A direct positioning method and system based on a rotating array

Abstract

The application provides a kind of direct positioning method and system based on rotating array, belong to passive positioning field based on space.The present application receives radiation source signal using array structure changing with time, and using less receiving station can obtain intercepted signal under different array structure, which is beneficial to increase the accuracy of positioning estimation, and can reduce equipment cost;The use of rotating array can make the system receive signals from different directions and angles in the same time, greatly improving the efficiency of signal acquisition and the response speed of the system;Make the application suitable for real-time positioning and dynamic tracking tasks, improve the overall work efficiency of the system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of space-based passive positioning, in particular to a direct positioning method and system based on a rotating array. BACKGROUND

[0002] Traditional positioning methods are usually two-step methods, that is, first estimate the parameters such as the angle of arrival, time difference, frequency difference, etc. of the received signal, and then calculate the position through geometric relationship, while the direct positioning method can directly estimate the position of the radiation source from the received signal, and is more accurate in low signal-to-noise ratio environment. For multi-satellite direct positioning, the cost function of positioning, the array structure of received signal, and the signal processing method directly affect the performance of positioning. However, the traditional array structure is generally a fixed array structure of the receiving station, and the single received signal limits the positioning performance. The present application uses a rotating array to receive signals, which can receive signals from different directions by adjusting the angle of the array surface, expand the range of received signals, and form more baseline structures by receiving signals from different directions, thereby improving the positioning accuracy. SUMMARY

[0003] The technical problem to be solved by the present application is:

[0004] To solve the problem that the traditional array structure is a fixed array structure and the single received signal limits the positioning performance.

[0005] The technical solution adopted by the present application to solve the above technical problem is:

[0006] The present application provides a direct positioning method based on a rotating array, comprising the following steps:

[0007] S100, constructing a rotating array structure, deploying a rotating linear array on each observation satellite, rotating clockwise around the center of the rotating linear array to obtain the position representation of each element in the rotating linear array;

[0008] S200, constructing an observation signal model, obtaining a positioning cost function based on the rotating array based on the MUSIC method;

[0009] S300, considering the influence of the rotating elements of the rotating array, optimizing the signal propagation time from the satellite to the target, including calculating the signal delay, interval length and phase of the collected signal in the rotating elements;

[0010] S400, estimating the position of the target based on the optimization of the signal propagation time in step S300 and considering the position of the satellite orbit through the positioning cost function constructed in step S200, and then determining the accurate position of the target by searching for the maximum value in the positioning cost function value.

[0011] Further, in step S100, comprising,

[0012] A rotating linear array with N elements arranged in one or more rows is deployed on each observation satellite, which rotates clockwise around the center of the rotating linear array with an angular velocity of ω; K signals are intercepted in each rotation period T=2π / ω, and the rotation angle of each interception is θ k , k=1, 2, …, K, and the duration of a single observation is T k ; during the kth observation, the position of each element is represented as:

[0013]

[0014] where d1 represents the position of all elements relative to the reference element at the first observation time, the matrix represents a rotation matrix, t k represents the kth observation time;

[0015]

[0016] d1=[ε1-ε0,ε2-ε0,…,ε N -ε0]

[0017] where ε0 and ε n represent the position of the reference element at the start time and the position of the nth element.

[0018] Further, in step S200, the jth sample output by the kth observation array is:

[0019] r k,j =A k (ρ)s k,j +w k,j

[0020] where s k,j represents the received signal, w k,j represents noise, and ρ represents the position parameter of the radiation source;

[0021] The array response is:

[0022]

[0023] where p represents the radiation source position, K k =2π×u k / λ is the wave number vector, u k represents the unit line-of-sight vector from the receiving station to the radiation source at the kth observation time, and λ is the wavelength;

[0024] A matrix is constructed by the array vectors corresponding to the jth sample in all observations: Define

[0025]

[0026] The observation signal model is:

[0027] r j = A(p) s + w j j

[0028] The positioning cost function based on the rotating array is obtained based on the MUSIC method:

[0029]

[0030] wherein a k (p) represents a steering vector at the kth observation, represents a noise subspace matrix at the kth observation;

[0031] Since the positioning cost function is only related to the position of the radiation source, the maximum radiation source position P in the above positioning cost function is the position estimation of the radiation source.

