LED attitude angle offset estimation method and visible light positioning method

Abstract

The invention discloses an LED attitude angle offset estimation method based on an indoor visible light environment and a positioning system. According to the method, a visible light propagation model containing deviation of an LED direction angle alpha and an inclination angle beta is constructed, optical power data of an indoor point to be measured are collected, and an error function of a measured value and an ideal model is established; a sequential quadratic programming (SQP) or L-BFGS-B optimization algorithm is introduced to solve a nonlinear minimization problem with constraints, and an attitude angle offset solution set is obtained; searching a maximum optical power point by adopting a particle swarm optimization (NA-PSO) algorithm of adaptive inertia weight, and determining an azimuth angle alpha; and finally, a generative fingerprint database is constructed in combination with the model, and visible light positioning is realized through a weighted k-nearest neighbor (WKNN) algorithm. According to the method, angle information is fused, the problems that in a traditional fingerprint database positioning method, the data volume collected by an offline fingerprint database is large, and attitude angle estimation in a model is fuzzy are solved, the attitude angle estimation precision and the visible light positioning precision in the complex indoor environment are remarkably improved, and the method has high robustness.

Description

Technical Field

[0001] This invention relates to the field of indoor visible light positioning, and in particular to a method for improving the accuracy of attitude angle offset estimation for LEDs. Specifically, this invention focuses on improving positioning accuracy in indoor visible light environments by using multiple algorithms to estimate the attitude angle offset of indoor LEDs and incorporating the estimated angle offset into a Lambertian model. Background Technology

[0002] With the rapid development of IoT technology and intelligent systems, indoor positioning technology has become an indispensable key technology in modern life and industrial applications. Compared with traditional outdoor positioning (such as GPS), the complexity and diversity of indoor environments make GPS unsuitable for indoor use. In recent years, visible light positioning (VLP) technology has gradually become a research hotspot due to its advantages of high accuracy, low power consumption, and no electromagnetic interference. Compared with traditional radio wave positioning technology, visible light positioning uses LED lights as a signal source and achieves centimeter-level or even higher positioning accuracy through methods such as received signal strength (RSS), time of arrival (TOA), angle of arrival (AOA), and end-to-end prediction based on neural networks. However, in practical applications, the non-uniformity of light intensity distribution, multipath interference, and noise have a significant impact on positioning accuracy, leading to large deviations or instability in positioning results. This accuracy problem not only limits the widespread application of visible light positioning technology but may also seriously affect user experience and system reliability in critical scenarios. Therefore, finding methods to improve indoor positioning accuracy in practical application scenarios is particularly urgent.

[0003] In his paper "Indoor visible light localization algorithm based on received signal strength ratio with multi-directional LED array", Lixuan Wang proposed a hemispherical positioning light based on multi-directional LED (MD-LED) and a positioning algorithm based on received signal strength ratio (RSSR). The paper analyzed the impact of various LED orientation combinations on positioning accuracy and constructed a new LED lighting structure. However, such a hemispherical structure lighting fixture is not easy to implement in practical applications.

[0004] In her paper "Multi-directional LED visible light positioning based on neural network" (2024), Li Qingxiang proposed a neural network method based on received signal strength ratio (RSSR). This positioning method introduces the angular offset of the LED as a factor affecting the positioning accuracy into the neural network for training. However, it is necessary to collect a large number of RSSR values ​​of LEDs with different offset angles in the early stage.

[0005] In his paper "Fingerprint Inference Model Calibration for Visible Light Wireless Positioning" (2024), Zhou Bingpeng proposed an efficient fingerprint weighting model calibration optimization method. This method establishes a fingerprint database by offline collection of visible light received signal strength and its corresponding position and attitude labels, and constructs a Gaussian fingerprint weighting model to improve the fingerprint inference accuracy of visible light positioning. This method has higher positioning performance, but its position and attitude angle labels rely on data directly collected in the offline stage.

