A method for locating multi-satellite electromagnetic signal sources based on overpass time acquisition

Abstract

This invention discloses a multi-satellite electromagnetic signal source localization method based on overpass time acquisition. It primarily addresses the problems of existing methods failing to achieve on-board positioning under conditions of low link bandwidth and limited payload resources, and also suffers from high algorithm complexity. The implementation scheme is as follows: S satellites are selected, and the frequency of the target signal is continuously recorded starting from the moment the target signal can be detected. The overpass time of each satellite is calculated based on the Doppler frequency change rate of the detected target signal. The region where the target signal source is located is calculated based on the time when the satellite begins to detect the target signal and the time when it stops receiving the target signal. This region is then divided into grids, and the shortest distance time between the grid and the satellite is calculated. Based on the overpass time and the shortest distance time, the average position deviation of each grid is calculated to determine the location of the target signal source. This invention simplifies the complexity of current satellite positioning technology, improves signal positioning accuracy, and can be used for real-time online on-board positioning of electromagnetic signal sources.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic spectrum monitoring, and in particular relates to a multi-satellite electromagnetic signal source localization method, which can be used to determine the location of ground electromagnetic signal radiation sources in real time from satellites. Background Technology

[0002] Compared with ground-based electromagnetic spectrum monitoring methods, satellite-based electromagnetic spectrum monitoring, especially passive location of radiation sources, has advantages such as wide coverage, no limitation by terrain or objects, and no multipath interference from ground channels. However, space-based satellites also face challenges such as weak received signals, difficulty in identifying signal characteristics, time-varying channel attenuation, narrow satellite backhaul channels, high algorithm complexity, and difficulty in online real-time processing onboard.

[0003] Currently, there are a series of methods for passive positioning of ground electromagnetic signals using spaceborne monitoring equipment. These methods can be categorized by the number of satellites involved: single-satellite positioning and multi-satellite positioning; and by signal feature extraction: direction-finding positioning, time-difference positioning, frequency-difference positioning, received signal strength indication positioning, Doppler rate of change positioning, and joint positioning. Single-satellite positioning often uses direction-finding or Doppler rate of change methods, but it requires high accuracy in direction finding and payload attitude control, and suffers from significant positioning errors. Multi-satellite positioning often uses time-difference, frequency-difference, or a combination of both methods, offering higher accuracy but with higher computational complexity and stringent requirements for clock synchronization between satellites.

[0004] In his master's thesis, "Research on Target Tracking Algorithm Based on Three-Star Passive Fusion Positioning System" (Harbin: Harbin Engineering University, 2021), Wang Chaoran proposed a three-star TDOA-FDOA-DOA fusion positioning method. Based on the traditional three-star time difference and frequency difference positioning system, this method obtains the arrival direction information of radiation sources by installing a one-dimensional interferometer device on the primary satellite, fusing it with the time difference and frequency difference information of the three satellites to achieve high-precision positioning of maneuvering targets at unknown elevations. However, due to the large detection range and numerous signals to be located on the satellite, it is difficult to achieve online real-time positioning of multiple signals on the satellite. If the spectrum data is transmitted back to the ground for calculation via satellite link, the bandwidth limitation will affect the implementation. Furthermore, the high computational complexity of this method will significantly impact the positioning timeliness. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of current satellite positioning technologies by proposing a multi-satellite electromagnetic signal positioning method based on overpass time acquisition. This method simplifies the complexity of current satellite positioning technologies, enables online real-time positioning of multiple signals on satellites, and improves positioning accuracy.

[0006] The technical idea of ​​this invention is to obtain the position deviation by using the overpass time of the satellite during the acquisition of the target signal and the shortest distance time of the target area from the satellite, thereby simplifying the algorithm complexity of the current satellite positioning technology and realizing online real-time positioning of multiple signals on the satellite under the current limited on-board payload conditions; by averaging all position deviations of each grid center, the grid center with the smallest average position deviation is selected as the positioning result to improve positioning accuracy.