[0032] Further, in step S300, including, S310, signal delay calculation, in order to specify the received signal, the collection time t c of each signal t e (t c ) is determined in a manner considering the movement of the rotating antenna:

[0033] t e (t c ) = t c - τ c (t c )

[0034] τ c (t c ) = τ c,stat (t c ) + τ c,v (t c )

[0035]

[0036] wherein c represents the speed of light; τ c,v (t c ) represents an additional time increment of the rotating antenna; represents a position vector from the emission source to the rotating collector; represents a direction vector of the antenna source;

[0037] The static propagation delay of the position vector from the emission source to the rotating collector is:​

[0038]

[0039] In the formula, The direction vector representing the static propagation delay time of the emission source; τ r，stat (t c ) represents the time required for the radio frequency waveform to form.

[0040] In the formula, the unit vector is the line-of-sight vector from the rotating collecting element to the source. for:

[0041]

[0042] The effective sampling rate of the source signal during a single sampling time at the collector is given by the following formula:

[0043] t s,ef (t c )=[τ c (t c )-τ c (t c -t s )]+t s

[0044] In the formula, t s，ef (t c ) is the nominal sampling time t s The sum; τ c (t c -t s () represents the time delay from the launch time to the single sampling time;

[0045]

[0046] In the formula, F s，ef (t) represents an expanded version of the source signal being collected.

[0047] Furthermore, step S300 also includes S320, interval length calculation, which is represented by a linear model within an angle range of 180°:

[0048] F s,ef (t)=F s,ef (t o )+F′ s,ef (t)(tt o ) = F s,ef (t o )+q×(tt o )

[0049] In the formula, F′ s，ef (t) is F s，efderivative of (t), q is a constant factor; t is the time of collecting signal; t0 is the time of initially transmitting signal;

[0050] At t o + t int , the slope of linear function in the time variation interval is:

[0051]

[0052] where t int is the task time;

[0053] Allowing the sample mismatch amount occurred in the interval, limit the error within a certain range of sample number, namely:

[0054]

[0055] For the collection process, the time is related to the rotation position, for the effective source sampling rate, repeat the process in the next time interval, and so on, until the rotating antenna completes half a circle of collection.

[0056] Further, in step S300, it also includes, S330, phase calculation of collected signal, the phase of collected signal is:

[0057] Φ ck (t) = Φ ck = -ωτ ck + ΔΦ

[0058] In the formula, the phase of each collection element is Φ ck , the angular velocity is ω, and the angle is ΔΦ; τ ck is the angle of static rod rotation;

[0059] For each sample Φ c (n), take a rate in the duration of interval τ c，stat (n = 1), the corresponding time is given by:

[0060]

[0061] In the formula, τ c represents the period of radio frequency carrier frequency;

[0062] The sampling at the receiver of the rotating collector, due to the expansion or compression effect, is represented as t s,ef on the transmitted signal waveform;

[0063] The collected signal has equivalence with Doppler phenomenon:

[0064]

[0065] wherein, is the direction vector of the rotating collector at time t cm is the velocity vector of the rotating collector at time t is the direction vector of the rotating collector at time t cm is the velocity vector of the rotating collector at time t

[0066] v r，rad is the radial velocity component, i.e. the component in the direction of the emission source; m is the radial velocity component, i.e. the component in the direction of the emission source; s is the radial velocity component, i.e. the component in the direction of the emission source;

[0067] During one cycle of on-board sampling, due to the radial movement of the collector, the sampling period of the incident signal has a very small time increment, i.e.

[0068]

[0069] The Doppler frequency f c is:

[0070]

[0071] wherein γ represents the wavelength of the radio frequency carrier frequency;

[0072] The phase of the signal collected in the interval is represented as:

[0073] Φ c (n) = -ωτ c,stat (n = 1) + ΔΦ + 2πf c (n - 1)t s

[0074] The effective Doppler frequency for one f c interval is:

[0075]

[0076] wherein f s represents the radio frequency carrier frequency.

[0077] Further, in step S400, the maximum value of the positioning cost function is searched using a particle swarm optimization algorithm, a Newton method or a genetic algorithm.

