Method for parameter calibration of a visible light lambertian radiation model for positioning direction finding

Abstract

The application provides a parameter calibration method for positioning and direction finding of a visible light Lambert radiation model, and relates to the technical field of visible light wireless positioning and direction finding. First, an LED light source is used as a transmitting end beacon to transmit visible light, a photodiode is used as a receiver to sense and receive the visible light, and an actual visible light channel Lambert radiation system is formed. Then, a visible light Lambert radiation model is constructed. When the parameters of the visible light Lambert radiation model are unknown or inaccurate, the parameters of the visible light Lambert radiation model are calibrated, the real values of the parameters can be estimated, the method has robustness to different signal-to-noise ratios, and the accuracy of subsequent visible light positioning and direction finding can be further ensured.

Description

Technical Field

[0001] This invention relates to the technical field of visible light wireless positioning and direction finding, and more specifically, to a parameter calibration method for a visible light Lambertian radiation model used for positioning and direction finding. Background Technology

[0002] With the development of light-emitting diode (LED) lighting technology, indoor positioning technology based on LED visible light is currently a research hotspot. Compared with other indoor positioning technologies, visible light positioning technology can utilize existing lighting systems, is easy to install, has low cost, fast signal transmission speed, and high accuracy. It can provide positioning functions in environments unsuitable for radio frequency propagation, such as underwater and underground mines. Due to its superior cost-effectiveness, robustness, durability, and controllability, LED-based visible light positioning (VLP) has also become a candidate for future wireless positioning technologies.

[0003] In visible light positioning and direction finding, propagation models are frequently used. This involves relying on the propagation channel model between a transmitter (such as an LED) and a receiver (a photodiode, PD) for positioning and direction finding. Multiple transmission links are established between multiple LEDs and the receiver. Based on the parameters of the transmission link channel model, algorithms deduce the receiver's position and orientation. Inaccurate or unrealistic channel models will negatively impact the positioning and direction finding results, leading to decreased positioning accuracy. To address this, existing technologies disclose an indoor positioning method and platform based on the fusion of visible light communication and inertial sensors. Based on visible light communication technology and combined with inertial sensors, high-precision positioning of mobile blind nodes is achieved indoors. According to the propagation characteristics of visible light, a propagation model of received signal strength (RSS) and distance, as well as an RSS normalization calibration model, are established. A calibration model for inertial sensor data and a linear model of error factors are established, and adaptive Kalman filtering is applied to the error factors to optimize model parameters. During the positioning process, visible light RSS data and inertial sensor data are calibrated and corrected. The distance between the blind node and the anchor node is obtained based on the RSS-distance model, and the displacement distance and direction per unit time are obtained based on the inertial sensor data. The visible light data and inertial sensor data are fused and calculated to finally obtain the blind node positioning result.

[0004] Currently, when building visible light positioning and direction finding systems, most systems assume that some parameters of the model are known and given, eliminating the need for parameter calibration. Alternatively, the calibration process is not specified, and the model parameter results are simply provided. In practice, due to environmental factors and the fact that some model parameters, such as LED emission power, Lambertian coefficient, and receiver photoelectric conversion efficiency, may be unknown, inaccurate, or unsuitable for the current environment when the equipment is purchased, these factors can cause discrepancies. Furthermore, the manufacturing processes of equipment used in different transmission links can lead to variations in the parameters of even identical equipment, and the emission power of different LEDs may not be identical. These factors can result in different channel models for each transmission link, further negatively impacting positioning and direction finding. Summary of the Invention

[0005] To address the issue of low positioning and direction finding accuracy in current visible light positioning and direction finding based on the Lambertian radiation model of the visible light propagation channel, which does not consider the calibration of model parameters, this invention proposes a parameter calibration method for the visible light Lambertian radiation model used for positioning and direction finding. The calibration estimation results are good, which can further ensure the accuracy of subsequent visible light positioning and direction finding.

[0006] To achieve the above-mentioned technical effects, the technical solution of the present invention is as follows:

[0007] A parameter calibration method for a visible light Lambertian radiation model used for positioning and orientation, the method comprising:

[0008] S1. Using an LED light source as a transmitting beacon to transmit visible light, and a photodiode as a receiver to sense and receive visible light, thus forming a visible light channel Lambertian radiation system;

[0009] S2. Combine the visible light channel Lambertian radiation system to construct a visible light Lambertian radiation model. The parameters of the visible light Lambertian radiation model include system constants and the Lambertian coefficients of the LED light source.

