Sensitivity integrated positioning method and system based on movable array

Abstract

The invention relates to a movable array-based communication and induction integrated positioning method and system. The method comprises the steps of (1) time division ISAC mode configuration; (2) establishing a mobile array continuous moment signal transceiving model in the sensing time slot; (3) establishing a discrete signal transceiving model of the movable array in the sensing time slot; (4) performing joint processing on the signals in the plurality of discrete sensing time slots, enabling Doppler-induced time phase change to be equivalent to space phase deviation, and constructing a space-time steering vector model; (5) converting the space-time steering vector model into an equivalent virtual array; and (6) modeling the received signal into a sparse representation model, and performing angle positioning on the target through a compressed sensing algorithm. Compared with the prior art, the method provided by the invention can realize angle positioning with higher precision under the same physical antenna array element.

Description

TECHNICAL FIELD

[0001] The present application relates to a mobile array-based integrated sensing and positioning method and system, belonging to the technical field of wireless communication. BACKGROUND

[0002] With the continuous evolution of the sixth generation mobile communication system (6G), integrated sensing and communication (ISAC) has become one of the core technology directions.

[0003] In the integrated sensing and communication system, direction of arrival (DoA) is one of the most basic and key sensing functions, which determines the spatial resolution capability of the sensing system and directly affects the accuracy and energy efficiency of core tasks such as target positioning, tracking, and beamforming. To improve the accuracy of DoA estimation, traditional methods rely on large-aperture arrays or dense multi-antenna deployment to enhance the angle resolution and robustness. However, this approach has many problems in practical systems, such as large device size, high hardware cost, and high power consumption.

[0004] Scholars have proposed a series of virtual aperture methods to achieve large aperture estimation performance with a small number of antenna elements. For example, the nested array in [Liu C L, Vaidyanathan P P. Super nested arrays: Linear sparse arrayswith reduced mutual coupling—Part I: Fundamentals[J]. IEEE Transactions on Signal Processing, 2016, 64(15): 3997-4012.] and the coprime array, which improve the virtual aperture through differential array technology by changing the array element arrangement. However, this special structure of the array still has certain requirements for the number of antennas, and it fails in extreme cases (such as a single antenna). Moreover, the special structure of the array often cannot be compatible with existing communication systems.

[0005] In addition, the movable antenna technology can also create new degrees of freedom through the movement of the antenna, for example, the document [Yang B, Wang C, Wang D. Direction-of-arrival estimation of strictly noncircular signal by maximum likelihood based on moving array[J]. IEEE Communications Letters, 2019, 23(6): 1045-1049.] proposes to use the Doppler effect brought by the moving array to improve the angle estimation performance, but it cannot explicitly create a virtual array, so many signal processing algorithms are not applicable. The document [Yang B, Wang C, Yang B, et al. A joint space-time array for communication signals-based on a moving platform and performance analysis[J]. Sensors, 2018, 18(10): 3388.] Although the Doppler effect of the array is established as an equivalent virtual array, it relies on the coherence of the signal source snapshot level, which is difficult to guarantee in practice. SUMMARY

[0006] The purpose of the present application is to overcome the shortcomings of the prior art, such as the dependence of the direction estimation system on large-scale antenna arrays, high hardware cost, and high power consumption, and to provide a sensing and communication integrated positioning method and system based on a movable array. The method models the two-way Doppler effect generated during the movement of the array as a spatial phase shift of the receiving steering vector, and then constructs a large-aperture virtual array signal model, and combines a compressed sensing algorithm to realize high-resolution angle estimation, thereby significantly improving the direction estimation performance under the premise of limited physical antenna number, and is widely applicable to ubiquitous sensing and precise positioning scenarios in future 6G sensing and communication integrated networks.