[0007] Based on the above ideas, the implementation steps of the present invention include the following:

[0008] (1) S satellites continuously monitor signals at time intervals τ, that is, each satellite monitors the signal at time t. ib The target signal is detected and its frequency is continuously recorded until it is too far from the target signal source at time t. ie Terminate monitoring of the target signal, i = 1, 2, ..., S;

[0009] (2) Calculate the overpass time of each satellite:

[0010] (2a) Calculate the change in Doppler frequency Δf between every two adjacent moments when the satellite receives the target signal. t ;

[0011] (2b) Calculate the Doppler frequency change Δf of the target signal received by the satellite. t The two largest adjacent times t * and t * +τ, and take the median of two adjacent moments as the overpass moment of the satellite for the target signal.

[0012] (2c) Repeat steps (2a) to (2b) to obtain the overpass time of each satellite.

[0013] (3) Calculate the region where the target signal source is located:

[0014] (3a) Establish a geocentric-ground-fixed coordinate system, and obtain the nadir coordinates (x, t) of each satellite at the moment it begins monitoring the target signal, based on the satellite orbit information. ib ),y(t ib ),z(t ib The coordinates of the nadir point (x(t)) at the moment when receiving the target signal is terminated. ie ),y(t ie ),z(t ie )), calculate t ib and t ie The observation range D(t) of satellite i at time i ib ) and D(t ie ):

[0015]

[0016]

[0017] in, For Earth's latitude and longitude coordinates, To convert latitude and longitude coordinates to geocentric coordinates, (x1, y1, z1) represents the satellite observation range D(t). ib The coordinates of the center of the crown base circle (x2, y2, z2) are the satellite observation range D(t). ie The coordinates of the center of the crown base circle;

[0018] (3b) According to t ib and t ie The observation range D(t) of satellite i at time i ib ) and D(t ie ), to extend the observation range D(t) of all satellites ib ) and D(t ie By taking the intersection, we can obtain the region D where the target signal source is located;

[0019] (4) Divide the area where the target signal source is located into a grid:

[0020] (4a) Divide region D into M×N grids at equal intervals according to latitude and longitude, and take the center point C of the kth grid. k latitude and longitude coordinates Where k = 1, 2, ..., M × N;

[0021] (4b) Set the latitude and longitude coordinates of each grid center point Convert to Earth-centered Earth-fixed coordinates (x k ,y k ,z k );

[0022] (5) Determine the location of the target signal source:

[0023] (5a) For each grid center point, calculate the distance d between it and satellite i at the time t when the target signal is detected, based on the satellite orbit information. ik (t);

[0024] (5b) Based on distance d ik (t) Obtain the time t when the distance between satellite i and the center point of each grid is shortest. ik ;

[0025] (5c) Based on satellite i and each grid center point C k The shortest time t ik and overpass moment Calculate the average positional deviation of each grid center:

[0026]

[0027] (5d) Based on the average positional deviation of each grid center, obtain the grid that minimizes the average positional deviation.

[0028]

[0029] (5e) The grid with the smallest deviation Determine the final grid center and its latitude and longitude coordinates The coordinates of the target signal source are used to determine the location of the target signal source.

[0030] Compared with the prior art, the present invention has the following advantages:

[0031] 1. This invention only requires calculating the time of the maximum frequency change obtained by satellite monitoring of the target signal, and the position deviation can be obtained by using the time of ...

[0032] 2. Since this invention only requires calculation of the overpass time and position deviation, it can achieve online positioning on satellites under conditions of low satellite link bandwidth and limited payload resources such as on-board computing and power consumption. Moreover, the amount of data that needs to be transmitted back to the ground is only the positioning result data. Compared with traditional satellite positioning methods that require a large amount of monitoring data to be transmitted back to the ground for data processing, this invention reduces the great communication pressure on the satellite link and solves the bottleneck problems of low satellite link bandwidth and limited payload resources.

[0033] 3. This invention improves the accuracy of satellite positioning by dividing the target area into fine grids, averaging the positional deviations of all positions at the center of each grid, and selecting the grid center with the smallest average positional deviation as the positioning result. Compared with the errors caused by the large number of matrix operations required for multiple equal-frequency surfaces in traditional satellite positioning methods, this invention improves the accuracy of satellite positioning. Attached Figure Description

[0034] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0035] Figure 2 This is a schematic diagram of the overlapping side and top views of the satellite's observation range at the moments when a single satellite begins to monitor the target signal and terminates monitoring the target signal in this invention;

[0036] Figure 3 This is a schematic diagram of the grid division of the target area in this invention. Detailed Implementation

[0037] The embodiments and effects of the present invention will be further described in detail below with reference to the accompanying drawings.

