A space-based positioning method, system, and storage medium combining direction finding and coherent cumulative positioning.

Abstract

This invention provides a space-based positioning method, system, and storage medium combining direction-finding positioning and coherent cumulative positioning, relating to the field of space-based passive positioning technology. It addresses the problems of low positioning accuracy, high computational cost, and long processing time in existing space-based positioning methods. The method includes: Step 1, constructing a target signal model received by the satellite and using a direction-finding positioning algorithm to perform coarse positioning of the target, obtaining a coarse estimate of the target's position; Step 2, using the coarse estimate of the target's position as the center, setting a traversal range, and using a coherent cumulative positioning algorithm to perform high-precision positioning of the target. This invention significantly reduces the computational load of space-based positioning methods, improves computational efficiency, and achieves high-precision and efficient space-based positioning.

Description

Technical Field

[0001] This invention relates to the field of space-based passive positioning technology, and more specifically, to a space-based positioning method, system, and storage medium that combines direction finding and coherent cumulative positioning. Background Technology

[0002] Accurately determining the location of ground targets using satellites is a crucial issue in aerospace electronic intelligence reconnaissance, spectrum surveillance, and remote sensing. Compared to ground-based reconnaissance methods, intercepting and tracking target radio signals using satellite platforms is unaffected by geographical location, offers a wide detection range, longer reconnaissance time, and higher cost-effectiveness. Common space-based positioning systems include single-satellite direction-finding positioning, two-satellite time-difference positioning, and multi-satellite positioning, each exhibiting unique advantages and limitations, collectively forming the current diverse landscape of space-based positioning technologies. Among these, multi-satellite positioning, especially the three-satellite time-difference positioning system, leverages the comprehensive use of signal information from multiple satellites and employs precise time difference measurement technology to achieve high-precision three-dimensional positioning of ground or air targets. This system offers advantages such as high positioning accuracy, wide coverage, and a degree of resistance to interference, improving positioning stability. However, this high precision comes with increased system complexity. It requires not only highly coordinated operation among multiple satellites to ensure the synchronization and accuracy of signal transmission but also imposes stringent requirements on satellite orbit design and configuration; any change in configuration can significantly impact positioning accuracy. In addition, the construction and maintenance costs of multi-satellite systems are high, including satellite launch, operation and maintenance, and the establishment of ground monitoring systems, all of which are significant economic burdens.

[0003] In contrast, single-satellite direction finding and positioning systems achieve basic positioning functions in a simpler way. This system mainly relies on the signal transmitted by a single satellite, and determines the approximate location of the target by measuring the direction of the signal through ground or air receivers. Due to its simple structure and low implementation cost, it is particularly suitable for applications with limited resources or low requirements for positioning accuracy. However, the inherent limitations of single-satellite direction finding and positioning lie in its relatively limited positioning accuracy and susceptibility to environmental factors such as terrain obstruction and multipath effects, leading to a certain degree of uncertainty in the positioning results and making it difficult to meet the needs of high-precision navigation and positioning. Summary of the Invention

[0004] The technical problem to be solved by this invention is:

[0005] Existing methods for space-based positioning suffer from low positioning accuracy, high computational cost, and long processing time.

[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0007] This invention provides a space-based positioning method combining direction finding and coherent cumulative positioning, comprising the following steps:

[0008] Step 1: Construct a target signal model received by the satellite, and use a direction finding and positioning algorithm to coarsely locate the target and obtain a coarse estimate of the target's position;

[0009] Step 2: Using the coarse estimate of the target location as the center, set the traversal range and use the coherent cumulative positioning algorithm to perform high-precision positioning of the target.

[0010] Further, step 1 includes the following steps:

[0011] Step 1.1: Construct a signal model;

[0012] Assume the target signal received by the satellite is r(t), with dimension Nx1; the noise is stationary, zero-mean Gaussian white noise, and the noise particles are independent of each other; its expression is:

[0013]

[0014] Where: M is the number of target signals, A m Let θ be the amplitude of the m-th target signal. m , Let ω be the spatial parameter of the m-th target signal. m Let φ be the frequency of the m-th target signal. m Let n(t) be the phase of the m-th target signal, and n(t) be the noise.