[0007] The technical scheme of the present application is: A sensing and communication integrated positioning method based on a movable array, applicable to a sensing and communication integrated system of a movable antenna array, the sensing and communication integrated system of the movable antenna array comprising a set of movable uniform linear arrays, i.e. movable arrays, moving along a straight line, the movable uniform linear array comprising N antenna elements, the antenna element spacing being d, and moving at a constant speed in a preset direction through a driving mechanism; the movable array is deployed in a communication base station with a slide rail and a control device, or installed on a drone, a robot or an intelligent platform with moving capability; it is assumed that there are A far-field target needs to be angle positioned; including: (1) Time division ISAC mode configuration; (2) Establishing a signal transmission and reception model of a movable array at a continuous time in a sensing time slot; (3) Establishing a signal transmission and reception model of a movable array at a discrete time in a sensing time slot; (4) Jointly processing signals at multiple discrete sensing time slots, equivalently converting Doppler-induced time phase changes into spatial phase offsets, and constructing a space-time steering vector model; (5) Converting the space-time steering vector model into an equivalent virtual array; (6) Modeling the received signal as a sparse representation model, and angle positioning the target through a compression sensing algorithm.

[0008] According to the application, preferably, in step (1), the time division ISAC mode configuration refers to: adopting a time division multiplexing ISAC working mode, dividing time resources into periodic communication time slots and sensing time slots; in the communication time slot, the movable array stops moving and is fixed at the position of the array at the end of the sensing time slot in the last frame, and a fixed array mode is used for data transmission with a communication user; in the sensing time slot, a sensing and positioning integrated method based on the movable array is adopted.

[0009] According to the application, preferably, in step (2), the signal transmission and reception model of the movable array at a continuous time in the sensing time slot refers to: according to the constant speed movement characteristics of the movable array, constructing a sensing signal transmission and echo reception model at each sensing time , which is expressed as formula (I): (I); In formula (I), represents the echo signal received by the movable array at the sensing time t; is the reflection coefficient of the kth target, is the Doppler shift of the kth target relative to the array, is the angle of the kth target relative to the array, is the wavelength, is an imaginary unit; , represents the transmission and reception steering vector, , represents the active sensing signal transmitted by the movable array at time t, is the complex Gaussian white noise received by the movable array at time t.

[0010] According to a preferred embodiment of the present invention, in step (3), establishing a discrete signal transceiver model for a movable array within a sensing time slot means: dividing the continuous sensing time, i.e., the sensing time slot, into M discrete sensing time slots, each discrete sensing time slot having a length of... The distance the movable array can move within each discrete sensing time slot is At the beginning of each discrete sensing time slot, the movable array transmits sensing signals and receives echo signals, and processes the echo signals. The time interval between each quick sample is [number]. Assuming the movable array is considered quasi-stationary during the L snapshot sampling period; the signal received at the l-th snapshot in the m-th discrete sensing time slot is used as... It means, or is interpreted as in Given the discrete samples of the continuous model in equation (I), the discretized signal transmission and reception model of the movable array within the sensing time slot becomes equation (II): (II); In formula (II), , indicating the Doppler phase shift introduced by the k-th target in the m-th time slot. This represents the transmitted signal at time slot m and snapshot l. Assuming an omnidirectional transmission mode, i.e., satisfying the condition that the autocorrelation matrix is ​​an identity matrix: for The autocorrelation matrix, This indicates the conjugate transpose. express Identity matrix.

[0011] A further preferred embodiment is to express equation (II) in matrix form: (III); In formula (III), This represents the transmission of active sensing signals in the L snapshots within the m-th discrete time slot. This represents the received noise of L snapshots in the m-th discrete time slot.

[0012] A further preferred embodiment sets the moving speed and the discrete sensing time slot interval to satisfy... .

[0013] More preferably, each time-slot movable array transmits the same active sensing signal, i.e.: (IV).

[0014] Where S represents the same active sensing signal used in M ​​discrete time slots.

[0015] According to the application, preferably, in step (4), the signals in the plurality of discrete sensing time slots are jointly processed to equivalently convert Doppler-induced time phase changes into spatial phase offsets to construct a space-time steering vector model; that is, the received signals in the M discrete sensing time slots shown in formula (III) are stacked to be represented as: (V); wherein the Doppler effect is decomposed into phase changes of the received steering vectors of each time slot, and a space-time steering vector with a dimension of is obtained by vertically stacking the Doppler-modulated received steering vectors in the M discrete sensing time slots.