[0038] Reference Figure 1 The implementation steps for the instance include the following:

[0039] Step 1: Select S satellites to monitor the frequency of the target signal.

[0040] In a satellite network, all satellites continuously monitor signal frequencies at time intervals τ during their operation. If a satellite detects a target signal within one operational cycle, that satellite is selected as the positioning satellite.

[0041] This example assumes there are a total of S positioning satellites, which are located at time t. ib The target signal is detected and its frequency is continuously recorded until it is too far from the target signal source at time t. ie Terminate monitoring of target signals, where i = 1, 2, ..., S.

[0042] Step 2: Calculate the overpass time of each satellite.

[0043] 2.1) Calculate the change Δf of the Doppler frequency between any two adjacent moments when the satellite receives the target signal. t :

[0044] Δf t =f t+τ -f t , t = t b , t b +τ,...,t e -τ

[0045] Among them, f t Let t be the frequency of the target signal received by the satellite at time t. b and t e These are the times when the satellite begins to detect the target signal and the times when it stops monitoring the target signal within one operational cycle;

[0046] 2.2) Calculate the Doppler frequency change Δf of the target signal received by the satellite. t The two largest adjacent times t * and t * +τ, and take the median of two adjacent moments as the overpass moment of the satellite for the target signal. The formula is expressed as follows:

[0047]

[0048]

[0049] 2.3) Repeat steps (2.1) to (2.2) to calculate the overpass time t for each satellite. i .

[0050] Step 3: Calculate the region where the target signal source is located.

[0051] 3.1) Establish a geocentric coordinate system and obtain the time t when each satellite begins monitoring the target signal based on the satellite orbit information. ib The coordinates of the sub-star point (x(t) ib ), y(t) ib ), z(t ib and the time t when receiving the target signal is terminated 1e The coordinates of the sub-star point (x(t) ie ), y(t) ie ), z(t ie ));

[0052] 3.2) Taking satellite 1 as an example, calculate its performance at time t. 1b The coverage range of time D(t) 1b ) and in t 1e The coverage range of time D(t) 1e ):

[0053] Reference Figure 2 (a) and Figure 2 (b) The implementation of this step is as follows:

[0054] 3.2.1) Calculate the time t when satellite 1 begins to detect the target signal. 1b Coverage range D(t) 1b ):

[0055] In the geocentric coordinate system, it is known that satellite 1 is at time t 1b The time is located at point A, and the sub-satellite point is A′(x). A′ y A′ , z A′ ), Observation range D(t) 1b The elevation angle θ1 of the nadir point A′, the azimuth angle θ2 of the nadir point A′, and the distance R1 between the nadir point A′ and the Earth's center are given. The distance d1 from the unknown crown base center A″ to the nadir point A′ needs to be calculated using the following formula:

[0056] 3×(d2+d1) 2 +(R1-d1) 2 =R1 2

[0057] Where d2 is the distance between position A of satellite 1 and the sub-satellite point A′;

[0058] Based on the above data, solve for the observation range D(t). 1b The coordinates of the center of the crown base circle A″(x) A″ y A″ , z A″ ):

[0059]

[0060] According to the observation range D(t) 1b The coordinates of the crown base center A″ are used to obtain the observation range D(t). 1b The expression for ) is:

[0061]

[0062] in, For any latitude and longitude coordinates on Earth, To convert latitude and longitude coordinates into geocentric and geofixed coordinates;

[0063] 3.2.2) Calculate the time t at which satellite 1 stops receiving the target signal. 1e Coverage range D(t) 1e ):

[0064] In the geocentric coordinate system, it is known that satellite 1 is at time t 1e The time is located at point B, and the sub-satellite point is B′(x). B′ y B′ , z B′ ), Observation range D(t) 1e The elevation angle θ3 of the nadir point B′, the azimuth angle θ4 of the nadir point B′, and the distance R2 between the nadir point B and the Earth's center are given. The distance d3 from the unknown crown base center B″ to the nadir point B′ needs to be calculated using the following formula:

[0065] 3×(d⁴+d³) 2 +(R2-d3) 2 =R2 2

[0066] Where d4 is the distance between position B of satellite 1 and the nadir point B′.

