Non-calibration wireless optical positioning method and system

Abstract

The invention discloses an uncalibrated wireless optical positioning method and system, and relates to the technical field of indoor positioning. The method comprises the following steps: acquiring optical signals of a plurality of LED light sources with known coordinates through a photoelectric detector at a receiving end, measuring the intensity of the received signals, sequencing and matching the coordinates, deducing an intensity and distance correlation formula based on a Lambert transmission model and a geometric position relationship, eliminating an unknown constant by utilizing an intensity ratio, and combining with known or unknown conditions of Lambert orders to obtain a distance value of the LED light sources. And constructing a nonlinear equation set about the position coordinates of the receiving end, and solving to obtain two-dimensional position coordinates. According to the method, Lambert model parameters and m values do not need to be calibrated in advance, the deployment and maintenance cost is reduced, 'installation and use 'is achieved, the positioning precision stability and the environment self-adaption capacity are improved, and an economic and efficient scheme is provided for practicability and large-scale indoor wireless light positioning.

Description

Technical Field

[0001] This invention relates to the field of indoor positioning technology, and in particular to a calibration-free wireless optical positioning method and system. Background Technology

[0002] With the widespread adoption of smart terminal devices, the demand for location-based services continues to grow, making indoor positioning technology a hot research topic. In complex indoor environments such as exhibition halls, warehouses, shopping malls, and underground parking lots, accurately acquiring the location information of items or staff is crucial for realizing numerous scenario-based applications.

[0003] However, the development of indoor positioning technology faces numerous challenges. While outdoor positioning systems can provide high positioning accuracy in open environments, factors such as wall obstructions and interference from electronic devices can severely affect their functionality in indoor scenarios, failing to meet the demand for precise positioning. Furthermore, the Global Positioning System (GPS) struggles to penetrate walls, further highlighting the importance of positioning technologies specifically designed for indoor environments.

[0004] With the rapid popularization of LED lighting technology, wireless optical positioning (WOP) technology based on indoor visible light communication (VLC) has gradually entered the research field. This technology can achieve indoor positioning using LED lighting fixtures, and with its advantages of high accuracy, low deployment cost, high security, and short response time, it has become a highly promising candidate technology in the field of indoor positioning. Currently, indoor wireless optical positioning technologies mainly include various implementation methods based on images, received signal strength (RSS), time of arrival (TOA) / time difference of arrival (TDOA), and angle of arrival (AOA) / angle difference of arrival (ADOA). Among them, WOP systems based on TOA / TDOA, AOA / ADOA, and images require additional auxiliary equipment to obtain time, angle, or image information, placing high demands on experimental equipment; while WOP systems based on received signal strength (RSS) can conveniently obtain RSS values ​​through photodiodes (PDs), offering a cost advantage and wider application.

[0005] However, existing WOP systems based on RSS trilateration have significant limitations in practical applications. Before operation, they require data acquisition through geometric measurements and cumbersome calibration procedures, resulting in high time and labor costs. Specifically, traditional RSS-calibrated trilateration systems require two core calibration steps before each positioning operation: The first part involves calibrating the constant parameters in the Lambertian model. Since LEDs generally exhibit beam divergence characteristics, they are typically modeled as Lambertian sources. The calibration process requires measuring a reference power directly beneath at least one LED, and then further calibrating the LED's emission power based on this reference power. The calibration method relies on prior information such as the physical area (A) of the PD detector, the optical concentrator gain (g), the optical filter gain (T), and the Lambertian order (m). However, this calibration method has significant shortcomings: the reference power measurement operation before positioning not only increases the manpower and time costs of system deployment but is also susceptible to environmental interference, equipment installation deviations, and differences in human operation, introducing additional measurement errors.

[0006] The second part involves calibrating the order *m* of the Lambertian model. With *m* unknown, the functional relationship needs to be fitted by changing the emission angle and collecting the corresponding received power, while maintaining a fixed incident angle and LED-PD spacing. Then, the value of m is determined. A common approach is to control the incident angle to be 90° and the LED-PD spacing d equal to the vertical height h. In this case, only m is a variable, and calibration is achieved through data fitting. However, this process relies on the collection of a large amount of experimental data, which is cumbersome, time-consuming, and labor-intensive, severely restricting the rapid deployment and practical application of the system.

[0007] After completing the above two calibration steps, the system can obtain the received power of the three LEDs via the PD, calculate the distance from each LED to the receiver, and finally calculate the actual position of the receiver based on the trilateration principle (such as the least squares method). Besides the problems inherent in the calibration process itself, the existing technology also has the following shortcomings: First, the system deployment cost is high: it relies on manual pre-measurement of reference power to calibrate relevant parameters, requires dedicated personnel to operate on-site, and involves a large investment of manpower and time, which is not conducive to the large-scale and rapid deployment of the system.

[0008] Second, it is inefficient in practice: the calibration of the order m of the Lambert model requires multiple adjustments to the emission angle, collection of power data and curve fitting, which takes a long time to prepare for the experiment and seriously affects the system's startup efficiency and practical experience.