[0016] According to the application, preferably, in step (5), the space-time steering vector model is converted into an equivalent virtual array; that is, the formula is substituted into , that is, , and the formula is equivalently converted into: (VI); wherein represents a virtual array manifold matrix, represents a steering vector of the virtual array, and is represented as: (VII); In addition, represents an equivalent source signal generated by the target reflection; at this time, the N-antenna moving array received signal is equivalently converted into an MN-antenna array received signal.

[0017] According to the application, preferably, in step (6), the received signal is modeled as a sparse representation model, and the target is located through a compressive sensing algorithm, and specifically includes: 1) the virtual array signal in the formula is represented as a sparse representation model, as shown in formula (VIII): (VIII); wherein is an over-complete basis matrix composed of a series of virtual steering vectors, contains Q possible discrete angles, is a sparse representation of the equivalent source signal, satisfies a row sparsity constraint, that is, only K rows have non-zero elements, corresponding to K real target angles; 2) in formula (VIII), the angle estimation problem is represented as a row sparse matrix reconstruction problem: (IX); wherein represents a noise threshold constraint.​ Solving formula (IX) by a compressive sensing algorithm, we obtain 3) After obtaining , a set of non-zero row sequence numbers of is extracted , and the angle estimation of the K targets is: (X); wherein is the target positioning result, , including Q possible discrete angles, is the sequence number set, indicates that the angle corresponding to the sequence number in is selected.

[0018] A computer device comprises a memory and a processor, the memory stores a computer program, and the processor implements the steps of the above-mentioned mobile array-based integrated sensing and positioning method when executing the computer program.

[0019] A computer-readable storage medium stores a computer program, and the computer program implements the steps of the above-mentioned mobile array-based integrated sensing and positioning method when executed by a processor.

[0020] A mobile array-based integrated sensing and positioning system comprises: A time division ISAC mode configuration module configured to implement time division ISAC mode configuration; A continuous time signal transceiver model establishment module configured to establish a mobile array continuous time signal transceiver model within a sensing time slot; A discretization signal transceiver model establishment module configured to establish a mobile array discretization signal transceiver model within a sensing time slot; A space-time steering vector model construction module configured to jointly process signals within multiple discrete sensing time slots, equivalent spatial phase shifts to Doppler-induced time phase changes, and construct a space-time steering vector model; A conversion module configured to convert the space-time steering vector model into an equivalent virtual array; A positioning module configured to model the received signal as a sparse representation model and position the target through a compressive sensing algorithm.

[0021] The beneficial effects of the present application are: ​​The application provides a mobile array-based integrated positioning method and system for sensing and communication, which is suitable for positioning applications in a sensing and communication network. The application introduces double-path Doppler effect caused by array movement into an equivalent spatial steering vector phase shift, constructs a high-dimensional virtual array model without relying on multi-antenna deployment, and introduces a compressed sensing algorithm to complete sparse angle reconstruction. Compared with existing schemes, the method can achieve higher-precision angle positioning with the same physical antenna elements. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 is a deployment schematic diagram of the mobile array-based integrated positioning system for sensing and communication; Figure 2 is a schematic diagram of the ISAC frame structure of the application and the relationship between the snapshot in the sensing time slot and the sampling in the discrete sensing time slot; Figure 3 is a schematic diagram of the angle estimation result of the scheme proposed by the application; Figure 4 is a schematic diagram of the angle positioning error comparison result of different schemes. DETAILED DESCRIPTION

[0023] The application will be further limited in combination with the accompanying drawings and examples of the specification, but is not limited thereto.

