A method for suppressing multipath effects in indoor visible light positioning

Abstract

A method for suppressing multipath effects in indoor visible light positioning, which relates to the fields of indoor visible light communication and positioning technology. To solve the problems existing in the prior art, this method: constructs a fractional-order chaotic signal generator and starts to generate a chaotic sequence signal; modulates and loads the chaotic sequence signal onto an LED array and its driving circuit to generate and emit an optical signal carrying fractional-order chaotic characteristics; after the optical signal propagates indoors, it is collected by a photodetector, preprocessed, and then transmitted to the on-site FPGA; in the FPGA, based on the compressed sensing theory, the received signal is modeled and an appropriate sensing matrix is constructed to obtain a compressed observation signal; the path focusing-guided orthogonal matching pursuit algorithm is used to iteratively recover the sparse channel response from the compressed observation signal; the FPGA extracts the main path information from the reconstructed sparse channel response and combines it with the time-of-arrival positioning model to calculate the final positioning coordinates. It has good ability to resist multipath effects in indoor visible light positioning.

Description

Technical Field

[0001] The present invention relates to the technical fields of indoor visible light communication and positioning technology, and uses the reflection and refraction of light waves for positioning detection, and is particularly applicable to indoor visible light positioning where the room positioning performance is greatly affected by the multipath effect. Background Art

[0002] As a new generation of high-precision indoor navigation solution, indoor visible light positioning technology has shown remarkable potential in recent years in fields such as intelligent warehousing, medical navigation, industrial Internet of Things, and large shopping mall navigation. This technology encodes position information in optical signals through the high-speed modulation characteristics of LED light sources, and the receiving end achieves centimeter-level positioning accuracy by analyzing parameters such as light intensity, phase, or time difference. Compared with traditional radio frequency positioning technology, its advantages are: no need for additional spectrum resources, strong anti-electromagnetic interference ability, and can be deeply integrated with the lighting system. However, the reliability and robustness of existing technologies still face multiple challenges in complex scenarios.

[0003] The current mainstream positioning methods are mainly divided into: trilateration based on geometric models and fingerprint matching based on signal characteristics. During the propagation of visible light signals, they are affected by the reflection and scattering of objects such as walls and furniture, resulting in the superposition of the direct signal received by the receiving end and multiple reflected signals, forming a complex multipath interference scenario. This interference will cause distance estimation deviation in the positioning method based on geometric models. Especially in areas with dense metal obstacles, the positioning error will increase significantly. At the same time, the time delay spread of multipath signals will cause inter-symbol interference, affecting the performance of the positioning system based on intensity fingerprint matching. It is necessary to increase the sampling frequency or optimize the signal modulation method to alleviate this, but this will significantly increase the system complexity and hardware cost.

[0004] The Chinese patent publication number is "CN 114690118 A", and the patent name is "An NLOS Suppression OCDMA Indoor Visible Light Positioning Method". The core of this method is to use optical code division multiple access (OCDMA) technology to assign orthogonal optical address codes to each LED. Subsequently, the receiving end calculates the correlation value between the mixed signal and the local optical address code to achieve positioning. By leveraging the low correlation between LOS signals and NLOS signals, the influence of NLOS signals on the positioning results is effectively reduced, and the positioning accuracy in areas with severe multipath reflections such as the edges and corners of the room is improved to a certain extent. Moreover, it does not require strict synchronization and complex filter design, and has the advantages of strong anti-interference ability and low equipment cost. However, this method has problems such as high requirements for address code adaptation, insufficient adaptability to dynamic environments, and the bottleneck of code set capacity for large-scale deployment. It is difficult to achieve high-precision indoor visible light positioning in complex multipath scenarios, stable in dynamic environments, and highly scalable for large-scale LED arrays. For scenarios such as large shopping malls with dense crowds, exhibition halls, industrial workshops with complex metal obstacles, and high-density intelligent lighting storage shelves, it still cannot meet the requirements of strong multipath interference suppression, stable real-time continuous positioning, and low-cost large-scale deployment. Summary of the Invention

[0005] In order to solve the problem in the prior art that indoor visible light positioning with high precision in complex multipath scenarios, stable in dynamic environments, and highly scalable for large-scale LED arrays cannot be achieved, the present invention provides a multipath effect suppression method for indoor visible light positioning, which can solve the problems of non-line-of-sight signal interference and multiple access interference in a dynamic multipath changing environment, improve the positioning accuracy and robustness in complex scenarios, realize adaptive positioning for the deployment of high-density LED arrays and the distribution environment of strong reflection obstacles, and meet the positioning requirements of centimeter-level positioning accuracy and real-time continuous tracking in public spaces with high-frequency personnel movement, industrial factories with complex metal structures, and high-density intelligent storage shelves in warehouses.