[0006] All the above references mention that the angular offset of LEDs is a factor affecting the positioning accuracy of visible light. The positioning accuracy can be improved by introducing the angular offset information of LEDs into neural networks or by establishing a fingerprint database. However, when acquiring the angular offset data of LEDs, direct measurement and acquisition methods are usually adopted, which faces challenges such as high data acquisition costs and insufficient scene generalization ability in actual deployment. Summary of the Invention

[0007] The main objective of this invention is to provide a method for estimating and locating the LED attitude angle offset under indoor visible light conditions, so as to effectively improve the positioning accuracy under indoor visible light conditions.

[0008] To achieve the above objectives, the method of this invention is as follows: The SQP algorithm and the L-BFGS-B algorithm are used to solve the constrained nonlinear optimization problem of visible light positioning under the Lambertian model to obtain the azimuth and tilt angles. Then, NA-PSO (Nonlinear Adaptive Particle Swarm Optimization) is used to fix the azimuth direction and achieve the final angle offset estimation. NA-PSO improves the traditional particle swarm optimization (PSO) algorithm used in visible light positioning by introducing nonlinear inertial weights and dynamic learning factors, significantly improving the convergence speed and global search capability of the optimization process. The angle offset estimate is then introduced into the Lambertian model and the Wknn algorithm is used to complete the positioning operation, thereby improving positioning accuracy.

[0009] The specific steps of the method of the present invention are as follows:

[0010] Step 1: Select the visible light propagation model P that includes the LED attitude angle offset. r(α, β, x, y, z), where α is the direction angle offset, β is the tilt angle offset, where α is the angle between the projection of the LED normal vector onto the XY axis and the x-axis, β is the angle between the LED normal vector and the z-axis, and (x, y, z) are the coordinates of the point to be measured where the PD (PhotoDiode) is located;

[0011] The visible light propagation model is as follows:

[0012]

[0013] Where m is the Lambert scattering coefficient, P t Let d be the LED emitted light power, d be the distance from the LED to the PD, and θ0 be the LED attitude angular offset. This parameter needs to be estimated in conjunction with the visible light received signal strength at the PD. θ+θ0 is the angle between the LED normal vector and the PD-to-LED direction vector. c The scattering coefficient m is the maximum field of view (FOV) of the PD, and is determined by the half-power intensity angle φ of the LED. 1 / 2 The decision, that is;

[0014]

[0015] The distance d from a measurement point on an indoor plane to the LED is expressed as:

[0016] The coordinates of the measurement point are (x, y, z), and the coordinates of the LED are (x, y, z). LED y LED , z LED )

[0017] Step 2: Set the space to be located S(0 <x s <x max , 0 <y s <y max , 0 <z s <z max A position coordinate (x, y, z) is generated in space S. The optical power value at the (x, y, z) coordinate is measured by PD to obtain the RSS. mea (x, y, z), where the position coordinates satisfy 0. <x<x s ,0 <y<y s , 0 <z<z s ;

[0018] Step 3: Based on the ideal visible light model P r Calculate the ideal optical power P at the position (x, y, z) given (α, β, x, y, z). r ;

[0019] Step 4: Select the discrimination criterion, based on the difference between the measured value and the ideal calculated value at the calculated location coordinates ||P r(α，β) -RSS mea || 2 <σ, calculate the solution set of (α, β) {(α1, β1), (α2, β2), ..., (α n ,β n )}, where σ is the tolerance threshold;

[0020] The problem (α, β) is subject to nonlinear constraints and boundary constraints. The solution problem is essentially a nonlinear optimization problem with constraints. The goal is to minimize the error by optimizing (α, β). Due to the nonlinear characteristics of the constraints, traditional linear optimization methods are difficult to handle, and the error model becomes more complex. By introducing the SQP method or the L-BFGS-B algorithm, the problem of minimizing light intensity error with nonlinear constraints can be solved efficiently.

[0021] By introducing the SQP (Sequential Quadratic Programming) method, the problem of minimizing light intensity error with nonlinear constraints can be solved efficiently.