[0024] Example 1 A mobile array-based integrated positioning method for sensing and communication is used in a mobile antenna array integrated sensing and communication system, which can achieve high-precision angle positioning under the condition of limited physical antenna number. The mobile antenna array integrated sensing and communication system includes a group of mobile arrays moving along a straight line, such as Figure 1 shown, the array is a uniform linear array (ULA), the mobile uniform linear array includes N antenna elements, the distance between the antenna elements is d, and the array moves at a constant speed along a preset direction through a driving mechanism; the mobile array is deployed in a communication base station with a slide rail and a control device, or is installed on a drone, a robot or an intelligent platform with a moving capability; flexible deployment and low-power operation are achieved. It is assumed that there are target scenes in the target scene that need to be positioned; the method includes the following steps:

[0025] (1) Time division ISAC mode configuration; (2) Establishing a mobile array continuous-time signal transmission and reception model in a sensing time slot; (3) Establishing a mobile array discretization signal transmission and reception model in a sensing time slot; (4) Joint processing of signals in multiple discrete sensing time slots, equivalent to time phase changes caused by Doppler into spatial phase shifts, and constructing a space-time steering vector model. (5) Transform the spacetime steering vector model into an equivalent virtual array; (6) The received signal is modeled as a sparse representation model, and the target is located by angle using a compressed sensing algorithm.

[0026] Example 2 The difference between the sensor-integrated positioning method based on a movable array described in Embodiment 1 and the one described in Embodiment 1 is as follows: In step (1), the time-division ISAC mode configuration refers to the following: In an integrated sensing system, to achieve efficient coordination between communication and sensing functions and avoid resource conflicts, this invention adopts the time-division multiplexing ISAC working mode, such as... Figure 2 As shown, time resources are divided into periodic communication time slots and sensing time slots. These can be flexibly allocated according to the importance or indicators of actual communication and sensing tasks. For example, when communication demand is high, the proportion of communication time slots is greater. During the communication time slot, the movable array stops moving and is fixed at the position of the array at the end of the sensing time slot in the previous frame. That is, during the communication time slot, the array remains stationary at the position at the end of the previous sensing time slot, and data is transmitted with the communication user using the fixed array mode. During the sensing time slot, a sensor-integrated positioning method based on the movable array is adopted.

[0027] In step (2), establishing a continuous time-series signal transmission and reception model for the movable array within the sensing time slot refers to: based on the constant-speed motion characteristic of the movable array, constructing a model for each sensing time slot. The sensing signal transmission and echo reception model within the system is expressed as equation (I): (I); In formula (I), This represents the echo signal received by the movable array at sensing time t; It is the reflection coefficient of the k-th target. , where is the Doppler frequency shift of the k-th target relative to the array. Let the angle of the k-th target relative to the array be . It's the wavelength. It is the imaginary unit; , Represents the transmit and receive steering vectors. , This represents the active sensing signal transmitted by the mobile array at time t. Let be the complex Gaussian white noise received by the movable array at time t.

[0028] In step (3), establishing a discrete signal transmission and reception model for a movable array within the sensing time slots means dividing the continuous sensing time, i.e., the sensing time slots, into M discrete sensing time slots, such as... Figure 2 As shown, the length of each discrete sensing time slot is , the distance of the movable array moving in each discrete sensing time slot is ; at the beginning of each discrete sensing time slot, the movable array transmits a sensing signal and receives a return signal, and the return signal is sampled for L times , and the time interval between the times of sampling is , it is assumed that the movable array is quasi-stationary during the L times of sampling; the signal received at the lth time of sampling in the mth discrete sensing time slot is denoted as , which is explained as a discrete sample of the continuous model of formula (I) at , therefore, the discrete signal transceiving model of the movable array in the sensing time slot becomes formula (II): (II); In formula (II), , represents the Doppler phase shift introduced by the kth target at the mth time slot, represents the transmitted signal at the time slot m, the time of sampling l, and the transmitted signal is assumed to be an omnidirectional transmission mode, that is, the autocorrelation matrix satisfies the unit matrix: is the autocorrelation matrix of , represents the conjugate transpose, represents , and represents the unit matrix.

[0029] Formula (II) is expressed in the form of a matrix: (III); In formula (III), represents the transmitted active sensing signal of L times of sampling in the mth discrete time slot, represents the received noise of L times of sampling in the mth discrete time slot.

