Multi-satellite direct positioning method based on CUDA (Compute Unified Device Architecture) parallel computing

Abstract

The invention discloses a multi-satellite direct positioning method based on CUDA (Compute Unified Device Architecture) parallel calculation, relates to the field of space-based electromagnetic signal positioning, and aims to be suitable for large-range and high-precision positioning of low-signal-to-noise-ratio signals. According to the technical key points, a positioning area is determined in a satellite coverage range according to prior information, and grid points are divided on the surface of the earth; two or more satellites with time-frequency synchronization obtain observed quantities of signals emitted by the same ground radiation source, a first signal model of the multiple observed quantities is constructed, and down-conversion is carried out on the first signal to obtain a second signal; constructing a cost function by using signal characteristics (such as time difference of arrival, frequency difference of arrival and the like) in a radiation source signal received by a satellite; a cost function corresponding to each grid point is subjected to multi-core parallel computing through the GPU; and summarizing results, and searching the maximum value of the cost function to determine the estimated position of the ground radiation source. According to the multi-satellite direct positioning method based on the CUDA, the characteristic that parallel calculation can be carried out when cost function grid searching optimization is carried out in direct positioning is utilized, calculation is directly carried out on satellites, satellite-ground data transmission is omitted, the positioning time is shortened by utilizing the independence of searching calculation among grids, and the real-time performance of a positioning system is guaranteed.

Description

Technical Field

[0001] The present invention relates to the field of space-based electromagnetic signal positioning, and in particular to a passive direct positioning method based on CUDA acceleration. Background Art

[0002] The passive positioning of ground radiation sources by satellite platforms usually adopts a two-step positioning method based on parameter measurement, that is, firstly estimating the signal parameters, and then estimating the position of the radiation source based on the signal parameters. In the current complex electromagnetic environment, this method is subject to many constraints, such as: parameter estimation error, positioning equation linearization solution error, etc., which will affect the positioning results. The direct positioning method breaks through the limitations of the two-step positioning and eliminates the parameter estimation process. Especially under low signal-to-noise ratio conditions, the positioning accuracy is better than the two-step positioning method. However, it requires unified processing of multi-channel observation signals, resulting in a large amount of inter-satellite and downlink data transmission. In particular, it adopts the grid search method. When positioning the ground radiation source based on the satellite, the satellite coverage is large, and a dense grid needs to be divided to achieve the positioning accuracy requirements, resulting in a large search volume, low algorithm optimization efficiency, and difficulty in meeting real-time requirements.

[0003] The existing patent document with the document number CN113721276B discloses a target positioning method, device, electronic device and computer-readable medium based on multiple satellites. The method includes: obtaining multiple direction-finding positioning data sets and multiple time-frequency difference data of multiple satellites for the target object according to the positioning request of the target object, wherein the direction-finding positioning data set includes direction-finding positioning data of multiple periods; training a machine learning model according to the multiple direction-finding positioning data sets and multiple time-frequency difference data to generate a multi-satellite positioning model; inputting the multiple direction-finding positioning data sets into the multi-satellite positioning model to obtain the precise position of the target object. The long-period positioning data of multiple satellites are fused to fully explore the correlation between the long-period data of multiple satellites of the same target, realize decision-making fusion and improve the accuracy of target positioning.

[0004] The existing patent document with document number CN115119142B discloses a distributed direct positioning method based on a sensor network. It solves the problem of low positioning accuracy of the current distributed direct positioning algorithm under low signal-to-noise ratio. In order to improve the accuracy of distributed direct positioning, it adopts the following scheme: First, a high-resolution direct positioning distributed optimization model based on the subspace data fusion algorithm is derived. Second, in order to solve the problem of solving the initial value of the target position, a particle swarm algorithm based on vector evaluation is used to obtain a rough estimate of the initial value of the target position iteration, and then the traditional clustering algorithm is used to obtain the initial value of the target position iteration, avoiding the problem of parameter matching of the traditional two-step positioning algorithm. Third, an accurate first-order algorithm in the field of distributed optimization is introduced, and the accuracy of centralized direct positioning is achieved through a two-step gradient information iteration solution, solving the problem of positioning accuracy loss caused by distributed processing.