[0010] S3. Calibrate the system constants and the Lambert coefficients of the LED light source.

[0011] Preferably, in step S1, a visible light positioning space is constructed, the number of LED light sources is selected, and the LED light sources are evenly installed and arranged, all perpendicular to the ceiling plane and facing downwards, while a single photodiode is placed on the ground, vertically upwards.

[0012] Preferably, let Let represent the three-dimensional position coordinates and three-dimensional orientation of the receiver at the k-th position, respectively. Let v represent the position coordinates and direction of the m-th LED light source, respectively, and ||v| ... m ||2=1, let rm This represents the Lambertian coefficient of the m-th LED light source, which is related to the half-power angle of the LED light source radiation; W m Let be the emission power of the m-th LED. For a photodiode, let its aperture size, optical concentrator gain, and optical filter gain be denoted as Φ. R ,Γ R and G R And all of them are constants;

[0013] Treating the non-line-of-sight component of visible light propagation as noise and considering only the line-of-sight propagation component, the LED emission angle between the m-th LED light source and the receiver at the k-th position is... and the angle of incidence of the receiver None of them exceed the maximum field of view φ of their corresponding transmitters. FOV and the receiver's maximum incident angle θ FOV At that time, the Received Signal Strength (RSS) value of the m-th LED at the k-th position of the receiver is obtained, denoted by z. m,k This indicates that the visible light Lambertian radiation model is thus formed as a whole, and its expression is:

[0014]

[0015] in, M represents the number of LED light sources, K represents the number of locations where the receiver receives signals, and r m ε represents the Lambertian coefficient of the LED light source. m,k This indicates that it includes non-line-of-sight propagation information and noise related to dark current, thermal noise, and diffuse reflection. Indicates the line-of-sight propagation component. This represents the system constant when the receiver receives the RSS value of the m-th LED light source. It is related to the optical concentrator gain, optical filter gain, LED emission power, and receiver aperture size. During calibration, both the system constant and the LED light source Lambertian coefficients are considered unknown or inaccurate and require calibration to solve for.

[0016] Preferably, the expression for the line-of-sight propagation component is:

[0017]

[0018] in, This represents the LED emission angle between the m-th LED light source and the receiver at the k-th position. Then, the receiver incident angle between the m-th LED light source and the receiver at the k-th position is expressed as:

[0019]

[0020]

[0021] The emission angle of the LED light source expressed by formula (3) The angle of incidence of the receiver is expressed by formula (4). Substituting the expression for the line-of-sight propagation component, we obtain the transformed line-of-sight propagation component. The expression is:

[0022]

[0023] The RSS of the received signal strength of the m-th LED at the k-th position of the receiver is expressed as:

[0024]

[0025] Preferably, in step S3, the process of calibrating the system constant and the Lambert coefficient of the LED light source is as follows:

[0026] S31. By receiving visible light signals through a photodiode, K sets of RSS value calibration data with known position coordinates and orientations can be obtained in a positioning space;

[0027] S32. Based on the RSS value vector of visible light transmitted by all LED light sources at the k-th position received by the receiver, a measurement vector composed of the RSS values ​​of all LED light sources at the k-th position is obtained, and the corresponding receiver coordinates and receiver direction are recorded. The corresponding receiver position coordinates and receiver direction are known in the vector composed of the RSS values ​​of all LED light sources at the k-th position, while the Lambert coefficient and system constant of the LED light source are unknown or inaccurate.

[0028] S33. Using the Lambert coefficients and system constants of the LED light source as parameters to be calibrated, construct an optimization problem and optimize the solution of the Lambert coefficients and system constants of the LED light source.

[0029] Preferably, let Let represent the RSS value vector of all LEDs at position k received by the receiver, where vec[] represents a stacked vector of all elements; then Let M represent the line-of-sight transmission components of all LED light sources at position k, where M is the number of LED light sources. Let κ represent the system constants of all line-of-sight transmission link models, respectively. m The Lambertian coefficient r of LED lights m The vector formed by the measured RSS values; according to the visible light Lambertian radiation model, the measured RSS value vector is theoretically represented as:

[0030]

[0031] in, It is a noise vector, which can be expressed by formula (5) as:

[0032]

[0033] in, Then formula (7) can be expressed as:

[0034]

[0035] in, Again Let RSS be a vector consisting of the RSS values ​​of all LEDs at K locations. Then:

[0036] z = A(r; x) R ,u R )κ+ε (10)

[0037] in, mat[] represents a matrix form where all elements are stacked. That is the noise vector.