[0022] To solve the above constrained nonlinear optimization problem, the Lagrangian function is introduced:

[0023]

[0024] Where λ is the Lagrange multiplier for equality constraints, and μ i Let I be the Lagrange multipliers of the inequality constraints, and let c be the set of indices of the inequality constraints. i (x) denotes the boundary inequality constraint;

[0025] The SQP method must satisfy the KKT conditions of the optimization problem. The following are necessary conditions for the optimization problem (and sufficient conditions for convex problems):

[0026]

[0027] In each iteration of SQP, the optimization variables are updated through the following steps: a first-order Taylor expansion of the nonlinear constraints is performed to obtain linearized constraints. Under the linearized constraints, the quadratic approximation of minimizing the Lagrange function can be expressed as:

[0028]

[0029] Where p = xx k It refers to the search direction, H. k The objective function yields an approximation of the Hessian matrix, and the search direction p is obtained by solving the QP subproblem. kUpdate and optimize variables:

[0030] x k+1 =x k +α k p k

[0031] Where α k It is the step size factor, which is used to check the current solution x after each iteration. k+1 Does it meet the KKT conditions or does it conform to the requirements? If the condition is met, the iteration stops; otherwise, the iteration continues. ε is a preset tolerance.

[0032] Through the above iterations, we can obtain the solution set {(α1, β1), (α2, β2), ..., (α...β1)} that satisfies the tolerance condition. n ,β n ));

[0033] By introducing the L-BFGS-B (Limited-memory Broyden-Fletcher-Goldfarb-Shanno with Boundary constraints) quasi-Newton algorithm, the problem of minimizing light intensity error with nonlinear constraints can be solved efficiently.

[0034] First, the gradient is projected to ensure the search direction is within the feasible region. For each variable x... i :

[0035]

[0036] Among them, l i and u i The variables x are respectively i The lower and upper bounds;

[0037] Update the approximate Hessian matrix using BFGS with limited memory. Define the difference vector:

[0038]

[0039] in, This represents the gradient of the objective function. The curvature condition must satisfy... To ensure Hessian is positive definite;

[0040] The search direction d is calculated using a double-loop recursive method. k This avoids explicitly storing the Hessian matrix. The recursive process utilizes the nearest m sets of {s} i ,y i} vectors, construct an approximation of the Hessian inverse;

[0041] Finally, the maximum feasible step size α was determined. max :

[0042]

[0043] In the interval [0, α] max The execution line search within the scope ensures that the objective function decreases sufficiently and does not go out of bounds.

[0044] Repeat the above steps until the convergence condition is met:

[0045] ||P r(α,β) -RSS mea || 2 <σ

[0046] Through the above iterations, we can obtain the solution set {(α1, β1), (α2, β2), ..., (α...β1)} that satisfies the tolerance condition. n ,β n ));

[0047] Step 5: Select a search algorithm and iteratively search for the point RSS with the maximum optical power on the positioning plane in the space S to be located. max According to the coordinates of the maximum point (x max y max , z max Determine the azimuth offset α;

[0048] Particle Swarm Optimization (PSO) is a swarm intelligence optimization algorithm that simulates the foraging behavior of bird flocks. In PSO, each particle moves through the search space, and its position and velocity are updated by the following formula:

[0049] v i (t+1)=wv i (t)+c1r i (p i (t)-x i (t))+c2r2(g i (t)-x i (t))

[0050] x i (t+1)=x i (t)+v i (t+1)

[0051] Where: w is the inertia weight, controlling the degree of influence of the particle's historical velocity; c1 and c2 are the individual learning factor and the social learning factor, respectively, controlling the particle's optimal position (pi(t)) and global optimal position (g). i The attractiveness of (t)); r1 and r2 are random numbers uniformly distributed in the range [0, 1], increasing the randomness of the algorithm; p i(t) is the best position of particle i so far; g i (t) is the global optimal position for all particles;

[0052] To avoid premature convergence of the traditional PSO algorithm in the early stages, leading to local optima, and to enhance the algorithm's global search capability, a nonlinear adaptive inertia factor is proposed. The adaptive inertia factor is adjusted dynamically based on changes in particle fitness, thereby improving the flexibility of the search process. The formula defines the average fitness and the upper and lower limits of the fitness interval in the current iteration:

[0053]

[0054]

[0055] fitA and fitB define the adjustment range in the current iteration, where fit avg The average fitness over all previous iterations, fit min The minimum fitness across all previous iterations, fit max This represents the maximum fitness across all previous iterations.