[0005] However, none of the above existing technologies proposes how to use the parallel computing capability of GPU to realize rapid processing and analysis of a large amount of calculations in the positioning search process. Summary of the invention

[0006] The technical problems to be solved by the present invention are:

[0007] The purpose of the present invention is to provide a multi-satellite direct positioning method based on CUDA parallel computing, which is suitable for large-scale, high-precision positioning of low signal-to-noise ratio signals, and realizes the rapid processing and analysis of a large number of calculations in the positioning search process by utilizing the parallel computing capability of GPU.

[0008] The technical solution adopted by the present invention to solve the above technical problems is:

[0009] A multi-satellite direct positioning method based on CUDA parallel computing comprises the following steps:

[0010] Step 1: Determine the positioning area within the satellite coverage area and divide the grid points on the earth's surface:

[0011] Divide the earth's surface into grids of uniform size within the specified range of longitude, latitude, and altitude;

[0012] Step 2: using two or more satellites synchronized in time and frequency to obtain observations of signals transmitted by the same ground radiation source, constructing a first signal model of multiple observations, and down-converting the first signal model to obtain a second signal model:

[0013] The first signal model is established based on time delay and frequency shift:

[0014]

[0015] In the above formula, r l,k (t) represents the signal received by the lth satellite in the kth time slot, β l,k is the channel attenuation, s k (t-τ l,k ) represents the target signal after transmission delay in the kth time slot, w l,k (t) is zero-mean Gaussian white noise, T is the observation time in each time slot, and f l,k is the Doppler shift:

[0016] f l,k =f c [1+μ l,k (p)]

[0017]

[0018] In the above formula, c is the signal propagation speed, f c is the signal carrier frequency, p l,k is the position of the lth satellite in the kth time slot, and p represents the position of the radiation source;

[0019] Satellite receiving signal delay:

[0020] τ l,k =||p l,k -p|| / c

[0021] After down-conversion and N sampling processes at the receiver, the second signal model is obtained:

[0022] r l.k =β l,k A l,k F l,k s k +w l,k (3)

[0023] In the above formula, β l,k is the channel attenuation matrix, A l,k is the frequency shift matrix, F l,k is a shift matrix, which means that s k Shift τ l,k / T s , T s is the sampling interval, w l,k is a zero-mean Gaussian noise matrix with variance σ 2 I;

[0024] Step 3: Use the signal characteristics of the satellite received radiation source signal to construct a cost function:

[0025] The maximum likelihood function is:

[0026]

[0027] Taking the logarithm of both sides of the above formula, we get:

[0028]

[0029] For σ 2 Take the partial derivative and set it to 0 to get the estimated value of the noise variance:

[0030]

[0031] Get the cost function:

[0032]

[0033] Assume||s k || 2=1, minimize equation (4) and obtain the maximum likelihood estimate of channel attenuation:

[0034]

[0035] Substituting formula (5) into formula (4), we get:

[0036]

[0037] In the above formula, is an independent parameter, transforming the minimization formula (6) into the maximization formula:

[0038]

[0039] Define the following N-order Hermitian matrix:

[0040]

[0041] Maximization (7) is transformed into maximizing every k The quadratic form of s k The matrix Q k When the eigenvector corresponding to the maximum eigenvalue of , the cost function value is the largest, so the above cost function is equivalent to:

[0042]

[0043] Q k Equivalent to a matrix of dimension L×L At this time, the cost function is equivalent to:

[0044]

[0045] Then the estimated position of the ground radiation source is:

[0046]

[0047] Step 4: Use GPU multi-core to parallelly calculate the cost function corresponding to each grid point;

[0048] Step 5: Summarize the results, search for the maximum value of the cost function, and replace the grid point with the maximum value of the cost function as the estimated position of the ground radiation source.

[0049] Furthermore, step 4 specifically includes:

[0050] Step 41, initialization data:

[0051] Copy the signal data and grid point division data from the host memory to the device memory, and use the CUDA memory allocation function to allocate the memory required for computing data on the device side;

[0052] Step 42, write the kernel function:

[0053] Design the kernel function based on the cost function in step 3;

[0054] Step 43, start the kernel function:

[0055] Call the CUDA kernel function on the device side, set the number of blocks according to the number of grid points, assume that each block contains M threads, each thread calculates the cost function value of a grid point, and transfers the calculation result data from the device-side video memory back to the host-side memory.