[0015] Step 1.2: Calculate the data covariance matrix;

[0016] The autocorrelation function of the received signal is:

[0017] R = E(r(t)r(t)) H (2)

[0018] Where: E() represents the mathematical expectation, and H is the conjugate transpose;

[0019] Step 1.3: Perform eigenvalue decomposition on the covariance matrix R to obtain the noise subspace U. n ;

[0020] Eigenvalue decomposition of the covariance matrix R yields:

[0021]

[0022] Among them: U s These are the eigenvectors of the signal subspace;

[0023] Let ∑ be a matrix consisting of the M largest eigenvalues ​​of R, corresponding to the eigenvalues ​​of the signal subspace, and we have:

[0024] ∑=diag{λ1 λ2 ... λ M} (4)

[0025] λ m Let M be the feature value corresponding to the m-th signal, where 1 ≤ m ≤ M;

[0026] U n These are the feature vectors of the noise subspace;

[0027] Let Λ be a matrix consisting of NM small eigenvalues ​​of R, corresponding to the eigenvalues ​​of the noise subspace, and we have:

[0028] Λ=diag{λ M+1 λ M+2 ... λ N} (5)

[0029] λ M+i Let be the eigenvalue of the (M+i)th eigenvalue, 1≤i≤NM;

[0030] Step 1.4: Perform spectral peak search on the target signal;

[0031] The steering vector in the signal subspace is orthogonal to the noise subspace, that is:

[0032]

[0033] Where: e(ω)=[1 e jω ... e jω(N-1) ] T ;

[0034] We obtain the following by minimizing the search:

[0035]

[0036] Step 1.5: Find the signal frequency and spatial parameters corresponding to the maximum point;

[0037] The formulas for estimating the frequency and spatial parameters of the target signal are as follows:

[0038]

[0039] Find the signal frequency and spatial parameters corresponding to the M maxima of formula (8);

[0040] Step 1.6: Calculate the target signal position;

[0041] Using the satellite position as the origin and the spatial parameters obtained in step 1.5 as the direction, construct a ray and calculate the intersection of the ray with the Earth's surface. When there are two intersections, select the intersection closer to the satellite position as the coarse estimate of the target position.

[0042] Furthermore, step 2 includes the following steps:

[0043] Step 2.1: Determine the positioning area based on the direction finding and positioning results;

[0044] The theoretical positioning error of the space-based direction finding and positioning algorithm is analyzed. Taking the coarse estimate of the target position as the center and the theoretical positioning error of multiples as the radius, the traversal range is determined, and grid points are divided on the Earth's surface.

[0045] Step 2.2: Construct the observation signal model;

[0046] The model for the received signal based on time delay and frequency shift is as follows:

[0047]

[0048] Where, r k (t) represents the signal received by the satellite in the k-th time slot, β k For channel attenuation, s k (t-τ k ) represents the target signal in the k-th time slot after transmission delay, n k (t) represents the zero-mean Gaussian white noise in the k-th time slot, T is the observation time in each time slot, and f k For Doppler frequency shift;

[0049] Step 2.3: Construct the cost function;

[0050] Utilizing the signal characteristics in the satellite-received radiation source signal, the unknown parameters are estimated based on maximum likelihood estimation. The cost function C(p) is derived as follows:

[0051]

[0052] Among them, A k Let F be the frequency shift matrix. k It is a shift matrix;

[0053] Assume ||s k || 2 =1, minimizing formula (10), we obtain the maximum likelihood estimate of channel attenuation:

[0054]

[0055] Substituting equation (11) into equation (10), we get:

[0056]

[0057] Step 2.4: Estimate the target location;

[0058] Target location estimation We obtain it from the following formula:

[0059]

[0060] This invention provides a space-based positioning system that combines direction finding and coherent cumulative positioning. The system has a program module corresponding to the steps of any of the above-described technical solutions, and executes the steps of the above-described space-based positioning method that combines direction finding and coherent cumulative positioning when running.

[0061] The present invention provides a computer-readable storage medium storing a computer program configured to, when called by a processor, implement the steps of the space-based positioning method combining direction finding and coherent cumulative positioning as described in any of the above technical solutions.