[0009] Third, positioning accuracy is affected: the on-site acquisition process of reference power is easily affected by environmental interference, equipment installation errors and human operation factors, which leads to deviations in calibration parameters. These deviations will accumulate and propagate in subsequent distance estimation and position calculation, ultimately reducing the overall positioning accuracy.

[0010] Fourth, insufficient flexibility and adaptability: The system relies heavily on pre-calibrated fixed parameters. When the lamps age, the performance of optical components drifts, or the deployment environment changes, the original calibration parameters become invalid, and the entire calibration process needs to be re-executed. It lacks the ability to update parameters online and is difficult to adapt to actual application scenarios with long-term operation or dynamic environmental changes.

[0011] Therefore, developing an indoor visible light positioning method that requires no complex pre-calibration, has low deployment costs, and is robust has significant practical implications and application value. Summary of the Invention

[0012] Therefore, this invention aims to solve the technical problems of existing wireless optical positioning systems based on received signal strength (RSS) that rely on manual pre-measurement and calibration of the constant parameters and order of the Lambertian model, have high deployment and maintenance costs, have cumbersome and time-consuming calibration processes, have positioning accuracy that is easily affected by measurement errors, and have insufficient adaptability to environmental and hardware changes. Thus, this invention provides a calibration-free wireless optical positioning method and system.

[0013] Specifically, the calibration-free wireless optical positioning method includes the following steps: Step S1: The receiver acquires light signals from multiple known coordinates of LED light sources through a photodetector and measures the received signal intensity value corresponding to each light signal; Step S2: Sort the received signal strength values ​​according to their amplitude, and identify the LED light source coordinates corresponding to each received signal strength value based on the time division multiplexing mechanism; Step S3: Based on the Lambertian transmission model and the geometric positional relationship between the LED light source and the photodetector, derive the correlation formula between the received signal strength and the distance between the LED light source and the receiver. Use the ratio of the received signal strength to eliminate unknown constant parameters and construct a system of nonlinear equations. When the Lambertian order m is known, the variables to be solved in the system of nonlinear equations include the receiver position coordinates; when the Lambertian order m is unknown, the variables to be solved in the system of nonlinear equations include both the receiver position coordinates and the Lambertian order m. Step S4: Solve the nonlinear equations numerically to obtain the two-dimensional position coordinates of the receiving end.

[0014] In one embodiment of the present invention, the geometrical positional relationship between the LED light source and the photodetector satisfies: ,in The straight-line distance between the LED light source and the receiver. The emission angle of the LED light source. The incident angle of the photodetector. The vertical distance between the plane containing the LED light source and the plane containing the photodetector.

[0015] In one embodiment of the present invention, the relationship between the received signal strength and the distance between the LED light source and the receiving end is as follows: ,in The received signal strength is represented by C, which is a constant parameter in the Lambertian transmission model after integrating the physical characteristics of the LED light source and the photodetector, and m is the Lambertian order. The straight-line distance between the LED light source and the receiver. The vertical distance between the plane containing the LED light source and the plane containing the photodetector.

[0016] In one embodiment of the present invention, when the Lambertian order m is known, the system needs to deploy at least three LED light sources with known coordinates; if three LED light sources with known coordinates are actually deployed, then the receiver position coordinates are used. The only variable to be solved Construct a system of nonlinear equations in the following form: , , in, , , These are the first three received signal strength values ​​after sorting, and ; , , These are the received signal strength values. , , The distance from the corresponding LED light source to the receiving end.

[0017] In one embodiment of the present invention, when the Lambertian order m is unknown, the system needs to deploy at least four LED light sources with known coordinates; if four LED light sources with known coordinates are actually deployed, then the receiver position coordinates are used. The Lambert order m is a common variable to be solved. Construct a system of nonlinear equations in the following form: , , , in, , , , The received signal strength values ​​are sorted, and ; , , , These are the received signal strength values. , , , The distance from the corresponding LED light source to the receiving end.