[0078] A direct positioning system based on a rotating array, which has program modules corresponding to the above steps, and when running, executes the steps in the above direct positioning method based on a rotating array.

[0079] A computer readable storage medium, which stores a computer program configured to realize the steps of the direct positioning method based on a rotating array when called by a processor.

[0080] Compared with the prior art, the present application has the following advantages:

[0081] The direct positioning method based on the rotating array provided by the present application receives the radiation source signal by using the array structure changing with time. Since the rotating array structure changes with time, the intercepted signals under different array structures can be obtained by using fewer receiving stations, which is beneficial to increase the positioning estimation accuracy and reduce the equipment cost. The use of the rotating array enables the system to receive signals from different directions and angles at the same time, greatly improving the signal acquisition efficiency and the system response speed. This makes the present application suitable for real-time positioning and dynamic tracking tasks, and improves the overall working efficiency of the system.

[0082] Since the rotating array can flexibly adjust the receiving angle and array configuration, it can better adapt to complex and dynamic environmental changes, and can still maintain high positioning accuracy and reliability under different geographical conditions and signal transmission environments, having strong environmental adaptability. By using the structural change of the rotating array, the need for multiple fixed array configurations is reduced, thereby reducing the consumption of space and energy. The operation and control are also more convenient, because the system does not need to rely on complex array layout and frequent adjustment, further simplifying the installation and operation process. The rotating array structure enables the device to complete accurate positioning tasks by using fewer receiving stations and lower power consumption, and compared with the traditional multi-array system, the method can significantly reduce energy consumption under the same performance, meeting the requirements of energy saving and emission reduction. BRIEF DESCRIPTION OF DRAWINGS

[0083] Figure 1 The flowchart of the direct positioning method based on the rotating array in an embodiment of the present application is shown in the figure.

[0084] Figure 2 The geometric structure diagram of the rotating array of the present application is shown in the figure. DETAILED DESCRIPTION

[0085] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0086] Specific implementation scheme one: combined with Figure 1 and Figure 2 The present application provides a direct positioning method based on a rotating array, which comprises the following steps:

[0087] S100, constructing a rotating array structure,

[0088] combined with Figure 2As shown, a rotating linear array with N elements arranged in one or more rows is deployed on each observation satellite, which rotates at an angular velocity of ω clockwise around the center of the rotating linear array; K signals are intercepted in each rotation period T = 2π / ω, and the rotation angle of each interception is θ k , k = 1, 2, …, K, and the duration of a single observation is T k , it is considered that the observation time is very short, that is, the array structure is considered unchanged in a single observation; during the kth observation, the position of each element is represented as:

[0089]

[0090] where d1 represents the position of all elements relative to the reference element (the first element in the array) at the first observation time, the matrix represents a rotation matrix, t k represents the kth observation time;

[0091]

[0092] d1 = [ε1-ε0,ε2-ε0,…,ε N -ε0]

[0093] where ε0 and ε n represent the position of the reference element at the start time and the position of the nth element;

[0094] S200, construct a signal model,

[0095] The jth sample of the kth observation array output is:

[0096] r k,j = A k (ρ) s k,j +w k,j

[0097] where s k,j represents the received signal, w k,j represents noise, and ρ represents the position parameter of the radiation source;

[0098] The array response is:

[0099]

[0100] where p represents the position of the radiation source, K k = 2π × u k / λ is the wave number vector, u k represents the unit line-of-sight vector from the receiving station to the radiation source at the kth observation time, and λ is the wavelength;

[0101] A matrix is constructed by the array vectors corresponding to the jth sample in all observations: Definitions where J is the total number of samples;

[0102]

[0103] The observed signal model is then:

[0104] r j = A (p) s j + w j

[0105] The MUSIC-based positioning cost function based on the rotating array is obtained as:

[0106]

[0107] where a k (p) represents the steering vector at the kth observation, represents the noise subspace matrix at the kth observation; the cost function is only related to the position of the radiation source, so that P which makes the above cost function maximum is the position estimation of the radiation source;

