Multi-track combined Doppler positioning method based on two-step solution

Abstract

The invention discloses a multi-track joint Doppler positioning method based on two-step solution, which aims at a scene of a multi-track Doppler positioning system, a receiver receives ground interference source information through a satellite signal, and processes data through the multi-track joint Doppler positioning method so as to realize more accurate positioning. The method comprises the following steps of: respectively solving Doppler frequency difference on each orbit, calculating and correcting frequency deviation caused by clock deviation, then carrying out joint solution on multi-orbit data, establishing a unified observation equation model, estimating the position of a target interference source by utilizing a least square method, gradually adjusting and optimizing estimated values of target parameters by adopting an iterative optimization method, and finally calculating and correcting the frequency deviation caused by clock deviation. And the convergence condition is reached. According to the method, the clock skew problem in multi-orbit combined positioning is effectively solved, the positioning precision and the convergence speed are improved, information can be more effectively integrated by combining two-orbit data, the influence of single satellite observation errors is reduced, and therefore higher positioning precision is achieved.

Description

Technical Field

[0001] The present invention relates to a satellite positioning technology, in particular to a multi-track joint Doppler positioning method based on two-step solution. Background Art

[0002] With the development of satellite navigation technology, multi-orbit joint positioning technology has attracted widespread attention due to its high precision and reliability. Among various positioning technologies, Doppler positioning is valued for its ability to provide velocity information. Multi-orbit joint Doppler positioning utilizes observation data of the same target from multiple satellites and determines the target's position and velocity by analyzing the Doppler frequency shift of the target relative to the satellites. While this method theoretically provides high positioning accuracy, it still faces numerous challenges in practical application. In actual operation, multi-orbit joint Doppler positioning systems can experience frequency variations due to complex factors such as atmospheric delay and multipath effects, which can disrupt the system's positioning results.

[0003] In multi-orbit LEO satellite Doppler positioning systems, clock bias between the satellite and the receiver is a critical issue. Clock bias causes a discrepancy between the received and transmitted frequencies, a discrepancy that is particularly pronounced in multi-orbit positioning. Since satellites in different orbits may have different clock biases, directly calculating the Doppler frequency difference can lead to positioning errors. In particular, in multi-orbit LEO problems, the frequency bias caused by clock bias is a step variable, and direct solutions often fail to converge. In practical applications, existing technologies suffer from slow convergence and low accuracy when addressing positioning problems under conditions of poor satellite geometric distribution (DOP). Currently, existing multi-orbit Doppler positioning methods require complex mathematical problems when processing observation data from multiple satellites, particularly when calculating the frequency difference. These methods require high computational complexity and often struggle to achieve ideal accuracy. Developing a multi-orbit Doppler positioning technology that can provide stable positioning services in various environments is crucial for advancing the state of the art in these fields. Summary of the Invention

[0004] Purpose of the invention: In response to the above-mentioned problems existing in the prior art, the present invention proposes a multi-track joint Doppler positioning method based on a two-step solution. Through the two-step solution method, multi-track observation data is effectively utilized, the convergence domain is expanded, the positioning accuracy is improved, and the complexity of centralized processing is avoided.

[0005] Technical solution: The present invention provides a multi-track joint Doppler positioning method based on a two-step solution, comprising the following steps:

[0006] (1) Using the receiver on the satellite, the frequency of the signal from the ground stationary radiation source is measured at regular intervals. Multiple satellites collect signals from the same ground radiation source and record the signal frequency data received by each satellite.

[0007] (2) Preprocess the signals received from each satellite and extract the Doppler shift characteristics;

[0008] (3) Perform preliminary processing on the frequency shift data of each satellite, calculate the difference between the received signal frequency and the transmitted signal frequency, and obtain the original frequency difference observation value; use the least squares method to filter the original frequency difference observation value of each satellite to eliminate the influence of random noise and obtain an accurate frequency difference estimate; based on the clock model of the satellite and receiver, calculate and correct the systematic frequency error caused by the clock bias; synchronize and merge the corrected frequency difference data of each satellite;

[0009] (4) Establish the Doppler shift observation equation. Based on the WGS-84 earth model, construct the matrix equation of the geodetic coordinates of the radiation source. Use the coordinate transformation relationship to realize the conversion from Cartesian coordinates to geodetic coordinates, and realize the unified mathematical modeling of multi-track observation data.