[0038] Preferably, during the calibration process, the receiver position coordinates x R and direction u R Given that the system constant κ and the Lambert coefficients r of the LEDs are unknown or inaccurate, the vector consisting of the RSS values ​​of all LEDs at K locations can theoretically be represented as:

[0039] z=A(r)κ+ε (11);

[0040] As described in step S33, the Lambert coefficients and system constants of the LED light source are used as the parameters that need to be calibrated and solved. Construct the following optimization problem:

[0041]

[0042] Preferably, when optimizing the solution for the Lambert coefficients and system constants of the LED light source, the transformed measurement vector form is decomposed into two sub-problems: a convex calibration sub-problem and a non-convex calibration sub-problem; the initial solution is then approximated. From the initial solution Begin, alternating updates and Two estimators are used until they converge. The converged estimators are used as estimates of the system constant κ and the Lambert coefficient r of all line-of-sight transmission links between LED light sources and receivers, thereby completing the calibration of all line-of-sight transmission channel model parameters.

[0043] Preferably, the Lambert coefficients obtained through approximate solution are used as the initial solution. The process of approximating the Lambert coefficients is as follows:

[0044] The RSS value of formula (1) can be approximated as:

[0045]

[0046] Set different LED lamp Lambertian coefficients and system constants They are approximately the same, i.e., r m =r0 and κ m =κ0, Let z 1,1 That is, m=1 and k=1 are the reference samples, let Let RSS be the logarithm for all m and k, but (m,k)≠(1,1), then:

[0047]

[0048] Among them, b m,k c m,k and d m.k All are constants, obtained by the following formula:

[0049]

[0050]

[0051]

[0052] Furthermore, let: have:

[0053] y≈br0 (15)

[0054] Based on the least squares method, we can conclude that: The final initial solution expression is:

[0055]

[0056] Among them, 1 M It is an M-dimensional vector consisting entirely of 1s.

[0057] The present invention also proposes a parameter calibration system for a visible light Lambertian radiation model for positioning and orientation. The calibration system is based on a parameter calibration method for a visible light Lambertian radiation model for positioning and orientation, and calibrates the system constants and the Lambertian coefficients of the LED light source.

[0058] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0059] This invention proposes a parameter calibration method for a visible light Lambertian radiation model used for positioning and direction finding. First, an LED light source is used as a transmitting beacon to transmit visible light, and a photodiode is used as a receiver to sense and receive the visible light, forming an actual visible light channel Lambertian radiation system. Then, a visible light Lambertian radiation model is constructed. When the parameters of the visible light Lambertian radiation model are unknown or inaccurate, the parameters of the visible light Lambertian radiation model are calibrated to estimate the true values ​​of the parameters. Furthermore, it is robust to different signal-to-noise ratios, which can further ensure the accuracy of subsequent visible light positioning and direction finding. Attached Figure Description

[0060] Figure 1 A flowchart illustrating the parameter calibration method for the visible light Lambertian radiation model for positioning and orientation proposed in Embodiment 1 of the present invention;

[0061] Figure 2 A schematic diagram of the visible light channel Lambertian radiation system proposed in Embodiment 2 of the present invention;

[0062] Figure 3 This is a flowchart illustrating the calibration of system constants and the Lambert coefficients of the LED light source as proposed in Embodiment 2 of the present invention;

[0063] Figure 4 This diagram illustrates the iterative convergence trend of the system constant loss and the Lambert coefficient loss of the LED light source during the calibration process, as presented in Embodiment 4 of this invention.

[0064] Figure 5 This is a trend graph showing the calibration results of the system constant loss and the Lambert coefficient loss of the LED light source at different signal-to-noise ratios between 20 and 60 dB, as proposed in Embodiment 4 of the present invention.

[0065] Figure 6 This is a trend graph showing the calibration results of the system constant loss and the Lambert coefficient loss of the LED light source at different calibration locations when the signal-to-noise ratio is 20dB and 40dB, as proposed in Embodiment 4 of the present invention.