[0062] Compared with the prior art, the beneficial effects of the present invention are:

[0063] This invention discloses a space-based positioning method, system, and storage medium that combines direction-finding positioning and coherent cumulative positioning. By combining these two algorithms and employing a phased processing strategy, it achieves both reduced computational complexity and improved positioning accuracy. First, a coarse positioning algorithm with lower computational requirements is used for preliminary coarse positioning to obtain a rough estimate of the target's location, quickly narrowing down the possible spatial range of the target. Then, a coherent cumulative positioning algorithm is used to perform fine positioning based on the coarse estimate. Unlike traditional methods that exhaustively search the entire search space, this invention limits the search range to a smaller area around the coarse estimate, significantly reducing computational load and ultimately achieving a high-precision estimate of the target's location.

[0064] This invention significantly reduces the computational load of positioning algorithms, improves computational efficiency, and achieves high-precision and efficient space-based positioning.

[0065] This invention provides a novel technical approach for building an efficient and accurate space-based positioning system, and has broad application prospects in multiple fields such as space-based navigation, emergency rescue, and environmental monitoring. Attached Figure Description

[0066] Figure 1 This is a flowchart of the space-based positioning process combining direction finding and coherent cumulative positioning in an embodiment of the present invention.

[0067] Figure 2 This is a schematic diagram of space-based direction finding and positioning in an embodiment of the present invention;

[0068] Figure 3 This is a schematic diagram of spatial parameter peak search in an embodiment of the present invention;

[0069] Figure 4 This is a schematic diagram of grid search in an embodiment of the present invention. Detailed Implementation

[0070] To enable those skilled in the art to better understand the present invention, exemplary embodiments or examples of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described embodiments or examples are merely some, not all, of the embodiments or examples of the present invention. All other embodiments or examples obtained by those skilled in the art based on the embodiments or examples of the present invention without inventive effort should fall within the scope of protection of the present invention.

[0071] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0072] This invention provides a space-based positioning method that combines direction finding and coherent cumulative positioning, such as... Figure 1 As shown, it includes the following steps:

[0073] Step 1: Construct a model of the target signal received by the satellite, and use a direction-finding and positioning algorithm to coarsely locate the target, obtaining a coarse estimate of the target's position; for example... Figure 2 As shown, the specific steps include the following:

[0074] Assuming the two targets are located at (120°E, 32°N) and (122°E, 28°N) respectively, the satellite orbital parameters are as follows.

[0075] Satellite orbital parameters

[0076] Serial Number parameter numerical values 1 Semi-long wheelbase (km) 6872 2 Track inclination angle (°) 89 3 Eccentricity 0 4 Right ascension of the ascending node (°) 102 5 Argument of perigee (°) 20 6 True nearest angle (°) 25

[0077] When the satellite passes over the target, it receives the target signal and locates the target.

[0078] Step 1.1: Construct a signal model;

[0079] Assume the target signal received by the satellite is r(t), with dimension N×1; the noise is stationary, zero-mean Gaussian white noise, and the noise particles are independent of each other; its expression is:

[0080]

[0081] Where: M is the number of target signals, in this implementation example M=2, A m Let θ be the amplitude of the m-th target signal. m , Let ω be the spatial parameter of the m-th target signal. mLet φ be the frequency of the m-th target signal. m Let n(t) be the phase of the m-th target signal, and n(t) be the noise.

[0082] Step 1.2: Calculate the data covariance matrix;

[0083] The autocorrelation function of the received signal is:

[0084] R = E(r(t)r(t)) H (2)

[0085] Where: E() represents the mathematical expectation, and H is the conjugate transpose;

[0086] Step 1.3: Perform eigenvalue decomposition on the covariance matrix R to obtain the noise subspace U. n ;

[0087] Eigenvalue decomposition of the covariance matrix R yields:

[0088]

[0089] Among them: U s These are the eigenvectors of the signal subspace;

[0090] Let ∑ be a matrix consisting of the M largest eigenvalues ​​of R, corresponding to the eigenvalues ​​of the signal subspace, and we have:

[0091] ∑=diag{λ1 λ2 ... λ M} (4)

[0092] λ m Let M be the feature value corresponding to the m-th signal, where 1 ≤ m ≤ M;

[0093] U n These are the feature vectors of the noise subspace;

[0094] Let Λ be a matrix consisting of NM small eigenvalues ​​of R, corresponding to the eigenvalues ​​of the noise subspace, and we have:

[0095] A = diag(λ) M+1 λ M+2 ... λ N} (5)

[0096] λ M+i Let be the eigenvalue of the (M+i)th eigenvalue, 1≤i≤NM;

[0097] Step 1.4: Perform spectral peak search on the target signal, such as... Figure 3 As shown;

[0098] Since the signal subspace and the noise subspace are orthogonal, the steering vector in the signal subspace is also orthogonal to the noise subspace, that is:

[0099]

[0100] Where: e(ω)=[1 e jω ... e jω(N-1) ] T ;

[0101] Due to the presence of noise, the steering vector in the signal subspace cannot be completely orthogonal to the noise subspace. Therefore, in practice, it is obtained through a minimization search, i.e.:

[0102]

[0103] Step 1.5: Find the signal frequency and spatial parameters corresponding to the maximum point;

[0104] The formulas for estimating the frequency and spatial parameters of the target signal are as follows:

[0105]

[0106] Find the signal frequency and spatial parameters corresponding to the M maxima points of Formula 8; these are the frequencies and directions of arrival of the M target signals.

[0107] Step 1.6: Calculate the target signal position;

[0108] Using the satellite position as the origin and the spatial parameters obtained in step 1.5 as the direction, construct a ray and calculate the intersection of the ray with the Earth's surface. When there are two intersections, select the intersection closer to the satellite position as the coarse estimate of the target position.

[0109] Step 2: Using the coarse positioning result as the center, set the traversal range, and use the coherent cumulative positioning algorithm to perform high-precision positioning of the target; for example... Figure 4 As shown, it includes the following steps:

[0110] Step 2.1: Determine the positioning area based on the direction finding and positioning results;

[0111] The theoretical positioning error of the space-based direction finding and positioning algorithm is analyzed. Taking the coarse estimate of the target position as the center and twice the theoretical positioning error as the radius, the traversal range of the coherent cumulative positioning algorithm is determined, and grid points are divided on the Earth's surface.

[0112] Step 2.2: Construct the observation signal model;

[0113] The model for the received signal based on time delay and frequency shift is as follows:

[0114]

[0115] Where, r k(t) represents the signal received by the satellite in the k-th time slot, β k For channel attenuation, s k (t-τ k ) represents the target signal in the k-th time slot after transmission delay, n k (t) represents the zero-mean Gaussian white noise in the k-th time slot, T is the observation time in each time slot, and f k For Doppler frequency shift;

[0116] Step 2.3: Construct the cost function;

[0117] By utilizing the signal characteristics (such as time difference of arrival, frequency difference of arrival, and amplitude difference of arrival) in the satellite-received radiation source signal, the unknown parameters are estimated based on maximum likelihood estimation. The cost function C(p) is derived as follows:

[0118]

[0119] Among them, A k Let F be the frequency shift matrix. k It is a shift matrix.

[0120] Without loss of generality, assume ||s k || 2 =1, minimizing formula (10), we obtain the maximum likelihood estimate of channel attenuation:

[0121]

[0122] Substituting equation (11) into equation (10), we get:

[0123]

[0124] Step 2.4: Estimate the target location;

[0125] Target location estimation We obtain it from the following formula:

[0126]

[0127] The space-based positioning method (algorithm) combining direction finding and coherent cumulative positioning proposed in this invention is the underlying technical core of this invention, and various products can be derived based on the algorithm.

[0128] Based on the method proposed in this invention, a space-based positioning system combining direction finding and coherent cumulative positioning is developed using a programming language. This system has program modules corresponding to the steps of the above-mentioned technical solution, and executes the steps in the above-mentioned space-based positioning method combining direction finding and coherent cumulative positioning when running.

[0129] The developed system (software) computer program is stored on a computer-readable storage medium. This computer program is configured to, when called by a processor, implement the steps of the aforementioned space-based positioning method combining direction finding and coherent cumulative positioning. In other words, the invention is materialized on a carrier, becoming a computer program product.