[0056] The beneficial effects of the present invention are:

[0057] The present invention proposes a fast and direct positioning method, which realizes the rapid processing and analysis of a large number of calculations in the positioning search process by making full use of the parallel computing power of the GPU. In order to meet the positioning accuracy requirements, the grid division needs to be relatively dense when using the grid search method to achieve the corresponding accuracy. Due to the CPU hardware structure, the number of CPU threads is small, and the CPU-based positioning calculation time is long, which makes it difficult to meet the real-time positioning. The present invention uses the parallel computing unit of the GPU to cut the positioning area into units in which each grid point runs independently, executes a copy of the cost function for each grid point, and assigns the key computing tasks in the positioning algorithm to multiple processing units for simultaneous processing, thereby keeping hundreds of GPU cores busy. The denser the search grid, the more obvious the advantage of this method in accelerating the calculation speed, which improves the real-time and response speed of the positioning system.

[0058] The method of the present invention utilizes the parallel computation characteristics of grid search optimization of cost function in direct positioning, proposes a multi-satellite direct positioning method based on CUDA, performs calculations directly on the satellite, eliminates satellite-to-ground data transmission, and utilizes the independence of search calculations between grids to shorten the positioning time, thereby ensuring the real-time performance of the positioning system. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 A schematic diagram of a satellite passive positioning scenario according to an embodiment of the present invention;

[0060] Figure 2 is a flow chart of a multi-satellite direct positioning method according to an embodiment of the present invention;

[0061] Figure 3 A schematic diagram of parallel calculation of a multi-satellite direct positioning method based on CUDA according to an embodiment of the present invention;

[0062] Figure 4 A schematic diagram of a grid search for Samsung direct positioning according to an embodiment of the present invention. DETAILED DESCRIPTION

[0063] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the following Figure 1-4 It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0064] The present invention provides a multi-satellite direct positioning method based on CUDA parallel computing (a multi-satellite passive positioning method based on CUDA), which realizes direct positioning based on GPU, and the method comprises: step 1, determining the positioning area according to prior information within the satellite coverage range, and dividing the grid points on the earth's surface. Step 2, two or more satellites synchronized in time and frequency obtain the observation quantity of the signal transmitted by the same ground radiation source, construct the first signal model of the multiple observation quantities, and down-convert the first signal to obtain the second signal; step 3, constructing the cost function by using the signal characteristics (such as arrival time difference, arrival frequency difference, etc.) in the signal received by the satellite radiation source; step 4, using GPU multi-core parallel calculation of the corresponding cost function at each grid point; step 5, summarizing the results, searching for the maximum value of the cost function to determine the estimated position of the ground radiation source.

[0065] According to the method provided by the present invention, step 1 specifically includes: determining the positioning area based on prior knowledge, specifying the longitude, latitude, and altitude ranges, dividing the earth's surface into grids of uniform size, and the density of the grids depends on the positioning accuracy requirements.

[0066] According to the method provided by the present invention, the step 2 specifically includes: Optionally, a model for receiving the first signal is established based on the time delay and the frequency shift:

[0067]

[0068] Among them, r l,k (t) represents the signal received by the lth satellite in the kth time slot, β l,k is the channel attenuation, s k (t-τ l,k ) represents the target signal after transmission delay in the kth time slot, w l,k (t) is zero-mean Gaussian white noise, T is the observation time in each time slot, and f l,k is the Doppler frequency shift, as shown below:

[0069] f l,k =f c [1+μ l,k (p)]

[0070]

[0071] Where c is the signal propagation speed, f c is the signal carrier frequency.

[0072] After down-conversion and N sampling processes at the receiver, the second signal model is obtained:

[0073] r l.k =β l,k A l,k F l,k s k +w l,k (3)

[0074] Among them, β l,k is the channel attenuation matrix, A l,k is the frequency shift matrix, F l,k is a shift matrix, which means that s k Shift τ l,k / T s , W l,k The variance of 2 I, the target position can be estimated based on the second signal model.

[0075] According to the method provided by the present invention, step 3 specifically includes: estimating the unknown parameters based on the maximum likelihood estimation principle, and obtaining the cost function through derivation as follows:

[0076]

[0077] Without loss of generality, assume that ||s k || 2 =1, minimizing equation (4), the maximum likelihood estimate of channel attenuation can be obtained as:

[0078]

[0079] Substituting formula (5) into formula (4), we get:

[0080]

[0081] in are independent parameters, so the minimization of equation (6) can be transformed into the maximization of the following equation:

[0082]

[0083] Define the following N-order Hermitian matrix:

[0084]