[0066] Figure 7 This figure shows a comparison of the positioning performance trends of the visible light positioning method based on the Lambert radiation model proposed in Embodiment 4 of the present invention, with a signal-to-noise ratio between 20 and 60 dB, under different signal-to-noise ratios, with and without calibration of the system constant and the Lambert coefficient of the LED light source. Detailed Implementation

[0067] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent.

[0068] To better illustrate this embodiment, some parts of the accompanying drawings may be omitted, enlarged, or reduced, and do not represent the actual dimensions;

[0069] It is understandable to those skilled in the art that some well-known details may be omitted from the accompanying drawings.

[0070] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0071] The positional relationships depicted in the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent.

[0072] Example 1

[0073] like Figure 1 As shown in the figure, this embodiment proposes a parameter calibration method for a visible light Lambertian radiation model used for positioning and direction finding. The method includes:

[0074] S1. Using an LED light source as a transmitting beacon to transmit visible light, and a photodiode as a receiver to sense and receive visible light, thus forming a visible light channel Lambertian radiation system;

[0075] S2. Combine the visible light channel Lambertian radiation system to construct a visible light Lambertian radiation model. The parameters of the visible light Lambertian radiation model include system constants and the Lambertian coefficients of the LED light source.

[0076] S3. Calibrate the system constants and the Lambert coefficients of the LED light source.

[0077] Example 2

[0078] like Figure 2 As shown, in step S1, a visible light positioning space is constructed, the number of LED light sources is selected, and the LED light sources are evenly installed and arranged, all perpendicular to the ceiling plane and facing downwards, while a single photodiode is placed on the ground, vertically upwards.

[0079] make Let represent the three-dimensional position coordinates and three-dimensional orientation of the receiver at the k-th position, respectively. Let v represent the position coordinates and direction of the m-th LED light source, respectively, and ||v| ... m ||2=1, let r m This represents the Lambertian coefficient of the m-th LED light source, which is related to the half-power angle of the LED light source radiation; W m Let be the emission power of the m-th LED. For a photodiode, let its aperture size, optical concentrator gain, and optical filter gain be denoted as Φ. R ,Γ R and G R And all of them are constants;

[0080] In this embodiment, the non-line-of-sight component of visible light propagation is treated as noise, and only the line-of-sight propagation component is considered. This refers to the LED emission angle between the m-th LED light source and the receiver at the k-th position. and receiver incident angle None of them exceed the maximum field of view φ of their corresponding transmitters. FOV and the receiver's maximum incident angle θ FOV At that time, the Received Signal Strength (RSS) value of the m-th LED at the k-th position of the receiver is obtained, denoted by z. m,k This indicates that the visible light Lambertian radiation model is thus formed as a whole, and its expression is:

[0081]

[0082] The received signal strength (RSS) of visible light depends on the emission angle gain, the incident angle gain, the transmission distance, and the characteristic constant. Among these, M represents the number of LED light sources, K represents the number of locations where the receiver receives signals, and r m ε represents the Lambertian coefficient of the LED light source. m,k This indicates that it includes non-line-of-sight propagation information and noise related to dark current, thermal noise, and diffuse reflection. Indicates the line-of-sight propagation component. This represents the system constant when the receiver receives the RSS value of the m-th LED light source. It is related to the optical concentrator gain, optical filter gain, LED emission power, and receiver aperture size. During calibration, both the system constant and the LED light source Lambertian coefficients are considered unknown or inaccurate and require calibration to solve for.

[0083] The expression for the line-of-sight propagation component is:

[0084]

[0085] in, This represents the LED emission angle between the m-th LED light source and the receiver at the k-th position. Then, the receiver incident angle between the m-th LED light source and the receiver at the k-th position is expressed as:

[0086]

[0087]

[0088] The emission angle of the LED light source expressed by formula (3) The angle of incidence of the receiver is expressed by formula (4). Substituting the expression for the line-of-sight propagation component, we obtain the transformed line-of-sight propagation component. The expression is:

[0089]

[0090] The RSS of the received signal strength of the m-th LED at the k-th position of the receiver is expressed as:

[0091]

[0092] In this embodiment, the system constant κ is to be calibrated. m The Lambertian coefficient r of LED lights m In step S3, the calibration process for the system constants and the Lambert coefficients of the LED light source is as follows:

[0093] S31. By receiving visible light signals through a photodiode, K sets of RSS values ​​with known position coordinates and directions can be obtained in a positioning space; that is, by receiving visible light signals through the PD photodiode at the receiving end, the received signal strength can be measured, thereby obtaining K sets of RSS value calibration data with known position coordinates and directions in a positioning space. The positions of these K sets of measured RSS values ​​need to be evenly selected in various locations in the space to fully reflect the RSS values ​​of each location, and it is generally better to select more than 30 location points for the K sets of data.