[0056] At the start of each iteration, the inertia factor is updated synchronously. If the current fitness is fit... i If the value is less than fitA, it is considered far from the optimal point, and the maximum inertia weight w is used. max If the current fitness is greater than fitB, it is considered far from the optimal point, and the maximum inertia weight w is adopted. min The current fitness is calculated according to the following formula if it is in the (fitA, fitB) interval:

[0057]

[0058] After searching the localization plane using the above nonlinear adaptive particle swarm algorithm, the coordinates of the maximum point (x) can be obtained. max y max , z max );

[0059] PD measurement points (x) max y max , z max The unit direction vector pointing to the LED can be represented as:

[0060] n PD =(sinβ) PD cosα PD sinβ PD sinα PD cosβ PD )

[0061] Where β PD α represents the angle between the PD direction vector d and the z-axis. PD The angle between the projection d′ of the PD-LED direction vector d onto the xy-plane and the x-axis is represented by the dot product formula and simplified using the cosine sum formula.

[0062] cosθ=sinβ LED sinβ PD cos(α LED -α PD )+cosβ LED cosβ PD

[0063] According to the formula, with a fixed distance and tilt angle, when α... LED =α PD When cosθ reaches its maximum value, it is derived that the azimuth angle of the LED angle offset is consistent with the direction angle at the maximum RSS point on the indoor plane. The azimuth angle value of the LED angle offset can be solved and expressed as:

[0064]

[0065] Step Six: Use azimuth offset α in the solution set {(α1, β1), (α2, β2), ..., (α... n ,β n The optimal solution min(||α-α1||) is selected from the options. 2 ,||α-α2|| 2 ,..,||α-α n || 2 ), thus obtaining an estimate of the LED attitude angle offset (α) es ,β es );

[0066] For the solution set {(α1, β1), (α2, β2), ..., (α... n ,β n Since LED light sources follow a Lambertian distribution, the symmetry of the RSS value distribution indoors under this distribution leads to multiple optimal solutions in the SQP algorithm iteration. To address this multiple-solution problem, the azimuth angle α obtained from the solution is used for selection.

[0067] min(||α-α1|| 2 ,|‖α-α2|| 2 , ..., ||α-α n || 2 )

[0068] By traversing the solution set to search for the closest solution to α, an estimate of the LED attitude angle offset (α) can be obtained. es ,β es); Attached Figure Description

[0069] Figure 1 Method and Flowchart for Estimating LED Attitude Angle Offset and Positioning in Indoor Visible Light Environment

[0070] Figure 2 Channel transmission model of indoor visible light system

[0071] Figure 3 The normal vector pointing diagram of the LED emitter with angular offset.

[0072] Figure 4 Traditional localization algorithms (WKNN, KNN), RBF neural networks, and the localization error of this method under different grid point segments at signal-to-noise ratios of 10-50 dB.

[0073] Figure 5 Graph of cumulative error distribution function between RBF neural network and the method in this paper Detailed Implementation

[0074] To better understand the technical solution of this invention, the following flowchart is attached. Figure 1 The present invention will be described in detail with reference to specific embodiments.

[0075] Step 1: For LEDs (LED1, LED2, ... LED) evenly distributed in an indoor environment n Each light source uses frequency division multiplexing (FDM) technology to achieve signal separation. Let the carrier frequency of the i-th LED be f. i Its modulated signal can be represented as:

[0076] s i (t)=A i [1+m·RSS i (t)]cos(2πf i t)

[0077] Where m is the modulation index, A i To determine the transmitted light intensity, the receiver uses a bandpass filter bank to separate the signal.

