A direct positioning method based on space-based ground fixed radiation source

Abstract

The present application relates to the technical field of passive positioning of radiation sources, and specifically discloses a direct positioning method for a ground fixed radiation source based on space-based positioning, comprising the following steps: S1, a double-satellite constellation is built according to two satellites operating in different orbits; S2, a signal receiving model in the double-satellite constellation is used to receive a signal sent by a ground radiation source, and a cost function is established according to a time difference and a phase of the signal; S3, a plurality of grid points are obtained by dividing a preset area, an estimated value of the time difference and the phase between each two grid points is calculated, a compensation signal is obtained by compensating the signal according to the estimated value; S4, the compensation signal is brought into the cost function, so that a peak point appears in the grid point where the ground radiation source is located; and S5, the peak point is found by adaptive traversal of the grid points, and positioning information of the ground radiation source is obtained. The present application expands the positioning coverage range, improves the positioning real-time performance, and reduces the system complexity and data processing difficulty while ensuring the positioning accuracy.

Description

Technical Field

[0001] This invention relates to the field of passive radiation source positioning technology, specifically to a direct positioning method for a space-based ground-based fixed radiation source. Background Technology

[0002] Space-based positioning of ground-based radiation sources can be categorized into active and passive positioning methods. Active positioning requires the satellite to actively transmit signals and receive the echoes reflected or scattered by the target to locate it; therefore, active positioning cannot locate non-cooperative targets. Passive positioning, on the other hand, does not transmit signals but locates the target solely by calculating the signals it emits.

[0003] In passive positioning, a two-step method is typically used. However, this method requires parameter estimation beforehand, resulting in poor positioning performance under low signal-to-noise ratio (SNR) conditions. Recent developments in direct positioning methods employ a single step, eliminating the parameter estimation step and reducing information loss from the received signal. Therefore, they offer better positioning accuracy even under low SNR conditions. In satellite-to-ground radiation source positioning scenarios, the low SNR of the received satellite signal makes the direct positioning method a suitable choice for passive positioning technologies.

[0004] Existing direct positioning methods based on satellite platforms have made some progress, mainly including two methods: First, a multi-satellite collaborative approach is employed, using multiple satellites to synchronously observe the radiation source. High-precision measuring equipment onboard the satellites acquires information such as the time difference and angle of arrival of the radiation source signal at different satellites. Complex algorithms are then used to solve a system of equations to determine the three-dimensional spatial coordinates of the radiation source. For example, some low-Earth orbit satellite constellation systems, through the coordinated work of multiple satellites within the constellation, can achieve effective positioning of ground-based and airborne radiation sources.

[0005] Second, single-satellite direct positioning technology is employed. This technology utilizes multiple sensors on a single satellite, such as a wideband receiving antenna and a high-precision direction finder, to locate the radiation source based on principles such as signal feature analysis and phase interferometry. Compared to multi-satellite positioning, single-satellite direct positioning has advantages such as faster response speed and lower system complexity, and has application potential in scenarios with high real-time requirements.

[0006] In the field of space-based platform research, early work primarily focused on single-satellite platforms, aiming to achieve positioning functionality with a minimal number of satellites. The design philosophy of single-satellite platforms was to accomplish target positioning tasks through sophisticated algorithms and technologies under resource constraints. However, with the rapid development of aerospace technology and the increasingly prominent trend of satellite networking, direct positioning methods using single-satellite platforms have revealed numerous shortcomings: First, data processing faces severe challenges. As the complexity of positioning tasks increases, the amount of data that a single satellite needs to process grows exponentially, resulting in reduced data processing efficiency and difficulty in meeting real-time requirements. Second, obtaining the time difference is quite difficult. Because the observation angle and range of a single satellite are limited, obtaining the precise time difference between the target and the satellite is easily affected by various factors, which in turn affects the positioning accuracy.