[0018] In one embodiment of the present invention, the method for numerically solving the nonlinear equations to obtain the two-dimensional position coordinates of the receiving end is as follows: S41: Initialize the iteration parameters, including: Setting initial estimates for the variables to be solved: When the Lambert order m is known, the only variable to be solved is the receiver position. Its initial estimate is set as When the Lambert order m is unknown, the variables to be solved are Its initial estimate is set as , is the initial value of the Lambert order; Initialize the iterative calculator Set the maximum number of iterations to Initial value of damping factor adjustment coefficient First convergence threshold Second convergence threshold and the initial coefficient of the damping factor ; Based on the current initial estimate Calculate the objective function vector Jacobian matrix Then, the approximate value of the Hessian matrix is ​​calculated. With gradient vector Wherein, when the Lambert order m is known, the objective function vector When the Lambert order m is unknown, the objective function vector ; Initialize damping factor , For matrix The diagonal elements; S42: Set the first convergence condition to the gradient vector. The infinite norm satisfies , This indicates taking the gradient vector. The maximum value among the absolute values ​​of all components; determine whether the first convergence condition is satisfied: If so, proceed to step S46; If not, further determine the current iteration number. Is it less than ; like Then proceed to step S46; like Execute step S43; S43: Order Construct a system of linear equations Solving this system of equations yields the step size vector. ,in It is the identity matrix; S44: Calculate the step size vector step size norm The second convergence condition is set as follows: Determine whether the second convergence condition is met: If so, proceed to step S46; If not, based on the current estimate With step vector Calculate candidate estimates : According to the candidate estimates and current estimate Calculate the ratio of the actual decrease to the model-predicted decrease. : ,in Let be the quadratic model function at the current location, and its expression is: ; S45: According to The value determines whether to accept the update and adjust the parameters accordingly: like This indicates that the iteration is valid and accepts the candidate position update: Let Recalculate the objective function vector Jacobian matrix Hessian matrix approximation With gradient vector Adjusting the damping factor Return to step S42 to re-perform the convergence judgment; like This indicates that the iteration is invalid, so the candidate position update is rejected, and the current position estimate is maintained. Unchanged; Damping factor adjusted And update the damping factor adjustment coefficient. Return to step S42 to re-perform the convergence judgment; S46: Output the current estimated value The position coordinates in the image represent the final horizontal coordinate positioning result of the receiving end.

[0019] In one embodiment of the present invention, when the Lambert order m is unknown, the iterative update method for the Lambert order m is as follows: S401: Define the search range for the Lambert order m. Search step size and correction factor ; S402: In the search range Within, with the search step size Iterate through the candidate order values ​​and perform the following steps for each candidate order value: Two different combinations of LED light sources are selected, and corresponding nonlinear equations are constructed based on the current candidate order. The Levenberg-Marquardt algorithm is used to solve the equations to obtain the two preliminary position estimates, and the Euclidean distance between the two preliminary position estimates is calculated. S403: Select a candidate order value that minimizes the Euclidean distance. Through formula Obtain the optimized Lambert order And use it as the initial value of the Lambert order in the next iteration calculation.

[0020] In one embodiment of the present invention, in the Lambertian transmission model, the expression for the line-of-sight transmission channel gain of wireless light from the LED light source to the photodetector is: , Where m is the Lambertian order, d is the straight-line distance between the LED light source and the photodetector, and A is the physical area of ​​the photodetector. The emission angle of the LED light source. The incident angle of the photodetector. The field-of-view threshold of the photodetector. For optical filter gain, This refers to the gain of the optical concentrator.

[0021] In one embodiment of the present invention, all the LED light sources are fixedly installed on the same horizontal plane, and the photodetector is placed horizontally, maintaining a fixed vertical height with the LED light sources.

[0022] Based on the same inventive concept, the present invention also provides a calibration-free wireless optical positioning system, comprising: an optical signal acquisition and intensity measurement module, an intensity sorting and light source coordinate matching module, an equation system construction module, and a positioning result output module; The optical signal acquisition and intensity measurement module is used to acquire optical signals from LED light sources at multiple known coordinates and measure the received signal intensity value corresponding to each optical signal. The intensity sorting and light source coordinate matching module is used to sort the received signal intensity values ​​according to their amplitude and identify the LED light source coordinates corresponding to each received signal intensity value based on the time division multiplexing mechanism. The equation system construction module is used to derive the correlation formula between the received signal strength and the distance between the LED light source and the receiver based on the Lambertian transmission model and the geometric positional relationship between the LED light source and the photodetector. It then uses the ratio of the received signal strength to eliminate unknown constant parameters and construct a nonlinear equation system. When the Lambertian order m is known, the unsolved variables of the nonlinear equation system include the receiver position coordinates; when the Lambertian order m is unknown, the unsolved variables of the nonlinear equation system include both the receiver position coordinates and the Lambertian order m. The positioning result output module is used to numerically solve the nonlinear equations to obtain the two-dimensional position coordinates of the receiving end.

[0023] Compared with the prior art, the above-described technical solution of the present invention has the following advantages: This invention constructs a nonlinear equation system that integrates the receiver location and Lambertian model parameters. Combined with the Levenberg-Marquardt algorithm and an ergonomic verification mechanism for unknown Lambertian orders, it completely eliminates the tedious manual calibration steps required by traditional positioning systems, such as measuring reference power directly below the LED and acquiring data from multiple angles to fit the Lambertian order. This significantly reduces the manpower and time costs of system deployment and maintenance, enabling quick "plug-and-play" startup. It also avoids errors introduced by manual measurement from the source, improving the stability of positioning accuracy. Furthermore, by simultaneously solving key parameters during each positioning operation, the system can adapt to environmental and hardware changes such as light source aging and optical component performance drift, exhibiting stronger long-term robustness and reliability. Moreover, without requiring additional calibration operations, it maintains positioning accuracy comparable to traditional manual calibration schemes, providing an economical and efficient solution for the practical and large-scale application of indoor wireless optical positioning technology. Attached Figure Description

[0024] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0025] Figure 1 This is a flowchart illustrating a calibration-free wireless optical positioning method provided in an embodiment of the present invention; Figure 2 This is a flowchart comparing existing calibration positioning technology solutions with the calibration-free positioning technology solution proposed in this invention. Figure 3 This is a comparison chart of the true coordinates of each test point and the positioning results of the uncalibrated WOP system of this invention, under the condition that the Lambert order m is known. Figure 4 This is a comparison chart of the actual coordinates of each test point and the positioning results of the traditional manually calibrated WOP system and the uncalibrated WOP system of this invention, under the condition that the Lambert order m is unknown. Figure 5 The curves show a comparison of the cumulative distribution function (CDF) of positioning errors between the traditional manually calibrated WOP system and the non-calibrated WOP system of this invention. Figure 6 This is a schematic diagram of the structure of a calibration-free wireless optical positioning system provided in an embodiment of the present invention.

