Space-time model direct positioning method and system based on low-mid earth orbit satellite fusion

Abstract

The application provides a space-time model direct positioning method and system based on medium and low orbit satellite fusion, comprising: position rough measurement; constructing a direct positioning scene and a satellite receiving data model; constructing a space-time model of satellite receiving data; deriving a maximum likelihood estimator target function based on a least square estimation criterion; introducing an optimal weight vector, solving the weight vector according to a minimum variance distortionless response criterion, and deriving a target function based on the minimum variance distortionless criterion; drawing a space spectrum diagram according to the target function value, performing spectrum peak search, and determining the position of a ground radiation source. The application reduces the search range and the calculation amount by using the rough estimation result of single satellite direction finding positioning to obtain the direct positioning area to be searched; the space-time direct positioning model based on the angle of arrival and the Doppler frequency shift is established by using Doppler information, high-precision positioning can be realized under low signal-to-noise ratio, and high resolution can still be realized when the ground radiation sources are very close.

Description

Technical Field

[0001] This invention belongs to the field of spaceborne passive positioning technology, specifically relating to a direct positioning method and system based on a space-time model fusion of medium and low orbit satellites. Background Technology

[0002] Passive positioning is a crucial research area in positioning technology, characterized by its strong concealment, wide range of application, and excellent positioning performance, playing a vital role in both civilian and military applications. Among these, high-precision spaceborne passive positioning technology, relying on satellite platforms and signal processing techniques, is unrestricted by territorial boundaries, airspace, territorial waters, or weather conditions. It boasts advantages such as long operating distance, strong environmental adaptability, and wide coverage, thus possessing broad application prospects and attracting widespread attention and high regard from scholars worldwide.

[0003] Because low- and medium-Earth orbit (LEO) satellites are relatively close to the Earth's surface, their signal transmission time is short and latency is minimal. Therefore, passive positioning technology based on LEO satellites is particularly suitable for applications requiring rapid response, such as emergency rescue and traffic navigation. Furthermore, LEO satellite systems typically involve multiple satellites that can communicate and network with each other, providing strong global coverage. Consequently, their signals exhibit good stability and can effectively resist noise and radio frequency interference.

[0004] However, the current passive positioning method based on the fusion of medium and low orbit satellites still has the following shortcomings: (1) Most of the existing spaceborne passive positioning methods adopt the classic two-step positioning method. Because the two-step positioning method needs to obtain intermediate parameters, it ignores the basic fact that the signals received by each satellite observation station come from the same target, and thus loses the correlation between the received signals of each satellite observation station, making it difficult to achieve the optimal solution for the positioning result and severely limiting the positioning accuracy; (2) Compared with stationary targets on the ground, medium and low orbit satellites are in a state of high-speed motion in the airspace above the Earth. The severe Doppler effect they generate will introduce positioning errors, thereby reducing the positioning performance. Summary of the Invention

[0005] The technical problem to be solved by the present invention is: the purpose of the present invention is to provide a direct positioning method and system based on the space-time model of medium and low orbit satellite fusion, which can effectively utilize Doppler frequency shift information and effectively improve positioning accuracy under low signal-to-noise ratio conditions.

[0006] To achieve the above objectives, the technical solution of this invention is implemented as follows: a direct positioning method based on a space-time model using low- and medium-Earth orbit satellite fusion, comprising:

[0007] By using any satellite to locate the ground radiation source, a rough estimate of the range of the ground radiation source can be found, and the rough estimate range can be determined as the area to be searched.

[0008] Establish a satellite reception data model for low- and medium-Earth orbit satellite observation stations receiving signals from ground radiation sources, where Doppler shift exists;

[0009] Based on the satellite receiving data model, a space-time steering vector is created using Doppler frequency shift information to establish the receiving data space-time model of the satellite receiving data model;

[0010] Using the received data space-time model, the sampling covariance matrix is ​​calculated; based on the least squares estimation criterion, the objective function of the maximum likelihood estimator for single ground radiation source estimation is obtained;

[0011] Based on the objective function of the maximum likelihood estimator for the single ground radiation source, an optimal weight vector is introduced, and the weight vector is obtained according to the minimum variance distortionless response criterion, thus obtaining the objective function based on the minimum variance distortionless criterion.

