Joint timing synchronization and optical wireless positioning method based on continuous linear least square

Abstract

The invention provides a joint timing synchronization and optical wireless positioning method based on continuous linear least square, and relates to the technical field of optical wireless positioning. An indoor optical wireless positioning system comprising a plurality of LED optical signal transmitting ends, a photodiode receiving end and user equipment located at the receiving end is constructed, an optical wireless communication signal waveform is used as measurement data of optical wireless positioning, and clock phase offset and clock frequency offset are used as time parameters; a time synchronization model is constructed by combining user equipment position parameters and user equipment direction parameters, then a time synchronization and positioning objective function is constructed based on measurement data of optical wireless positioning and the time synchronization model, and finally, the objective function is solved based on continuous linear least square and iterative update alternate optimization. The timing synchronization and optical wireless positioning joint estimation is realized, the optimal user equipment direction parameter, time parameter and user equipment position parameter are obtained, and the positioning precision is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of optical wireless positioning, and more specifically, to a joint timing synchronization and optical wireless positioning method based on continuous linear least squares. Background Art

[0002] In recent years, with the rapid development of 6G wireless networks, the need for multi-dimensional integration of mobile communications, sensing, and computing networks has become increasingly urgent. This trend is driving the rapid development of integrated communication and sensing technologies. Among the many applications that utilize integrated communication and sensing technologies for indoor positioning, optical wireless communication has attracted considerable attention. Optical wireless positioning uses optical signals to determine the location of target objects or devices. It combines optical sensing and wireless communication technologies to achieve high-precision positioning by analyzing the propagation characteristics of optical signals. In addition to its extremely low cost for long-distance data transmission, it experiences almost negligible interference in the signal transmission link, with the only interference coming from opaque obstacles and ambient light. This demonstrates its excellent communication and sensing performance in ultra-dense environments.

[0003] Existing optical wireless positioning technologies, such as those based on received signal strength (RSS), angle of arrival (AOA), and time of arrival (TOA), all demonstrate that achieving high positioning accuracy relies on perfect timing synchronization. However, due to measurement noise and low-cost clock equipment, timing errors inevitably occur in actual signal transmission, leading to significant performance degradation in optical wireless positioning. Existing research on positioning based on transmission delay mostly assumes precise time synchronization between the signal transmitter and receiver. Consequently, the resulting systems are overly idealized and have limited practical application value. Other studies have only considered clock phase offset or clock frequency offset, without fully considering parameters that affect clock synchronization.

[0004] To address the performance loss of optical wireless positioning due to timing errors, a method for real-time positioning of mobile targets based on visible light communication (VLC) has been proposed. This method employs a cellular topology to divide indoor LED nodes into multiple cells. A network source central node is selected to apply for time slots through competition, and the LEDs transmit optical signals according to these time slots. The terminal adaptively selects three LED reference nodes. A RSS positioning algorithm is used to calculate the transmission distance from the LED reference nodes to the terminal based on the received optical power. The optical power at the receiving end is corrected using a mean model. Finally, the terminal coordinates are calculated using the coordinates of the LED reference nodes and the transmission distance, achieving indoor positioning. This method resolves the conflict between frame length and the large number of LED nodes, minimizes the latency of the communication system, and addresses the impact of LED light obstruction and channel attenuation on positioning. However, the RSS positioning algorithm used in the prior art is susceptible to multipath effects, ambient light interference, and channel attenuation, and positioning accuracy is significantly reduced due to clock synchronization errors between the transmitter and receiver. Summary of the Invention

[0005] In order to solve the problem of reduced positioning accuracy due to clock synchronization errors at both ends of the transmitter and receiver in traditional optical wireless positioning methods based on transmission delay, the present invention proposes a joint timing synchronization and optical wireless positioning method based on continuous linear least squares, constructs a time synchronization and positioning objective function based on the measurement data and time synchronization model of optical wireless positioning, iteratively updates and alternately optimizes the objective function to achieve joint estimation of timing synchronization and optical wireless positioning, obtain the optimal timing synchronization parameters, user device position parameters and user device direction parameters, and improve positioning accuracy.