[0007] Meanwhile, satellites have a large coverage area, and when implementing direct positioning algorithms, the entire search area is wide, which requires high computing power. Therefore, an algorithm that reduces computational complexity is needed. Summary of the Invention

[0008] To address the aforementioned problems, the purpose of this invention is to provide a direct positioning method for ground-based fixed radiation sources based on space-based systems. This method is primarily used for precise geographic location positioning of ground-based fixed radiation sources. By adaptively adjusting the search range, it improves positioning accuracy while reducing computational complexity. This method can be widely applied in scenarios such as interference source investigation in the communications field, environmental monitoring, signal optimization for intelligent transportation, and electromagnetic anomaly detection in industrial production, providing accurate radiation source location information to support the smooth operation of related work.

[0009] This invention provides a direct positioning method for a space-based ground-based fixed radiation source, comprising: Step S1: Construct a binary constellation based on two satellites orbiting in different orbits; Step S2: Receive signals transmitted from ground radiation sources using the signal receiving model in the binary constellation, and establish a cost function based on the time difference and phase of the signals; Step S3: Divide the preset area to obtain multiple grid points, calculate the estimated time difference and phase between every two grid points, and compensate the signal according to the estimated values ​​to obtain the compensated signal; Step S4: Substitute the compensation signal into the cost function to make a peak point appear at the grid point where the ground radiation source is located; Step S5: Find the peak point by adaptively traversing the grid points to obtain the location information of the ground radiation source.

[0010] In one possible implementation, step S2 includes: The time-domain model of the signal reception model is established based on the following formula. : In the formula, Indicates the first The receiving device received the first One signal Indicates the first The receiving device received the first Channel attenuation of each signal, For the first Each transmitted signal, For carrier frequency, For transmitting noise, For signal delay, Indicates time, Indicates the sampling interval.

[0011] In one possible implementation, step S2 further includes: Performing a Discrete Fourier Transform on the time-domain model yields the frequency-domain model of the signal receiving model, as shown in the following formula: In the formula, Indicates the first The receiving device received the first One signal Indicates the phase change of the signal, For transmitting noise.

[0012] In one possible implementation, step S2 further includes: The signal delay is determined using the following formula. : In the formula, Indicates the location of ground radiation sources, Indicates the first The location of each receiving device It represents the speed of light.

[0013] In one possible implementation, step S2 further includes: The cost function is determined according to the following formula. : In the formula, Indicates the first The receiving device received the first Channel attenuation of each signal, Indicates the phase change of the signal, For the first Each transmitted signal, Indicates the first The receiving device received the first One signal Indicates the number of signals, This indicates the number of receiving devices.

[0014] In one possible implementation, the locations of the ground radiation sources and grid points are represented using the WGS-84 coordinate system.

[0015] In one possible implementation, step S3 includes: The location of the ground radiation source can be transformed from the latitude, longitude, and altitude coordinate system (LLA) to the geocentric, earth-fixed coordinate system (ECEF) according to the following formula: In the formula, The location of the ground radiation source in the geocentric-earth-fixed coordinate system. The extreme flattening of the reference ellipsoid. The semi-major axis of the reference ellipsoid, For the longitude of the ground radiation source, Latitude of ground radiation source, The elevation of the ground-based radiation source.

[0016] In one possible implementation, step S4 includes: The peak point is determined using the following formula. : In the formula, For cost function, This is a position matrix.

[0017] In one possible implementation, step S4 further includes: The cost function is transformed using the following formula to obtain a new cost function: In the formula, Representing Hermitian matrices, Indicates the number of receivers. This indicates the number of pulses received.

[0018] In one possible implementation, step S4 further includes: The Hermitian matrix is ​​determined using the following formula. : In the formula, express conjugate transpose This represents an N×N matrix.