[0108] S300, due to the certain complexity of the signal processing brought by the rotating antenna element, the properties and parameters related to the concept of arrival time need to be distinguished and adjusted, the rotating elements considered by the present application include signal delay, interval length and phase of collected signal;

[0109] S310, signal delay calculation,

[0110] In order to specify the received (baseband) signal, the transmission time t e (t c ) needs to be determined for each signal collection time t c , in order to consider the way of movement of the rotating antenna:

[0111] t e (t c ) = t c - τ c (t c )

[0112] τ c (t c ) = τ c,stat (t c ) + τ c,v (t c )

[0113]

[0114] where c represents the speed of light; τ c,v (t c) represents the additional time increment of the rotating antenna; represents the position vector from the emission source to the rotating collector; represents the direction vector of the antenna source;

[0115] position vector from the emission source to the rotating collector The static propagation delay is:

[0116]

[0117] wherein, represents the direction vector of the static propagation delay time of the emission source; the time τ r，stat (t c ) required for the radio frequency wave to travel from the light source to the collection point at the speed of light, the collector itself being in motion, so that it is possible to correctly determine the emission time of the signal with respect to t c it is necessary to include an additional increment of the signal flight time due to this movement of the collector; the additional time increment τ r，v (t c ) is the radial distance of the rotating antenna with respect to the light source divided by the speed of light;

[0118] In the formula, the unit vector in the line of sight direction from the rotating collection element to the source

[0119]

[0120] The compression and expansion effect produced by the rotating collector on the source signal is very similar to the Doppler effect, considering the source signal sampled on the ground at a certain rate and then at the rotating collector, even if the sampling takes place at that point, very slight movements towards or away from the source produce a collected signal with expansion or compression aspects with respect to the emitted source signal; in other words, it produces a version of the source signal, effectively resampled at a slightly different sampling rate;

[0121] From this point in the source signal stream, the collected signal is a compressed or expanded version of the subsequent signal; to make a high-fidelity simulation, this compression / expansion feature is implemented by resampling the source signal at the effective sampling rate; the effective sampling rate of the source signal in a single sampling time at the collector is given by the following formula:

[0122] t s,ef (t c ) = [τ c (t c ) - τ c (t c - t s )] + t s

[0123] wherein, ts，ef (t c ) is the sum of nominal sampling time t s ; τ c (t c -t s ) represents the time delay from the emission time to the single sampling time;

[0124]

[0125] In the formula, F s，ef (t) represents the extended version of the source signal being collected; at this time t = t c ;

[0126] S320, interval length calculation,

[0127] Before the approximation of constant sampling rate leads to too much loss of fidelity, such as 10%~20%; the maximum change rate appears around 180°, in the angle range, a linear model can be used to represent:

[0128] F s,ef (t) = F s,ef (t o ) + F′ s,ef (t)(t-t o ) = F s,ef (t o ) + q × (t-t o )

[0129] In the formula, F′ s，ef (t) is the derivative of F s，ef (t), q is a constant; t is the time of collecting the signal; t0 is the initial emission signal time;

[0130] The slope of the linear function in the time change interval t o +t int is:

[0131]

[0132] Where t int is the task time;

[0133] Allow the sample mismatch amount occurring in the interval, limit this error within a certain range of the number of samples:

[0134]

[0135] ​For the collection process, the time is determined in relation to the rotation position, for an effective source sampling rate, it can be 158 ms after a certain time length, the process is repeated in the next time interval, and so on, until the rotating antenna completes a half circle of collection;

[0136] S330, phase calculation of the collected signal,

[0137] The phase of the collected (baseband) signal is:

[0138] Φck(t) = Φck = -ωτck + ΔΦ

[0139] In the formula, the phase of each collection element is Φ ck , the angular velocity ω, the angle ΔΦ; τ ck is the angle of rotation of the static rod;

[0140] For the rotating collection element, as has been described before, the motion produces an expansion / compression effect on the complex envelope of the transmitted signal, and the phase of the RF carrier is also disturbed accordingly; this effect is also evident in the baseband collected signal, but it is not automatically imposed on this signal through the resampling process; on the contrary, it must be numerically imposed based on an analytical model; this effect is usually interpreted as a Doppler shift of the carrier frequency, but in order to obtain maximum clarity in the following derivation, the same quantities are used as always, and the following formula is mathematically derived, which is equivalent to the expression of the Doppler shift:

[0141] For the phase of the collected signal from a certain time, for each sample Φ c (n), a rate is taken within the duration of the interval τ c，stat (n = 1), where the corresponding time is given by:

[0142]

[0143] In the formula, τ c represents the period of the radio frequency carrier frequency;

[0144] The sampling performed at the receiver of the rotating collector, due to the expansion / compression effect, manifests itself on the transmitted signal waveform as

[0145] t s,ef ; in order to demonstrate the equivalence with the Doppler phenomenon, the formula is as follows:

[0146]

[0147] In the formula, is the velocity vector of the rotating collector at time t cm ; and represents the direction vector of the rotating collector at time t cm ;

[0148] v r，rad (tc m )t s is the radial velocity component, i.e., its component in the direction of the emission source; during one cycle of on-board sampling, due to the radial movement of the collector, the sampling period of the incident signal has a very small time increment:

[0149]

[0150] Doppler frequency f c is:

[0151]

[0152] where γ represents the wavelength of the radio frequency carrier frequency;

[0153] In terms of the Doppler frequency, the phase of the signal collected in the interval can be expressed as:

[0154] Φ c (n)=-ωτ c,stat (n=1)+ΔΦ+2πf c (n-1)t s

[0155] One f c The effective Doppler frequency of an interval is:

[0156]

[0157] where f s represents the radio frequency carrier frequency;

[0158] Specific implementation scheme two: the present application provides a direct positioning system based on a rotating array, which has program modules corresponding to the above steps, and when running, executes the steps in the direct positioning method based on a rotating array described above.

[0159] Other combinations and connection relationships of the present embodiment are the same as those of specific implementation scheme one.

[0160] Specific implementation scheme three: the present application provides a computer readable storage medium, which stores a computer program, and the computer program is configured to realize the steps of the direct positioning method based on a rotating array when called by a processor.

[0161] Other combinations and connection relationships of the present embodiment are the same as those of specific implementation scheme one.

[0162] Simulation experiment

[0163] Dynamic target positioning in urban environment

[0164] Step 1: Set up a dual-satellite positioning scenario with a rotating array, where each satellite is equipped with a rotating array antenna composed of multiple antenna elements that can adjust the receiving direction by rotation. The rotating array antenna is used to receive the radiation source signals from a dynamic target on the ground. In the simulation environment, assume the target is a fast-moving vehicle emitting radar pulse signals at a frequency of 1 GHz. Assume there are no multipath effects in the environment, and the propagation of radar pulse signals is only affected by the target's speed and distance. The radar pulse signals are emitted from the target vehicle, propagate through free space to the satellites. The signal propagation time τ is determined by the distance d between the target and the satellite, with the formula: where c is the speed of light;

[0165] Step 2: At each observation time, the dual-satellite array receives radar pulse signals from the target vehicle through the rotating array. Each satellite collects 100 signals per second to ensure that enough signals are received for positioning estimation in the case of target dynamics. At each sampling time, the rotating array antenna adjusts the receiving direction according to the pre-set rotation pattern to capture signals from different directions. The received signals are demodulated to extract time delay and phase information. By comparing the time difference between the signals received by the two satellites, the distance difference between the target and the two satellites can be calculated.

[0166] Step 3: Based on the received signal data, a cost function is constructed, which is optimized based on the possible position of the target and the signal propagation time from the satellite to the target. The cost function calculates the possible coordinates of the target by considering the time delay of the satellite signals and the known orbital position. For each satellite, the distance d i between the target position (x, y) and the satellite position (x i ,y i ,z i ) is calculated:

[0167] signal propagation time

[0168] cost function where is the actual propagation time calculated from the received signal. The goal is to find the most likely position of the target by minimizing J(x, y).

[0169] Step 4: Determine the estimated position of the target by searching for the point with the maximum cost function value. During the search process, a particle swarm optimization algorithm can be used to improve the calculation efficiency and accuracy, and finally obtain the accurate coordinates of the target position. For each particle, calculate its corresponding cost function value J(x, y). According to the rules of the particle swarm optimization algorithm, update the position and velocity of the particle: v k+1 ​k + cl - r1 - (p best - x k ) + c2 - r2 - (g best - x k )

[0170] + x k+1 = x k + v k+1

[0171] where w is the inertia weight, cl and c2 are learning factors, r1 and r2 are random numbers, p best is the particle's historical best position, g best is the global best position.