[0067] Based on the above data, solve for the observation range D(t). 1e The coordinates of the center of the crown base circle B″(x) B″ y B″ , z B″ ):

[0068]

[0069] According to the observation range D(t)1e The coordinates of the crown base center B″ are used to obtain the observation range D(t). 1e The expression for ) is:

[0070]

[0071] in, For any latitude and longitude coordinates on Earth, To convert latitude and longitude coordinates into geocentric and geofixed coordinates;

[0072] 3.3) Repeat step (3.2) to calculate the observation range D(t) of the S satellites. ib ) and D(t ie );

[0073] 3.4) Based on the time t when satellite i begins monitoring the target signal ib and the time t when receiving the target signal is terminated 1e The observation range D(t) ib ) and D(t ie ), extending the observation range D(t) of S satellites. ib ) and D(t ie Taking the intersection, we obtain the region where the target signal source is located: D = D(t) ib )∩D(t ie ), where ∩ represents the intersection of the observation ranges.

[0074] Step 4: Divide the area where the target signal source is located into grids.

[0075] 4.1) Reference Figure 3 Divide region D into M×N grids at equal intervals according to latitude and longitude, and take the center point C of the k-th grid. k latitude and longitude coordinates Where k = 1, 2, ..., M × N;

[0076] 4.2) Set the latitude and longitude coordinates of each grid center point. Convert to Earth-centered Earth-fixed coordinates (x k y k , z k ):

[0077]

[0078] Where e is the first eccentricity of the Earth. Let λ be the latitude of the center point of the grid. k The longitude of the center point of this grid. denoted as y, the length from the center point of the grid along the normal to the y-axis of the meridian plane in the rectangular coordinate system, where a is the length of the Earth's semi-major axis.

[0079] Step 5: Calculate the average position deviation of each grid to determine the location of the target signal source.

[0080] 5.1) For each grid center point, calculate its distance d from satellite i at the time t when the target signal is detected, based on the satellite orbit information. ik (t):

[0081]

[0082] Among them, [x i (t), y i (t), z i [(t)] represents the geocentric and Earth-fixed coordinates of satellite i at time t, (x k y k , z k ) is the center point C of the grid. k Geocentric coordinates;

[0083] 5.2) Based on distance d ik (t) Obtain the time t when the distance between satellite i and the center point of each grid is shortest. ik :

[0084]

[0085] Among them, t ib t is the time when satellite i begins monitoring the target signal. ie τ is the time when satellite i stops monitoring the target signal, and τ is the time interval during which the satellite monitors the signal;

[0086] 5.3) Based on satellite i and each grid center point C k The shortest time t ik and overpass moment Calculate the average positional deviation of each grid center:

[0087]

[0088] 5.4) Based on the average positional deviation of each grid center, obtain the grid that minimizes the average positional deviation.

[0089]

[0090] 5.5) The grid with the smallest deviation Determine the final grid center and its latitude and longitude coordinates Using the coordinates of the target signal source, the location of the target signal source is determined; that is, the final location result of the target signal source is...

[0091] The order of the above steps is not limited.

[0092] The effects of this invention will be further illustrated below with simulation experiments:

[0093] 1. Simulation parameter settings:

[0094] The parameter settings for the signal source, communication environment, and satellite are shown in Table 1:

[0095] Table 1 Signal Source, Communication Environment, and Satellite Parameter Settings

[0096] parameter Value Earth Model WGS-84 Rain attenuation model ITU-R_P618-8 Ionospheric scintillation model ITU-R_P618-12 Atmospheric loss model ITU-R_P676-9 ground temperature 293.15K Ground signal source transmission frequency 1.3GHz signal power 100dBW Signal modulation type BPSK signal bandwidth 10MHz Antenna type Non-directional Gaussian antenna Antenna gain 15.6dB Tropospheric refractive index 4 / 3 satellite model Ningxia-1 (ten satellites in total) Satellite observation angle 60° Monitoring time interval 0.02s Actual location of the signal source (35.34N, 93.81E)

[0097] 2. Simulation Content and Results

[0098] Under the above environmental configuration and parameter settings, 2, 4, 6, 8 and 10 satellites were selected as positioning satellites, and the present invention was used to locate the target signal source. The results are shown in Table 2.

[0099] Table 2. Positioning results and deviations of this invention for different numbers of satellites.

