-1. is the three-dimensional position vector of the i-th satellite; is the three-dimensional velocity vector of the i-th satellite. Using the extended Kalman filter, combined with the initial state , Doppler observation and ephemeris information of satellite, weight matrix The precise state vector of the carrier to be located at any k time can be derived The precise state vector includes the position of the carrier to be positioned, three-bit speed and clock drift information.

[0159] Second embodiment (experimental scenario)

[0160] The experimental scenario includes a hybrid constellation consisting of OneWeb, Iridium and Globalstar satellites, with a total of 801 LEO satellites. The relevant parameter settings are shown in Table 1.

[0161]

[0162] A typical sky picture of this experimental scenario is shown in Figure 2 .

[0163] The present invention obtains the satellite ephemeris and Doppler observation of the experimental scene and then starts the positioning solution. When the initial position is unknown, the present invention and iterative least squares are used to determine the initial state of the carrier to be positioned. The loss (Loss) of the solution process is shown in Figure 3a and Figure 3b The loss is the binary norm of the difference between the state quantities before and after.

[0164] It can be seen from the loss curve that when the initial position is unknown, the method of the present invention can converge, while the iterative least squares algorithm diverges and cannot converge.

[0165] To further illustrate the performance of the method of the present invention when the initial position is unknown, the method of the present invention and the grid method are used to perform Doppler positioning in a dynamic situation, and the granularity of the grid method is 50m. The latitude range of the experimental path is: [28.215˚, 28.230˚]; the longitude range is: [112.987˚, 112.992˚]; the altitude range is: [10 (m), 1000 (m)]. Figure 4 As shown, the trajectories of the benchmark value, the method of the present invention and the grid method are given. Figure 4 It can be clearly seen that this method has great advantages over the grid method.

[0166] In order to further illustrate the influence of the method of the present invention on the positioning accuracy, when the initial state of the carrier to be positioned is known, the Doppler positioning solution is respectively performed using the method of the present invention and the traditional elevation angle weighting. Figure 5 As shown, the trajectories of the benchmark value, the method of the present invention and the traditional weighting method are given. The method of the present invention is closer to the benchmark value than the traditional weighting method.

[0167] In order to qualitatively verify the superiority of the positioning performance of the method of the present invention, Figure 6a , Figure 6b , Figure 7a , Figure 7bThe position and velocity errors of the method of the present invention and the traditional weighted method are given respectively. Among them: RMSE (Root Mean Squared Error) represents the root mean square error, which is used to measure the difference between the solution result and the simulation true value; NED represents the north-east ground coordinate system; V_N represents the north velocity; V_E represents the east velocity; V_D represents the ground velocity. The average positioning error and average fixed velocity error of the two methods are shown in Table 2.

[0168]

[0169] In this embodiment, the method of the present invention improves the positioning performance by 52.35% and the speed-fixing performance by 37.70%. This embodiment further illustrates the adaptability of the present invention in dynamic situations and improves the Doppler positioning accuracy.

[0170] A second aspect of the present invention discloses a low-orbit satellite Doppler positioning device, the device comprising a processing module, the processing module being configured to execute:

[0171] Step S1, according to the visible satellites of the carrier to be positioned, obtain the satellite ephemeris information of the visible satellites at the same time and the Doppler observation value corresponding to the satellite frequency point;

[0172] Step S2, using the satellite ephemeris information in combination with the iterative matrix eigenvalue to calculate the damping term;

[0173] Step S3, based on the satellite ephemeris information and the Doppler observation quantity, combined with the damping term, determining the position, velocity and clock drift of the carrier to be positioned as an initial state vector;

[0174] Step S4: According to the initial state vector, the Doppler observation quantity is weighted filtered using the line-of-sight angle between the visible satellite and the carrier to be positioned and the visible satellite velocity contained in the satellite ephemeris information to calculate the precise positioning and constant speed result of the carrier to be positioned.

[0175] The third embodiment (Low-orbit satellite Doppler positioning device)

[0176] The device comprises:

[0177] The data input module is used to obtain satellite ephemeris information and Doppler observations according to the satellite ephemeris protocol file and the observation protocol file as input data for subsequent processing steps.

[0178] The damping factor construction module is used to calculate the damping factor according to the satellite ephemeris information and the iteration matrix, so as to solve the algorithm divergence problem of the iteration process when the initial state is unknown.

[0179] The initial state quantity estimation module is used to iteratively estimate the initial state quantity of the carrier to be positioned according to the Doppler observation quantity and satellite ephemeris information in combination with the damping factor construction module, as input data for subsequent processing steps.

[0180] The weighted filtering positioning solution module is used to obtain the position coordinates, three-dimensional velocity and clock drift of the carrier to be positioned at any time through forward weighted filtering according to the initial state quantity, state equation, observation equation and weight matrix.