[0026] Explanation of the reference numerals in the instruction manual: 1. Optical signal acquisition and intensity measurement module; 200. Intensity sorting and light source coordinate matching module; 300. Equation system construction module; 400. Positioning result output module. Detailed Implementation

[0027] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0028] Example 1: Reference Figure 1 As shown, the present invention provides a calibration-free wireless optical positioning method, which specifically includes the following steps: Step S1: The receiver acquires light signals from multiple known coordinates of LED light sources through a photodetector and measures the received signal intensity value corresponding to each light signal; Step S2: Sort the received signal strength values ​​according to their amplitude, and identify the LED light source coordinates corresponding to each received signal strength value based on the time division multiplexing mechanism; Step S3: Based on the Lambertian transmission model and the geometric positional relationship between the LED light source and the photodetector, derive the correlation formula between the received signal strength and the distance between the LED light source and the receiver. Use the ratio of the received signal strength to eliminate unknown constant parameters and construct a system of nonlinear equations. When the Lambertian order m is known, the variables to be solved in the system of nonlinear equations include the receiver position coordinates; when the Lambertian order m is unknown, the variables to be solved in the system of nonlinear equations include both the receiver position coordinates and the Lambertian order m. Step S4: Numerically solve the nonlinear equations to obtain the two-dimensional position coordinates of the receiver. The entire positioning process does not require pre-calibration of the Lambert model parameters or the received signal strength reference value.

[0029] Furthermore, in step S1, the transmitter of the indoor wireless optical positioning system is constructed, using multiple identical LED light sources as positioning beacons. All LED light sources are non-collinearly distributed and fixedly installed on the same horizontal plane of the ceiling. When the Lambertian order m is known, at least three LED light sources need to be deployed; when m is unknown, at least four LED light sources need to be deployed.

[0030] The coordinates of each LED light source are pre-calibrated and stored, and the calibration results are also stored. (Note: The original text contains some inconsistencies and inconsistencies. A more accurate translation would require the full context.) The three-dimensional coordinates of each LED light source are ,in Its horizontal coordinate, For vertical height, and all LED light sources The values ​​are the same.

[0031] The transmitter employs a unified driving scheme, where a PC controls an arbitrary waveform generator (AWG) to generate an on / off keying (OOK) modulation signal. This modulation signal is then superimposed on a DC bias signal by a bias T-shaped circuit to drive all LED light sources to emit light, ensuring the emission power of each LED light source. Maintain consistency.

[0032] The receiving end is equipped with a horizontally placed photodetector (PD), with its receiving surface parallel to the ground and a fixed installation height (0 cm for the z-axis in this embodiment). The field of view of the photodetector must meet the following requirements. , The incident angle of the photodetector. This is the field-of-view threshold of the photodetector. Furthermore, the receiver does not have an optical filter or optical concentrator configured, thus satisfying... , For optical filter gain, This refers to the gain of the optical concentrator.

[0033] Vertical height between the plane where the LED light source is located and the plane where the PD is located During system deployment, ensure that the optical links between all LED light sources and photodetectors meet the line-of-sight transmission requirements and that there is no transmission interference caused by obstructions.

[0034] The receiver captures the light signals emitted by the four LED light sources through a photodetector, converts the light signals into corresponding electrical signals, and after signal amplification, extracts and measures the raw received signal strength (RSS) data corresponding to each LED light source, i.e., the raw received power data.

[0035] Further, in step S2, the multiple received signal strength values ​​measured in step S1 are sorted in descending order of amplitude to obtain the sorted results. Based on the time-division multiplexing mechanism, the LED light source corresponding to each sorted received signal strength value is identified, and the known three-dimensional coordinates of each LED light source are obtained. .

[0036] Further, in step S3, in the Lambertian transmission model, the expression for the line-of-sight transmission channel gain of wireless light from the LED light source to the photodetector is: , Where m is the Lambert order, its expression is: , denoted as the half-power angle of the LED light source; d is the straight-line distance between the LED light source and the photodetector; and A is the physical area of ​​the photodetector. The emission angle of the LED light source.