[0006] In order to achieve the above technical effects, the technical solutions of the present invention are as follows:

[0007] This application proposes a joint timing synchronization and optical wireless positioning method based on continuous linear least squares, including the following steps:

[0008] S1. Construct an indoor optical wireless positioning system, the system comprising: multiple LED optical signal transmitters, a photodiode receiving end, and a user device located at the receiving end, the receiving end receiving the optical wireless communication signal emitted by the transmitting end;

[0009] S2. Use the optical wireless communication signal waveform as the measurement data for optical wireless positioning, use the clock phase offset and clock frequency offset as time parameters, and combine the user device location parameters and user device direction parameters to construct a time synchronization model;

[0010] S3. Construct a time synchronization and positioning objective function based on the measurement data and time synchronization model of optical wireless positioning;

[0011] S4. Based on continuous linear least squares, the objective function is solved by iterative updating and alternating optimization to achieve joint estimation of timing synchronization and optical wireless positioning, and obtain the optimal user device direction parameters, time parameters and user device location parameters.

[0012] In this technical solution, an indoor optical wireless positioning system is constructed, which includes multiple LED light signal transmitters, a photodiode receiver, and a user device located at the receiver. The waveform of the optical wireless communication signal is used as the measurement data of the optical wireless positioning, and the clock phase deviation and clock frequency deviation are used as time parameters. In combination with the user device position parameters and the user device direction parameters, a time synchronization model is constructed. Then, based on the measurement data and the time synchronization model of the optical wireless positioning, a time synchronization and positioning objective function is constructed. Finally, based on the continuous linear least squares, the objective function is iteratively updated and alternately optimized to solve the objective function, thereby realizing joint estimation of timing synchronization and optical wireless positioning, and obtaining the optimal user device direction parameters, time parameters, and user device position parameters, thereby improving the positioning accuracy.

[0013] Preferably, the indoor optical wireless positioning system in step S1 includes M LED light signal transmitting ends, and the photodiode receives the optical wireless communication signal emitted by the LED light signal transmitting end; wherein the coordinate parameter of the mth LED light signal transmitting end is p m , the direction parameter is v m ; The location parameter of the user equipment at the receiving end is x R , the user equipment direction parameter is u R ;v m with u R are all unit vectors, and the expressions are:

[0014] ‖v m ‖2=1

[0015] ‖u R ‖2=1.

[0016] Preferably, before constructing the time synchronization model, the process further includes constructing a time synchronization model for a single signal, and the process is as follows:

[0017] The time parameter α R Expressed as: α R =[ζ R ,θ R ], where ζ R represents the clock phase deviation, θ R Indicates clock frequency deviation;

[0018] Define the time delay of the mth LED optical signal transmitter received by the user equipment at the standard time as τ m , the expression is:

[0019]

[0020] Among them, x R is the user equipment location parameter, p m is the coordinate parameter of the mth LED light signal transmitting end, c is the speed of light;

[0021] Using the time parameter α R Synchronize the time of the user equipment and delay the time of the mth LED light signal transmitter received by the user equipment at the standard time by τ m Mapped to the actual time delay when the user device has clock deviation The expression is:

[0022]

[0023] Calculate the emission angle φ of the mth LED light signal transmitter pointing to the user equipment m , the receiving angle θ of the user equipment receiving the mth LED light signal transmitter m , the expression is:

[0024]

[0025] Among them, T represents the transpose operation, x R is the user equipment location parameter, u R is the user equipment direction parameter, p m is the coordinate parameter of the mth LED light signal transmitting end, v m is the direction parameter of the mth LED light signal transmitting end;

[0026] Based on the emission angle φ m and the receiving angle θ m , construct the channel transfer function h ′ m , the expression is:

[0027]

[0028] Among them, h R is the response coefficient that depends on the photodiode aperture and gain, γ is the order of the channel transfer function;

[0029] Constructing a time-synchronous model for a single signal The expression is:

[0030]

[0031] in, is the nth pilot signal emitted by the mth LED light signal transmitter, n=1,…,N C , N Cis the total number of signals sent by the LED light signal transmitter at one time, m=1,…,M, M is the number of LED light signal transmitters, ι is a unit imaginary number, f m is the carrier frequency emitted by the mth LED optical signal transmitter, h ′ m is the channel transfer function.

[0032] Preferably, a time synchronization model that integrates all individual signals Construct the final time synchronization model g(α R β R ), the expression is:

[0033]

[0034] Among them, vec[] represents the operation of integrating the time synchronization models of all signals into a column vector.