[0100] Location results latitude longitude Positional deviation Two satellites 35.19N 93.94E 20.4488km Four satellites 35.27N 93.87E 9.5064km Six satellites 35.30N 93.84E 5.2186km Eight satellites 35.35N 93.80E 1.4361km Ten satellites 35.35N 93.80E 1.4361km

[0101] As can be seen from Table 2, the latitude and longitude of the positioning results obtained by selecting 2, 4, 6, 8, and 10 positioning satellites are all close to the actual location of the target signal source (35.34N, 93.81E). Moreover, the distance deviation between the positioning result and the actual location of the target signal source along the Earth's surface decreases continuously as the number of positioning satellites increases. For example, the positioning error is 20.4488km when two satellites are selected, and 1.4361km when ten satellites are selected, which is more than ten times less than the previous error.

[0102] The simulation results above show that the multi-satellite electromagnetic signal source positioning method based on overpass time acquisition proposed in this invention can effectively solve the bottleneck problems of low satellite link bandwidth and limited payload resources with low algorithm complexity. Moreover, the positioning accuracy is significantly improved with the increase of the number of satellites, and the positioning accuracy can be guaranteed in long-distance satellite positioning scenarios.

Claims

1. A multi-satellite electromagnetic signal source localization method based on overhead time acquisition, characterized in that, Includes the following steps: (1) S satellites continuously monitor signals at time intervals τ, that is, each satellite monitors the signal at time t. ib The target signal is detected and its frequency is continuously recorded until it is too far from the target signal source at time t. ie Terminate monitoring of the target signal, i = 1, 2, ..., S; (2) Calculate the overpass time of each satellite: (2a) Calculate the change in Doppler frequency Δf between every two adjacent moments when the satellite receives the target signal. t ; (2b) Calculate the Doppler frequency change Δf of the target signal received by the satellite. t The two largest adjacent times t * and t * +τ, and take the median of two adjacent moments as the overpass moment of the satellite for the target signal. (2c) Repeat steps (2a) to (2b) to obtain the overpass time of each satellite. (3) Calculate the region where the target signal source is located: (3a) Establish a geocentric-ground-fixed coordinate system, and obtain the nadir coordinates (x, t) of each satellite at the moment it begins monitoring the target signal, based on the satellite orbit information. ib ),y(t ib ),z(t ib The coordinates of the nadir point (x(t)) at the moment when receiving the target signal is terminated. ie ),y(t ie ),z(t ie )), calculate t ib and t ie The observation range D(t) of satellite i at time i ib ) and D(t ie ): in, For Earth's latitude and longitude coordinates, To convert latitude and longitude coordinates to geocentric coordinates, (x1, y1, z1) represents the satellite observation range D(t). ib The coordinates of the center of the crown base circle (x2, y2, z2) are the satellite observation range D(t). ie The coordinates of the center of the crown base circle; (3b) According to t ib and t ie The observation range D(t) of satellite i at time i ib ) and D(t ie ), to extend the observation range D(t) of all satellites ib ) and D(t ie By taking the intersection, we can obtain the region D where the target signal source is located; (4) Divide the area where the target signal source is located into a grid: (4a) Divide region D into M×N grids at equal intervals according to latitude and longitude, and take the center point C of the kth grid. k latitude and longitude coordinates Where k = 1, 2, ..., M × N; (4b) Set the latitude and longitude coordinates of each grid center point Convert to Earth-centered and Earth-fixed coordinates (x k ,y k ,z k ); (5) Determine the location of the target signal source: (5a) For each grid center point, calculate the distance d between it and satellite i at the time t when the target signal is detected, based on the satellite orbit information. ik (t); (5b) Based on distance d ik (t) Obtain the time t when the distance between satellite i and the center point of each grid is shortest. ik ; (5c) Based on satellite i and each grid center point C k The shortest time t ik and overpass moment Calculate the average positional deviation of each grid center: (5d) Based on the average positional deviation of each grid center, obtain the grid that minimizes the average positional deviation. (5e) The grid with the smallest deviation Determine the final grid center and its latitude and longitude coordinates The coordinates of the target signal source are used to determine the location of the target signal source.