[0037] Since both the LED light source and the photodetector are horizontally placed, they satisfy the following geometric positional relationship: This system does not use optical filters or concentrators, i.e. Based on the Lambertian transmission model, the relationship between the received signal strength and the distance between the LED light source and the receiver can be derived as follows: ,in The received signal strength is represented by C, which is a constant parameter in the Lambertian transmission model after integrating the physical characteristics of the LED light source and the photodetector, and m is the Lambertian order. The straight-line distance between the LED light source and the receiver. The vertical distance between the plane containing the LED light source and the plane containing the photodetector.

[0038] like Figure 2 As shown, in traditional calibration schemes, determining the constant parameter C requires measuring the reference power directly below the LED light source and then using the correlation between the received power and the reference power to complete the calibration. This process suffers from high manual costs and is prone to introducing errors. In contrast, this invention proposes a calibration-free positioning method that eliminates the need for explicit calibration of the constant parameter C by manually measuring the reference power. The position of the receiver can be calculated directly based on the raw data of the received signal strength, significantly simplifying the positioning process.

[0039] When the Lambert order m is known, if three LED light sources with known coordinates are actually deployed, then the receiver position coordinates are used. The only variable to be solved By combining the above correlation formula with the ratio of received signal strength, a system of nonlinear equations is constructed. This system of equations establishes an equivalence relationship between the ratio of the difference in received signal strength and the ratio of the difference in distance, naturally eliminating the influence of the unknown constant parameter C. The specific form is as follows: , , in, , , These are the top three received signal strength values ​​sorted in descending order of amplitude; These are the received signal strength values. , , The distance from the corresponding LED light source to the receiver, , The horizontal coordinates corresponding to the LED light source; The horizontal coordinate of PD The vertical distance between the plane containing the LED light source and the plane containing the photodetector.

[0040] When the Lambertian order m is unknown, if four LED light sources with known coordinates are actually deployed, then the receiver position coordinates are used. The Lambert order m is a common variable to be solved. Based on the correlation formula between received signal strength and the distance between the LED light source and the receiver. By combining the ratio of received signal strengths, a system of three nonlinear equations can be constructed. This system establishes equivalent constraints through the ratio of the difference in received signal strengths to the ratio of the difference in distance, which naturally cancels out the influence of the unknown constant parameter C. Simultaneously, it achieves a joint solution for the position coordinates and the Lambert order, as shown in the following form: , , , in, , , , These are the received signal strength values ​​sorted in descending order of amplitude. , , , These are the received signal strength values. , , , The distance from the corresponding LED light source to the receiver is calculated using the same formula as above.

[0041] Further, in step S4, the Levenberg-Marquardt algorithm is used to numerically solve the nonlinear equations to obtain the two-dimensional position coordinates of the receiving end. The specific process is as follows: S41: Initialize the iteration parameters, including: Set initial estimates for the variables to be solved: When the Lambert order m is known, the only variable to be solved is the position of the receiver. Its initial estimate is set as The initial position can be reasonably preset according to the distribution range of the LED light source; When the Lambert order m is unknown, the variable to be solved is Its initial estimate is set as , is the initial value of the Lambert order; Initialize the iterative calculator Set the maximum number of iterations to Initial value of damping factor adjustment coefficient First convergence threshold Second convergence threshold and the initial coefficient of the damping factor ; Based on the current initial estimate Calculate the objective function vector Jacobian matrix Then, the approximate value of the Hessian matrix is ​​calculated. With gradient vector Wherein, when the Lambert order m is known, the objective function vector When the Lambert order m is unknown, the objective function vector ; Initialize damping factor , For matrix The diagonal elements; S42: Set the first convergence condition to the gradient vector. The infinite norm satisfies , This indicates taking the gradient vector. The maximum value among the absolute values ​​of all components; determine whether the first convergence condition is satisfied: If so, proceed to step S46; If not, further determine the current iteration number. Is it less than ; like Then proceed to step S46; like Execute step S43; S43: Order Construct a system of linear equations Solving this system of equations yields the step size vector. ,in It is the identity matrix; S44: Calculate the step size vector step size norm The second convergence condition is set as follows: Determine whether the second convergence condition is met: If so, proceed to step S46; If not, based on the current estimate With step size vector Calculate candidate estimates : According to the candidate estimates and current estimate Calculate the ratio of the actual decrease to the model-predicted decrease. : ,in Let be the quadratic model function at the current location, and its expression is: ; S45: According to The value determines whether to accept the update and adjust the parameters accordingly: like This indicates that the iteration is valid and accepts the candidate position update: Let Recalculate the objective function vector Jacobian matrix Hessian matrix approximation With gradient vector Adjusting the damping factor Return to step S42 to re-perform the convergence judgment; like This indicates that the iteration is invalid, so the candidate position update is rejected, and the current position estimate is maintained. Unchanged; Damping factor adjusted And update the damping factor adjustment coefficient. Return to step S42 to re-perform the convergence judgment; S46: Output the current estimated value The position coordinates in the image represent the final horizontal coordinate positioning result of the receiving end.