[0030] The moving speed and the interval of the discrete sensing time slot are set to satisfy .

[0031] The movable array transmits the same active sensing signal in each time slot, that is: (IV).

[0032] wherein S represents the same active sensing signal adopted in the M discrete time slots.

[0033] In step (4), the signals in multiple discrete sensing time slots are jointly processed, the time phase change induced by Doppler is equivalent to the spatial phase offset, and the space-time steering vector model is constructed; that is: the received signals of the M discrete sensing time slots shown in formula (III) are stacked up and represented as: (V); Among them, the Doppler effect Decomposed into a receive steering vector for each time slot The phase change is obtained by vertically stacking the Doppler-modulated receive steering vectors within the M discrete sensing time slot, resulting in a dimension of The spacetime steering vector.

[0034] In step (5), transforming the spacetime steering vector model into an equivalent virtual array means: Substitution ,Right now The formula is equivalent to: (VI); In the formula, Represents a virtual array manifold matrix. The steering vector of the virtual array is represented as: (VII); in addition, This represents the equivalent source signal generated by the target reflection; at this point, the signal received by the N-antenna mobile array has been equivalent to the signal received by the MN virtual antenna array.

[0035] In step (6), the received signal is modeled as a sparse representation model, and the target is located using a compressed sensing algorithm, specifically including: 1) Represent the virtual array signal in the formula as a sparse representation model, as shown in Equation (VIII): (VIII); in, It is an overcomplete basis matrix composed of a series of virtual steering vectors. It contains Q possible discrete angles. It is a sparse representation of the equivalent source signal. It satisfies the row sparsity constraint, meaning that only K rows have non-zero elements, corresponding to K real target angles; 2) In equation (VIII), the angle estimation problem is expressed as a row sparse matrix reconstruction problem: (IX); in, Indicates noise threshold constraint; due to Since sparsity is shared between different columns, problem (IX) can be solved using existing compressed sensing methods, such as the Simultaneous Orthogonal Matching Pursuit (SOMP) algorithm.

[0036] Solving formula (IX) by a compression sensing algorithm, we obtain ; 3) After obtaining , the set of non-zero row sequence numbers of is extracted , and the angle estimation of the K targets is: (X); wherein is the target positioning result, , the Q possible discrete angles, is the sequence number set, indicates the angle corresponding to the sequence number in .

[0037] In the embodiment, the parameters are set as follows: frequency 10 GHz, wavelength , number of array antennas , array moving speed v = 20 m / s, M = 27, L = 10, , and the root mean square error (RMSE) is used as an index.

[0038] Figure 3 The scheme of the application is shown in the angle estimation result diagram. Figure 3 In the diagram, the signal-to-noise ratio (SNR) is set to 10 dB, and the number of targets K = 7. Figure 3 The results show that the scheme of the application can realize high-precision angle positioning with only 4 physical antennas.

[0039] Figure 4 The diagram shows the comparison results of angle positioning errors of different schemes. Figure 4 In the diagram, the horizontal axis is the signal-to-noise ratio (SNR), and the vertical axis is the root mean square error (RMSE). The SNR varies from -10 dB to 10 dB, the number of targets K = 1, the comparison schemes are a fixed array scheme (i.e., a fixed uniform linear array with N = 4) and an extended fixed array scheme (i.e., a uniform linear array deployed within the moving range of the movable antenna array), and the Cramer-Rao bound (CRB) of different schemes is used as the error lower limit. Figure 4 The results show that the three schemes can all reach the corresponding Cramer-Rao bound at high signal-to-noise ratios, the proposed scheme has the smallest estimation error, which is reflected in the lowest RMSE in the diagram, and the comparison shows the superiority of the proposed scheme.

[0040] Embodiment 3​ A computer device comprising a memory and a processor, the memory storing a computer program, the processor implementing the steps of the method for integrated positioning based on movable array according to embodiment 1 or 2 when executing the computer program.