[0019] The direct positioning method for ground-based fixed radiation sources based on space provided by this invention can expand the positioning coverage and improve the real-time positioning while ensuring positioning accuracy, and at the same time reduce system complexity and data processing difficulty, providing an efficient and reliable solution for the positioning of ground-based fixed radiation sources. Attached Figure Description

[0020] Figure 1 A flowchart illustrating the direct positioning method provided in an embodiment of the present invention; Figure 2 This is a schematic diagram showing the positions of the satellite and the ground radiation source provided in an embodiment of the present invention; Figure 3 A contour map showing the calculation results of the cost function provided in an embodiment of the present invention; Figure 4 A comparison chart of existing algorithms and RMSE data provided in this embodiment of the invention. Detailed Implementation

[0021] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. The following detailed description of the embodiments and the accompanying drawings are used to illustrate the principles of the present invention by way of example, but should not be used to limit the scope of the present invention. That is, the present invention is not limited to the described preferred embodiments, and the scope of the present invention is defined by the claims.

[0022] In the description of this invention, it should be noted that, unless otherwise stated, "a plurality of" means two or more; the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance; those skilled in the art can understand the specific meaning of the above terms in this invention as appropriate.

[0023] To facilitate understanding, the technical terms involved in this invention will first be explained.

[0024] Radiation source: refers to a substance or device that can emit ionizing radiation. In this invention, it mainly refers to ground-based fixed equipment that emits electromagnetic signals, such as communication base stations and radar stations.

[0025] Passive positioning: a technique that determines the location of a target by receiving electromagnetic wave signals emitted by the target. Unlike active positioning, passive positioning devices do not emit signals themselves, but only passively receive external signals, thus possessing good stealth capabilities.

[0026] Direct position determination (DPD) uses raw or simply preprocessed signal data to construct a cost function, and then obtains the optimal solution of the cost function to obtain the target position. This avoids information loss caused by parameter estimation, and the positioning accuracy is closer to the Cramer-Rao boundary than the traditional two-step method.

[0027] Figure 1 A flowchart illustrating the direct positioning method provided in an embodiment of the present invention is shown below. Figure 1 As shown, this invention provides a direct positioning method for a space-based ground-based fixed radiation source, comprising: Step S1: Construct a binary constellation based on two satellites orbiting in different orbits; This invention utilizes a dual-satellite platform consisting of two satellites. By receiving signals emitted from a fixed ground-based radiation source, measuring the time difference of arrival (TDOA) and angle of arrival (AOA) of the signals to the two satellites, and combining this with the satellites' orbital position information, a specific algorithm is used to directly calculate the geographical location of the ground-based radiation source. Figure 2 This is a schematic diagram showing the positions of the satellite and the ground radiation source provided in an embodiment of the present invention.

[0028] The dual-satellite platform consists of two satellites operating in different orbits. Each satellite is equipped with high-precision receiving equipment, time synchronization devices, and orbit measurement equipment. The satellite's orbital parameters are precisely known and can be updated in real time.

[0029] The receiving equipment is installed on the satellite to receive signals emitted by fixed ground-based radiation sources. This equipment features high sensitivity and wide bandwidth reception capabilities, enabling it to accurately capture weak radiation source signals and convert them into electrical signals for further processing.

[0030] Time synchronization devices are used to ensure that the time synchronization accuracy between two satellites reaches the nanosecond level, thereby guaranteeing the accuracy of the arrival time difference of measurement signals. Time synchronization can be achieved through inter-satellite laser links or high-precision atomic clocks.

[0031] Orbit measurement equipment is used to measure the orbital position information of satellites in real time, including parameters such as the satellite's three-dimensional coordinates and velocity vector. The accuracy of the orbit measurement must meet the positioning accuracy requirements, and onboard GPS receivers or other high-precision orbit measurement technologies can be used.

[0032] The data processing unit is located on the satellite or in the ground control center. It is responsible for processing and analyzing the received signal data, time information, and orbital position information, and using specific positioning algorithms to calculate the position coordinates of the radiation source.