[0010] (5) The area under the satellite track is divided into grids according to longitude and latitude, and the least squares solution is obtained. A cost function is constructed to achieve a rough estimate of the radiation source position and determine the search range;

[0011] (6) Optimal estimation is solved to minimize the cost function, find the grid point that minimizes the cost function, and output the optimal estimated radiation source position.

[0012] Furthermore, the implementation process of step (1) is as follows:

[0013] The receiver has high-precision signal capture and Doppler shift measurement capabilities, and its position is defined as s i =(x i ,y i ,z i ) T , the speed is The receiver monitors a specific frequency point f0 and records the Doppler observation f of the interference source. d ;

[0014] The receiver's observation data, including Doppler frequency shift measurements, satellite position and velocity information, and observation time, provides basic data for subsequent frequency difference processing and positioning calculations.

[0015] Furthermore, the implementation process of step (3) is as follows:

[0016] The distance r between the receiver and the ground interference source received by the observation stationi It is expressed as follows:

[0017] r i =(x i -x0,y i -y0,z i -z0) T (1)

[0018] By estimating the Doppler frequency f received by the satellite d Calculate the radial velocity of the satellite, calculate the radial distance, and calculate the location of the interference source by counting the radial distance information at multiple times; the Doppler frequency is expressed as:

[0019]

[0020] in, Represents the speed of relative motion, which is the derivative of the distance between the two. It is negative when moving towards each other and positive when moving away from each other:

[0021]

[0022] use is expressed as a unit vector in the distance direction between the two; then the i-th moment The relationship between the target coordinates is established by the following formula:

[0023]

[0024] in,

[0025]

[0026] The true Doppler observation value measured at time i should be:

[0027]

[0028] From this we can get:

[0029]

[0030] Among them, n i The noise of the frequency measurement at time i follows Gaussian distribution, δ f It is the frequency deviation caused by the clock;

[0031] δ f Make corrections:

[0032] f i =f d,i -δ f (8)

[0033] Among them, f i is the corrected frequency.

[0034] Furthermore, the implementation process of step (4) is as follows:

[0035] The Doppler frequency shift observation equation is established, and the frequencies measured at N moments are expressed in matrix form as follows:

[0036] Γ=f0F+n (9)

[0037] The value F of the Doppler frequency shift function at different positions and the noise measured at N moments are specifically expressed as:

[0038]

[0039] Set the solution variable to x = [s j ′δ f ] T′ , the initial solution is x0=[s j0 ′δ f0 ]′ T Simultaneous observation equations:

[0040]

[0041] Where G is the state update matrix and Δf is the error matrix;

[0042] The WGS-84 earth model coordinate system is used to represent the position of the radiation source, and the following conversion relationship is used:

[0043]

[0044] Among them, H is the weight matrix, is the radius of curvature of the circle at that point, and e is the first eccentricity; the position coordinates of the target source are replaced by the transformation of expression (18) to obtain the matrix equation of the geodetic coordinates (L, B), realizing the geodetic surface positioning of the WGS-84 model.

[0045] Furthermore, the state update matrix G is:

[0046]

[0047] The error matrix Δf is:

[0048]

[0049] Furthermore, the weight matrix H is expressed as follows:

[0050] H=(G T G) -1 (14)

[0051] According to the definition of geometric dilution of positioning error:

[0052]

[0053]

[0054] Among them, H ii are the diagonal elements of the weight matrix, PDOP is the positional dilution of precision, HDOP is the horizontal dilution of precision, and GDOP is the geometric dilution of precision.