[0006] The technical solution of the present invention to solve the technical problem is as follows:

[0007] A multipath effect suppression method for indoor visible light positioning, comprising the following steps:

[0008] S1. Construct a fractional-order chaotic signal generator and start generating a non-periodic chaotic sequence signal.

[0009] S2. Modulate and load the chaotic sequence signal onto the LED array and its driving circuit to generate an optical signal carrying fractional-order chaotic characteristics and transmit it.

[0010] S3. During the propagation of the optical signal in the room, a multipath mixed signal including direct paths and multiple reflection and refraction paths is formed, and is collected by a photodetector, preprocessed, and then transmitted to a field programmable gate array circuit (FPGA).

[0011] S4. In the FPGA, based on the compressive sensing theory, the received signal is modeled as a linear convolution form of a sparse channel response vector and a chaotic excitation signal, and an appropriate sensing matrix is constructed by using the characteristics of the chaotic sequence to obtain a compressive observation signal that satisfies the compressive sensing theory.

[0012] S5. The path concentration ratio-orthogonal matching pursuit algorithm (PCR-OMP) is used to reconstruct the sparse channel response, iteratively recover the sparse channel response from the compressive observation signal, and suppress the interference of non-main paths by dynamically evaluating the path concentration ratio.

[0013] S6. The FPGA extracts the main path delay information from the reconstructed sparse channel response, combines it with the time of arrival (TOA) positioning model, and calculates the spatial coordinates of the target terminal through the geometric relationship of multiple light sources with unique identification IDs.

[0014] The beneficial effects of the present invention are as follows:

[0015] 1. The anti-multipath interference ability is significantly enhanced: By introducing a fractional-order Lorenz chaotic system to generate an aperiodic chaotic sequence signal, and using the multi-dimensional control characteristics of the fractional-order derivative, the chaotic sequence has stronger parameter sensitivity and spectral sparsity. Compared with the traditional integer-order chaotic system, the signal of the present invention presents the characteristics of "local oscillation + global aperiodicity" in the time domain, and the autocorrelation function only has a spike at zero delay, and the correlation at other delay values is extremely low, effectively reducing the aliasing interference between multipath signals and improving the signal recognition ability in a complex reflection environment.

[0016] 2. The path separation and the accuracy of main path extraction are improved: A sparse channel model is constructed by combining the compressive sensing theory, and a Toeplitz-type sensing matrix is constructed by using the chaotic signal. Its column incoherence and frequency domain expansion satisfy the conditions of the restricted isometry property (RIP), ensuring the efficient reconstruction of the sparse channel response. The improved PCR-OMP algorithm dynamically screens the main path through the path concentration ratio index, avoiding the support set contamination problem of the traditional OMP algorithm, accurately capturing the main path energy in a multipath aliasing environment, greatly reducing the path delay estimation error, and significantly improving the input accuracy of the positioning geometric model.

[0017] 3. System Robustness and Adaptability Optimization: The non-integer order derivative characteristics of the fractional-order chaotic system provide a more flexible parameter adjustment space. For example, when the order is close to 1, it shows quasi-integer order strong chaotic characteristics, and when the order decreases, the spectral sparsity increases. The order can be adjusted to adapt to the linear response interval and bandwidth limit of different LED models. The normalized mapping and clipping filter design ensure the reliable transmission of signals in LED non-linear devices. Combining with the first-order inertia model to compensate for the LED bandwidth limit improves the system's robustness to fluctuations in the light source hardware parameters and is applicable to multi-brand and multi-model LED networking environments. Moreover, it supports the dynamic expansion of the light source layout. For example, when adding new LED nodes, only the construction rule of the sensing matrix needs to be updated, and there is no need to reconstruct the algorithm parameters, reducing the system expansion cost.