[0012] Based on the objective function value, a spatial spectrum is plotted, spectral peaks are searched, and the location of the ground radiation source is determined.

[0013] Furthermore, the satellite reception data model for receiving ground radiation source signals from a medium- and low-Earth orbit satellite observation station with Doppler frequency shift includes:

[0014] The ground radiation source signal data received by the nth satellite is modeled as follows:

[0015]

[0016] in, This is the vector data of the kth sample snapshot observed by the nth satellite receiving antenna array, where M represents the number of array elements of the receiving antenna on the satellite, k = 0, 1, 2, ..., K-1, and there are a total of K sample snapshots;

[0017] p q Let K be the coordinate vector of the q-th ground radiation source, where q = 1, 2, ..., Q, and there are a total of Q ground radiation sources; K and Q are both positive integers; j is the imaginary unit.

[0018] β is the steering vector when the q-th ground radiation source reaches the n-th satellite observation station, determined by the relative positions of the ground radiation source and the satellite observation station. n,q This represents the unknown complex channel attenuation parameter required for the q-th ground radiation source to reach the n-th satellite observation station;

[0019] s n,q (k) represents the complex Gaussian signal envelope received by the satellite observation station, T s This is expressed as the sampling interval time. Let f be the Gaussian white noise with a mean of 0 for the nth satellite observation station. n (p qThe Doppler frequency shift is caused by relative motion.

[0020]

[0021] Where f0 is the carrier frequency. Let u be the velocity vector of the nth satellite. n represents the current position vector information of the nth satellite, where c is the speed of light.

[0022] Furthermore, the space-time model for the received data in the satellite receiving data model is as follows:

[0023]

[0024] in, For Q ground-based radiation source signals:

[0025]

[0026] Divide the K sample snapshots into L segments.

[0027]

[0028] coefficient matrix

[0029] The spacetime steering vector is

[0030]

[0031]

[0032] in, This represents the Kronen product operation of matrices.

[0033] Furthermore, using the received data spatiotemporal model, the sampling covariance matrix is ​​calculated; based on the least squares estimation criterion, the maximum likelihood objective function for estimating a single ground radiation source is derived, including:

[0034] The least squares objective function is constructed as follows:

[0035]

[0036] Among them, constraint terms β is the path loss from the ground radiation source to the satellite observation station;

[0037] The transmitter p that minimizes the least-squares estimated objective function is the location of the ground radiation source.

[0038]

[0039] According to the least squares estimation criterion, the least squares estimation objective function is minimized. satisfy:

[0040]

[0041] The objective function of the maximum likelihood estimator is obtained as follows:

[0042]

[0043] in, The sampling covariance matrix is ​​of size ML×ML;

[0044] λ max (·) represents the operation of finding the largest eigenvalue.

[0045] Furthermore, the objective function of the maximum likelihood estimator based on the single ground radiation source is used to introduce an optimal weight vector. The weight vector is then obtained according to the minimum variance distortionless response criterion, resulting in an objective function based on the minimum variance distortionless criterion, including:

[0046] According to the minimum variance distortionless response criterion, we obtain:

[0047]

[0048] The target location satisfies

[0049] Wherein, the weight function w opt (β,p) satisfies:

[0050] Weight vector w opt (β,p) makes p the only one q The total output energy at all locations outside the ground is minimized, making the ground radiation source p q The signal output at that point is distortion-free, q = 1, ..., Q;

[0051] right Solve for w opt The optimal solution for (β,p) is as follows:

[0052]

[0053] According to w opt The optimal solution of (β,p) yields the objective function based on the minimum variance distortion-free criterion:

[0054]

[0055] Make the objective function The location of the ground radiation source is where p reaches its maximum value.

[0056] A direct positioning system based on a space-time model using low- and medium-Earth orbit satellite fusion, based on the above method, includes:

[0057] The first module is used to locate ground radiation sources using any satellite, find a rough estimate of the range of the ground radiation sources, and determine the rough estimate range as the search area.