[0041] Embodiment 4 A computer readable storage medium having stored thereon a computer program, the computer program implementing the steps of the method for integrated positioning based on movable array according to embodiment 1 or 2 when executed by a processor.

[0042] Embodiment 5 A system for integrated positioning based on movable array, comprising: A time division ISAC mode configuration module configured to implement time division ISAC mode configuration; A continuous time signal transceiver model establishment module configured to establish a movable array continuous time signal transceiver model within a sensing time slot; A discretization signal transceiver model establishment module configured to establish a movable array discretization signal transceiver model within a sensing time slot; A space-time steering vector model construction module configured to jointly process signals within multiple discrete sensing time slots, to equivalently convert Doppler-induced time phase changes into spatial phase shifts, and to construct a space-time steering vector model; A conversion module configured to convert the space-time steering vector model into an equivalent virtual array; A positioning module configured to model the received signal as a sparse representation model, and to position the target through a compressive sensing algorithm.

Claims

1. A sensor-integrated positioning method based on a movable array, characterized in that, This is applicable to a movable antenna array sensing integrated system, which includes a movable uniform linear array (i.e., a movable array) that moves along a straight line. The movable uniform linear array comprises N antenna elements with a spacing of d between the antenna elements, and is driven by a mechanism at a constant speed. The movable array moves along a preset direction; it is deployed on a communication base station equipped with a sliding rail and control device, or installed on a mobile drone, robot, or intelligent platform; assuming that the target scene contains... Each far-field target requires angle positioning; including: (1) Time-division ISAC mode configuration; (2) Establish a continuous time-series signal transmission and reception model for the movable array within the sensing time slot; (3) Establish a discrete signal transmission and reception model for a movable array within the sensing time slot; (4) Jointly process the signals in multiple discrete sensing time slots, and convert the Doppler-induced time phase change into a spatial phase shift to construct a space-time steering vector model; (5) Transform the spacetime steering vector model into an equivalent virtual array; (6) The received signal is modeled as a sparse representation model, and the target is located by angle using a compressed sensing algorithm.

2. The sensor-integrated positioning method based on a movable array according to claim 1, characterized in that, In step (1), the time-division ISAC mode configuration refers to: adopting the time-division multiplexing ISAC working mode to divide time resources into periodic communication time slots and sensing time slots; within the communication time slot, the movable array stops moving and is fixed at the position of the array after the end of the sensing time slot in the previous frame, and uses the fixed array mode to transmit data with the communication user; within the sensing time slot, the integrated sensing positioning method based on the movable array is adopted.

3. The integrated sensing positioning method based on a movable array according to claim 1, characterized in that, In step (2), establishing a continuous time-series signal transmission and reception model for the movable array within the sensing time slot refers to: based on the constant-speed motion characteristic of the movable array, constructing a model for each sensing time slot. The sensing signal transmission and echo reception model within the system is expressed as equation (I): （I）； In formula (I), This represents the echo signal received by the movable array at sensing time t; It is the reflection coefficient of the k-th target. , where is the Doppler frequency shift of the k-th target relative to the array. Let the angle of the k-th target relative to the array be denoted as . It's the wavelength. It is the imaginary unit; , Represents the transmit and receive steering vectors. , This represents the active sensing signal transmitted by the mobile array at time t. Let be the complex Gaussian white noise received by the movable array at time t.