[0172] Offshore platform positioning

[0173] Step 1: Set up a dual-star positioning system with a rotating array of satellites that are equipped to receive radar pulse signals transmitted from an offshore platform. The carrier frequency of the radar signals is set to 1 GHz, and the signal propagation is assumed to be straight-line propagation without multipath effects. The offshore platform moves at a constant speed on the sea surface and transmits radar pulse signals for positioning.

[0174] Step 2: Each satellite receives the radar signals from the offshore platform at different observation times through the rotating array. Since the platform is located in the sea area far from the land, the signal propagation is mainly affected by the sea surface reflection, so the quality of the received signal is high and is not disturbed by urban buildings and other obstacles.

[0175] Step 3: Based on the received radar signals, a cost function is constructed. This cost function estimates the position of the offshore platform by modeling the signal propagation delay between the satellite and the offshore platform and considering the orbital position of the satellite. For each satellite, the distance d i between the target position (x, y) and the satellite position (x i , y i , z i ) is calculated:

[0176] Signal propagation time

[0177] Cost function where T is the actual propagation time calculated from the received signal. The goal is to find the most likely position of the target by minimizing J(x, y).

[0178] Step 4: Use optimization algorithms (such as Newton's method or genetic algorithm) to search for the maximum value of the cost function, thus determining the precise position of the offshore platform. This process can effectively eliminate signal noise and obtain more accurate positioning results. Newton's method uses iterative approximation to find the optimal solution, which is suitable for local search. Genetic algorithm simulates the natural selection process for global search, which is suitable for complex nonlinear problems.

[0179] Newton's method search process:

[0180] Initialize platform position estimate (x0, y0);

[0181] Calculate the gradient of the cost function And the Hessian matrix H(J(x, y));

[0182] Update platform position estimate:

[0183] Repeat the iteration until convergence, and get the optimal position estimate of the platform.

[0184] Genetic algorithm search process:

[0185] Initialize a group of individuals, each representing a possible platform position (x, y);

[0186] Calculate the fitness of each individual (i.e. the value of the cost function);

[0187] Generate new individuals through selection, crossover and mutation operations;

[0188] Repeat the iteration until convergence, and get the optimal position estimate of the platform;

[0189] When the optimization algorithm converges, the optimal position (x*, y*) is the estimated position of the platform;

[0190] Through multiple iterations and optimization, the precise coordinates of the platform position can be obtained.

[0191] Although the present invention is disclosed as above, the protection scope of the present invention is not limited to this. The skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the protection scope of the present invention.

Claims

1. A direct positioning method based on a rotating array, characterized in that, The method comprises the following steps: S100, constructing a rotating array structure, deploying a rotating linear array on each observation satellite, rotating clockwise around the center of the rotating linear array to obtain the position representation of each array element in the rotating linear array; S200, constructing an observation signal model, and obtaining a positioning cost function based on the rotating array based on a MUSIC method; The positioning cost function based on the rotating array is obtained based on the MUSIC method: wherein, denotes the steering vector at the kth observation, denotes the noise subspace matrix at the kth observation; S300, considering the influence of the rotating element of the rotating array, optimizing the signal propagation time from the satellite to the target, including calculating the signal delay, interval length and phase of the collected signal in the rotating element; S400, estimating the position of the target based on the optimization of the signal propagation time in step S300 and the position of the satellite orbit by the positioning cost function constructed in step S200, and determining the accurate position of the target by searching for the maximum value in the positioning cost function value.

2. A direct positioning method based on a rotating array according to claim 1, characterized in that: In step S100, comprising, A rotating line array with N elements arranged in one or more rows is deployed on each observation satellite, so that The rotating angle of the line array is clockwise around the center of the line array with an angular velocity; in each rotation period K signals are intercepted, and the rotating angle of each interception is The duration of a single observation is During the kth observation, the position of each element is represented as: wherein, represents the position of all array elements relative to the reference array element at the first observation time, matrix represents a rotation matrix, represents the kth observation time; wherein and denotes the position of the reference element at the start and the position of the n-th element.