[0130] Various implementations of the systems and techniques described herein can be implemented in digital electronic circuit systems, integrated circuit systems, application-specific integrated circuits (ASICs), computer hardware, firmware, software, and / or combinations thereof. These various implementations may include: implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0131] The computational programs (also referred to as programs, software, software applications, or code) of this invention include machine instructions of a programmable processor and can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. As used herein, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, device, and / or apparatus (e.g., disk, optical disk, memory, programmable logic device PLD) for providing machine instructions and / or data to a programmable processor, including machine-readable media that receive 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.

[0132] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A space-based positioning method combining direction-finding positioning and coherent integration positioning, characterized in that, Comprising the following steps: Step 1, constructing a target signal model received by a satellite, using a direction finding positioning algorithm to coarsely position the target, to obtain a coarse estimation result of the target position; Step 2, setting a traversal range with the coarse estimation result of the target position as the center, using a coherent accumulation positioning algorithm to highly accurately position the target; Step 1 comprises the following steps: Step 1.1, constructing a signal model; Suppose that the target signal received by the satellite is r(t), and its dimension is ; the noise is stationary, zero-mean Gaussian white noise, and the noises are independent of each other, and its expression is: （1） wherein: is the number of target signals, is the amplitude of the th target signal, is the spatial parameter of the th target signal, is the frequency of the th target signal, is the phase of the th target signal, is the noise; Step 1.2, calculating a data covariance matrix; The autocorrelation function of the received signal is: （2） where E() denotes the mathematical expectation, is the conjugate transpose; Step 1.

3. Perform eigen decomposition of the covariance matrix R to obtain the noise subspace ; Eigenvalue decomposition is performed on the covariance matrix R to obtain: （3） wherein: is an eigenvector of the signal subspace; For The The matrix of the largest eigenvalues, corresponding to the eigenvalues of the signal subspace, has: （4） is the eigenvalue corresponding to the mth signal pair, 1≤m≤M; is the eigenvector of the noise subspace; For The The matrix of the small eigenvalues, corresponding to the noise subspace, has eigenvalues with: （5） M+i, 1≤i≤N-M; Step 1.4, performing spectral peak search on the target signal; The steering vector in the signal subspace is orthogonal to the noise subspace, that is: （6） wherein: ; The maximum value point is obtained by minimization search: （7） Step 1.5, finding the signal frequency and spatial parameters corresponding to the maximum value point; The estimation formula of the frequency and spatial parameters of the target signal is: （8） M maximum value points corresponding to the signal frequency and spatial parameters of formula (8) are found; Step 1.6, calculating the target signal position; A ray is constructed with the satellite position as the origin and the spatial parameter obtained in step 1.5 as the direction, the intersection of the ray and the earth's surface is calculated, when there are two intersection points, the intersection point close to the satellite position is selected as the coarse estimation result of the target position; Step 2 comprises the following steps: Step 2.1, determining the positioning area based on the direction finding positioning result; The theoretical positioning error of the space-based direction finding positioning algorithm is analyzed, the traversal range is determined with the coarse estimation result of the target position as the center and the theoretical positioning error multiplied by a plurality of times as the radius, and the grid points on the earth's surface are divided; Step 2.2, constructing an observation signal model; The model of the received signal is established based on time delay and frequency shift as: （9） wherein, denotes the signal received by the satellite in the kth time slot, is the channel attenuation, denotes the target signal after the transmission delay in the kth time slot, is the zero-mean Gaussian white noise in the kth time slot, T is the observation time in each time slot, is the Doppler shift; Step 2.3, constructing a cost function; By using the signal characteristics in the satellite received radiation source signal, unknown parameters are estimated based on maximum likelihood estimation, and a cost function is obtained through derivation is: （10） wherein is a frequency shift matrix, is a shift matrix; Assume Minimizing equation (10) gives the maximum likelihood estimate of the channel attenuation as （11） Substitute formula (11) into formula (10) to obtain: （12） Step 2.4, estimating the target position; Estimation of target position is obtained from the equation: （13）。 2. A space-based positioning system combining direction-finding positioning and coherent integration positioning, characterized in that, The system has program modules corresponding to the steps of the method of claim 1, and when running, executes the steps in the space-based positioning method combining direction finding positioning and coherent accumulation positioning.

3. A computer-readable storage medium, characterized in that, The computer readable storage medium stores a computer program, and the computer program is configured to realize the steps in the space-based positioning method combining direction finding positioning and coherent accumulation positioning of claim 1 when called by the processor.

Images