[0018] 4. Breakthrough in Positioning Accuracy and Stability: Using the main path delay information after sparse reconstruction to calculate the coordinates can greatly suppress the energy superposition interference of multipath signals. Especially in strong reflection areas (such as glass curtain walls and smooth floor scenarios), the positioning accuracy and stability can be significantly improved to meet the actual needs of high-precision indoor positioning.

[0019] 5. Spectrum Efficiency and Energy Utilization Optimization: The broad-spectrum energy distribution characteristics of chaotic signals (the power spectral density decays with frequency but covers a wide frequency band) match the limited bandwidth response of LEDs, reducing the loss of high-frequency components while ensuring signal integrity. The intensity modulation method directly maps the light intensity signal, avoiding the problem of chaotic structure loss in OOK modulation, reducing the LED switching loss compared to PWM modulation, improving the system energy efficiency ratio, and being applicable to low-power indoor positioning scenarios. Description of the Drawings

[0020] Figure 1 It is a schematic diagram of a multipath effect suppression system for indoor visible light positioning according to the present invention.

[0021] Figure 2 It is a flowchart of a multipath effect suppression method for indoor visible light positioning according to the present invention.

[0022] Figure 3 It is a curve diagram of the LED light intensity modulation signal after the chaotic sequence generated by the fractional-order Lorenz system according to the present invention is normalized and mapped. Figure 3 (a) is the curve diagram of the original fractional-order Lorenz chaotic sequence x(t); Figure 3 (b) is the curve diagram of the normalized LED light intensity modulation signal.

[0023] Figure 4 It is a schematic diagram of the sensing matrix construction and sparse signal flow based on the fractional-order Lorenz chaotic system according to the present invention.

[0024] Figure 5It is the flow chart of the PCR-OMP algorithm described in the present invention.

[0025] Figure 6 It is the schematic diagram of the positioning performance simulation results of the basic method and the method of the present invention under the multipath intensity of 0.3 environment. Figure 6 (a)is the positioning effect diagram of the basic method; Figure 6 (b)is the positioning effect diagram of the method of the present invention. Detailed implementation manners

[0026] The present invention will be further described in detail below with reference to the accompanying drawings.

[0027] As Figure 1 shown, a multipath effect suppression system for indoor visible light positioning includes a fractional-order chaotic signal generator 1, an LED array driving circuit 2, an LED light source array 3 (m×n), a photodetector 5, and an FPGA 6; the indoor environment includes a smooth wall 4 (including the ceiling and four walls) with the ability to reflect and refract light, and a smooth floor 7 with the ability to reflect and refract light. In an indoor environment with strong multipath interference, the fractional-order chaotic signal generator 1 is connected to the LED array driving circuit 2 to drive the uniformly distributed LED light source array 3 to emit light carrying chaotic characteristics. During the propagation of the light, it includes a direct path and non-direct paths such as reflection and refraction through the smooth wall 4 and the smooth floor 7; after being received by the photodetector 5, it is photoelectrically converted and processed by the FPGA 6. Among them, the photodetector 5 and the FPGA 6 are located at any place on the smooth floor 7 within the indoor range.

[0028] As Figure 2 shown, a multipath effect suppression method for indoor visible light positioning, the method process is as follows:

[0029] S1. Construct and start the fractional-order chaotic signal generator 1: In an indoor environment with strong multipath interference, the LED light source array 3 is uniformly distributed, and the photodetector 5 is located at any place on the smooth floor 7 within the indoor range. Based on the fractional-order Lorenz derivative, a fractional-order chaotic signal generator is constructed to generate an aperiodic chaotic sequence signal.

[0030] S2. Modulate and drive the LED light source array 3 to emit an optical signal: Map the generated aperiodic chaotic sequence signal to the value range of [0,1] through the min-max normalization method, and then linearly map it to the LED drive current range to make the current fluctuate within the linear region of the current-light intensity curve of the LED; finally, load the chaotic signal onto the LED array driving circuit 2 through intensity modulation to drive the LED light source array 3 to generate a continuous optical intensity modulation signal carrying fractional-order chaotic characteristics and emit it.