[0094] S32. Based on the RSS value vector of visible light transmitted by all LED light sources at the k-th position received by the receiver, a measurement vector composed of the RSS values ​​of all LED light sources at the k-th position is obtained, and the corresponding receiver coordinates and receiver direction are recorded. The corresponding receiver position coordinates and receiver direction are known in the vector composed of the RSS values ​​of all LED light sources at the k-th position, while the Lambert coefficient and system constant of the LED light source are unknown or inaccurate.

[0095] S33. Using the Lambert coefficients and system constants of the LED light source as parameters to be calibrated, construct an optimization problem and optimize the solution of the Lambert coefficients and system constants of the LED light source.

[0096] Specifically: Order Let represent the RSS value vector of all LEDs at position k received by the receiver, where vec[] represents a stacked vector of all elements; then Let M represent the line-of-sight transmission components of all LED light sources at position k, where M is the number of LED light sources. Let κ represent the system constants of all line-of-sight transmission link models, respectively. m The Lambertian coefficient r of LED lights mThe vector formed by the measured RSS values; according to the visible light Lambertian radiation model, the measured RSS value vector is theoretically represented as:

[0097]

[0098] in, It is a noise vector, since formula (5) can be expressed as,

[0099]

[0100] in, Then formula (7) can be expressed as:

[0101]

[0102] in, Again Let RSS be a vector consisting of the RSS values ​​of all LEDs at K locations. Then:

[0103] z = A(r; x) R ,u R )κ+ε(10)

[0104] in, mat[] represents a matrix form where all elements are stacked. That is the noise vector.

[0105] During calibration, the receiver position coordinates x R and direction u R Given that the system constant κ and the Lambert coefficients r of the LEDs are unknown or inaccurate, the vector consisting of the RSS values ​​of all LEDs at K locations can theoretically be represented as:

[0106] z=A(r)κ+ε (11);

[0107] As described in step S33, the Lambert coefficients of the LED light source and the system constants are used as the parameters that need to be calibrated and solved. Construct the following optimization problem:

[0108]

[0109] When optimizing the solution for the Lambert coefficients and system constants of the LED light source, the transformed measurement vector form is decomposed into two subproblems: a convex calibration subproblem and a non-convex calibration subproblem; the initial solution is then approximated. From the initial solution Begin, alternating updates and Two estimators are used until they converge. The convergent estimators are then used as estimates of the system constant κ and the Lambert coefficients r of the line-of-sight transmission link between all LED light sources and receivers, thus completing the calibration of all line-of-sight transmission channel model parameters. Here, the approximately solved Lambert coefficients are used as the initial solution. The process of approximating the Lambert coefficients is as follows:

[0110] The RSS value of formula (1) can be approximated as:

[0111]

[0112] Set different LED lamp Lambertian coefficients and system constants They are approximately the same, i.e., r m =r0 and κ m =κ0, Let z 1,1 That is, m=1 and k=1 are the reference samples, let Let RSS be the logarithm for all m and k, but (m,k)≠(1,1), then:

[0113]

[0114] Among them, b m,k c m,k and d m.k All are constants, obtained by the following formula:

[0115]

[0116]

[0117]

[0118] Furthermore, let: have:

[0119] y≈br0 (15)

[0120] Based on the least squares method, we can conclude that: The final initial solution expression is:

[0121]

[0122] Among them, 1 M It is an M-dimensional vector consisting entirely of 1s.