[0058] The second module is used to establish a satellite reception data model for receiving signals from ground radiation sources by a medium- and low-orbit satellite observation station with Doppler frequency shift; based on the satellite reception data model, a space-time steering vector is created using Doppler frequency shift information to establish a space-time model of the received data of the satellite reception data model;

[0059] The third module is used to calculate the sampling covariance matrix using the received data space-time model; obtain the maximum likelihood estimator objective function for single ground radiation source estimation according to the least squares estimation criterion; introduce the optimal weight vector according to the maximum likelihood estimator objective function for single ground radiation source estimation, obtain the weight vector according to the minimum variance distortionless response criterion, and obtain the objective function based on the minimum variance distortionless criterion.

[0060] The fourth module is used to draw a spatial spectrum based on the objective function value, perform spectral peak search, and determine the location of ground radiation sources.

[0061] The advantages of this invention compared to the prior art are:

[0062] (1) In order to solve the above-mentioned shortcomings of the existing passive positioning technology based on medium and low orbit satellites, this invention proposes a direct positioning method based on the space-time model of medium and low orbit satellite fusion. It does not require intermediate parameter estimation steps and has the advantages of high accuracy and automatic parameter correlation. It solves the problem of unsatisfactory positioning effect under low signal-to-noise ratio in the existing two-step positioning method.

[0063] (2) This invention addresses the problem of severe Doppler effect during positioning of medium and low orbit satellites moving at high speeds in the Earth's atmosphere. The method of this invention establishes a space-time direct positioning model based on the angle of arrival and Doppler frequency shift, which not only avoids the positioning error caused by Doppler but also effectively utilizes the Doppler frequency shift information of moving satellite observation stations, thereby improving the positioning accuracy and resolution.

[0064] (3) This invention provides a direct positioning method based on a space-time model using low- and medium-orbit satellite fusion. By first using the coarse estimation results of direction finding positioning using a single satellite, the search area to be directly located is obtained, reducing the search range and computational load. Compared with existing technologies, the method provided by this invention can achieve high-precision positioning under low signal-to-noise ratio, while still achieving high resolution when ground radiation sources are very close together.

[0065] (3) When locating multiple ground radiation sources using the method of the present invention, it is not necessary to perform iterative calculations or estimate the number of sources in advance, thus reducing engineering costs. Attached Figure Description

[0066] Figure 1 This is a flowchart illustrating the positioning implementation of the method of the present invention;

[0067] Figure 2 A map of the search area determined by a coarse estimate of the direction finding and positioning of a single satellite;

[0068] Figure 3 This is a localization spectrum peak diagram from a simulation experiment of an embodiment of the present invention;

[0069] Figure 4 This is a positioning thermogram from a simulation experiment of an embodiment of the present invention;

[0070] Figure 5 This is a comparison chart of the root mean square error curves of the simulation experiment of the embodiment of the present invention and the traditional two-step positioning method. Detailed Implementation

[0071] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0072] like Figure 1 As shown, a direct positioning method based on a space-time model using low- and medium-Earth orbit satellite fusion includes the following steps:

[0073] Step 1: Roughly measure the location of ground radiation sources.

[0074] like Figure 2 As shown, by using the signal emitted by the ground radiation source obtained by measuring a single satellite, and based on the direction of the satellite antenna and the location of the maximum radiation power, the approximate spatial location information of the ground radiation source can be roughly determined, so as to reduce the spatial size of the direct location search in subsequent steps and reduce the computational cost.

[0075] Step 2: Construct a direct positioning scenario and satellite reception data model.

[0076] Assuming there are Q ground-based radiation sources in space, the method of this invention uses N satellites in medium and low Earth orbits for positioning, with M elements forming a linear array on each satellite. The signal data received by the nth satellite can then be modeled as follows:

[0077]

[0078] in, This represents the vector data of the k-th snapshot observed by the n-th satellite receiving antenna array, where M represents the number of array elements on the satellite receiving antenna, k = 0, 1, 2, ..., K-1, and there are a total of K sampling snapshots; p q Let be the coordinate vector of the q-th ground radiation source, where q = 1, 2, ..., Q, and there are a total of Q ground radiation sources; β is the steering vector when the q-th ground radiation source reaches the n-th satellite observation station, mainly determined by the relative positional relationship between the ground radiation source and the satellite observation station. n,q s represents the unknown complex channel attenuation parameter required for the q-th ground radiation source to reach the n-th satellite observation station; n,q (k) represents the envelope of the complex Gaussian signal received by the satellite observation station, and T represents the sampling interval. Let f be the Gaussian white noise with a mean of 0 for the nth satellite observation station. n (p q The Doppler frequency shift caused by relative motion is expressed as follows:

[0079]

[0080] In the above formula, f0 is the carrier frequency. Let u be the velocity vector of the nth satellite. n This provides the current position vector information for the nth satellite. and u n All of these can be obtained through satellite GPS positioning information, where c is the speed of light.