[0031] S3. Optical signal propagation and preprocessing: When the optical signal propagates indoors, it is mixed and superimposed by the direct path and the non-direct path formed by the reflection of the smooth wall 4 and the smooth floor 7. After the optical signal is converted into an electrical signal by the photoelectric detector 5, signal amplification, band-pass filtering, and analog-to-digital conversion preprocessing are performed in sequence to generate a digital baseband signal and transmit it to the FPGA 6. During the preprocessing process, the signal amplitude is ensured to be within the input dynamic range of the FPGA 6 through automatic gain control.

[0032] S4. Processing the received signal based on the compressive sensing theory: In the FPGA 6, the electrical signal received after photoelectric conversion and preprocessing is processed based on the compressive sensing theory. The received signal is modeled as a linear convolution form of a sparse channel response vector and a chaotic excitation signal. Utilizing the unique properties of the chaotic sequence, an appropriate sensing matrix is constructed by row displacement and satisfies the RIP condition that the column correlation is less than a certain threshold; the high-dimensional original received signal is mapped to a low-dimensional space to obtain a compressive observation signal that satisfies the compressive sensing theory.

[0033] S5. Main path focusing and sparse reconstruction: The PCR-OMP algorithm is used to perform sparse reconstruction on the compressive observation signal. The sparse channel response is recovered and reconstructed from the compressive observation signal through iterative calculation. During the iterative process, the main path focusing degree is dynamically evaluated to suppress non-main path interference and enhance the main path focusing, achieving high-precision channel estimation.

[0034] S6. Output the final positioning position: The FPGA 6 extracts the time delay corresponding to the component with the largest amplitude from the reconstructed sparse channel response as the LOS path time delay, converts it into a distance through the TOA positioning model, combines the coordinates of three or more LED light sources with unique IDs to construct a trilateration ranging equation set, and uses the Gauss-Newton iterative method to solve it, finally calculating the three-dimensional space coordinates of the target terminal to achieve high-precision and strong-stable indoor positioning in an indoor environment with strong multipath interference.

[0035] In S1, the fractional-order chaotic signal generator 1 is constructed based on the fractional-order Lorenz derivative, and its dynamic model is defined by the Caputo fractional-order derivative, specifically including:

[0036]

[0037] Among them: is the Caputo-type fractional-order derivative, and the superscript C is used to distinguish other fractional-order definitions; is the integer-order derivative; is the order; is the Gamma function; is the current time point, the upper limit of integration; is the integration variable; is the smallest integer satisfying 。

[0038] In the integer order, the Lorenz system is as follows:

[0039]

[0040] Deducing to the fractional-order Lorenz chaotic system, its model is expressed as:

[0041]

[0042] Where: is the order of the fractional derivative; is the system control parameter.

[0043] In S2, each LED light source in the LED light source array 3 is assigned a unique identification ID, specifically including:

[0044] The chaotic modulation signal is subjected to min-max normalization so that its value range matches the LED control input range, expressed as:

[0045]

[0046] Where: is the normalized chaotic signal of the ith light source; i is the unique identification ID of the light source, representing the ith light source in the system; is the original chaotic modulation signal generated by the ith light source, which changes with time t; 、 is the chaotic signal of the ith light source The maximum and minimum values within the observation time window.

[0047] Subsequently, it is remapped to the LED drive current range :

[0048]

[0049] Where: is the drive current actually loaded by the ith light source, which changes with time t; is the normalized chaotic signal of the ith light source; 、 are the maximum and minimum drive currents allowed for the ith light source.

[0050] As Figure 3 shown is the LED light intensity modulation signal curve after normalization mapping of the chaotic sequence generated by the fractional-order Lorenz system. The curve of the original fractional-order Lorenz chaotic sequence is as Figure 3 (a) shown; Figure 3(b) is the normalized LED light intensity modulation signal curve; as can be seen from the figure, the signal fluctuation range is stable, retaining the "local oscillation + global non-periodic" characteristics of the original chaotic structure and having the actual light emission modulation ability.