[0085] The maximization formula (7) can be transformed into maximizing every k The quadratic form of , therefore, when s k The matrix Qk When the eigenvector corresponding to the maximum eigenvalue of , the cost function value is the largest. Therefore, the above cost function is equivalent to:

[0086]

[0087] Q k The dimension is N×N. As the number of sampled data increases, the amount of calculation becomes larger. According to matrix theory, it is equivalent to a matrix with a dimension of L×L. At this time, the cost function is equivalent to:

[0088]

[0089] The estimation of the radiation source position is obtained by the following formula:

[0090]

[0091] According to the method provided by the present invention, the step 4 specifically comprises:

[0092] 1) Initialize data: Use the cudaMemcpy function to copy signal data, grid division data and other data required for positioning from the host (CPU) memory to the device (GPU) memory, store them in the GPU's global memory, and use the CUDA memory allocation function to allocate the memory required for computing data on the device side;

[0093] 2) Write kernel function: Design kernel function according to the cost function in step 3;

[0094] 3) Start the kernel function: Call the CUDA kernel function on the host side (GPU), set the number of blocks according to the number of grid points, assume that each block contains M threads, and each thread calculates the cost function value of a grid point. To maximize parallelism and make full use of computing resources, maximize the number of threads as much as possible and make each used thread active. Assign the computing task to the GPU thread, perform numerical calculations, and transfer the calculation result data from the device memory back to the host memory.

[0095] According to the method provided by the present invention, step 5 specifically includes: analyzing the copied calculation results on the host side, searching for the maximum value of the cost function value, and selecting the grid point with the maximum cost function value as the radiation source position estimation point.

[0096] Example

[0097] Figure 2The present invention is a flow chart of a multi-satellite direct positioning method according to an embodiment of the present invention. The method comprises: step 1, determining the positioning area according to prior information within the satellite coverage pattern, and dividing the grid points on the surface of the earth. Step 2, two or more satellites synchronized in time and frequency obtain the observation quantity of the signal transmitted by the same ground radiation source, construct the first signal model of the multiple observation quantities, and down-convert the first signal to obtain the second signal; step 3, constructing the cost function using the time difference and frequency difference information in the satellite receiving radiation source signal; step 4, using GPU multi-core parallel calculation of the corresponding cost function at each grid point; step 5, finding the maximum value of the cost function to determine the estimated position of the ground radiation source.

[0098] Step 1: Figure 4 A schematic diagram of a possible three-dimensional grid search for direct three-star positioning of a single radiation source according to an embodiment of the present invention. The positioning area is determined based on prior knowledge, and the longitude, latitude, and altitude ranges are specified to divide the earth's surface into grids of uniform size. The density of the grid depends on the accuracy requirements of the positioning. Optionally, a suitable coordinate system is selected to represent the earth's surface, such as the longitude and latitude high coordinate system in the WGS-84 coordinate system. The geostationary Cartesian coordinate system is used in the positioning calculation process, so the longitude and latitude high coordinate system is converted to the geostationary Cartesian coordinate system, which is defined as:

[0099]

[0100] Among them, L is the geodetic longitude, B is the geodetic latitude, H is the geodetic height, a=6378137m±2m is the major axis of the earth ellipsoid model, e 2 =0.00669437999013 is the square of the first eccentricity, N is the radius of curvature of the local yoke, which is defined as:

[0101]

[0102] Step 2: Optionally, a model for receiving the first signal is established based on the time delay and the frequency shift:

[0103]

[0104] Among them, r l,k (t) represents the signal received by the lth satellite in the kth time slot, β l,k is the channel attenuation, s k (t-τ l,k ) represents the target signal after transmission delay in the kth time slot, w l,k (t) is zero-mean Gaussian white noise, and T is the observation time in each time slot.

[0105] c is the signal propagation speed, p l,krepresents the position of the lth satellite in the kth time slot, and p represents the position of the radiation source. Then the satellite receiving signal delay is given by the following formula:

[0106] τ l,k =||p l,k -p|| / c (4)

[0107] f lk is the Doppler shift, given by:

[0108]

[0109] Among them, f c is the signal carrier frequency.

[0110] After down-conversion and N sampling processes at the receiver, the vector is defined as:

[0111]

[0112] Get the second signal model:

[0113] r l.k =β l,k A l,k F l,k s k +w l,k (7)

[0114] Among them, β l,k is the channel attenuation matrix, A l,k is the frequency shift matrix, F l,k is a shift matrix, which means that s k Shift τ l,k / T s , T s is the sampling interval, w is the zero-mean Gaussian noise matrix, and the variance is σ 2 I, the target position can be estimated based on the second signal model.