[0123] For details, please refer to [link / reference]. Figure 3 Alternate updates and Two estimators are used until both estimators converge. The process is as follows:

[0124] (1) Estimation of the system constant κ: First, a given... Given the initial solution, the Lambert coefficients obtained in the i-th iteration can be expressed as: System constants The estimate can be obtained by solving the following optimization subproblems:

[0125]

[0126] In each iteration, the optimization problem of equation (13) is strictly convex, therefore the closed-form solution has

[0127]

[0128] in, Indicates a false reversal;

[0129] (2) Estimation of the Lambert coefficient r: Once determined We will determine based on the following calibration sub-problems

[0130]

[0131] The optimization problem in formula (19) is a non-convex problem. To solve this problem, the cost function of formula (19) can be approximated as convex. Specifically, in each iteration, the cost function of formula (19) is approximated as convex. exist The cost function of the deconvex approximation formula (19) is obtained by performing a first-order Taylor expansion, which yields formula (20):

[0132]

[0133] Thus, each iteration is a convex expression, where... Is The derivative with respect to r,

[0134]

[0135] in, This indicates that for the corresponding r m Differentiate, and therefore, The closed-form solution can be obtained from the following formula.

[0136]

[0137] Example 3

[0138] This embodiment proposes a parameter calibration system for a visible light Lambertian radiation model used for positioning and orientation. The calibration system is based on a parameter calibration method for a visible light Lambertian radiation model used for positioning and orientation, and calibrates the system constants and the Lambertian coefficients of the LED light source.

[0139] Example 4

[0140] In this embodiment, a multi-transmitter, single-receiver visible light positioning scenario is considered. Specifically, a 6*6*4m visible light positioning space is constructed using MATLAB simulation. M=6 LEDs are installed on the ceiling, with the six LEDs evenly distributed and perpendicular to the ceiling plane, facing downwards. m =[0,0,-1] T , The positions of all LEDs are also known. We use one PD receiver to receive the RSS values ​​of six LEDs, and the receiver is moved on the ground to measure the RSS values ​​at different locations, with the PD receiver facing vertically upwards. Meanwhile, we pre-set the actual values ​​of the system constant κ as κ1=10, κ2=9, κ3=11, κ4=12, κ5=11 and κ6=10, respectively, and the actual values ​​of the Lambert coefficients r of the LED lights as r1=0.4865, r2=0.532, r3=0.528, r4=0.476, r5=0.4801 and r6=0.532, respectively.

[0141] Based on the Lambertian propagation model of the visible light channel, K=64 location points were selected and measured. The RSS value is used as calibration data. The received visible light received signal intensity value RSS at the m-th LED and the RSS value received at the k-th position of the receiver follows the following:

[0142]

[0143] make It can obtain the MK-dimensional visible light received signal intensity vector required for calibration.

[0144] The calibration cost loss is calculated using the L2 norm of the difference between the estimated system constant vector or the Lambert coefficient vector of the LED and its corresponding true value vector. Specifically, the cost loss for system constant estimation is equal to... The cost of estimating the Lambert coefficients is equal to In a given After initializing the values, the proposed calibration algorithm is used to adjust the known position coordinates. and direction Substituting the measured visible light received signal intensity vector z into formula (18):

[0145]

[0146] The system constants can be estimated. Then estimate Substitute the corresponding position coordinates, direction, and RSS value into formula (21).

[0147]

[0148] To estimate the Lambert coefficient The system constant κ and the Lambert coefficients r of the visible light channel Lambertian radiation model are calculated iteratively until the algorithm converges. Figure 4 It can be seen that, under noise-free conditions, after 1500 iterations, the system constant κ and the Lambert coefficient r both converge to the preset true values, and the iterative solution results are also relatively accurate. This demonstrates that the proposed calibration algorithm is convergent and can iterate to the preset true values.

[0149] In noisy conditions, this embodiment simulated the calibration performance with a signal-to-noise ratio between 20 and 60 dB, using the results after 1500 iterations as the output. Figure 5 As shown, with the increase of the signal-to-noise ratio, the calibration performance also improves, and the parameter calibration accuracy is relatively high within the range of 20dB to 60dB. Meanwhile, from... Figure 5 It can be seen that the calibration algorithm still maintains a certain robustness under different signal-to-noise ratios and can achieve relatively good calibration estimation results.

[0150] like Figure 6 The simulation compares the model parameter calibration results with different numbers of calibration points at signal-to-noise ratios of 20dB and 40dB. It shows that as the number of calibration points increases, the cost of model parameter calibration decreases, meaning the accuracy of the calibration results improves. Typically, 30 calibration points are sufficient to achieve satisfactory calibration results; further increasing the number of calibration points leads to performance saturation.