[0081] Step 3: Construct a space-time model of satellite received data.

[0082] Converting equation (1) into matrix form, we have:

[0083]

[0084] Wherein, the coefficient matrix (Formula (4)) is the extended array manifold matrix, α=[β1,β2,…β N ]、 All are extended steering vectors that take path loss parameters into account. For Q ground-based radiation source signals:

[0085]

[0086] To fully utilize the ground radiation source location information hidden in spatial angles and Doppler frequency shifts, a joint two-dimensional spatiotemporal processing model was chosen for direct localization. Based on the above received data model, the K sampling snapshots were divided into L segments. To simplify the model, the signal envelope and spatial attenuation information of these L segments can be considered approximately invariant, thus obtaining the spatiotemporal model of the received data:

[0087]

[0088] in,

[0089]

[0090] coefficient matrix

[0091]

[0092] intermediate quantity matrix

[0093] noise matrix

[0094] in, This represents the Kronen product operation of matrices. Note that... The space-time steering vector established by the method of the present invention. As mentioned above, in the signal receiving model of a high-speed moving satellite observation station, the Doppler frequency cannot be ignored. The purpose of the method of the present invention is to obtain the highly accurate positions of multiple ground radiation sources based on the space-time expression (6) of the received signal.

[0095] Step 4: Obtain the objective function of the maximum likelihood estimator.

[0096] Since the noise samples are independent and identically distributed, circular, complex Gaussian variables, the maximum likelihood estimator for single-source estimation is consistent with the least squares estimator expression.

[0097] For a single-source scenario, we assume the ground radiation source is located at point p, and its complex envelope at the nth satellite observation station is s. n (k). Therefore, the spatiotemporal measurement in expression (6) is simplified as follows:

[0098]

[0099] The least squares objective function is constructed as follows:

[0100]

[0101] Where N is the number of satellite observation stations, and the constraint term is... The p that minimizes the above equation is the location of the ground radiation source, i.e.:

[0102]

[0103] According to the least squares estimation criterion, the one that minimizes equation (13) is... Satisfy the following formula:

[0104]

[0105] Without loss of generality, assume ||b n (β,p)|| 2 =1, substituting equation (15) into the objective function (13), we get:

[0106]

[0107] because Keeping it constant, further simplifying formula (16) yields the simplified least squares estimated objective function:

[0108]

[0109] in, Let be the sampling covariance matrix of size ML×ML. Further simplifying equation (17), we obtain the simplified least-squares estimation objective function:

[0110]

[0111] Since β follows the condition ||β||=1, according to the Rayleigh entropy criterion, the maximum likelihood estimator result can be obtained as follows:

[0112]

[0113] Where, λ max (·) represents the operation of finding the maximum eigenvalue. By searching within the locked spatial range, the location of the ground radiation source is the p that maximizes the above expression.

[0114] Step 5: Obtain the objective function based on the minimum variance distortion-free criterion;

[0115] As shown in the above formula, the maximum likelihood is the extreme value of a nonlinear cost function, and its optimal solution can be obtained through a simple grid search. However, we expect to obtain higher resolution and more accurate positioning results. Therefore, the method of this invention applies the minimum variance distortion-free criterion (MVDR) to the above direct positioning model to achieve even higher positioning accuracy and resolution.

[0116] If the signals received by N satellite observation stations are integrated together, then equation (17) can be further rewritten as:

[0117]

[0118] in,

[0119]

[0120]

[0121] The symbol blkdiag(·) represents the block diagonal operation on a matrix.