[0055] Furthermore, the process of gridding the area under the satellite track according to longitude and latitude in step (5) is as follows:

[0056] The simulation environment was launched, with m circular orbit satellites at approximately 550 km altitude and varying inclination angles configured to generate varying frequency deviation data. 60 seconds of continuous data observations were recorded during the target source positioning analysis. Any 60 seconds of data within a specific time range was then extracted and retained. Phase modeling was used to analyze the signal and estimate the frequency and frequency rate of change. Considering the inevitable effects of frequency stability, a GDOP plot was obtained for the area below the satellites. The GDOP curve distribution was analyzed to determine the area with the best positioning performance. The impact of varying frequency measurement accuracies on positioning error was analyzed. By applying mean square error processing to the frequency measurement error, the theoretical lower limit of the position deviation of the radiating source at a given location was determined.

[0057] The area below the satellite orbit is divided into longitude and latitude grids, and the two-dimensional grid points are defined as the set ∑. For each grid point (L k ,B l )∈∑, calculate its least squares solution:

[0058]

[0059] Where k and l represent the horizontal and vertical counts of the grid respectively.

[0060] Furthermore, the implementation process of step (6) is as follows:

[0061] The optimal estimate is solved as follows:

[0062]

[0063] in, is the optimal estimated location parameter, is the least squares solution of the grid points that minimizes the cost function;

[0064] Find the optimal estimated radiation source position. The cost function is expressed as follows:

[0065]

[0066] Output to minimize (L k ,B l ) as the optimal estimate of the interference source location.

[0067] Beneficial effects: Compared with the prior art, the present invention has the following beneficial effects: the present invention improves the accuracy of multi-orbit joint positioning by first solving the frequency difference separately and then jointly solving it; by processing the multi-orbit observation data in two steps, first independently estimating the frequency difference between each satellite and the ground interference source, because the frequency deviation caused by the clock deviation is not a constant in the multi-orbit case, direct solution will cause the result to fail to converge, so the observation data needs to be corrected, and then a comprehensive model is used to combine the two-orbit data for solution, and the position estimation of the ground interference source is iteratively optimized to improve the positioning accuracy; the two-step solution effectively solves the clock deviation problem in multi-orbit joint positioning, improves the positioning accuracy and convergence speed, and by combining the two-orbit data, it can more effectively integrate information and reduce the influence of single satellite observation errors, thereby achieving higher positioning accuracy; in addition, the present invention allows it to be carried out without the need for centralized processing, reducing the demand for computing resources, making it more effective in dynamic and real-time application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 Flowchart of the present invention. DETAILED DESCRIPTION

[0069] The present invention is described in further detail below with reference to the accompanying drawings.

[0070] The present invention proposes a multi-track joint Doppler positioning method based on a two-step solution. For the scenario of a multi-track joint low-orbit satellite Doppler positioning system, the receiver receives ground interference source information through satellite signals, and solves the frequency difference separately first, and then corrects the multi-track data for joint solution to achieve more accurate positioning. First, the satellite signal received by the receiver contains information about the ground interference source, and the frequency shift data of each satellite is preliminarily processed to obtain a preliminary frequency difference. The observation data of each satellite is processed using the least squares method to obtain the frequency difference result of each satellite. Correct the frequency deviation caused by the clock deviation to ensure the accuracy of the observation data of each satellite. Put the corrected multi-track data together for joint solution, and iterate the position of the interference source using the least squares method. Figure 1 As shown, the specific steps include:

[0071] Step 1: Using a reconnaissance receiver on a satellite, measure the frequency of signals from a ground-based stationary radiation source at regular intervals. Multiple satellites collect signals from the same ground-based radiation source, and each satellite records the frequency data of the signal received.