[0078]

[0079] In the formula h i (t) is the corresponding f i The impulse response of the matched filter;

[0080] Step 2: Select the visible light propagation model that includes LED attitude angle offset, i.e., the Lambertian model. See details below. Figure 2 , represented as P r(α, β, x, y, z), where α is the orientation angle offset, β is the tilt angle offset, and α is the angle between the LED normal vector projected onto the XY axis and the x-axis, and β is the angle between the LED normal vector and the z-axis. For a detailed representation of the transmitter angle offset model, see [link to relevant documentation]. Figure 3 As shown, (x, y, z) are the coordinates of the point to be measured where the PD (PhotoDiode) is located;

[0081] Step 3: Set the space to be located S(0 <x s <x max , 0 < y s <y max , 0 <z s <z max A position coordinate (x, y, z) is generated in space S. The optical power value at the (x, y, z) coordinate is measured by PD to obtain the RSS. mea (x, y, z), where the position coordinates satisfy 0. <x<x s , 0 <y<y s , 0 <z<z s ;

[0082] Step 4: Based on the ideal visible light model P r Calculate the ideal optical power Pr at the position (x, y, z) (α, β, x, y, z);

[0083] Step 5: Select the discrimination criterion, using the SQP algorithm or the L-BFGS-B algorithm, and calculate the difference between the measured value and the ideal calculated value at the calculated position coordinates, ‖P. r(α，β) -RSS mea || 2 <σ, calculate the solution set of (α, β) {(α1, β1), (α2, β2), ..., (α n ,β n )}, where σ is the tolerance threshold;

[0084] Step Six: Select the NA-PSO search algorithm and iteratively search for the point RSS with the maximum optical power on the localization plane in the space S to be localized. max According to the coordinates of the maximum point (x max y max , z max Determine the azimuth offset α;

[0085] Step 7: Use azimuth offset α in the solution set {(α1, β1), (α2, β2), ..., (α... n ,β n The optimal solution min(||α-α1||) is selected from the options. 2 ,|‖α-α2|| 2 ,…,||α-αn || 2 ), thus obtaining an estimate of the LED attitude angle offset (α) es ,β es );

[0086] Repeat steps two through seven above to obtain the estimated values ​​of the attitude angle offset of n LEDs in the positioning space S, and introduce the corresponding attitude angle offset estimates into the Lambert model to obtain the corresponding attitude angle estimation modified Lambert model for each LED.

[0087] Step 8: Calculate the indoor RSS distribution map under the current state using the attitude angle offset compensated visible light positioning model, and construct the fingerprint database:

[0088]

[0089] The fingerprint database is established without relying on offline collection, but is obtained directly based on the angle compensation model;

[0090] Step 9: Using the fingerprint database and the WkNN algorithm, indoor location estimation can be performed. The WkNN algorithm is based on the idea of ​​distance weighting. For an indoor coordinate observation point (RSS... mea，1 …RSS mea,n The RSS difference between the observation point and each coordinate in the fingerprint database is calculated and expressed using the Euclidean distance metric:

[0091]

[0092] The weights are calculated based on the inverse relationship between the points and their distances; points that are closer to each other have a higher weight. The weights can be calculated as follows:

[0093]

[0094] Where Wi is the weight of the i-th point, and Di is the distance from the i-th point to the observation point;

[0095] The location of the query point is estimated using weighted distance and position coordinates. Specifically, the coordinates of the query point are estimated based on the weighted positions of its k nearest neighbors.

[0096]

[0097] Among them, P query Pi is the estimated location of the query point, Pi is the actual location of the i-th point in the fingerprint database, and W is the estimated location of the query point. i is the weight of the i-th point. The above steps can be used to complete visible light positioning in indoor spaces.

[0098] Step 10: Divide the acquisition points into 50*50 and 100*100 areas for the positioning plane, and compare the indoor positioning accuracy of this method with that of WKNN, KNN, and RBF neural networks under different signal-to-noise ratio conditions.