[0115] l,k

[0116] Step 3: Estimate the unknown parameters based on the maximum likelihood estimation principle. The maximum likelihood function is:

[0117]

[0118] Taking the logarithm of both sides of the above formula, we get:

[0119]

[0120] For σ in formula (9), 2 Take the partial derivative and set it to 0 to get the estimated value of the noise variance:

[0121]

[0122] Substituting into formula (9) we get the cost function:

[0123]

[0124] Without loss of generality, assume that ||s k || 2 =1, minimizing equation (11), the maximum likelihood estimate of channel attenuation can be obtained as:

[0125]

[0126] Substituting formula (12) into formula (11), we get:

[0127]

[0128] in are independent parameters, so the minimization formula (13) can be transformed into the maximization formula:

[0129]

[0130] Define the following N-order Hermitian matrix:

[0131]

[0132] When the signal is unknown, the maximization formula (14) can be transformed into maximizing every k The quadratic form of , therefore, when s k The matrix Q k When the eigenvector corresponding to the maximum eigenvalue of , the cost function value is the largest. Therefore, the cost function is equivalent to:

[0133]

[0134] Q k The dimension is N×N. As the number of sampled data increases, the amount of calculation becomes larger. According to matrix theory, it is equivalent to a matrix with a dimension of L×L. At this time, the cost function is equivalent to:

[0135]

[0136] The estimation of the radiation source position is obtained by the following formula:

[0137]

[0138] According to the method provided by the present invention, the step 4 specifically comprises:

[0139] 1) Initialize data: Use the cudaMemcpy function to copy signal data, grid division data and other data required for positioning from the host (CPU) memory to the device (GPU) memory, store them in the GPU's global memory, and use the CUDA memory allocation function to allocate the memory required for computing data on the device side;

[0140] 2) Write kernel function: Design kernel function according to the cost function in step 3;

[0141] 3) Start the kernel function: Call the CUDA kernel function on the host side (GPU). Each thread calculates the cost function value of a grid point. The required thread blocks and number of threads are specified according to the number of grids. The computing resources are fully utilized, the computing tasks are assigned to the GPU, numerical calculations are performed, and the calculation result data is transferred from the device memory back to the host.

[0142] According to the method provided by the present invention, step 5 specifically includes: analyzing the calculation results transmitted back at the host end, searching for the maximum value of the cost function value, and selecting the grid point with the maximum cost function value as the radiation source position estimation point.

[0143] The above embodiments further illustrate the purpose, technical solutions and advantages of the present invention in detail. It should be understood that the above embodiments are only preferred implementation modes of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made to the present invention within the spirit and principles of the present invention should be included in the protection scope of the present invention.

[0144] It has been verified that the method proposed in the present invention solves the technical problem proposed in the present invention. The method of the present invention has been verified through practical application of the technical effect and practicality claimed by the present invention.

[0145] The method of the present invention has been verified through simulation experiments and practical applications, and the technical effects claimed by the present invention have been verified.

[0146] The algorithm (method) proposed in the present invention is the underlying technical core of the present invention. Based on the algorithm (method) proposed in the present invention, a multi-star direct positioning system based on CUDA parallel computing is developed using a programming language. The system has program modules corresponding to the steps of the above-mentioned technical solution, and executes the steps in the above-mentioned multi-star direct positioning method based on CUDA parallel computing during operation.

[0147] The computer program of the developed system (software) is stored on a computer-readable storage medium, and the computer program is configured to implement the steps of the multi-star direct positioning method based on CUDA parallel computing when called by a processor. That is, the present invention is materialized on a carrier to become a computer program product.

[0148] A multi-satellite direct positioning method device based on CUDA parallel computing, the device comprising at least one processor and a memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the above-mentioned multi-satellite direct positioning method based on CUDA parallel computing.

[0149] Various implementations of the systems and techniques described herein can be realized in digital electronic circuit systems, integrated circuit systems, dedicated ASICs (application specific integrated circuits), computer hardware, firmware, software, and / or combinations thereof. These various implementations can include: being implemented in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which can be a special purpose or general purpose programmable processor that can receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit data and instructions to the storage system, the at least one input device, and the at least one output device.