[0051] In S3, the preprocessing includes:

[0052] S31. Signal amplification: Use a transimpedance amplifier to convert the photocurrent output by the photodetector 5 into a voltage signal.

[0053] S32. Band-pass filtering: Filter out the environmental noise and interference outside the frequency band range.

[0054] S33. Analog-to-digital conversion: Digitalize at a sampling rate not lower than twice the bandwidth of the chaotic signal.

[0055] As Figure 4 shown, it is a schematic diagram of the construction of the sensing matrix and the sparse signal flow based on the fractional-order Lorenz chaotic system. In S4, the FPGA 6 processes the received electrical signal after photoelectric conversion and preprocessing based on the compressed sensing theory. The channel response vector at the receiving end shows obvious sparse characteristics on the time axis and can be expressed as:

[0056]

[0057] Among them: y is the sampling signal at the receiving end; x is the chaotic modulation excitation sequence; h is the sparse channel response vector to be recovered; n is the additive noise.

[0058] Utilize the unique properties of the chaotic sequence to construct an adapted sensing matrix by row displacement and satisfy the RIP condition that the column correlation is less than a certain threshold. The sensing matrix is constructed as a Toeplitz matrix and is expressed as:

[0059]

[0060] Among them: is the sensing matrix, with dimensions M×N; M is the number of rows of the sensing matrix, corresponding to the observation dimension in compressed sensing; N is the number of columns of the sensing matrix, corresponding to the dimension of sparse representation; is the value of the i-th chaotic sequence generated by the fractional-order Lorenz chaotic system.

[0061] And the sensing matrix should satisfy the "restricted isometry property":

[0062]

[0063] Among them: k is the sparsity; h k is an arbitrary k-sparse channel response vector; is the isometric constant when the sensing matrix satisfies the RIP property for k-sparse vectors; is the square of the L2 norm, that is, the sum of the squares of the vector elements.

[0064] Map the high-dimensional original received signal to a low-dimensional space to obtain a compressed observation signal that satisfies the compressed sensing theory:

[0065]

[0066] where: is the received signal sampling vector, that is, the compressed observation signal; is the sensing matrix; h is the sparse channel response vector to be recovered; n is the additive noise.

[0067] In S5, based on the reconstruction optimization reduction theory of compressed sensing, accurately recover the sparse channel response h from the compressed observation signal L :

[0068]

[0069] where: h is the sparse channel response vector to be recovered; is the L1 norm; is the square of the L2 norm; is the sensing matrix; is the received signal sampling vector, that is, the compressed observation signal; is the sparse regularization parameter, weighing the residual and sparsity; is the upper limit of the reconstruction error, controlling the reconstruction accuracy tolerance.

[0070] In the process of recovering the sparse channel response, introduce the optimized PCR-OMP algorithm, that is, use the path concentration ratio index PCR as the judgment basis, guide the update of the support set during the algorithm operation, and dynamically evaluate the reliability of the estimation result, enhancing the accuracy of the main path extraction and the system robustness. Define the current estimated path response as , and its path concentration ratio PCR is calculated as follows:

[0071]

[0072] where: is the component with the largest amplitude in the current estimated vector; the denominator is the total energy of the current estimated channel response.

[0073] As Figure 5 shown, the PCR-OMP algorithm includes the following steps:

[0074] S51. Initialization: Residual , support set , iteration number 。

[0075] S52. Maximum projection search: Calculate the correlation between the residual and the sensing matrix , and select the maximum term 。

[0076] S53. Support set update: 。

[0077] S54. Least squares estimation: Solve the least squares estimation for the sub-matrix within the support set 。 。

[0078] S55. PCR discrimination: Calculate the path concentration ratio PCR. If PCR < threshold, trigger correction.

[0079] S56. Residual update: Eliminate the reconstructed signal components, approximate the true channel response, and update the residual in real time 。

[0080] S57. Termination condition: If or the number of iterations exceeds the upper limit, terminate the iteration.

[0081] Where: is the residual after the t-th iteration; is the received signal sampling vector, i.e., the compressed observation signal; S is the support set, storing the indices of the currently selected channel response components; p is the projection correlation vector; is the transpose of the sensing matrix; j is the index corresponding to the maximum projection value, representing the path component with the strongest energy in the current residual; is the j-th element of the projection correlation vector p; is the parameter index for taking the maximum value; is the support set sub-matrix of the sensing matrix; is the estimated value vector of the path components within the support set; is the L2 norm of the residual; is the preset residual threshold.