[0181] The third aspect of the present invention discloses an electronic device. The electronic device includes a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, the low-orbit satellite Doppler positioning method described in the first aspect of the present disclosure is implemented.

[0182] The fourth aspect of the present invention discloses a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the low-orbit satellite Doppler positioning method described in the first aspect of the present disclosure is implemented.

[0183] The beneficial technical effects brought about by the present invention include: (1) Through the damping term construction scheme of the present invention, the divergence of the positioning algorithm can be limited when the initial error is too large. (2) Through the iterative estimation of the initial state quantity of the carrier to be positioned scheme of the present invention, the initial position and speed of the carrier to be positioned can be quickly estimated. (3) Through the satellite speed and line of sight weighted and forward filtered positioning solution scheme of the present invention, the state vector can converge quickly, and can simultaneously estimate the position coordinates, three-dimensional velocity and clock drift of the carrier to be positioned. (4) Through the method of the present invention, the applicability and positioning performance of the satellite Doppler positioning system can be significantly improved. (5) Through the method of the present invention, it can be widely used in low-orbit satellite receivers and measurement stations.

[0184] Please note that the technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, all possible combinations of the technical features in the above embodiments are not described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification. The above-mentioned embodiments only express several implementation methods of the present application, and their descriptions are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that for ordinary technicians in this field, without departing from the concept of the present application, several variations and improvements can be made, which all belong to the scope of protection of the present application. Therefore, the scope of protection of the patent in this application shall be based on the attached claims.

Claims

1. A low-orbit satellite Doppler positioning method, characterized in that: The method comprises: Step S1, according to the visible satellites of the carrier to be positioned, obtain the satellite ephemeris information of the visible satellites at the same time and the Doppler observation value corresponding to the satellite frequency point; Step S2, using the satellite ephemeris information in combination with the iterative matrix eigenvalue to calculate the damping term; The calculation formula of the iteration matrix is: Among them, G m represents the iteration matrix in the mth iteration; represents the Jacobian matrix of the observation equation in the mth iteration; Wherein, the calculation formula of the damping term is: Among them, λ m I is the damping term in the mth iteration, I is the identity matrix; λ max is the iteration matrix G m The maximum eigenvalue of min is the iteration matrix G m The minimum eigenvalue of ; C is the condition number coefficient; Step S3, based on the satellite ephemeris information and the Doppler observation quantity, combined with the damping term, determining the position, velocity and clock drift of the carrier to be positioned as an initial state vector; Step S4: According to the initial state vector, the Doppler observation quantity is weighted filtered using the line-of-sight angle between the visible satellite and the carrier to be positioned and the visible satellite velocity contained in the satellite ephemeris information to calculate the precise positioning and constant speed result of the carrier to be positioned.

2. A low-orbit satellite Doppler positioning method according to claim 1, characterized in that: In the method: The satellite ephemeris information refers to a protocol file used to calculate the position coordinates and three-dimensional velocity of visible satellites in the Earth-centered Earth-fixed coordinate system; The visible satellite indicators refer to low-orbit communication satellites or low-orbit navigation satellites with consistent frequencies.

3. A low-orbit satellite Doppler positioning method according to claim 2, characterized in that: In step S1: Acquire satellite ephemeris information of n visible satellites at time k and Doppler observation quantities corresponding to satellite frequencies according to the visible satellites of the carrier to be positioned; Wherein, when the carrier to be positioned is in a stationary state, n≥4; when the carrier to be positioned is in a moving state, n≥7.