[0122] Based on the minimum variance distortion-free response criterion, equation (20) can be rewritten as:

[0123]

[0124] At this point, the target position satisfies Among them, w opt (β,p) satisfies:

[0125]

[0126] Weight vector w opt (β,p) makes p the only one q The total output energy at all locations outside (q=1,...,Q) is minimized, thus minimizing the total output energy at the ground radiation source p. q The signal output at (q=1,...,Q) is distortion-free. Therefore, it can produce a high-resolution solution.

[0127] Solving equation (24) yields w. opt The optimal solution for (β,p) is as follows:

[0128]

[0129] Substituting the above optimal solution into the objective expression (23), we obtain the updated objective function:

[0130]

[0131] in, Further simplifying the above equation, we get:

[0132]

[0133] The location of the ground radiation source is the p that maximizes the above objective function.

[0134]

[0135] Step 6: Search the target space to determine the location of the ground radiation source.

[0136] Based on the above objective function values, a spatial spectrum is plotted, spectral peaks are searched, and the location of the ground radiation source is determined.

[0137] The direct positioning system based on the space-time model fusion of medium and low orbit satellites, according to the above method, includes:

[0138] The first module is used to locate ground radiation sources using any satellite, find a rough estimate of the range of the ground radiation sources, and determine the rough estimate range as the search area.

[0139] The second module is used to establish a satellite reception data model for receiving signals from ground radiation sources by a medium- and low-orbit satellite observation station with Doppler frequency shift; based on the satellite reception data model, a space-time steering vector is created using Doppler frequency shift information to establish a space-time model of the received data of the satellite reception data model;

[0140] The third module is used to calculate the sampling covariance matrix using the received data space-time model; obtain the maximum likelihood estimator objective function for single ground radiation source estimation according to the least squares estimation criterion; introduce the optimal weight vector according to the maximum likelihood estimator objective function for single ground radiation source estimation, obtain the weight vector according to the minimum variance distortionless response criterion, and obtain the objective function based on the minimum variance distortionless criterion.

[0141] The fourth module is used to draw a spatial spectrum based on the objective function value, perform spectral peak search, and determine the location of ground radiation sources.

[0142] Example 1

[0143] The simulation experiment platform in this embodiment was run on MATLAB R2022b in Windows 11 operating system. The simulation conditions were as follows: 5 satellites with an orbital altitude of 800km, satellite positions imported by STK software; each satellite had an 8-element uniform linear array; the observation time for each satellite was divided into L=10 segments; the number of sampling snapshots was 1200; and the channel fading of each ground radiation source and each array element was modeled as a complex Gaussian distribution with a mean of 0 and a variance of 0.1. A northeast-sky coordinate system was established with the nadir point of the primary satellite A as the origin. In this coordinate system, the positions of the ground radiation sources were [-1.2km, 1.2km], [0km, 0km].

[0144] With a signal-to-noise ratio (SNR) of 5 dB, the localization spectrum peak diagram of the method of this invention is obtained as follows: Figure 3 As shown, the location thermal distribution map is as follows: Figure 4 As shown. By Figure 3 and Figure 4 It can be seen that the position corresponding to the spectral peak The positions of the ground radiation sources p0 and p1 were consistent with the established locations, verifying the positioning accuracy of the method of the present invention. The positioning spectral peaks were very sharp and the resolution was high.

[0145] With the signal-to-noise ratio set from -20dB to 30dB, the root mean square error curves of the method of this invention and the two-step positioning method are obtained as follows: Figure 5 As shown. By Figure 5 It can be seen that when the signal-to-noise ratio of the received signal is low, the method of the present invention can still locate the position of the ground radiation source, and the positioning accuracy is higher than that of the traditional two-step positioning method.

[0146] This article uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only for the purpose of helping to understand the method and core ideas of the present invention. The above descriptions are only preferred embodiments of the present invention. It should be noted that due to the limitations of textual expression, while there are objectively infinite specific structures, those skilled in the art can make several improvements, modifications, or changes without departing from the principles of the present invention, and can also combine the above technical features in an appropriate manner. These improvements, modifications, changes, or combinations, or the direct application of the inventive concept and technical solution to other situations without modification, should all be considered within the scope of protection of the present invention.

[0147] The parts of this invention not described in detail are well-known to those skilled in the art.