[0035] Preferably, the waveform of a single optical wireless communication signal is used as the measurement data of the optical wireless positioning of a single signal, and the expression is:

[0036]

[0037] in, is a time synchronization model for a single signal, To measure noise,

[0038] The measurement data of optical wireless positioning of all optical wireless communication signals are integrated into the measurement data z, which is expressed as:

[0039]

[0040] Among them, ∈ represents the set of all measurement noises, g(α R β R ) represents the time synchronization model.

[0041] Preferably, the expression of the time synchronization and positioning objective function is:

[0042]

[0043] When the measurement data z is synchronized with the time-synchronized model g(α R β R ) is minimized, the optimal timing synchronization parameters are obtained. User device status collection parameters

[0044] Preferably, when iteratively updating and alternately optimizing the time synchronization and positioning objective functions, let and They are parameters μ R , α R and x R The state at the i-th iteration, at the i+1-th iteration, the parameter μ R , α R and x R The direction estimation algorithm, time parameter correction algorithm and positioning algorithm are used to update in sequence respectively.

[0045] Preferably, the iterative update alternately optimizes and solves the objective function to obtain the optimal user equipment direction parameter, and the process is:

[0046] Update the parameter μ using the direction estimation algorithm R , the update process satisfies:

[0047]

[0048] in, is the equivalent directional gain vector μ R The state at the i+1th iteration, The user device location parameter x R The state at the i-th iteration, is the timing synchronization parameter α R The state at the i-th iteration, and has been obtained in the i-th iteration;

[0049] Based on the equivalent directional gain vector μ R The optimal estimate of the user equipment direction parameter at the i+1th iteration is solved The expression is:

[0050]

[0051] Preferably, the iterative update alternately optimizes and solves the objective function to obtain the optimal time parameter, and the process is:

[0052] Update the time parameter α using the time parameter correction algorithm R , the update process satisfies:

[0053]

[0054] in, is the time parameter α R The state at the i+1th iteration, The user device location parameter x R The state at the i-th iteration, is the equivalent directional gain vector μ R The state at the i-th iteration, is the timing synchronization parameter α R The cost function of

[0055] Based on the continuous linear least squares method, the time parameter a at the i+1th iteration is obtained by iterative solution. R The best estimate of

[0056] Preferably, the iterative update alternately optimizes and solves the objective function to obtain the optimal user equipment location parameter, and the process is:

[0057] Use the positioning algorithm to update the user equipment location parameter x R ,The update process satisfies:

[0058]

[0059] in, The user device location parameter x R The state at the i+1th iteration, is the timing synchronization parameter α R The state at the i-th iteration, is the equivalent directional gain vector μ R The state at the i-th iteration, The user device location parameter x R The cost function of

[0060] Based on the continuous linear least squares method, the iterative solution is obtained to obtain the user equipment location parameter x at the i+1th iteration R The best estimate of

[0061] Compared with the prior art, the present invention has the following beneficial effects:

[0062] The present invention proposes a joint timing synchronization and optical wireless positioning method based on continuous linear least squares, constructs an indoor optical wireless positioning system for optical wireless communication signal transmission, uses the optical wireless communication signal waveform as the measurement data of optical wireless positioning, uses clock phase deviation and clock frequency deviation as time parameters, and combines user device position parameters and user device direction parameters to construct a time synchronization model. Then, based on the measurement data of optical wireless positioning and the time synchronization model, a time synchronization and positioning objective function is constructed. Finally, based on continuous linear least squares, the objective function is iteratively updated and alternately optimized to solve the objective function, thereby realizing joint estimation of timing synchronization and optical wireless positioning, obtaining the optimal user device direction parameters, time parameters and user device position parameters, and improving positioning accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1A schematic diagram showing a process flow of a method for joint timing synchronization and optical wireless positioning based on continuous linear least squares proposed in embodiment 1 of the present invention;

[0064] Figure 2 A schematic diagram showing the structure of the indoor optical wireless positioning system proposed in Example 2 of the present invention;

[0065] Figure 3 A schematic diagram showing a comparison of positioning performances of different positioning methods proposed in Example 3 of the present invention under different signal-to-noise ratios;

[0066] Figure 4 A schematic diagram showing a comparison of positioning performances of different positioning methods proposed in Example 3 of the present invention under different bandwidths;

[0067] Figure 5 A schematic diagram showing a comparison of clock frequency offset estimation errors of different time synchronization methods proposed in Example 3 of the present invention under different signal-to-noise ratio environments;