[0072] A multi-orbit joint satellite system model is established to accurately locate the ground interference source. The system includes a receiver with high-precision signal capture and Doppler shift measurement capabilities. Its position is defined as s i =(x i ,y i ,z i ) T , the speed is The receiver monitors a specific frequency point f0 and records the Doppler observation f of the interference source. d , which serves as the basis for subsequent positioning calculations. The data processing unit estimates the true position of the interference source s0 = (x0, y0, z0) from the data collected by the receiver. T and the frequency deviation δ caused by the clock f The data processing unit is responsible for collecting the observation data of the receiver, including Doppler frequency shift measurement values, satellite position and velocity information, observation time, etc., providing basic data for subsequent frequency difference processing and positioning calculation.

[0073] Step 2: Preprocess the signal received from each satellite, including filtering and demodulation, to extract the Doppler frequency shift characteristics.

[0074] Step 3: Preliminary frequency offset processing: Perform preliminary processing on the frequency shift data of each satellite to obtain the preliminary frequency offset. Use the least squares method to process the observation data of each satellite and obtain the frequency offset result of each satellite.

[0075] The distance r between the receiver and the ground interference source received by the observation station i It is expressed as follows:

[0076] r i =(x i -x0,y i -y0,z i -z0) T (1)

[0077] By estimating the Doppler frequency f received by the satellite d The radial velocity of the satellite can be calculated, and the radial distance can be calculated by combining the time delay and other information. The location of the interference source can be calculated by counting the radial distance information at multiple times. The Doppler frequency can be expressed as:

[0078]

[0079] in, Represents the speed of relative motion, which is the derivative of the distance between the two. It is negative when moving towards each other and positive when moving away from each other:

[0080]

[0081] use is represented as a unit vector in the distance direction between the two. Then the i-th moment The relationship between the target coordinates can be established by the following formula:

[0082]

[0083] in,

[0084]

[0085] Therefore, the true Doppler observation value measured at the i-th time slot should be:

[0086]

[0087] From this we can get:

[0088]

[0089] Among them, n i The noise of the frequency measurement at time i follows Gaussian distribution, δ f It is the frequency deviation caused by the clock.

[0090] In the case of multiple tracks f Corresponding to a step variable, direct solution cannot converge, so after performing the above steps on the two tracks of data respectively, the two tracks of data need to be corrected:

[0091] f i =f d,i -δ f (8)

[0092] Among them, f i is the corrected frequency.

[0093] Step 4: Establish the observation equation. Based on the WGS-84 earth model, construct the matrix equation of the geodetic coordinates of the radiation source. Use the coordinate transformation relationship to realize the conversion from Cartesian coordinates to geodetic coordinates, and realize the unified mathematical modeling of multi-track observation data.

[0094] The Doppler frequency shift observation equation is established, and the frequencies measured at N moments are expressed in matrix form as follows:

[0095] Γ=f0F+n(9)

[0096] The value of the Doppler frequency shift function at different positions and the noise measured at N moments can be specifically expressed as:

[0097]

[0098] Set the solution variable to x = [s j ′δ f ]T′ , the initial solution is x0=[s j0 ′δ f0 ]′ T Simultaneous observation equations:

[0099]

[0100] The state update matrix G is:

[0101]

[0102] The error matrix Δf is:

[0103]

[0104] The weight matrix H is defined as follows:

[0105] H=(G T G) -1 (14)

[0106] According to the definition of geometric dilution of positioning error:

[0107]

[0108] Among them, H ii are the diagonal elements of the weight matrix, PDOP is the positional dilution of precision, HDOP is the horizontal dilution of precision, and GDOP is the geometric dilution of precision.

[0109] The WGS-84 earth model coordinate system is used to represent the position of the radiation source, and the following conversion relationship is used:

[0110]

[0111] Its location coordinates are expressed in latitude, longitude and height (L, B, H). is the radius of curvature of the circle at this point, and e is the first eccentricity, which is approximately 0.08182. Substituting the position coordinates of the target source into the transformation of expression (18), the matrix equation of the geodetic coordinates (L, B) can be obtained.

[0112] Step 5: Divide the area under the satellite track into grids according to longitude and latitude, find the least squares solution, and construct a cost function to achieve a rough estimate of the radiation source position and determine the search range.