[0042] Furthermore, when the Lambert order m is unknown, the iterative update method for the Lambert order m is as follows: S401: Define the search range for the Lambert order m. Search step size and correction factor ; S402: In the search range Within, with the search step size Iterate through the candidate order values ​​and perform the following steps for each candidate order value: Two different combinations of LED light sources are selected, and a set of corresponding nonlinear equations is constructed based on the current candidate order. The Levenberg-Marquardt algorithm is used to solve the equations to obtain the two sets of preliminary position estimates, and the Euclidean distance between the two sets of preliminary position estimates is calculated. S403: Select a candidate order value that minimizes the Euclidean distance. Through formula Obtain the optimized Lambert order And use it as the initial value of the Lambert order in the next iteration calculation.

[0043] To fully verify the positioning performance of the indoor wireless optical calibration-free positioning method proposed in this invention, a closed indoor experimental platform was built. The experimental environment was a closed space with dimensions of 2m × 2m × 1.9m (length × width × height). Four identical LED positioning beacons were deployed at the transmitting end, non-collinearly distributed and fixed on the ceiling plane, with preset coordinates of (50, 50, 190), (50, 150, 190), (150, 50, 190), and (150, 150, 190) (unit: cm).

[0044] The transmitter uses a PC-controlled arbitrary waveform generator (AWG) to generate an on / off keying (OOK) modulation signal. This signal, after being superimposed with a DC bias signal by a bias T-shaped circuit, provides a uniform driving condition for all LEDs, ensuring the consistency of the emitted signal characteristics of each LED. The receiver uses a photodiode (PD) as the optical signal detection device. Its receiving surface is parallel to the ground, with an installation height of 0cm (z-axis coordinate 0), and a field of view parameter set to 60°. The horizontal coordinate of the receiver is... The core quantity to be estimated.

[0045] To rigorously verify the system's effectiveness under conditions without prior calibration, the optical filter gain was adjusted in the experiment. Optical concentrator gain LED light source emission power Key physical parameters such as the effective receiving area A of the PD and the order m of the Lambertian model are all considered unknowns. The electrical signal output by the PD is acquired by a real-time oscilloscope and then transmitted to a computer for offline data processing and positioning calculation.

[0046] In terms of test design, six test points were selected to construct an evaluation sample set. The test area covered half of a square area (a triangular plane area) of [0,100]cm × [0,100]cm. Given the symmetry of the experimental space structure, this test area (occupying 1 / 8 of the total room area) is sufficiently representative, and its test results can equivalently reflect the positioning performance of the system throughout the entire indoor space. Each test point was repeatedly measured 15 times independently, and the average of the multiple positioning results was taken as the final positioning output for that point to reduce the impact of random errors on the evaluation results.

[0047] The experiment was conducted under a fixed LED driving voltage of 17.2V. Figure 3 and Figure 4 A visual comparison diagram of the positioning results (the horizontal and vertical axes correspond to the X and Y axes of the positioning plane, respectively, in cm).

[0048] Quantitative analysis shows that, in scenarios where the Lambertian order m is known, the average positioning error of the uncalibrated WOP system of this invention is 8.7 cm; in scenarios where the Lambertian order m is unknown, the average positioning error of the traditional manually calibrated WOP system is 10.0 cm, while the average positioning error of the uncalibrated WOP system of this invention is only 9.7 cm. The difference between the two errors is less than 0.3 cm, indicating that this invention can still maintain positioning accuracy comparable to traditional calibration schemes without any manual calibration operations.

[0049] Figure 5The curves show a comparison of the cumulative distribution function (CDF) of positioning errors between the traditional manually calibrated WOP system and the non-calibrated WOP system of this invention. The horizontal axis represents the positioning error (unit: cm), and the vertical axis represents the cumulative probability. As can be seen from the curve characteristics, the CDF curves of both systems exhibit a monotonically increasing trend, consistent with the statistical distribution law of positioning errors.

[0050] Further quantitative analysis shows that the traditional manually calibrated WOP system has a positioning error of less than 15.2 cm in 90% of the samples; while the positioning error of the calibration-free WOP system of this invention is less than 14.5 cm under the same cumulative probability, a reduction of approximately 4.6% compared to the traditional method. This result verifies the advantages of this invention in error control. The core reason is that by eliminating the on-site manual calibration step, systematic errors introduced by environmental interference, equipment installation deviations, and human operational errors are eliminated from the source, thereby improving the stability and reliability of the positioning results.

[0051] Experimental verification and analysis results show that the calibration-free wireless optical positioning system proposed in this invention has successfully replaced the independent and cumbersome manual calibration process (including the measurement of reference power directly below the LED, and the fitting of the Lambert order to multi-angle data acquisition) in the traditional WOP system by innovatively constructing a nonlinear equation system containing location information and Lambert model parameters and directly solving it using optimization algorithms such as Levenberg-Marquardt (LM).

[0052] Without incorporating any geometric measurements or model parameter calibration, the average positioning error of this system is not significantly different from that of traditional manual calibration systems, and its positioning accuracy is superior in high cumulative probability scenarios. Simultaneously, this system significantly reduces manpower and time costs during deployment and maintenance, possesses rapid deployment capabilities, and exhibits inherent online adaptive capabilities to environmental and hardware changes such as light source aging and optical component performance drift. This provides a cost-effective solution for the practical and large-scale application of indoor wireless optical positioning technology.