[0099] Figure 4 The comparison results show that as the receiving plane grid acquisition point division is increased from 50*50 to 100*100 and the amount of fingerprint database and neural network data increases, the positioning accuracy of WKNN, KNN and RBF are all improved to a certain extent. As the signal-to-noise ratio increases from 10dB to 50dB, the accuracy of all positioning methods continues to increase, but this method is better than the other three methods under all signal-to-noise ratio conditions.

[0100] Figure 5 The CDF error cumulative distribution functions of the RBF neural network and the proposed method were plotted in an indoor environment with a signal-to-noise ratio of 20 dB. The figure shows that the cumulative error of the RBF neural network is 0.12 m at the median and 0.49 m at the 90th percentile. The proposed method improves the error by 16.7% at the median and 40.8% at the 90th percentile. The cumulative error of the proposed method is better than that of the RBF neural network.

Claims

1. A method for estimating and locating the attitude angle offset of a light-emitting diode (LED) under indoor visible light conditions, characterized in that, Includes the following steps: (1) Select the visible light propagation model P that includes the LED attitude angle offset. r (α, β, x, y, z), where α is the direction angle offset, β is the tilt angle offset, where α is the angle between the projection of the LED normal vector onto the XY axis and the x-axis, β is the angle between the LED normal vector and the z-axis, and (x, y, z) are the coordinates of the point to be measured where the PD (PhotoDiode) is located; (2) Set the space to be located S(0 <x s <x max ,0 <y s <y max 0 <z s <z max A position coordinate (x, y, z) is generated in space S. The optical power value at the (x, y, z) coordinate is measured by PD to obtain the RSS. mea (x, y, z), where the position coordinates satisfy 0. <x<x s ,0 <y<y s ,0 <z<z s ; (3) Based on the ideal visible light model P r Calculate the ideal optical power Pr at the position (x, y, z) (α, β, x, y, z); (4) Select the discrimination criterion, based on the difference between the measured value and the ideal calculated value under the calculated position coordinates ||P r(ɑ，β) -RSS mea || 2 <σ, calculate the solution set of (α, β) {(α1, β1), (α2, β2), ..., (α n ,β n )}, where σ is the tolerance threshold; (5) Select a search algorithm and iteratively search for the point RSS with the maximum optical power on the positioning plane in the space S to be located. max According to the coordinates of the maximum point (x max y max , z max Determine the azimuth offset α; (6) Using azimuth offset α in the solution set {(α1, β1), (α2, β2), ..., (α1, β1), ..., (α2, β2) n ,β n The optimal solution min(||α-ɑ1||) is selected from the options. 2 ,||α-α2|| 2 ,…,||α-α n || 2 ), thus obtaining an estimate of the LED attitude angle offset (α). es ,β es ).

2. The method according to claim 1, characterized in that, In step (1), the selected visible light propagation model is constructed: Where m is the Lambert scattering coefficient, P t Let d be the LED emitted light power, d be the distance from the LED to the PD, θ0 be the LED attitude angular offset (this parameter needs to be estimated in conjunction with the visible light received signal strength at the PD), and θ+θ0 be the angle between the LED normal vector and the PD-to-LED direction vector. c The scattering coefficient m is the maximum field of view (FOV) of the PD, and is determined by the half-power intensity angle φ of the LED. 1 / 2 Decision, that is The distance d from a measurement point on an indoor plane to the LED is expressed as: The coordinates of the measurement point are (x, y, z), and the coordinates of the LED are (x, y, z). LED y LED , z LED ).