[0068] Figure 6 A schematic diagram showing a comparison of the estimation errors of clock phase offsets by different time synchronization methods proposed in Example 3 of the present invention under different signal-to-noise ratio environments;

[0069] Figure 7 A schematic diagram showing a comparison of clock frequency offset estimation errors of different time synchronization methods proposed in Example 3 of the present invention at different bandwidths;

[0070] Figure 8 A schematic diagram showing a comparison of the estimation errors of clock phase offsets under different bandwidths using different time synchronization methods proposed in Example 3 of the present invention. DETAILED DESCRIPTION

[0071] The accompanying drawings are for illustrative purposes only and are not to be construed as limiting this patent;

[0072] In order to better illustrate this embodiment, some parts of the drawings may be omitted, enlarged, or reduced, and do not represent the actual size;

[0073] It is understandable to those skilled in the art that descriptions of certain well-known contents may be omitted in the drawings.

[0074] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0075] The positional relationships described in the drawings are for illustrative purposes only and should not be construed as limiting this patent;

[0076] Example 1

[0077] This embodiment proposes a method for joint timing synchronization and optical wireless positioning based on continuous linear least squares. The flowchart of this method is shown in FIG. Figure 1 , including the following steps:

[0078] S1. Construct an indoor optical wireless positioning system, the system comprising: multiple LED optical signal transmitters, a photodiode receiving end, and a user device located at the receiving end, the receiving end receiving the optical wireless communication signal emitted by the transmitting end;

[0079] S2. Use the optical wireless communication signal waveform as the measurement data for optical wireless positioning, use the clock phase offset and clock frequency offset as time parameters, and combine the user device location parameters and user device direction parameters to construct a time synchronization model;

[0080] S3. Construct a time synchronization and positioning objective function based on the measurement data and time synchronization model of optical wireless positioning;

[0081] S4. Based on continuous linear least squares, the objective function is solved by iterative updating and alternating optimization to achieve joint estimation of timing synchronization and optical wireless positioning, and obtain the optimal user device direction parameters, time parameters and user device location parameters.

[0082] In this embodiment, an indoor optical wireless positioning system is constructed, including multiple LED optical signal transmitting ends, a photodiode receiving end, and a user device located at the receiving end. The waveform of the optical wireless communication signal is used as the measurement data of the optical wireless positioning, and the clock phase deviation and clock frequency deviation are used as time parameters. In combination with the user device position parameters and the user device direction parameters, a time synchronization model is constructed. Then, based on the measurement data of the optical wireless positioning and the time synchronization model, a time synchronization and positioning objective function is constructed. Finally, based on continuous linear least squares, the objective function is iteratively updated and alternately optimized to solve the objective function, thereby realizing joint estimation of timing synchronization and optical wireless positioning, obtaining the optimal user device direction parameters, time parameters, and user device position parameters, and improving positioning accuracy.

[0083] Example 2

[0084] In this embodiment, the structural diagram of the indoor optical wireless positioning system described in step S1 is as follows: Figure 2 As shown;

[0085] The system includes M LED light signal transmitting ends, and the photodiode receives the optical wireless communication signal emitted by the LED light signal transmitting end; wherein the coordinate parameter of the mth LED light signal transmitting end is p m , the direction parameter is v m ; The location parameter of the user equipment at the receiving end is x R , the user equipment direction parameter is u R ;v m with uR are all unit vectors, and the expressions are:

[0086] ‖v m ‖2=1

[0087] ‖u R ‖2=1.

[0088] In this embodiment, before constructing the time synchronization model, a time synchronization model for a single signal is also constructed. The process is as follows:

[0089] The time parameter α R Expressed as: α R =[ζ R ,θ R ], where ζ R represents the clock phase deviation, θ R Indicates clock frequency deviation;

[0090] Define the time delay of the mth LED optical signal transmitter received by the user equipment at the standard time as τ m , the expression is:

[0091]

[0092] Among them, x R is the user equipment location parameter, p m is the coordinate parameter of the mth LED light signal transmitting end, c is the speed of light;

[0093] Using the time parameter α R Synchronize the time of the user equipment and delay the time of the mth LED light signal transmitter received by the user equipment at the standard time by τ m Mapped to the actual time delay when the user device has clock deviation The expression is:

[0094]