[0151] At the same time, such as Figure 7As shown in the figure, this embodiment simulates and compares the positioning performance under different signal-to-noise ratios for positioning without model parameter calibration and positioning with model parameter calibration. The positioning method used is a visible light positioning method based on the Lambertian radiation model. This method mainly utilizes the mathematical relationship (Lambertian model) between observed data such as the intensity of the received visible light signal and the position parameters of the wireless terminal. Based on optimization criteria such as minimum sample error, it inversely calculates the receiver's position and orientation. This method requires high accuracy of the Lambertian radiation model parameters. In positioning without model parameter calibration, the model-based positioning uses inaccurate LED Lambertian coefficients; all LEDs are assumed to have r = 0.5, while the system constant uses the actual accurate value set in the simulation. In positioning with model parameter calibration, the model-based positioning method uses the calibrated system constant and LED Lambertian coefficients. Figure 7 As can be seen, within the given noise range of 20 to 60 dB, positioning using the model parameter calibration method of this invention before positioning achieves better positioning performance compared to positioning without model parameter calibration. Positioning without model parameter calibration, due to the use of inaccurate model parameters for visible light positioning, eventually reaches the lower limit of error caused by model parameter errors. In contrast, the positioning error of visible light positioning using the method of this invention to calibrate the Lambertian radiation model parameters gradually decreases with increasing signal-to-noise ratio. This is because the model parameter errors are reduced through the calibration procedure of this invention, thus breaking the lower limit of error.

[0152] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A parameter calibration method for a visible light Lambertian radiation model used for positioning and direction finding, characterized in that, The method includes: S1. Using an LED light source as a transmitting beacon to transmit visible light, and a photodiode as a receiver to sense and receive visible light, thus forming a visible light channel Lambertian radiation system; S2. Combine the visible light channel Lambertian radiation system to construct a visible light Lambertian radiation model. The parameters of the visible light Lambertian radiation model include system constants and the Lambertian coefficients of the LED light source. S3. Calibrate the system constants and the Lambert coefficients of the LED light source; In step S3, the calibration process for the system constants and the Lambert coefficients of the LED light source is as follows: S31. Receive visible light signals through a photodiode and obtain [the signal] in a positioning space. A set of calibration data with known position coordinates and orientation RSS values; S32. Based on the first received by the receiver k The RSS value vectors of visible light transmitted by all LED light sources at each location are obtained from... The measurement vector is composed of the RSS values ​​of all LED light sources at each location point, and the corresponding receiver coordinates and receiver orientation are recorded. The vector composed of the RSS values ​​of all LED light sources at a given location point contains the corresponding receiver location coordinates and receiver orientation, while the Lambert coefficients and system constants of the LED light sources are unknown or inaccurate. S33. Using the Lambert coefficients and system constants of the LED light source as parameters to be calibrated, construct an optimization problem and optimize the solution of the Lambert coefficients and system constants of the LED light source.

2. The parameter calibration method for the visible light Lambertian radiation model used for positioning and direction finding according to claim 1, characterized in that, In step S1, a visible light positioning space is constructed, the number of LED light sources is selected, and the LED light sources are evenly installed and arranged, all perpendicular to the ceiling plane and facing downwards, with a single photodiode placed on the ground, vertically upwards.

3. The parameter calibration method for the visible light Lambertian radiation model used for positioning and direction finding according to claim 1, characterized in that, make , These represent the receiver at the 1st... k The three-dimensional position coordinates and three-dimensional orientation of each location, where , , They represent the first m The position coordinates and orientation of each LED light source, and ,make Indicates the first m The Lambertian coefficient of an LED light source is related to the half-power angle of the LED light source's radiation; Represented as the first m The emission power of an LED lamp, and for a photodiode, let its aperture size, optical concentrator gain, and optical filter gain be expressed as... , and And all of them are constants; Treating the non-line-of-sight component of visible light propagation as noise, and considering only the line-of-sight propagation component, when the... m The LED light source and receiver are in the first k LED light emission angle between positions and receiver incident angle None of them exceed the maximum field of view of their corresponding transmitters. and receiver maximum incident angle At that time, the first m The LED light is on the receiver. k The received signal strength (RSS value) at each location is expressed as "Received Signal Strength". This indicates that the visible light Lambertian radiation model is thus formed as a whole, and its expression is: （1） in, , , The number of LED light sources. Indicates the number of locations where the receiver receives signals. This represents the Lambertian coefficient of the LED light source. This indicates that it includes non-line-of-sight propagation information and noise related to dark current, thermal noise, and diffuse reflection. Indicates the line-of-sight propagation component. This indicates that the receiver received the first... m The system constant for the RSS value of an LED light source is related to the gain of the optical concentrator, the gain of the optical filter, the LED emission power, and the size of the receiver aperture. During the calibration process, the system constant and the Lambert coefficient of the LED light source are considered to be unknown or inaccurate and need to be calibrated and solved.