[0150] The computer programs (also referred to as programs, software, software applications, or codes) of the present invention include machine instructions for programmable processors, and these computer programs can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. As used in the present invention, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, device, and / or device (e.g., disk, optical disk, memory, programmable logic device PLD) for providing machine instructions and / or data to a programmable processor, including a machine-readable medium that receives machine instructions as machine-readable signals. The term "machine-readable signal" refers to any signal for providing machine instructions and / or data to a programmable processor.

[0151] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps recorded in this application can be executed in parallel, sequentially or in different orders, as long as the expected results of the technical solution disclosed in this application can be achieved, they are all within the scope of protection of the present invention.

Claims

1. A multi-satellite direct positioning method based on CUDA parallel computing, characterized in that: The steps include: Step 1: Determine the positioning area within the satellite coverage area and divide the grid points on the earth's surface: Divide the earth's surface into grids of uniform size within the specified range of longitude, latitude, and altitude; Step 2: using two or more satellites synchronized in time and frequency to obtain observations of signals transmitted by the same ground radiation source, constructing a first signal model of multiple observations, and down-converting the first signal model to obtain a second signal model: The first signal model is established based on time delay and frequency shift: In the above formula, r l,k (t) represents the signal received by the lth satellite in the kth time slot, β l,k is the channel attenuation, s k (t-τ l,k ) represents the target signal after transmission delay in the kth time slot, w l,k (t) is zero-mean Gaussian white noise, T is the observation time in each time slot, and f l,k is the Doppler shift: In the above formula, c is the signal propagation speed, f c is the signal carrier frequency, p l,k is the position of the lth satellite in the kth time slot, p represents the position of the radiation source; v l,k The speed of the lth satellite in the kth time slot; Satellite receiving signal delay: τ l,k J||p l,k -p|| / c After down-conversion and N sampling processes at the receiver, the second signal model is obtained: r l.k =β l,k A l,k F l,k s k +w l,k (3) In the above formula, β l,k is the channel attenuation matrix, A l,k is the frequency shift matrix, F l,k is a shift matrix, which means that s k Shift τ l,k / T s , T s is the sampling interval, w l,k is a zero-mean Gaussian noise matrix with variance σ 2 I; Step 3: Use the signal characteristics of the satellite received radiation source signal to construct a cost function: The maximum likelihood function is: Taking the logarithm of both sides of the above formula, we get: K is the total number of time slots, L is the total number of observed satellites; S k is the matrix form of the received signal; For σ 2 Take the partial derivative and set it to 0 to get the estimated value of the noise variance: Get the cost function: Assume||s k || 2 =1, minimize equation (4) and obtain the maximum likelihood estimate of channel attenuation: Substituting formula (5) into formula (4), we get: In the above formula, is an independent parameter, transforming the minimization formula (6) into the maximization formula: Define the following N-order Hermitian matrix: Maximization (7) is transformed into maximizing every k The quadratic form of s k The matrix Q k When the eigenvector corresponding to the maximum eigenvalue of , the cost function value is the largest, so the above cost function is equivalent to: Q k Equivalent to a matrix of dimension L×L At this time, the cost function is equivalent to: Then the estimated position of the ground radiation source is: λ max Representation Matrix The maximum eigenvalue of Step 4: Use GPU multi-core to parallelly calculate the cost function corresponding to each grid point; Step 5: Summarize the results, search for the maximum value of the cost function, and replace the grid point with the maximum value of the cost function as the estimated position of the ground radiation source.

2. The multi-satellite direct positioning method based on CUDA parallel computing according to claim 1, characterized in that: Step 4 specifically includes: Step 41, initialization data: Copy the signal data and grid point division data from the host memory to the device memory, and use the CUDA memory allocation function to allocate the memory required for computing data on the device side; Step 42, write the kernel function: Design the kernel function based on the cost function in step 3; Step 43, start the kernel function: Call the CUDA kernel function on the device side, set the number of blocks according to the number of grid points, assume that each block contains M threads, each thread calculates the cost function value of a grid point, and transfers the calculation result data from the device-side video memory back to the host-side memory.

3. A multi-satellite direct positioning method system based on CUDA parallel computing, characterized in that: The system has a program module corresponding to the steps of any one of claims 1-2 above, and executes the steps of the multi-satellite direct positioning method based on CUDA parallel computing when running.

4. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of a multi-satellite direct positioning method based on CUDA parallel computing according to any one of claims 1 to 2 when called by a processor.

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