[0082] In S6, the positioning calculation of FPGA6 specifically includes the following steps:

[0083] S61. Main path delay extraction: Select the delay corresponding to the component with the maximum amplitude from the reconstructed sparse channel response as the direct path delay 。

[0084] S62. Distance conversion: Convert the delay to distance according to the speed of light c , where is the delay corresponding to the k-th light source.

[0085] S63. Trilateration ranging modeling: Based on the light source coordinates With the coordinates of the receiving end , a geometric positioning equation set is constructed.

[0086]

[0087] S64. Coordinate calculation: Solve the equation set through the Gauss-Newton iterative algorithm to obtain the spatial coordinates of the receiving end , where K≥4 is the number of effective direct paths.

[0088] Such as Figure 6 shown is a schematic diagram of the positioning performance simulation results of the basic method and the method of the present invention in an environment with a multipath intensity of 0.3. Figure 6 (a) is the positioning effect diagram of the basic method; Figure 6 (b) is the positioning effect diagram of the method of the present invention. It can be seen from the figure that in the case of multipath interference, the method of the present invention significantly improves the positioning accuracy and has good ability to resist multipath effects in indoor visible light positioning.

Claims

1. A method for suppressing multipath effects in indoor visible light positioning, characterized in that The method includes the following steps: S1. Construct a fractional-order chaotic signal generator and start generating an aperiodic chaotic sequence signal; S2. Modulate and load the chaotic sequence signal onto the LED array and its driving circuit to generate and emit an optical signal carrying fractional-order chaotic characteristics; S3. During the propagation of the optical signal in the room, a multipath mixed signal including a direct path and multiple reflection and refraction paths is formed, and is collected by a photodetector, preprocessed, and then transmitted to the FPGA; S4. In the FPGA, based on the compressed sensing theory, model the received signal as a linear convolution form of a sparse channel response vector and a chaotic excitation signal, and construct an appropriate sensing matrix using the characteristics of the chaotic sequence to obtain a compressed observation signal that satisfies the compressed sensing theory; S5. Use the PCR-OMP algorithm to reconstruct the sparse channel response, iteratively recover and reconstruct the sparse channel response from the compressed observation signal, and suppress non-primary path interference by dynamically evaluating the path focusing degree; In the step S5, based on the reconstruction optimization reduction theory of compressive sensing, the sparse channel response h is accurately recovered from the compressed observation signal L : ； where: h is the sparse channel response vector to be restored; is the L1 norm; is the square of the L2 norm; is the sensing matrix; is the received signal sampling vector, i.e., the compressed observation signal; is the sparse regularization parameter, weighing the residual and sparsity; is the upper limit of the reconstruction error, controlling the reconstruction accuracy tolerance; During the process of recovering the sparse channel response, the newly proposed path focusing-guided orthogonal matching pursuit, namely the PCR-OMP algorithm, is adopted. In the iterative process, a path focusing degree index is introduced as a judgment basis to guide the update of the support set and dynamically evaluate the reliability of the estimation result, enhancing the accuracy of the primary path extraction and the system robustness. It includes the following steps: S51. Initialization: residuals , support set , number of iterations ; S52. Maximum projection search: Calculate the correlation between the residual and the sensing matrix , and select the maximum term ; S53, Support set update: ; S54, Least Squares Estimation: For the sub-matrix within the support set Solve the least squares estimation ; S55. PCR discrimination: Calculate the path focusing degree PCR. If PCR < threshold, trigger correction; S56. Residual update: Eliminate the reconstructed signal components, approximate the true channel response, and update the residual in real time ; S57. Termination condition: If or the number of iterations exceeds the upper limit, terminate the iteration; Wherein: is the residual after the t-th iteration; is the received signal sampling vector, i.e., the compressed observation signal; S is the support set, storing the indices of the currently selected channel response components; p is the projection correlation vector; is the transpose of the sensing matrix; j is the index corresponding to the maximum projection value, representing the path component with the strongest energy in the current residual; is the j-th element of the projection correlation vector p; is the parameter index for taking the maximum value; is the support set sub-matrix of the sensing matrix; is the estimated value vector of the path components within the support set; is the L2 norm of the residual; is the preset residual threshold; S6. The FPGA extracts the primary path delay information from the reconstructed sparse channel response, combines it with the TOA positioning model, and calculates the spatial coordinates of the target terminal through the geometric relationship of multiple light sources with unique identification IDs.