[0033] Step S2: Receive signals transmitted from the ground radiation source using the signal receiving model in the binary constellation, and establish a cost function based on the signal's time difference and phase; In one possible implementation, it is assumed that the start time of the first pulse signal emitted by the ground radiation source is time 0, and the initial phase of each pulse signal is set to 0. For a single radiation source, One pulse, In the case of individual receiving devices, the ground radiation source is located at... The receiving device maintains time-frequency synchronization. A receiving device at The first received A pulse signal. Considering only the time delay information of the received signal, the time-domain model of the signal reception model is established according to the following formula. : In the formula, Indicates the first The receiving device received the first One signal Indicates the first The receiving device received the first Channel attenuation of each signal, For the first Each transmitted signal, For carrier frequency, For transmitting noise, For signal delay, Indicates time, Indicates the sampling interval.

[0034] In one possible implementation, a discrete Fourier transform is performed on the time-domain model to obtain the frequency-domain model of the signal receiving model, as shown in the following formula: The matrix form of the frequency domain model is as follows: In the formula, Indicates the first The receiving device received the first One signal Indicates the phase change of the signal, For transmitting noise.

[0035] In one possible implementation, the signal delay is determined according to the following formula. : In the formula, Indicates the location of ground radiation sources, Indicates the first The location of each receiving device It represents the speed of light.

[0036] Assumption It is zero-mean Gaussian white noise, distributed according to .

[0037] The signal delay can be expressed in vector form as follows: in In the time domain, move Each sampling time, Indicates rounding down.

[0038] Assuming the delay can be approximated as an integer multiple of the sampling interval, , , The sampled sequence, expanded, can be represented by the following formula: In one possible implementation, the cost function is determined according to the following formula. : In the formula, Indicates the first The receiving device received the first Channel attenuation of each signal, Indicates the phase change of the signal, For the first Each transmitted signal, Indicates the first The receiving device received the first One signal Indicates the number of signals, This indicates the number of receiving devices.

[0039] Specifically, the following is the derivation of the cost function in the localization algorithm.

[0040] The matrix form of the frequency domain model can be written as follows: Assume that the noise in the received signals of each channel is independent and identically distributed zero-mean Gaussian white noise in time and space, i.e. That is equivalent to From this, the covariance matrix can be obtained. The maximum likelihood estimation function is expressed as follows: Taking the natural logarithm of both sides of the above equation yields the following formula: For the noise variance in the above formula Find the partial derivatives, and then make the partial derivatives equal to 0. The noise variance estimate is then given by the following formula: Substituting the above equation into the maximum likelihood estimation function yields the cost function. : Step S3: Divide the preset area to obtain multiple grid points, calculate the estimated time difference and phase between every two grid points, and compensate the signal based on the estimated values ​​to obtain the compensated signal; The higher the similarity of the compensation signals, the larger the output value of the cost function, and thus a peak value will appear at the grid point where the radiation source is located.

[0041] In one possible implementation, for ease of calculation and representation, the positions of ground radiation sources and grid points are represented using the WGS-84 coordinate system. Satellite positions and positioning calculations are performed using the ECEF coordinate system. Positioning calculations require transformation from the LLA coordinate system to the ECEF coordinate system using equation (4-5).

[0042] In one possible implementation, the location of the ground radiation source is transformed from the latitude, longitude, and height coordinate system (LLA) to the Earth-centered Earth-fixed coordinate system (ECEF) according to the following formula: In the formula, The location of the ground radiation source in the geocentric-earth-fixed coordinate system. The extreme flattening of the reference ellipsoid. The semi-major axis of the reference ellipsoid, For the longitude of the ground radiation source, Latitude of ground radiation source, The elevation of the ground-based radiation source.