4. A low-orbit satellite Doppler positioning method according to claim 3, characterized in that: In step S2: At the initial moment, construct the Doppler observation equation: Among them, f c is the nominal carrier frequency of the satellite signal; c is the speed of light in vacuum; f i (s) is the Doppler observation of the i-th satellite; s is the state vector of the carrier to be positioned; p i s is the three-dimensional position vector of the i-th satellite, p i s =[x i s ,y i s , z i s ], x i s ,y i s , z i s Corresponding to the position vectors in the x, y, and z directions respectively; v i s is the three-dimensional velocity vector of the i-th satellite, v i s =[v xi s , v yi s , v zi s ],v xi s , v yi s , v zi s Corresponding to the velocity vectors in the x, y, and z directions respectively; ε i is the observation noise of the i-th satellite; K T , Q T , J T To select the matrix, the expressions are: J T ＝[0 0 0 0 0 0 -1] The state vector s of the carrier to be located is expressed as p x , p y , p z , v x , v y , v z are the three-dimensional position coordinates and three-dimensional velocity coordinates of the carrier to be positioned in the Earth-centered Earth-fixed coordinate system, respectively, and x, y, and z correspond to the x, y, and z directions respectively; is the clock drift of the carrier to be positioned; the iteration matrix is ​​a 7×7 symmetric square matrix; The Jacobian matrix of the observation equation in the mth iteration has a matrix size of n×7 and is expressed as: Among them, S m is the state quantity of the carrier to be positioned calculated in the mth iteration; Where I is a 7×7 unit matrix; the calculation formula of the condition number coefficient C is: C=10 6 (36.116e (-0.3063n) +963.69e (-0.0033n) )。 5. A low-orbit satellite Doppler positioning method according to claim 4, characterized in that: In step S3: Construct the linearized system of Doppler observation equations: in, is the linearized Doppler observation of the ith satellite; f i (s m ) is the Doppler observation of the ith satellite in the mth iteration calculation, is the partial derivative of the Doppler observation of the ith satellite at the state quantity of the carrier to be positioned in the mth iteration calculation, and its calculation formula is: in: Among them, p m r is the position coordinate of the carrier to be located in the mth iteration calculation, p m r =[x m r , z m r ,y m r ], x m r , z m r ,y m r Corresponding to the position coordinates in the x, y, and z directions respectively, v m r is the three-dimensional velocity of the carrier to be positioned in the mth iteration calculation, v m r =[v m x ,v m y ,v m z ],v m x ,v m y ,v m z Corresponding to the speed in the x, y, and z directions respectively; is the clock drift of the carrier to be located in the mth iteration calculation; is the direction cosine, is the velocity cosine, Compute the Jacobian matrix of the observation equation in the mth iteration And calculate the iteration matrix G m ; According to the iteration matrix G m and the condition number coefficient C to calculate the damping term; according to the state quantity s of the carrier to be positioned in the mth iteration calculation m , calculate the state quantity s of the carrier to be located in the m+1th iteration calculation m+1 : Determine whether the residual value of the solution state is less than the initial set iteration termination condition ∈; if so, output the solution result s * ; If not, continue iterating; the state residual value is calculated as follows: s m+1 -s m ; Iteration termination condition∈<0.0001.

6. A low-orbit satellite Doppler positioning method according to claim 5, characterized in that: In step S4: The initial state vector is the solution result s * , the weighted filter is an extended Kalman filter, and its state equation is: in, is the predicted state vector of the carrier to be located at the kth moment; is the estimated state vector of the carrier to be located at the k-1th moment; A is the state transfer matrix, the matrix size is 7×7; w k is the process noise; when k-1=0, The observation equation of the extended Kalman filter is the Doppler observation equation; the observation weight matrix of the extended Kalman filter at the kth moment is: Among them, α i ,i=1…n k , α i is the line-of-sight angle of the ith satellite, n k is the number of satellites observed at the kth moment; α i The calculation formula is: in, is the position coordinate of the carrier to be located estimated by the extended Kalman filter at the k-1th moment, and the extended Kalman filter is combined with the initial state vector s * , Doppler observations, satellite ephemeris information, observation weight matrix R k , the estimated state vector of the carrier to be located at the kth moment is deduced The information includes the precise position, precise three-dimensional velocity and precise clock drift of the carrier to be positioned.

7. A low-orbit satellite Doppler positioning method according to claim 1, characterized in that: The carrier to be positioned is a low-orbit satellite receiver or an observation station.

8. A low-orbit satellite Doppler positioning device, characterized in that: The apparatus comprises a processing module configured to perform: Step S1, according to the visible satellites of the carrier to be positioned, obtain the satellite ephemeris information of the visible satellites at the same time and the Doppler observation value corresponding to the satellite frequency point; Step S2, using the satellite ephemeris information in combination with the iterative matrix eigenvalue to calculate the damping term; The calculation formula of the iteration matrix is: Among them, G m represents the iteration matrix in the mth iteration; represents the Jacobian matrix of the observation equation in the mth iteration; Wherein, the calculation formula of the damping term is: Among them, λ m I is the damping term in the mth iteration, I is the identity matrix; λ max is the iteration matrix G m The maximum eigenvalue of min is the iteration matrix G m The minimum eigenvalue of ; C is the condition number coefficient; Step S3, based on the satellite ephemeris information and the Doppler observation quantity, combined with the damping term, determining the position, velocity and clock drift of the carrier to be positioned as an initial state vector; Step S4: According to the initial state vector, the Doppler observation quantity is weighted filtered using the line-of-sight angle between the visible satellite and the carrier to be positioned and the visible satellite velocity contained in the satellite ephemeris information to calculate the precise positioning and constant speed result of the carrier to be positioned.

9. An electronic device, characterized in that: The electronic device includes a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, a low-orbit satellite Doppler positioning method as described in any one of claims 1-7 is implemented.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by the processor, the low-orbit satellite Doppler positioning method described in any one of claims 1-7 is implemented.

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