[0095] Calculate the emission angle φ of the mth LED light signal transmitter pointing to the user equipment m , the receiving angle θ of the user equipment receiving the mth LED light signal transmitter m , the expression is:

[0096]

[0097] Among them, T represents the transpose operation, x R is the user equipment location parameter, u R is the user equipment direction parameter, p m is the coordinate parameter of the mth LED light signal transmitting end, v mis the direction parameter of the mth LED light signal transmitting end;

[0098] Based on the emission angle φ m and the receiving angle θ m , construct the channel transfer function h ′ m , the expression is:

[0099]

[0100] Among them, h R is the response coefficient that depends on the photodiode aperture and gain, γ is the order of the channel transfer function;

[0101] Constructing a time-synchronous model for a single signal The expression is:

[0102]

[0103] in, is the nth pilot signal emitted by the mth LED light signal transmitter, n=1,…,N C , N C is the total number of signals sent by the LED light signal transmitter at one time, m=1,…,M, M is the number of LED light signal transmitters, ι is a unit imaginary number, f m is the carrier frequency emitted by the mth LED optical signal transmitter, h ′ m is the channel transfer function.

[0104] In this embodiment, the time synchronization model of all individual signals is integrated Construct the final time synchronization model g(α R β R ), the expression is:

[0105]

[0106] Among them, vec[] represents the operation of integrating the time synchronization models of all signals into a column vector.

[0107] In this embodiment, the waveform of a single optical wireless communication signal is used as the measurement data of the optical wireless positioning of the single signal, and the expression is:

[0108]

[0109] in, is a time synchronization model for a single signal, To measure noise,

[0110] The measurement data of optical wireless positioning of all optical wireless communication signals are integrated into the measurement data z, which is expressed as:

[0111]

[0112] Among them, ∈ represents the set of all measurement noises, g(α R β R ) represents the time synchronization model.

[0113] In this embodiment, the expression of the time synchronization and positioning objective function is:

[0114]

[0115] When the measurement data z is synchronized with the time-synchronized model g(α R β R ) is minimized, the optimal timing synchronization parameters are obtained. User device status collection parameters

[0116] In this embodiment, when iteratively updating and alternately optimizing the time synchronization and positioning objective functions, let and They are parameters μ R , α R and x R The state at the i-th iteration, at the i+1-th iteration, the parameter μ R , α R and x R The direction estimation algorithm, time parameter correction algorithm and positioning algorithm are used to update in sequence respectively;

[0117] Specifically, before iteratively updating and alternatingly optimizing the time synchronization and positioning objective functions, the time synchronization and positioning objective functions are reconstructed. The process is as follows:

[0118] Define the equivalent directional gain vector μ R , the expression is:

[0119] μ R =h R *u R

[0120] in, h R is the responsivity that depends on the photodiode aperture and gain, u R is the user device direction parameter;

[0121] The time synchronization model g(α R β R ) is reconstructed into an equivalent directional gain vector μ RThe linear correlation expression is:

[0122] g(α R β R )=Γ(x R ,α R )*μ R

[0123] in,

[0124] The total time domain signal model z is reconstructed as the equivalent directional gain vector μ R The linear correlation expression is:

[0125] z=Γ(x R ,α R )*μ R +∈

[0126] The timing synchronization and optical wireless positioning objective function are reconstructed. The expressions of the reconstructed timing synchronization and optical wireless positioning objective function are:

[0127]

[0128] In this embodiment, the iterative update alternate optimization solves the objective function to obtain the optimal user equipment direction parameter. The process is as follows:

[0129] Update the parameter μ using the direction estimation algorithm R , the update process satisfies:

[0130]

[0131] in, is the equivalent directional gain vector μ R The state at the i+1th iteration, The user device location parameter x R The state at the i-th iteration, is the timing synchronization parameter α R The state at the i-th iteration, and has been obtained in the i-th iteration;

[0132] Because the measured data z depends linearly on the equivalent directional gain vector μ R , the update process is about μ R convex problem, so the estimated value of the i+1th iteration is It can be obtained by matrix solution, the expression is:

[0133]

[0134] in, is the symbol of the pseudo-inverse matrix;

[0135] Based on the equivalent directional gain vector μ R The optimal estimate of the user equipment direction parameter at the i+1th iteration is solved The expression is:

[0136]

[0137] In this embodiment, the iterative update alternate optimization solves the objective function to obtain the optimal time parameter, and the process is:

[0138] Update the time parameter α using the time parameter correction algorithm R , the update process satisfies:

[0139]

[0140] in, is the time parameter α R The state at the i+1th iteration, The user device location parameter x R The state at the i-th iteration, is the equivalent directional gain vector μ R The state at the i-th iteration, is the timing synchronization parameter α R The cost function of

[0141] Based on the continuous linear least squares method, the time parameter α at the i+1th iteration is obtained by iterative solution. R The best estimate of The specific process is:

[0142] The timing synchronization parameter α is constructed using the continuous linear least squares method. R The cost function Convex proxy function of The expression is:

[0143]

[0144] in, for exist α R The derivative of is expressed as:

[0145]

[0146] in, for exist α R The derivative of is expressed as:

[0147]

[0148] in, and Represents α R The derivative of two elements in is expressed as:

[0149]

[0150] The timing synchronization objective function is reconstructed into a convex optimization timing synchronization objective function, which is expressed as:

[0151]

[0152] The convex optimization timing synchronization objective function is solved by multiple iterations to obtain the timing synchronization parameter α at the i+1th iteration R The best estimate of The expression is:

[0153]

[0154] in, Indicates the pseudo-inverse matrix operation, and H indicates the conjugate transpose operation of the complex matrix;

[0155] Specifically, the clock phase deviation ζ R and clock frequency deviation θ R The expression at the i-th iteration is:

[0156]

[0157] in, Indicates taking the real part of a vector, [■]1 represents the first element of the vector, and [■]2 represents the second element of the vector.

[0158] In this embodiment, the iterative update alternate optimization solves the objective function to obtain the optimal user equipment location parameter. The process is as follows:

[0159] Use the positioning algorithm to update the user equipment location parameter x R ,The update process satisfies:

[0160]

[0161] in, The user device location parameter x R The state at the i+1th iteration, is the timing synchronization parameter α R The state at the i-th iteration, is the equivalent directional gain vector μ R The state at the i-th iteration, The user device location parameter x R The cost function of

[0162] Based on the continuous linear least squares method, the iterative solution is obtained to obtain the user equipment location parameter x at the i+1th iteration R The best estimate of The specific process is:

[0163] Use the continuous linear least squares method to construct the user equipment location parameter x R The cost function Convex proxy function of The expression is:

[0164]

[0165] in, for exist x R The derivative of is expressed as:

[0166]

[0167] in, for exist x R The derivative of is expressed as:

[0168]

[0169] in, represents the i-th incident vector, s m,[i] and w m,[i] The expressions are:

[0170]

[0171] The position estimation objective function is reconstructed into a convex optimization position estimation objective function, which is expressed as:

[0172]

[0173] The convex optimization position estimation objective function is solved by multiple iterations to obtain the user equipment position parameter x at the i+1th iteration R The best estimate of The expression is:

[0174]

[0175] in, represents the pseudo-inverse matrix operation, and H represents the conjugate transpose operation on the complex matrix.

[0176] Example 3

[0177] In this embodiment, the positioning performance of different positioning methods under different signal-to-noise ratio environments is compared. The comparison results are as follows: Figure 3 As shown, the TDOA method without time synchronization represented by baseline 4 is robust to changes in signal-to-noise ratio and performs well in low signal-to-noise ratio scenarios. The root mean square RSS method represented by baseline 1 and the TOA method without time positioning represented by baseline 2 tend to show better performance at high signal-to-noise ratios, wherein the root mean square RSS method has an inherent lower limit of error, and the TOA method without time positioning can continue to improve accuracy as the signal-to-noise ratio increases. The joint timing synchronization and optical wireless positioning method based on continuous linear least squares proposed in the present invention is better than all baseline methods in positioning error clock in the entire signal-to-noise ratio range, and the positioning performance steadily improves with the improvement of the signal-to-noise ratio.

[0178] In this embodiment, the positioning performance of different positioning methods under different bandwidth conditions is compared. The comparison results are as follows: Figure 4 As shown, the fixed subcarrier frequency interval is 1 MHz, and the transmission bandwidth varies with the number of subcarriers. As the bandwidth increases, the joint timing synchronization based on continuous linear least squares proposed by the present invention always maintains performance advantages over baseline methods 1, 2, and 4 compared with the optical wireless positioning method. The baseline method 1 based on RSS is superior to the algorithm in that it is insensitive to frequency changes and exhibits the worst positioning performance, while the positioning errors of the remaining methods decrease with the increase of bandwidth, thanks to the fact that more subcarriers improve the spatial resolution. Compared with the baseline method 4 using the cross-correlation method for timing, the baseline method 2 based on the SLLS method and the method proposed by the present invention show better convergence performance, verifying the advantages of the SLLS-based method in positioning accuracy. At the same time, compared with the baseline method 2 without clock calibration, the method proposed by the present invention achieves higher convergence accuracy, confirming the key role of precise time synchronization.