2. A multipath effect suppression method for indoor visible light positioning according to claim 1, characterized in that In the step S1, the fractional-order chaotic signal generator is constructed based on the fractional-order Lorenz derivative, and its dynamic model is defined by the Caputo fractional-order derivative, specifically including: ； Wherein: is the Caputo fractional derivative, and the superscript C is used to distinguish it from other fractional definitions; is the integer-order derivative; is the order; is the Gamma function; is the current time point, the upper limit of integration; is the integration variable; is the smallest integer satisfying ; Deduced to the fractional-order Lorenz chaotic system, its model is expressed as: ； Wherein: is the order of the fractional derivative, ; is the system control parameter.

3. A multipath effect suppression method for indoor visible light positioning according to claim 1, characterized in that In the step S2, the modulation method is intensity modulation, and a unique identification ID is assigned to each LED light source, specifically including: Perform min-max normalization on the chaotic modulation signal to make its value range match the LED control input range, expressed as: ； Wherein: is the chaotic signal after normalization of the i-th light source; i is the unique identification ID of the light source, representing the i-th light source in the system; is the original chaotic modulation signal generated by the i-th light source, which changes with time t; and is the chaotic signal of the i-th light source the maximum and minimum values within the observation time window; Subsequently, it is mapped to the LED drive current range : ； Wherein: is the driving current actually loaded by the i-th light source, which varies with time t; is the normalized chaotic signal of the i-th light source; , are the maximum and minimum driving currents allowed for the i-th light source.

4. A multipath effect suppression method for indoor visible light positioning according to claim 1, characterized in that In the step S3, the preprocessing includes: S31. Signal amplification: Use a transimpedance amplifier to convert the photocurrent output by the photodetector into a voltage signal; S32. Band-pass filtering: Filter out environmental noise and interference outside the frequency band range; S33. Analog-to-digital conversion: Perform digitization at a sampling rate not lower than twice the bandwidth of the chaotic signal.

5. A multipath effect suppression method for indoor visible light positioning according to claim 1, characterized in that, In the step S4, the sensing matrix is constructed as a Toeplitz matrix, expressed as: ； Wherein: is a sensing matrix with dimensions M×N; M is the number of rows of the sensing matrix, corresponding to the observation dimension in compressive sensing; N is the number of columns of the sensing matrix, corresponding to the dimension of sparse representation; is the value of the i-th chaotic sequence generated by the fractional-order Lorenz chaotic system; And the sensing matrix should satisfy the "restricted isometry property": ； where: k is the sparsity; h k is an arbitrary k-sparse channel response vector; is the isometric constant when the sensing matrix satisfies the RIP property for the k-sparse vector; is the square of the L2 norm, that is, the sum of the squares of the vector elements; Obtain a compressed observation signal that satisfies the compressed sensing theory: ； Wherein: is the received signal sampling vector, i.e., the compressed observation signal; is the sensing matrix; h is the sparse channel response vector to be recovered; n is the additive noise.

6. A multipath effect suppression method for indoor visible light positioning according to claim 1, characterized in that In the step S6, the positioning calculation of the FPGA specifically includes the following steps: S61. Main path delay extraction: Select the delay corresponding to the component with the maximum amplitude from the reconstructed sparse channel response as the direct path delay ; S62. Distance conversion: Convert the time delay into distance according to the speed of light c , where is the time delay corresponding to the k-th light source; S63, Triangulation ranging modeling: Based on the light source coordinates and the coordinates of the receiving end , construct a geometric positioning equation system: ； S64. Coordinate calculation: Solve the equations through the Gauss-Newton iterative algorithm to obtain the spatial coordinates of the receiving end , where K≥4 is the number of effective direct paths.

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