Claims

1. A direct positioning method based on a space-time model using low- and medium-Earth orbit satellite fusion, characterized in that, include: By using any satellite to locate the ground radiation source, a rough estimate of the range of the ground radiation source can be found, and the rough estimate range can be determined as the area to be searched. Establish a satellite reception data model for low- and medium-Earth orbit satellite observation stations receiving signals from ground radiation sources, where Doppler shift exists; Based on the satellite receiving data model, a space-time steering vector is created using Doppler frequency shift information to establish the receiving data space-time model of the satellite receiving data model; Using the received data space-time model, the sampling covariance matrix is ​​calculated; based on the least squares estimation criterion, the objective function of the maximum likelihood estimator for single ground radiation source estimation is obtained; Based on the objective function of the maximum likelihood estimator for the single ground radiation source, an optimal weight vector is introduced, and the weight vector is obtained according to the minimum variance distortionless response criterion, thus obtaining the objective function based on the minimum variance distortionless criterion. Based on the objective function value, a spatial spectrum is plotted, and a spectral peak search is performed to determine the location of the ground radiation source; The space-time model for the satellite data reception model is as follows: ， in, for Q Signals from ground-based radiation sources: , This represents the envelope of the complex Gaussian signal received by the satellite observation station. ,common K One sampling snapshot; For the first q The coordinate vector of a ground radiation source ,common Q One ground-based radiation source; K , Q All are positive integers; j For imaginary units; This is expressed as the sampling interval time; Will K Each sampling snapshot is divided into L part, , For the first n The first satellite receiving antenna array observed the first k Vector data of a sample snapshot, M This indicates the number of array elements on the receiving antenna of the satellite; coefficient matrix , Indicates the first q The ground radiation source reached the first n The unknown complex channel attenuation parameters required for each satellite observation station The spacetime steering vector is , For the first q The ground radiation source reached the first n The steering vector for each satellite observation station is determined by the relative positional relationship between the ground radiation source and the satellite observation station; ， ， in, This represents the Kronen product operation of matrices; For the first n Gaussian white noise with a mean of 0 for each satellite observation station The Doppler frequency shift caused by relative motion: ， in, For carrier frequency, For the first n The velocity vector of each satellite For the first n The current position vector information of each satellite. It is the speed of light.

2. The direct positioning method based on a space-time model using low- and medium-orbit satellite fusion as described in claim 1, characterized in that: The satellite reception data model for receiving ground radiation source signals from a medium- and low-Earth orbit satellite observation station with Doppler frequency shift includes: No. n The ground radiation source signal data received by the satellite is modeled as follows: 。 3. The direct positioning method based on a space-time model using low- and medium-Earth orbit satellite fusion as described in claim 2, characterized in that: Using the received data space-time model, the sampling covariance matrix is ​​calculated; based on the least squares estimation criterion, the maximum likelihood objective function for estimating a single ground radiation source is derived, including: The least squares objective function is constructed as follows: ， Among them, constraint terms ; This refers to the path loss from the ground radiation source to the satellite observation station; The transmitter that minimizes the least squares estimated objective function This refers to the location of the ground-based radiation source: ， According to the least squares estimation criterion, the least squares estimation objective function is minimized. satisfy: ， The objective function of the maximum likelihood estimator is obtained as follows: ， in, for The size of the sampling covariance matrix; This is an operation to obtain the maximum eigenvalue.

4. The direct positioning method based on a space-time model using low- and medium-Earth orbit satellite fusion as described in claim 3, characterized in that: The objective function of the maximum likelihood estimator based on the single ground radiation source is used to introduce an optimal weight vector. The weight vector is then obtained according to the minimum variance distortionless response criterion, resulting in an objective function based on the minimum variance distortionless criterion, including: According to the minimum variance distortionless response criterion, we obtain: ， The target location satisfies , Wherein, weight function satisfy: ; Weight vector Make except Minimize the total output energy at all locations outside the ground radiation source, thus minimizing the total output energy at all locations outside the ground radiation source. The signal output at that location is distortion-free. ; right Solve the problem to obtain the results. The optimal solution is as follows: ， according to The optimal solution yields the objective function based on the minimum variance distortion-free criterion: ， Make the objective function Reaching the maximum value Location of ground radiation source .