[0179] In this embodiment, the estimation errors of clock frequency offsets of different time synchronization methods under different signal-to-noise ratio environments are compared. The comparison results are as follows: Figure 5 As shown in the figure, the estimation errors of clock phase offsets of different time synchronization methods under different signal-to-noise ratio environments are compared. The comparison results are shown in Figure 6 As shown in the figure, due to inherent algorithm limitations, the STS scheme-based method represented by baseline 3 and the TDOA method without time synchronization represented by baseline 4 both show a lower limit of estimation error in the high SNR region, while the method proposed in the present invention maintains high performance for both clock frequency deviation and clock phase deviation in the entire test SNR range, and gradually reduces the error as the SNR increases.

[0180] In this embodiment, the estimation errors of clock frequency offsets under different bandwidths using different time synchronization methods are compared. The comparison results are as follows: Figure 7 As shown in the figure, the estimation error of clock phase offset of different time synchronization methods under different bandwidths is compared. The comparison results are shown in the figure. Figure 8 As shown in the figure, the clock frequency and phase offset errors of the proposed method decrease continuously with increasing bandwidth, and the clock phase offset estimation accuracy reaches the nanosecond level. Although the convergence curve fluctuates, the timing performance of the proposed method consistently outperforms the STS scheme-based method (Baseline 3) and the TDOA method without time synchronization (Baseline 4) as the carrier frequency increases.

[0181] Obviously, the above embodiments of the present invention are merely examples for the purpose of clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the claims of the present invention.

Claims

1. A joint timing synchronization and optical wireless positioning method based on continuous linear least squares, characterized in that: The following steps are involved: S1. Construct an indoor optical wireless positioning system, the system comprising: multiple LED optical signal transmitters, a photodiode receiving end, and a user device located at the receiving end, the receiving end receiving the optical wireless communication signal emitted by the transmitting end; S2. Use the optical wireless communication signal waveform as the measurement data for optical wireless positioning, use the clock phase offset and clock frequency offset as time parameters, and combine the user device location parameters and user device direction parameters to construct a time synchronization model; S3. Construct a time synchronization and positioning objective function based on the measurement data and time synchronization model of optical wireless positioning; S4. Based on continuous linear least squares, the objective function is solved by iterative updating and alternating optimization to achieve joint estimation of timing synchronization and optical wireless positioning, and obtain the optimal user device direction parameters, time parameters and user device location parameters.

2. The method of joint timing synchronization and optical wireless positioning based on continuous linear least squares according to claim 1, characterized in that: Step S1: The indoor optical wireless positioning system includes M LED light signal transmitting ends, and the photodiode receives the optical wireless communication signal emitted by the LED light signal transmitting end; wherein the coordinate parameter of the mth LED light signal transmitting end is p m , the direction parameter is v m ; The location parameter of the user equipment at the receiving end is x R , the user equipment direction parameter is u R ;v m with u R are all unit vectors, and the expressions are: ‖v m ‖2＝1 ‖u R ‖2＝1。 3. The method of joint timing synchronization and optical wireless positioning based on continuous linear least squares according to claim 2, characterized in that: Before constructing the time synchronization model, a time synchronization model for a single signal is also constructed. The process is as follows: The time parameter α R Expressed as: Among them, R Indicates the clock phase deviation, Indicates clock frequency deviation; Define the time delay of the mth LED optical signal transmitter received by the user equipment at the standard time as τ m , the expression is: Among them, x R is the user equipment location parameter, p m is the coordinate parameter of the mth LED light signal transmitting end, c is the speed of light; Using the time parameter α R Synchronize the time of the user equipment and delay the time of the mth LED light signal transmitter received by the user equipment at the standard time by τ m Mapped to the actual time delay when the user device has clock deviation The expression is: Calculate the emission angle φ of the mth LED light signal transmitter pointing to the user equipment m , the receiving angle θ of the user equipment receiving the mth LED light signal transmitter m , the expression is: Among them, T represents the transpose operation, x R is the user equipment location parameter, u R is the user equipment direction parameter, p m is the coordinate parameter of the mth LED light signal transmitting end, v m is the direction parameter of the mth LED light signal transmitting end; Based on the emission angle φ m and the receiving angle θ m , construct the channel transfer function h ′ m , the expression is: Among them, h R is the response coefficient that depends on the photodiode aperture and gain, γ is the order of the channel transfer function; Constructing a time-synchronous model for a single signal The expression is: in, is the nth pilot signal emitted by the mth LED light signal transmitter, N C is the total number of signals sent by the LED light signal transmitter at one time, m=1,…,M, M is the number of LED light signal transmitters, ι is a unit imaginary number, f m is the carrier frequency emitted by the mth LED optical signal transmitter, h ′ m is the channel transfer function.