[0043] right Perform normalization, then calculate the cost function. The minimum value, then The maximum likelihood estimate is given by the following formula: Step S4: Substitute the compensation signal into the cost function to make peak points appear at the grid points where the ground radiation source is located; Figure 3 A contour map showing the calculation results of the cost function provided in an embodiment of the present invention; In one possible implementation, the maximum likelihood estimate is substituted into the cost function. The cost function is minimized as follows: in, Since the parameters are independent, the above equation can be transformed into the following cost-maximizing function: Among them, the definition Hermitian matrix The formula is as follows: For the case of unknown signals, maximizing the cost function can be achieved by maximizing each expression related to the unknown signal. This is achieved using a quadratic form. Therefore, a set of vectors needs to be selected. To maximize the cost function, that is, to need As Maximum eigenvalue The corresponding feature vector. Therefore, the cost function This can be converted into the following formula: but The dimension is The computational cost of finding eigenvalues ​​increases with the number of sampling points. According to matrix theory, for a given matrix... , and The non-zero eigenvalues ​​are equal. Therefore, for a Hermitian matrix... It can Vie Replace with Vie That is, the matrix dimension is consistent with the number of receivers, and the Hermitian matrix is ​​determined according to the following formula. : In the formula, express conjugate transpose Represents an N×N matrix. .

[0044] Then the cost function Equivalent to the following formula: In the formula, Representing Hermitian matrices, Indicates the number of receivers. This indicates the number of pulses received.

[0045] In one possible implementation, the peak point is determined according to the following formula. : In the formula, For cost function, This is a position matrix.

[0046] Step S5: Find the peak point by adaptively traversing the grid points to obtain the location information of the ground radiation source.

[0047] In one possible implementation, the error statistic uses the root mean square error (RMSE). The root mean square error represents the deviation between the observed value and the true value, and is calculated using the following formula: Figure 4 A comparison chart of existing algorithms and RMSE data provided for embodiments of the present invention is shown, such as... Figure 4 As shown, the RMSE data of this invention is significantly lower than that of existing algorithms.

[0048] This invention relies on the collaborative operation of two satellites to locate fixed ground-based radiation sources through precise measurements of the time difference of arrival (TDOA) and angle of arrival (AOA). Compared to single-satellite systems, this mechanism utilizes triangulation principles to effectively eliminate azimuth ambiguity in single-satellite positioning, significantly improving the accuracy of radiation source location. Compared to multi-satellite constellation positioning, this mechanism requires only simple communication and cooperation between two satellites, eliminating the need for complex inter-satellite links and large-scale data interaction, greatly reducing system complexity. Furthermore, it is more efficient in data processing and positioning calculations, effectively ensuring the real-time performance and reliability of positioning.

[0049] The positioning algorithm used in this invention combines TDOA and AOA information. By establishing hyperbola equations and direction vector equations and using iterative solution and optimization algorithms, it can accurately calculate the position coordinates of the radiation source when only a single pulse is received.

[0050] The direct positioning method for a space-based ground-based fixed radiation source provided by this invention has the following advantages: 1) Reduced positioning time. The dual-satellite platform can receive radiation source signals in real time and quickly process and calculate data through a high-speed communication link between the satellite and the ground control center to obtain the position coordinates of the radiation source in a timely manner. Compared with ground positioning systems, this reduces intermediate data transmission and processing steps, greatly improving the real-time performance of positioning and enabling timely response to changes in the radiation source, meeting the needs for real-time monitoring and tracking. The efficient data processing algorithm and communication link allow for rapid acquisition of positioning results. Furthermore, the lightweight structure of this method ensures its timeliness; experimental simulations show that the average time required for a single positioning operation is 0.9543 seconds.

[0051] 2) Reduced signal resource requirements. This method only needs to receive a single pulse of signal to achieve high-precision positioning. Unlike traditional positioning methods, this method does not require long-term signal monitoring or the accumulation and analysis of multi-pulse data, greatly reducing its dependence on signal resources. This characteristic has significant advantages in complex environments where signal resources are scarce, effectively reducing the complexity and computational load of data processing, and improving the overall performance and response speed of the positioning system.

[0052] 3) Expanded positioning coverage. Compared to terrestrial positioning systems, space-based dual-satellite platforms are not limited by ground infrastructure construction and can cover ground areas globally, especially in remote areas, oceans, deserts, and other regions where ground base stations are difficult to cover. They can also effectively locate fixed ground-based radiation sources, greatly expanding the positioning coverage. Through precise orbit setting and signal reception capabilities, positioning of radiation sources in different geographical locations can be achieved.