[0053] Furthermore, the wireless optical positioning method protected by this invention has no strong binding relationship between its core technical principle and the characteristics of optical bands. Its applicable spectral range is not limited to the visible light band, but can also be extended to other optical bands such as the infrared band, thus possessing cross-band universality and compatibility.

[0054] Example 2: like Figure 6 As shown, based on the same inventive concept as Embodiment 1, the present invention also provides a calibration-free wireless optical positioning system, including: an optical signal acquisition and intensity measurement module 100, an intensity sorting and light source coordinate matching module 200, an equation system construction module 300, and a positioning result output module 400. The optical signal acquisition and intensity measurement module 100 is used to acquire optical signals from multiple known coordinates of LED light sources and measure the received signal intensity value corresponding to each optical signal. The intensity sorting and light source coordinate matching module 200 is used to sort the received signal intensity values ​​according to their amplitude and identify the LED light source coordinates corresponding to each received signal intensity value based on the time division multiplexing mechanism. The equation system construction module 300 is used to derive the correlation formula between the received signal strength and the distance between the LED light source and the receiving end based on the Lambertian transmission model and the geometric positional relationship between the LED light source and the photodetector. It then uses the ratio of the received signal strength to eliminate unknown constant parameters and construct a nonlinear equation system. When the Lambertian order m is known, the unsolved variables of the nonlinear equation system include the receiving end position coordinates; when the Lambertian order m is unknown, the unsolved variables of the nonlinear equation system include both the receiving end position coordinates and the Lambertian order m. The positioning result output module 400 is used to numerically solve the nonlinear equation system to obtain the two-dimensional position coordinates of the receiving end.

[0055] This embodiment proposes a calibration-free wireless optical positioning system to implement the aforementioned calibration-free wireless optical positioning method. Therefore, the specific implementation of the calibration-free wireless optical positioning system can be found in the embodiment section of the aforementioned calibration-free wireless optical positioning method. For example, the optical signal acquisition and intensity measurement module 100, the intensity sorting and light source coordinate matching module 200, the equation system construction module 300, and the positioning result output module 400 are respectively used to implement steps S1 to S4 in the method described in Embodiment 1. Therefore, the specific implementation can be referred to the description of the corresponding embodiments. To avoid redundancy, it will not be repeated here.

[0056] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0057] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0058] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0059] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0060] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A calibration-free wireless optical positioning method, characterized in that, include: Step S1: The receiver acquires light signals from multiple known coordinates of LED light sources through a photodetector and measures the received signal intensity value corresponding to each light signal; Step S2: Sort the received signal strength values ​​according to their amplitude, and identify the LED light source coordinates corresponding to each received signal strength value based on the time division multiplexing mechanism; Step S3: Based on the Lambertian transmission model and the geometric positional relationship between the LED light source and the photodetector, derive the correlation formula between the received signal strength and the distance between the LED light source and the receiver. Use the ratio of the received signal strength to eliminate unknown constant parameters and construct a system of nonlinear equations. When the Lambertian order m is known, the variables to be solved in the system of nonlinear equations include the receiver position coordinates; when the Lambertian order m is unknown, the variables to be solved in the system of nonlinear equations include both the receiver position coordinates and the Lambertian order m. Step S4: Solve the nonlinear equations numerically to obtain the two-dimensional position coordinates of the receiving end.

2. The calibration-free wireless optical positioning method according to claim 1, characterized in that: The geometric positional relationship between the LED light source and the photodetector satisfies: ,in The straight-line distance between the LED light source and the receiver. The emission angle of the LED light source. The incident angle of the photodetector. The vertical distance between the plane containing the LED light source and the plane containing the photodetector.

3. The calibration-free wireless optical positioning method according to claim 1, characterized in that: The formula relating the received signal strength to the distance between the LED light source and the receiver is as follows: ,in The received signal strength is represented by C, which is a constant parameter in the Lambertian transmission model after integrating the physical characteristics of the LED light source and the photodetector, and m is the Lambertian order. The straight-line distance between the LED light source and the receiver. The vertical distance between the plane containing the LED light source and the plane containing the photodetector.

4. The calibration-free wireless optical positioning method according to claim 1, characterized in that: When the Lambert order m is known, the system needs to deploy at least three LED light sources with known coordinates; if three LED light sources with known coordinates are actually deployed, then the receiver position coordinates are used. The only variable to be solved Construct a system of nonlinear equations in the following form: ， ， in, , , These are the first three received signal strength values ​​after sorting, and ; , , These are the received signal strength values. , , The distance from the corresponding LED light source to the receiving end.

5. The calibration-free wireless optical positioning method according to claim 4, characterized in that: When the Lambertian order m is unknown, the system needs to deploy at least four LED light sources with known coordinates; if four LED light sources with known coordinates are actually deployed, then the receiver position coordinates are used. The Lambert order m is a common variable to be solved. Construct a system of nonlinear equations in the following form: ， ， ， in, , , , The received signal strength values ​​are sorted, and ; , , , These are the received signal strength values. , , , The distance from the corresponding LED light source to the receiving end.