4. The method of joint timing synchronization and optical wireless positioning based on continuous linear least squares according to claim 3, characterized in that: A time-synchronous model that integrates all individual signals Construct the final time synchronization model g(α R β R ), the expression is: Among them, vec[] represents the operation of integrating the time synchronization models of all signals into a column vector.

5. The method of joint timing synchronization and optical wireless positioning based on continuous linear least squares according to claim 3, characterized in that: The waveform of a single optical wireless communication signal is used as the measurement data of optical wireless positioning of a single signal, and the expression is: in, is a time synchronization model for a single signal, To measure noise, The measurement data of optical wireless positioning of all optical wireless communication signals are integrated into the measurement data z, which is expressed as: Among them, ∈ represents the set of all measurement noises, g(α R β R ) represents the time synchronization model.

6. The method of joint timing synchronization and optical wireless positioning based on continuous linear least squares according to claim 5, characterized in that: The expression of the time synchronization and positioning objective function is: When the measurement data z is synchronized with the time-synchronized model g(α R β R ) is minimized, the optimal timing synchronization parameters are obtained. User device status collection parameters 7. The method of joint timing synchronization and optical wireless positioning based on continuous linear least squares according to claim 6, characterized in that: When iteratively updating and alternatingly optimizing the time synchronization and positioning objective functions, let and They are parameters μ R , α R and x R The state at the i-th iteration, at the i+1-th iteration, the parameter μ R , α R and x R The direction estimation algorithm, time parameter correction algorithm and positioning algorithm are used to update in sequence respectively.

8. The method of joint timing synchronization and optical wireless positioning based on continuous linear least squares according to claim 7, characterized in that: The iterative update alternately optimizes and solves the objective function to obtain the optimal user equipment direction parameter. The process is: Update the parameter μ using the direction estimation algorithm R , the update process satisfies: in, is the equivalent directional gain vector μ R The state at the i+1th iteration The user device location parameter x R The state at the i-th iteration, is the timing synchronization parameter α R The state at the i-th iteration, and has been obtained in the i-th iteration; Based on the equivalent directional gain vector μ R The optimal estimate of the user equipment direction parameter at the i+1th iteration is solved The expression is:

9. The method of joint timing synchronization and optical wireless positioning based on continuous linear least squares according to claim 8, characterized in that: The iterative update alternately optimizes and solves the objective function to obtain the optimal time parameter. The process is: Update the time parameter α using the time parameter correction algorithm R , the update process satisfies: in, is the time parameter α R The state at the i+1th iteration, The user device location parameter x R The state at the i-th iteration, is the equivalent directional gain vector μ R The state at the i-th iteration, is the timing synchronization parameter α R The cost function of Based on the continuous linear least squares method, the time parameter α at the i+1th iteration is obtained by iterative solution. R The best estimate of 10. The method of joint timing synchronization and optical wireless positioning based on continuous linear least squares according to claim 9, characterized in that: The iterative update alternately optimizes and solves the objective function to obtain the optimal user equipment location parameter. The process is as follows: Use the positioning algorithm to update the user equipment location parameter x R ,The update process satisfies: in, The user device location parameter x R The state at the i+1th iteration, is the timing synchronization parameter α R The state at the i-th iteration, is the equivalent directional gain vector μ R The state at the i-th iteration, The user device location parameter x R The cost function of Based on the continuous linear least squares method, the iterative solution is obtained to obtain the user equipment location parameter x at the i+1th iteration R The best estimate of

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