4. The integrated sensing positioning method based on a movable array according to claim 1, characterized in that, In step (2) and step (3), establishing the discrete signal transmission and reception model of the movable array within the sensing time slot means: dividing the continuous sensing time slot into M discrete sensing time slots, each discrete sensing time slot having a length of... The distance the movable array can move within each discrete sensing time slot is At the beginning of each discrete sensing time slot, the movable array transmits sensing signals and receives echo signals, and processes the echo signals. The time interval between each quick sample is [number]. Assuming the movable array is considered quasi-stationary during the L snapshot sampling period; the signal received at the l-th snapshot in the m-th discrete sensing time slot is used as... It means, or is interpreted as in Given the discrete samples of the continuous model in equation (I), the discretized signal transmission and reception model of the movable array within the sensing time slot becomes equation (II): (II); In formula (II), , indicating the Doppler phase shift introduced by the k-th target in the m-th time slot. This represents the transmitted signal at time slot m and snapshot l. Assuming an omnidirectional transmission mode, i.e., satisfying the condition that the autocorrelation matrix is ​​an identity matrix: for The autocorrelation matrix, This indicates the conjugate transpose. express identity matrix; A further preferred embodiment is to express equation (II) in matrix form: (III); In formula (III), This represents the transmission of active sensing signals in the L snapshots within the m-th discrete time slot. This represents the received noise of L snapshots in the m-th discrete time slot; A further preferred embodiment sets the moving speed and the discrete sensing time slot interval to satisfy... ; More preferably, each time-slot movable array transmits the same active sensing signal, i.e.: (IV); Where S represents the same active sensing signal used in M ​​discrete time slots.

5. The integrated sensing positioning method based on a movable array according to claim 1, characterized in that, In step (2), in step (4), the signals in multiple discrete sensing time slots are jointly processed, and the Doppler-induced time phase change is equivalent to the spatial phase shift, and a space-time steering vector model is constructed; this means: stacking the received signals of the M discrete sensing time slots shown in equation (III), which is expressed as: （V）； Among them, the Doppler effect Decomposed into a receive steering vector for each time slot The phase change is obtained by vertically stacking the Doppler-modulated receive steering vectors within the M discrete sensing time slot, resulting in a dimension of The spacetime steering vector.

6. The integrated sensing positioning method based on a movable array according to claim 1, characterized in that, In step (2), and in step (5), transforming the spacetime guided vector model into an equivalent virtual array means: transforming the spacetime guided vector model into an equivalent virtual array. Substitution ,Right now The formula is equivalent to: (WE); In the formula, Represents a virtual array manifold matrix. The steering vector of the virtual array is represented as: (VII); in addition, This represents the equivalent source signal generated by the target reflection; at this point, the signal received by the N-antenna mobile array has been equivalent to the signal received by the MN virtual antenna array.

7. A sensor-integrated positioning method based on a movable array according to any one of claims 1-6, characterized in that, In step (2), and in step (6), the received signal is modeled as a sparse representation model, and the target is located using a compressed sensing algorithm, specifically including: 1) Represent the virtual array signal in the formula as a sparse representation model, as shown in Equation (VIII): (VIII); in, It is an overcomplete basis matrix composed of a series of virtual steering vectors. It contains Q possible discrete angles. It is a sparse representation of the equivalent source signal. It satisfies the row sparsity constraint, meaning that only K rows have non-zero elements, corresponding to K real target angles; 2) In equation (VIII), the angle estimation problem is expressed as a row sparse matrix reconstruction problem: (IX); in, Indicates noise threshold constraint; Solving equation (IX) using the compressed sensing algorithm yields the following results. ; 3) After obtaining Then, extract The set of non-zero row indices The angle estimates for the K targets are: （X）； in, It is the result of target positioning. This includes Q possible discrete angles. It is a set of ordinal numbers. This means that in Selected from The angle corresponding to the serial number in the table.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the sensor-integrated positioning method based on a movable array as described in any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the sensor-integrated positioning method based on a movable array as described in any one of claims 1-7.

10. A sensor-integrated positioning system based on a movable array, characterized in that, include: The time-division ISAC mode configuration module is configured to implement time-division ISAC mode configuration. The continuous-time signal transmission and reception model establishment module is configured to: establish a continuous-time signal transmission and reception model of the movable array within the sensing time slot; The discrete signal transceiver model establishment module is configured to: establish a discrete signal transceiver model for a movable array within a sensing time slot; The space-time steering vector model construction module is configured to: jointly process signals from multiple discrete sensing time slots, equate Doppler-induced temporal phase changes to spatial phase shifts, and construct a space-time steering vector model. The transformation module is configured to transform the spacetime guided vector model into an equivalent virtual array. The localization module is configured to model the received signal as a sparse representation model and locate the target using a compressed sensing algorithm.

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