3. A direct positioning method based on a rotating array according to claim 2, characterized in that: In step S200, the jth sample output by the kth observation array is: wherein denotes a received signal, denotes a noise, denotes a position parameter of the radiation source; The array response is: where p represents the position of the radiation source, is the wave number vector, is the unit line of sight vector from the receiving station to the radiation source at the kth observation, is the wavelength; A matrix is constructed from the array vectors corresponding to the jth sample in all observations: , define , The observation signal model is: Since the positioning cost function is only related to the position of the radiation source, the position of the radiation source that maximizes the positioning cost function in the above positioning cost function is the position estimate of the radiation source.

4. A direct positioning method based on a rotating array according to claim 3, characterized in that: In step S300, including, S310, signal delay calculation, in order to specify the received signal, it is necessary to collect the time for each signal , determine the transmission time In a manner that takes into account the movement of the rotating antenna: where c represents the speed of light; represents the additional time increment for the rotating antenna; represents the position vector from the launch source to the rotating collector; represents the direction vector of the antenna source; Position vector from launch source to location of rotating collector The static propagation delay is: In the formula, a direction vector representing the static propagation delay time of the emission source; a time required for the radio frequency waveform In the formula, the unit vector in the direction of the line of sight from the rotating collection element to the source is: The effective sampling rate of the source signal in a single sampling time at the collector is given by the following formula: wherein is the sum of the nominal sampling times ; and represents the time delay from the transmission time to the individual sampling times; wherein represents an extended version of the source signal being collected.

5. A direct positioning method based on a rotating array according to claim 4, characterized in that: In step S300, further comprising, S320, interval length calculation, using a linear model to represent the angle range of 180°: wherein is the derivative of q is a constant; t is the time of collection of the signal; t0 is the initial signal transmission time; In the slope of the linear function within the time variation interval is: wherein t int is the task time; Allowing the sample mismatch amount occurring in the interval, limiting the error within a certain range of the number of samples, that is: For the collection process, the time is related to the rotating position, and for the effective source sampling rate, the process is repeated in the next time interval, and so on, until the rotating antenna completes a half circle of collection.

6. A direct positioning method based on a rotating array according to claim 5, characterized in that: In step S300, further comprising, S330, phase calculation of the collected signal, the phase of the collected signal is: where each collection element phase is , angular velocity is , and angle is ; is the angle of rotation of the static bar. For each sample A rate is taken over the duration of the interval The corresponding time is given by In the formula, represents a period of the radio carrier frequency; Sampling at the receiver of the rotating collector, due to expansion or compression effects, manifests as a time shift, Δt, on the transmitted signal waveform 𝑠,𝑒𝑓 ; The collected signal has equivalence with the Doppler phenomenon: wherein is the direction vector of the rotating collector at time the velocity vector of the rotating collector; is the direction vector of the rotating collector at time cm t is the radial velocity component, i.e. the component in the direction of the discharge source; In a period of on-board sampling, due to the radial motion of the collector, the sampling period of the incident signal has a very small time increment, that is: Doppler frequency is: wherein wavelength representative of the radio frequency carrier frequency; The phase of the collected signal in the interval is represented as: One The effective Doppler frequency of the interval is: wherein represents the radio frequency carrier frequency.

7. A direct positioning method based on a rotating array according to claim 6, characterized in that: In step S400, the maximum value of the positioning cost function is searched by using a particle swarm optimization algorithm, a Newton method or a genetic algorithm.

8. A direct positioning system based on a rotating array, characterized by: The system has program modules corresponding to the steps of any one of claims 1-7, and executes the steps in the above-mentioned direct positioning method based on the rotating array.

9. A computer-readable storage medium, characterized in that: The computer readable storage medium stores a computer program configured to implement the steps of the direct positioning method based on the rotating array in any one of claims 1-7 when called by the processor. The computer readable storage medium stores a computer program configured to implement the steps of the direct positioning method based on the rotating array in any one of claims 1-7 when called by the processor.

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