5. A direct positioning system based on a space-time model using low- and medium-Earth orbit satellite fusion, characterized in that, include: The first module is used to locate ground radiation sources using any satellite, find a rough estimate of the range of the ground radiation sources, and determine the rough estimate range as the search area. The second module is used to establish a satellite reception data model for receiving signals from ground radiation sources by a medium- and low-orbit satellite observation station with Doppler frequency shift; based on the satellite reception data model, a space-time steering vector is created using Doppler frequency shift information to establish a space-time model of the received data of the satellite reception data model; The space-time model for the satellite data reception model is as follows: ， in, for Q Signals from ground-based radiation sources: , This represents the envelope of the complex Gaussian signal received by the satellite observation station. ,common K One sampling snapshot; For the first q The coordinate vector of a ground radiation source ,common Q One ground-based radiation source; K , Q All are positive integers; j For imaginary units; This is expressed as the sampling interval time; Will K Each sampling snapshot is divided into L part, , For the first n The first satellite receiving antenna array observed the first k Vector data of a sample snapshot, M This indicates the number of array elements on the receiving antenna of the satellite; coefficient matrix , Indicates the first q The ground radiation source reached the first n The unknown complex channel attenuation parameters required for each satellite observation station The spacetime steering vector is , For the first q The ground radiation source reached the first n The steering vector for each satellite observation station is determined by the relative positional relationship between the ground radiation source and the satellite observation station; ， ， in, This represents the Kronen product operation of matrices; For the first n Gaussian white noise with a mean of 0 for each satellite observation station The Doppler frequency shift caused by relative motion: ， in, For carrier frequency, For the first n The velocity vector of each satellite For the first n The current position vector information of each satellite. The speed of light; The third module is used to calculate the sampling covariance matrix using the received data space-time model; obtain the maximum likelihood estimator objective function for single ground radiation source estimation according to the least squares estimation criterion; introduce the optimal weight vector according to the maximum likelihood estimator objective function for single ground radiation source estimation, obtain the weight vector according to the minimum variance distortionless response criterion, and obtain the objective function based on the minimum variance distortionless criterion. The fourth module is used to draw a spatial spectrum based on the objective function value, perform spectral peak search, and determine the location of ground radiation sources.

6. A direct positioning system based on a space-time model using low- and medium-Earth orbit satellite fusion as described in claim 5, characterized in that: The satellite reception data model for receiving ground radiation source signals from a medium- and low-Earth orbit satellite observation station with Doppler frequency shift includes: No. n The ground radiation source signal data received by the satellite is modeled as follows: 。 7. A direct positioning system based on a space-time model using low- and medium-Earth orbit satellite fusion as described in claim 6, characterized in that: The process involves using the received data spatiotemporal model to calculate the sampling covariance matrix; and deriving the maximum likelihood objective function for estimating a single ground radiation source based on the least squares estimation criterion, including: The least squares objective function is constructed as follows: ， Among them, constraint terms ; This refers to the path loss from the ground radiation source to the satellite observation station; The transmitter that minimizes the least squares estimated objective function This refers to the location of the ground-based radiation source: ， According to the least squares estimation criterion, the least squares estimation objective function is minimized. satisfy: ， The objective function of the maximum likelihood estimator is obtained as follows: ， in, for The size of the sampling covariance matrix; This is an operation to obtain the maximum eigenvalue.

8. A direct positioning system based on a space-time model using low- and medium-Earth orbit satellite fusion as described in claim 7, characterized in that: The objective function of the maximum likelihood estimator based on the single ground radiation source is used to introduce an optimal weight vector. The weight vector is then obtained according to the minimum variance distortionless response criterion, resulting in an objective function based on the minimum variance distortionless criterion, including: According to the minimum variance distortionless response criterion, we obtain: ， The target location satisfies , Wherein, weight function satisfy: ; Weight vector Make except Minimize the total output energy at all locations outside the ground radiation source, thus minimizing the total output energy at all locations outside the ground radiation source. The signal output at that location is distortion-free. ; right Solve the problem to obtain the results. The optimal solution is as follows: ， according to The optimal solution yields the objective function based on the minimum variance distortion-free criterion: ， Make the objective function Reaching the maximum value Location of ground radiation source .

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