4. The parameter calibration method for the visible light Lambertian radiation model used for positioning and direction finding according to claim 3, characterized in that, The expression for the line-of-sight propagation component is: （2） in, Indicates the first m The LED light source and receiver are in the first k The LED light emission angle between each position Then it means the first m The LED light source and receiver are in the first k The angles of incidence of the receiver between the three locations are expressed as follows: （3） （4） The emission angle of the LED light source expressed by formula (3) The angle of incidence of the receiver is expressed by formula (4). Substituting the expression for the line-of-sight propagation component, we obtain the transformed line-of-sight propagation component. The expression is: (5) Then the first m The LED light is on the receiver. k The received signal strength RSS at each location is expressed as: (6)。 5. The parameter calibration method for the visible light Lambertian radiation model used for positioning and direction finding according to claim 4, characterized in that, make Indicates the number of times the receiver receives the first... k The RSS value vector of all LED light sources at each location, where, Represents a vector form where all elements are stacked; then Indicates the first k All LED light sources at each location Group line-of-sight transmission components, Let be the number of LED light sources, where , Represent the system constants of all line-of-sight transmission link models. The Lambertian coefficient of LED lights The vector formed by the measured RSS values; according to the visible light Lambertian radiation model, the measured RSS value vector is theoretically represented as: （7） in, It is a noise vector, as expressed by formula (5): （8） in, Then formula (7) can be expressed as: （9） in, , and then Indicates by The vector composed of the RSS values ​​of all LEDs at each location point is then: （10） in, , Represents a matrix form where all elements are stacked. , , That is the noise vector.

6. The parameter calibration method for the visible light Lambertian radiation model used for positioning and direction finding according to claim 5, characterized in that, During calibration, receiver position coordinates and direction Given the system constants The Lambertian coefficient of LED lights If it is unknown or inaccurate, then by The vector consisting of the RSS values ​​of all LEDs at each location point can theoretically be represented as: （11）； As described in step S33, the Lambert coefficients and system constants of the LED light source are used as the parameters that need to be calibrated and solved. Construct the following optimization problem: （12）。 7. The parameter calibration method for the visible light Lambertian radiation model used for positioning and direction finding according to claim 6, characterized in that, When optimizing the solution for the Lambert coefficients and system constants of the LED light source, the transformed measurement vector form is decomposed into two subproblems: a convex calibration subproblem and a non-convex calibration subproblem; the initial solution is then approximated. From the initial solution Begin, alternating updates ,and Two estimators are used until both estimators converge. The convergent estimators are used as the system constants for the line-of-sight transmission link between all LED light sources and receivers. And Lambert coefficient The estimation is then used to complete the calibration of all line-of-sight transmission channel model parameters.

8. The parameter calibration method for the visible light Lambertian radiation model used for positioning and direction finding according to claim 7, characterized in that, The Lambert coefficients obtained through approximate solution are used as the initial solution. The process of approximating the Lambert coefficients is as follows: The RSS value of formula (1) can be approximated as: （13） Set different LED lamp Lambertian coefficients and system constants Approximately the same, that is and , ;set up ,Right now m =1 and k =1 is the reference sample, let For logarithmic RSS, it is for all m and k In other words, but ,but: （14） in, , and All are constants, obtained by the following formula. Furthermore, let: , , ,have: （15） Based on the least squares method, we can conclude that: The final initial solution expression is: （16） in, yes A vector of dimension 1.

9. A parameter calibration system for a visible light Lambertian radiation model used for positioning and orientation, characterized in that, The calibration system calibrates the system constants and the Lambert coefficients of the LED light source based on the parameter calibration method of the visible light Lambertian radiation model for positioning and direction finding as described in any one of claims 1 to 8.

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