[0113] A simulation environment was launched, configuring m circular orbital satellites at approximately 550 km altitude and varying inclination angles to generate diverse frequency deviation data. 60 seconds of continuous data observations were recorded during the target source positioning analysis. Any 60 seconds of data within a specific timeframe was then extracted from these reports and retained. Phase modeling was used to analyze the signal and estimate the frequency and frequency rate of change. Taking into account the inevitable effects of frequency stability, a geometric dilution factor (GDOP) plot was generated for the area below the satellites. The GDOP curve distribution was analyzed to identify the area with the best positioning performance. The impact of varying frequency measurement accuracies on positioning error was analyzed. By applying mean square error (MSE) processing to the frequency measurement error, a theoretical lower limit for the positional deviation of a radiation source at a given location was derived.

[0114] The two-dimensional grid points divided by longitude and latitude are defined as a collection ∑. For each grid point (L k ,B l )∈∑, calculate its least squares solution, the calculation formula is as follows:

[0115]

[0116] Where k and l represent the horizontal and vertical counts of the grid respectively.

[0117] Step 6: Optimal estimation is solved to minimize the cost function, find the grid point that minimizes the cost function, and output the optimal estimated radiation source position, including longitude and latitude and other relevant parameters.

[0118] Using the result of formula (19), the least squares solution of the grid points is obtained, which is expressed as follows:

[0119]

[0120] in, is the optimal estimated location parameter, is the least squares solution of the grid points that minimizes the cost function.

[0121] Find the optimal estimated radiation source position. The cost function is expressed as follows:

[0122]

[0123] Output to minimize (L k ,B l ) as the optimal estimate of the interference source location.

[0124] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art could make various modifications and improvements without departing from the spirit of the present application, all of which fall within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be determined by the appended claims.

Claims

1. A multi-track joint Doppler positioning method based on two-step solution, characterized in that: The following steps are involved: (1) Using the receiver on the satellite, the frequency of the signal from the ground stationary radiation source is measured at regular intervals. Multiple satellites collect signals from the same ground radiation source and record the signal frequency data received by each satellite. (2) Preprocess the signals received from each satellite and extract the Doppler shift characteristics; (3) Perform preliminary processing on the frequency shift data of each satellite, calculate the difference between the received signal frequency and the transmitted signal frequency, and obtain the original frequency difference observation value; use the least squares method to filter the original frequency difference observation value of each satellite to eliminate the influence of random noise and obtain an accurate frequency difference estimate; based on the clock model of the satellite and receiver, calculate and correct the systematic frequency error caused by the clock bias; synchronize and merge the corrected frequency difference data of each satellite; (4) Establish the Doppler shift observation equation. Based on the WGS-84 earth model, construct the matrix equation of the geodetic coordinates of the radiation source. Use the coordinate transformation relationship to realize the conversion from Cartesian coordinates to geodetic coordinates, and realize the unified mathematical modeling of multi-track observation data. (5) The area under the satellite track is divided into grids according to longitude and latitude, and the least squares solution is obtained. A cost function is constructed to achieve a rough estimate of the radiation source position and determine the search range; (6) Optimal estimation is solved to minimize the cost function, find the grid point that minimizes the cost function, and output the optimal estimated radiation source position.

2. The multi-track joint Doppler positioning method based on two-step solution according to claim 1, characterized in that: The implementation process of step (1) is as follows: The receiver has high-precision signal capture and Doppler shift measurement capabilities, and its position is defined as s i =(x i ,y i ,z i ) T , the speed is The receiver monitors a specific frequency point f0 and records the Doppler observation f of the interference source. d ; The receiver's observation data, including Doppler frequency shift measurements, satellite position and velocity information, and observation time, provides basic data for subsequent frequency difference processing and positioning calculations.