3. The method according to claim 1, characterized in that, The solution to minimize the difference between the measured value and the ideal calculated value (α, β) and the discrimination criterion described in step (4) are as follows: By introducing the Sequential Quadratic Programming (SQP) method, the problem of minimizing light intensity error with nonlinear constraints can be solved efficiently. To solve the above constrained nonlinear optimization problem, the Lagrangian function is introduced: f(x)=||P r (a, b)-RSS mea || 2 c1(x)=||n|| 2 -1 Where λ is the Lagrange multiplier for equality constraints, and μ i Let I be the Lagrange multipliers of the inequality constraints, and let c be the set of indices of the inequality constraints. i (x) denotes the boundary inequality constraint; The SQP method must satisfy the KKT conditions of the optimization problem. The following are necessary conditions for the optimization problem (and sufficient conditions for convex problems): In each iteration of SQP, the optimization variables are updated through the following steps: a first-order Taylor expansion of the nonlinear constraints is performed to obtain linearized constraints. Under the linearized constraints, the quadratic approximation of minimizing the Lagrange function can be expressed as: Where p = xx k It refers to the search direction, H. k The objective function yields an approximation of the Hessian matrix, and the search direction p is obtained by solving the QP subproblem. k Update and optimize variables: x k+1 =x k +a k p k Where a k It is the step size factor, which is used to check the current solution x after each iteration. k+1 Does it meet the KKT conditions or does it conform to the requirements? If the condition is met, the iteration stops; otherwise, the iteration continues. ε is a preset tolerance. Through the above iterations, we can obtain the solution set {(α1, β1), (α2, β2), ..., (α...β1)} that satisfies the tolerance condition. n ,β n )}.

4. The method according to claim 1, characterized in that, The solution to minimize the difference between the measured value and the ideal calculated value (α, β) and the discrimination criterion described in step (4) are as follows: By introducing the memory-constrained quasi-Newton algorithm L-BFGS-B (Limited-memory Broyden-Fletcher-Goldfarb-Shanno with Boundary constraints), the problem of minimizing light intensity error with nonlinear constraints can be solved efficiently. First, the gradient is projected to ensure that the search direction is within the feasible region. For each variable x... i : Among them, l i and u i The variables x are respectively i The lower and upper bounds; Update the approximate Hessian matrix using BFGS with limited memory, defining the difference vector: in, The gradient of the objective function, the curvature condition must satisfy... To ensure Hessian is positive definite; The search direction d is calculated using a double-loop recursive method. k To avoid explicitly storing the Hessian matrix, the recursive process utilizes the nearest m groups {s} i ,y i } vectors, construct an approximation of the Hessian inverse; Finally, the maximum feasible step size α was determined. max : In the interval [0, α] max The execution line search within the scope ensures that the objective function decreases sufficiently and does not go out of bounds. Repeat the above steps until the convergence condition is met: ||P r(α,β) -RSS mea || 2 <s Through the above iterations, we can obtain the solution set {(α1, β1), (α2, β2), ..., (α...β1)} that satisfies the tolerance condition. n ,β n )}.

5. The method according to claim 1, characterized in that, The iterative search for the coordinates of the maximum optical power point on the positioning plane and the search method described in step (5) are as follows: Particle Swarm Optimization (PSO) is a swarm intelligence optimization algorithm that simulates the foraging behavior of bird flocks. In PSO, each particle moves through the search space, and its position and velocity are updated by the following formula: v i (t+1)=wv i (t)+c1r1(p i (t)-x i (t))+c2r2(g i (t)-x i (t)) x i (t+1)=x i (t)+v i (t+1) Where: w is the inertia weight, controlling the degree of influence of the particle's historical velocity; c1 and c2 are the individual learning factor and the social learning factor, respectively, controlling the particle's position relative to the individual's optimal position (p). i (t)) and the global optimal position (g) i The attractiveness of (t)); r1 and r2 are random numbers uniformly distributed in the range [0, 1], increasing the randomness of the algorithm; p i (t) is the best position of particle i so far; g i (t) is the global optimal position for all particles; The introduction of a nonlinear adaptive inertia factor aims to dynamically adjust the inertia weights based on changes in particle fitness, thereby improving the flexibility of the search process. The formula defines the average fitness and the upper and lower limits of the fitness range in the current iteration: fitA and fitB define the adjustment range in the current iteration, where fit avg The average fitness over all previous iterations, fit min The minimum fitness across all previous iterations, fit max This represents the maximum fitness across all previous iterations. At the start of each iteration, the inertia factor is updated synchronously. If the current fitness is fit... i If the value is less than fitA, it is considered far from the optimal point, and the maximum inertia weight w is used. max If the current fitness is greater than fitB, it is considered far from the optimal point, and the maximum inertia weight w is adopted. min The current fitness is calculated according to the following formula if it is in the (fitA, fitB) interval: After searching the localization plane using the above nonlinear adaptive particle swarm algorithm, the coordinates of the maximum point (x) can be obtained. max y max , z max ); PD measurement points (x) max y max , z max The unit direction vector pointing to the LED can be represented as: n PD =(sinβ PD cosɑ PD ,sinβ PD sinα PD ,cosβ PD ) Where β PD α represents the angle between the PD direction vector d and the z-axis. PD The angle between the projection d′ of the PD-LED direction vector d onto the xy-plane and the x-axis is represented by the dot product formula and simplified using the cosine sum formula. cosθ=sinβ LED sinβ PD cos(a LED -a PD )+cosβ LED cosβ PD According to the formula, with a fixed distance and tilt angle, when α... LED =ɑ PD When cosθ reaches its maximum value, it is derived that the azimuth angle of the LED angle offset is consistent with the direction angle at the maximum RSS point on the indoor plane. The azimuth angle value of the LED angle offset can be solved and expressed as:

6. The method according to claim 1, characterized in that, The estimated value (α) of the LED attitude angle offset obtained in step (6) is obtained. es ,β es ): For the solution set {(α1, β1), (α2, β2), ..., (α... n ,β n Since LED light sources follow a Lambertian distribution, the symmetry of the RSS value distribution indoors under this distribution leads to multiple optimal solutions in the SQP algorithm iteration. To address this multiple-solution problem, the azimuth angle α obtained from the solution is used for selection. min(||α-α1|| 2 ,||α-ɑ2|| 2 ,...,||a-a n || 2 ) By traversing the solution set to search for the closest solution to α, an estimate of the LED attitude angle offset (α) can be obtained. es ,β es ); 7. The method according to claim 1, characterized in that, The angle offset estimation method described above can be used to calculate attitude angle offset and applied to visible light models to complete indoor visible light positioning. (1) For LEDs (LED1, LED2, ... LED) uniformly distributed in an indoor environment n Each light source uses frequency division multiplexing (FDM) technology to achieve signal separation. Let the carrier frequency of the i-th LED be f. i Its modulated signal can be represented as: s i (t)=A i [1+m·RSS i (t)]cos(2πf i t) Where m is the modulation index and Ai is the transmitted light intensity; signal separation is achieved at the receiver through a bandpass filter bank. In the formula h i (t) is the corresponding f i The impulse response of the matched filter; (2) The estimated value of the LED attitude angle offset (α) is obtained by estimating through the steps of the above claims. es ,β es This model is then applied to the visible light propagation model to obtain an attitude angle offset compensation propagation model. (3) Calculate the indoor RSS distribution map under the current state using the attitude angle offset compensated visible light positioning model, and construct fingerprint database data: The fingerprint database is established without relying on offline collection, but is obtained directly based on the angle compensation model; (4) Indoor location estimation can be performed using a fingerprint database and the WkNN algorithm. The WkNN algorithm is based on the idea of ​​distance weighting. For an indoor coordinate observation point (RSS... mea，1 …RSS mea,n The RSS difference between the observation point and each coordinate in the fingerprint database is calculated and expressed using the Euclidean distance metric: The weights are calculated based on the inverse relationship between the points and their distances; points that are closer together have a higher weight. The weights can be calculated in the following ways: Where Wi is the weight of the i-th point, and Di is the distance from the i-th point to the observation point; The location of the query point is estimated using weighted distance and position coordinates. Specifically, the coordinates of the query point are estimated based on the weighted positions of its k nearest neighbors. Among them, P query Pi is the estimated location of the query point, Pi is the actual location of the i-th point in the fingerprint database, and W is the estimated location of the query point. i It is the weight of the i-th point. The above steps can complete the visible light positioning of indoor space.

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