[0053] Meanwhile, the modeling method of this invention allows for the self-setting of the coverage area, providing a certain degree of freedom.

[0054] 4) Improved relative positioning accuracy. By accurately measuring the time difference and angle of arrival of signals to two satellites, and combining this with high-precision satellite orbital position information, the positioning algorithm of this invention can effectively improve the accuracy of radiation source positioning. Under ideal conditions, the positioning accuracy can reach the meter level or even higher, meeting the needs for precise positioning of radiation sources and providing more accurate location information support for subsequent decision-making and actions. Compared with existing algorithms, the method of this invention has better positioning accuracy in low signal-to-noise ratio environments.

[0055] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A direct positioning method for a space-based ground-based fixed radiation source, characterized in that, include: Step S1: Construct a binary constellation based on two satellites orbiting in different orbits; Step S2: Receive signals transmitted from ground radiation sources using the signal receiving model in the binary constellation, and establish a cost function based on the time difference and phase of the signals; Step S3: Divide the preset area to obtain multiple grid points, calculate the estimated time difference and phase between every two grid points, and compensate the signal according to the estimated values ​​to obtain the compensated signal; Step S4: Substitute the compensation signal into the cost function to make a peak point appear at the grid point where the ground radiation source is located; Step S5: Find the peak point by adaptively traversing the grid points to obtain the location information of the ground radiation source.

2. The direct positioning method according to claim 1, characterized in that, Step S2 includes: The time-domain model of the signal reception model is established based on the following formula. : In the formula, Indicates the first The receiving device received the first One signal Indicates the first The receiving device received the first Channel attenuation of each signal, For the first Each transmitted signal, For carrier frequency, For transmitting noise, For signal delay, Indicates time, Indicates the sampling interval.

3. The direct positioning method according to claim 2, characterized in that, Step S2 further includes: Performing a Discrete Fourier Transform on the time-domain model yields the frequency-domain model of the signal receiving model, as shown in the following formula: In the formula, Indicates the first The receiving device received the first One signal Indicates the phase change of the signal, For transmitting noise.

4. The direct positioning method according to claim 2, characterized in that, Step S2 further includes: The signal delay is determined using the following formula. : In the formula, Indicates the location of ground radiation sources, Indicates the first The location of each receiving device, It represents the speed of light.

5. The direct positioning method according to claim 1, characterized in that, Step S2 further includes: The cost function is determined using the following formula. : In the formula, Indicates the first The receiving device received the first Channel attenuation of each signal, Indicates the phase change of the signal, For the first Each transmitted signal, Indicates the first The receiving device received the first One signal Indicates the number of signals, This indicates the number of receiving devices.

6. The direct positioning method according to claim 1, characterized in that, The locations of the ground radiation sources and grid points are represented using the WGS-84 coordinate system.

7. The direct positioning method according to claim 1, characterized in that, Step S3 includes: The location of the ground radiation source can be transformed from the latitude, longitude, and altitude coordinate system (LLA) to the geocentric, earth-fixed coordinate system (ECEF) according to the following formula: In the formula, The location of the ground radiation source in the geocentric-earth-fixed coordinate system. The extreme flattening of the reference ellipsoid. The semi-major axis of the reference ellipsoid, Longitude of the ground radiation source Latitude of ground radiation source, The elevation of the ground-based radiation source.

8. The direct positioning method according to claim 1, characterized in that, Step S4 includes: The peak point is determined using the following formula. : In the formula, For cost function, This is a position matrix.

9. The direct positioning method according to claim 8, characterized in that, Step S4 further includes: The cost function is transformed using the following formula to obtain a new cost function: In the formula, Representing Hermitian matrices, Indicates the number of receivers. This indicates the number of pulses received.

10. The direct positioning method according to claim 9, characterized in that, Step S4 further includes: The Hermitian matrix is ​​determined using the following formula. : In the formula, express conjugate transpose This represents an N×N matrix.

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