2. The method according to claim 1, characterized in that: In step (2a), the change in Doppler frequency Δf between every two adjacent moments of the target signal received by the satellite is calculated. t The formula is as follows: Δf t =f t+τ -f t ,t=t b ,t b +τ,...,t e -τ Among them, f t Let t be the frequency of the target signal received by the satellite at time t. b and t e These are the times when the satellite began monitoring the target signal and the times when it stopped monitoring the target signal, respectively.

3. The method according to claim 1, characterized in that: In step (2b), the Doppler frequency change Δf of the target signal received by the satellite is calculated. t The two largest adjacent times t * and t * +τ, and take the median of two adjacent moments as the overpass moment of the satellite for the target signal. The formula is expressed as follows: Among them, t b and t e These are the times when the satellite began monitoring the target signal and the times when it stopped monitoring the target signal, respectively.

4. The method according to claim 1, characterized in that: Step (3a) in formula D(t) ib The coordinates (x1, y1, z1) of the crown base circle in the figure are calculated using the following formula: Where θ1 is the target detection start time t of satellite i. ib Sub-star point (x(t) ib ),y(t ib ),z(t ib The angle of elevation of )) θ2 represents the time t at which satellite i begins target detection. ib Sub-star point (x(t) ib ),y(t ib ),z(t ib )) azimuth angle, R1 represents the satellite i at the target detection start time t. ib Sub-star point (x(t) ib ), y(t) ib ), z(t ib The distance between the Earth's core and the Earth's center. d1 is D(t) ib The distance from the crown base center (x1, y1, z1) of satellite i to the target detection start time t is... ib Sub-star point (x(t) ib ), y(t) ib ), z(t ib The distance is calculated using the formula 3×(d2+d1). 2 +(R1-d1) 2 =R1 2 Calculated d2 represents the time t at which target detection begins for satellite i. ib The position and the distance from the point below the star at this moment.

5. The method according to claim 1, characterized in that: Step (3a) in formula D(t) ie The coordinates (x2, y2, z2) of the center of the crown base circle in the figure are calculated using the following formula: Where θ3 is the target monitoring termination time t of satellite i. ie Sub-star point (x(t) ie ), y(t) ie ), z(t ie The angle of elevation of )) θ4 represents the time t at which satellite i terminates target monitoring. ie Sub-star point (x(t) ie ), y(t) ie ), z(t ie )) azimuth angle, R2 represents the time t at which satellite i terminates target monitoring. ie Sub-star point (x(t) ie ), y(t) ie ), z(t ie The distance between the Earth's core and the Earth's center. d3 is D(t ie The distance from the center of the crown base (x2, y2, z2) to satellite i at the target monitoring termination time t ie Sub-star point (x(t) ie ), y(t) ie ), z(t ie The distance is given by the formula 3×(d⁴+d³). 2 +(R2-d3) 2 =R2 2 Calculated d4 represents satellite i at t ie The position at that moment and the distance from the point below the star at that moment.

6. The method according to claim 1, characterized in that: In step (3b), the region D where the target signal source is located is obtained, as shown below: D=D(t ib )∩D(t ie ) Wherein, D(t) ib Let ) represent satellite i at time t. ib The observation range, D(t) ie Let ) represent satellite i at time t. ie The observation range.

7. The method according to claim 1, characterized in that: In step (4b), the latitude and longitude coordinates of each grid center point are... Convert to Earth-centered and Earth-fixed coordinates (x k y k , z k The formula is as follows: Where e is the first eccentricity of the Earth. Let λ be the latitude of the center point of the grid. k The longitude of the center point of this grid. denoted as y, the length from the center point of the grid along the normal to the y-axis of the meridian plane in the rectangular coordinate system, where a is the length of the Earth's semi-major axis.

8. The method according to claim 1, characterized in that: In step (5a), the distance d between each grid center point and satellite i at the time t when the target signal is detected is calculated. ik (t), the formula is as follows: Among them, [x i (t), y i (t), z i [(t)] represents the geocentric and geofixed coordinates of satellite i at time t.

9. The method according to claim 1, characterized in that: In step (5b), the distance d of satellite i at the time t when the target signal is detected is used as the basis for the calculation. ik (t), which gives the time t when the distance between satellite i and the center point of each grid is shortest. ik , means as follows: Among them, t ib t is the time when satellite i begins monitoring the target signal. ie τ represents the time when satellite i stops monitoring the target signal, and τ is the time interval during which the satellite monitors the signal.

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