6. The calibration-free wireless optical positioning method according to claim 5, characterized in that: The method for numerically solving the nonlinear equations to obtain the two-dimensional position coordinates of the receiving end is as follows: S41: Initialize the iteration parameters, including: Setting initial estimates for the variables to be solved: When the Lambert order m is known, the only variable to be solved is the receiver position. Its initial estimate is set as When the Lambert order m is unknown, the variables to be solved are Its initial estimate is set as , is the initial value of the Lambert order; Initialize the iterative calculator Set the maximum number of iterations to Initial value of damping factor adjustment coefficient First convergence threshold Second convergence threshold and the initial coefficient of the damping factor ; Based on the current initial estimate Calculate the objective function vector Jacobian matrix Then, the approximate value of the Hessian matrix is ​​calculated. With gradient vector Wherein, when the Lambert order m is known, the objective function vector When the Lambert order m is unknown, the objective function vector ; Initialize damping factor , For matrix The diagonal elements; S42: Set the first convergence condition to the gradient vector. The infinite norm satisfies , This indicates taking the gradient vector. The maximum value among the absolute values ​​of all components; determine whether the first convergence condition is satisfied: If so, proceed to step S46; If not, further determine the current iteration number. Is it less than ; like Then proceed to step S46; like Execute step S43; S43: Order Construct a system of linear equations Solving this system of equations yields the step size vector. ,in It is the identity matrix; S44: Calculate the step size vector step size norm The second convergence condition is set as follows: Determine whether the second convergence condition is met: If so, proceed to step S46; If not, based on the current estimate With step size vector Calculate candidate estimates : According to the candidate estimates and current estimate Calculate the ratio of the actual decrease to the model-predicted decrease. : ,in Let be the quadratic model function at the current location, and its expression is: ; S45: According to The value determines whether to accept the update and adjust the parameters accordingly: like This indicates that the iteration is valid and accepts the candidate position update: Let Recalculate the objective function vector Jacobian matrix Hessian matrix approximation With gradient vector Adjusting the damping factor Return to step S42 to re-perform the convergence judgment; like This indicates that the iteration is invalid, so the candidate position update is rejected, and the current position estimate is maintained. Unchanged; Damping factor adjusted And update the damping factor adjustment coefficient. Return to step S42 to re-perform the convergence judgment; S46: Output the current estimated value The position coordinates in the image represent the final horizontal coordinate positioning result of the receiving end.

7. The calibration-free wireless optical positioning method according to claim 6, characterized in that: When the Lambert order m is unknown, the iterative update method for the Lambert order m is as follows: S401: Define the search range for the Lambert order m. Search step size and correction factor ; S402: In the search range Within, with the search step size Iterate through the candidate order values ​​and perform the following steps for each candidate order value: Two different combinations of LED light sources are selected, and corresponding nonlinear equations are constructed based on the current candidate order. The Levenberg-Marquardt algorithm is used to solve the equations to obtain the two preliminary position estimates, and the Euclidean distance between the two preliminary position estimates is calculated. S403: Select a candidate order value that minimizes the Euclidean distance. Through formula Obtain the optimized Lambert order And use it as the initial value of the Lambert order in the next iteration calculation.

8. The calibration-free wireless optical positioning method according to claim 1, characterized in that: In the Lambertian transmission model, the expression for the line-of-sight transmission channel gain of wireless light from the LED light source to the photodetector is: ， Where m is the Lambertian order, d is the straight-line distance between the LED light source and the photodetector, and A is the physical area of ​​the photodetector. The emission angle of the LED light source. The incident angle of the photodetector. The field-of-view threshold of the photodetector. For optical filter gain, This refers to the gain of the optical concentrator.

9. The calibration-free wireless optical positioning method according to claim 1, characterized in that: All the LED light sources are fixedly installed on the same horizontal plane, and the photodetector is placed horizontally, maintaining a fixed vertical height with the LED light sources.

10. A calibration-free wireless optical positioning system, characterized in that, Includes the following modules: The optical signal acquisition and intensity measurement module is used to acquire optical signals from LED light sources at multiple known coordinates and measure the received signal intensity value corresponding to each optical signal. The intensity sorting and light source coordinate matching module is used to sort the received signal intensity values ​​according to their amplitude and identify the LED light source coordinates corresponding to each received signal intensity value based on the time division multiplexing mechanism. The equation system construction module is used to derive the correlation formula between the received signal strength and the distance between the LED light source and the receiver based on the Lambertian transmission model and the geometric positional relationship between the LED light source and the photodetector. It then uses the ratio of the received signal strength to eliminate unknown constant parameters and construct a nonlinear equation system. When the Lambertian order *m* is known, the variables to be solved in the nonlinear equation system include the receiver's position coordinates; when the Lambertian order *m* is unknown, the variables to be solved in the nonlinear equation system include both the receiver's position coordinates and the Lambertian order *m*. And a positioning result output module, which is used to numerically solve the nonlinear equations to obtain the two-dimensional position coordinates of the receiving end.

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