3. The multi-track joint Doppler positioning method based on two-step solution according to claim 1, characterized in that: The implementation process of step (3) is as follows: The distance r between the receiver and the ground interference source received by the observation station i It is expressed as follows: r i =(x i -x0,y i -y0,z i -z0) T (1) By estimating the Doppler frequency f received by the satellite d Calculate the radial velocity of the satellite, calculate the radial distance, and calculate the location of the interference source by counting the radial distance information at multiple times; the Doppler frequency is expressed as: in, Represents the speed of relative motion, which is the derivative of the distance between the two. It is negative when moving towards each other and positive when moving away from each other: use is expressed as a unit vector in the distance direction between the two; then the i-th moment The relationship between the target coordinates is established by the following formula: in, The true Doppler observation value measured at time i should be: From this we can get: Among them, n i The noise of the frequency measurement at time i follows Gaussian distribution, δ f is the frequency deviation caused by the clock; δ f Make corrections: f i =f d,i -d f (8) Among them, f i is the corrected frequency.

4. The multi-track joint Doppler positioning method based on two-step solution according to claim 1, characterized in that: The implementation process of step (4) is as follows: The Doppler frequency shift observation equation is established, and the frequencies measured at N moments are expressed in matrix form as follows: Γ=f0F+n(9) The value F of the Doppler frequency shift function at different positions and the noise measured at N moments are specifically expressed as: Set the solution variable to x = [s j′ δ f ] T ′, the initial solution is x0=[s j0′ δ f0 ]′ T Simultaneous observation equations: Where G is the state update matrix and Δf is the error matrix; The WGS-84 earth model coordinate system is used to represent the position of the radiation source, and the following conversion relationship is used: Among them, H is the weight matrix, is the radius of curvature of the circle at this point, and e is the first eccentricity; the position coordinates of the target source are replaced by the transformation of expression (18) to obtain the matrix equation of the geodetic coordinates (L, B), realizing the geodetic surface positioning of the WGS-84 model.

5. The multi-track joint Doppler positioning method based on two-step solution according to claim 4 is characterized in that: The state update matrix G is: The error matrix Δf is:

6. The multi-track joint Doppler positioning method based on two-step solution according to claim 4, characterized in that: The weight matrix H is expressed as follows: H=(G T G) -1 (14) According to the definition of geometric dilution of positioning error: Among them, H ii are the diagonal elements of the weight matrix, PDOP is the positional dilution of precision, HDOP is the horizontal dilution of precision, and GDOP is the geometric dilution of precision.

7. The multi-track joint Doppler positioning method based on two-step solution according to claim 1, characterized in that: The process of gridding the area under the satellite track according to longitude and latitude in step (5) is as follows: Start the simulation environment and configure m circular orbit satellites with an orbital altitude of approximately 550 km and different inclination angles to ensure the generation of different frequency difference data; when performing positioning analysis on the target source, continuously record data observation values ​​for 60 seconds; Then, any 60 seconds of data within a specific time range is extracted and retained. Phase modeling is used to analyze the signal and estimate the frequency and frequency change rate. Taking into account the inevitable influence of frequency stability, a GDOP plot is obtained for the area below the satellite. The GDOP curve distribution is analyzed to determine the area with the best positioning effect. The impact of different frequency measurement accuracies on positioning error is analyzed. By applying mean square error processing to the frequency measurement error, the theoretical lower limit of the position deviation of the radiating source at a given location is obtained. The area below the satellite orbit is divided into longitude and latitude grids, and the two-dimensional grid points are defined as the set ∑. For each grid point (L k ,B l )∈∑, calculate its least squares solution: Where k and l represent the horizontal and vertical counts of the grid respectively.

8. The multi-track joint Doppler positioning method based on two-step solution according to claim 1, characterized in that: The implementation process of step (6) is as follows: The optimal estimate is solved as follows: in, is the optimal estimated location parameter, is the least squares solution of the grid points that minimizes the cost function; Find the optimal estimated radiation source position. The cost function is expressed as follows: Output to minimize (L k ,B l ) as the optimal estimate of the interference source location.

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