A new type of basic surveying and mapping equipment positioning method and system based on Beidou technology

Abstract

This invention discloses a novel positioning method and system for basic surveying and mapping equipment based on BeiDou technology, relating to the field of surveying and mapping positioning technology. The method includes receiving radio frequency signals and position coordinates from BeiDou satellites, preprocessing them to generate a baseband signal; demodulating and calculating the baseband signal to generate a complex-form observation signal, and calculating the signal-to-noise ratio for validity detection and sampling verification, obtaining verification results, including whether the current sample is undersampled or complete; when the current sample is undersampled, extracting an instantaneous frequency set based on the baseband signal and generating a preliminary phase coefficient vector, and using a polynomial phase function and residual judgment mechanism to determine the feasibility of the preliminary phase coefficient vector; this invention achieves robust recovery and high-precision positioning calculation for incomplete signals, significantly improving the stability and accuracy of surveying and mapping equipment positioning in complex environments.

Description

Technical Field

[0001] This invention relates to the field of surveying and mapping positioning technology, and in particular to a new positioning method and system for basic surveying and mapping equipment based on BeiDou technology. Background Technology

[0002] With the rapid development of Global Navigation Satellite Systems (GNSS), satellite positioning and navigation technologies have been widely applied in basic surveying and mapping, engineering construction, geographic information systems, and unmanned telemetry and control. Among them, the BeiDou Navigation Satellite System (BDS), as my country's independently constructed and operated global navigation satellite system, has demonstrated significant value in high-precision surveying and mapping and geographic information acquisition due to its multi-frequency, global coverage, and regional enhancement features. Traditional GNSS surveying equipment positioning methods are mostly based on the joint calculation of code pseudorange observations and carrier phase observations. Satellite orbit parameters are obtained by demodulating the navigation message through the receiver, and the position of the surveying equipment is iteratively solved using the pseudorange equation. However, in complex environments, BeiDou signals are easily affected by the ionosphere, troposphere, multipath effects, and obstruction interference, resulting in inconsistent signal quality, low signal-to-noise ratio, incomplete sampling points, and disrupted phase continuity. These uncertainties and noise interference severely restrict the reliability and robustness of high-precision surveying and mapping, making it difficult for existing technologies to stably achieve centimeter-level or even sub-meter-level positioning accuracy in undersampling and high-noise environments. Summary of the Invention

[0003] In view of the aforementioned existing problems, the present invention is proposed.

[0004] Therefore, this invention provides a novel positioning method and system for basic surveying and mapping equipment based on BeiDou technology, which solves the problem that the reliability and robustness of high-precision surveying and mapping are severely restricted by the uncertainty and noise interference of existing technologies, making it difficult for existing technologies to stably achieve centimeter-level or even sub-meter-level positioning accuracy in undersampling and high-noise environments.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0006] Firstly, the present invention provides a novel positioning method for basic surveying and mapping equipment based on BeiDou technology, which includes,

[0007] The radio frequency signals and position coordinates received from BeiDou satellites are preprocessed to generate baseband signals;

[0008] Based on the baseband signal, demodulation and decomposition are performed to generate the complex form of the observation signal. The signal-to-noise ratio is calculated for validity detection and sampling verification to obtain the verification results, including whether the current sample is undersampled or complete.

[0009] When the current sample is undersampled, the instantaneous frequency set is extracted based on the baseband signal, and a preliminary phase coefficient vector is generated. The preliminary phase coefficient vector is then judged as feasible or infeasible by combining the polynomial phase function and the residual judgment mechanism.

[0010] Based on the feasible results, a correction operation is performed to generate the final phase correction value vector. The maximum likelihood criterion function is constructed and combined with a hybrid optimization algorithm to update the final phase correction value vector, and the optimal correction vector is output. The positioning solution is performed based on the optimal correction vector to obtain the coordinate position and clock difference of the surveying equipment as the positioning basis.

[0011] The hybrid optimization algorithm refers to a combination of particle swarm optimization algorithm and gravity search algorithm.

[0012] As a preferred embodiment of the novel basic surveying and mapping equipment positioning method based on BeiDou technology described in this invention, the method involves: demodulating and solving the baseband signal to generate a complex form observation signal, calculating the signal-to-noise ratio (SNR) for validity detection and sampling verification, and obtaining the verification result. Specifically, based on the baseband signal, envelope demodulation and phase calculation are performed to generate the amplitude and phase of the baseband signal. The amplitude and phase are used as observation signals, and a timestamp is added. All observation signals are uniformly modeled to generate complex form observation signals at different times. The SNR of the complex form observation signal is then obtained using the standard SNR formula, and validity detection is performed to generate a detection result. Sampling verification is then performed based on the detection result.

[0013] As a preferred embodiment of the positioning method for a novel basic surveying and mapping equipment based on BeiDou technology described in this invention, the step of extracting an instantaneous frequency set based on the baseband signal and generating a preliminary phase coefficient vector, and combining a polynomial phase function and a residual judgment mechanism to perform a feasibility-infeasibility judgment on the preliminary phase coefficient vector, refers to using a sliding window to divide the baseband signal into frames when the current sample is undersampled, and using a short-time Fourier transform to perform time-frequency conversion on the baseband signal in each frame to obtain the frequency variable under each frame signal, and then maximizing it to generate the instantaneous frequency of each frame signal at different times, and recording the timestamp;

[0014] Instantaneous frequencies from different times are integrated to form a set of instantaneous frequencies for the current baseband signal. Random numbers are generated using a uniformly distributed random number generator, and non-repeating instantaneous frequencies are randomly selected from the set of instantaneous frequencies based on the random numbers to generate the observation vector of the current baseband signal. Based on the selected instantaneous frequencies, the timestamps corresponding to the instantaneous frequencies are integrated into a regression matrix. The observation vector and the regression matrix are fitted using the least squares method to generate a preliminary phase coefficient vector.

[0015] The preliminary phase coefficients are extracted from the preliminary phase coefficient vector, a polynomial phase function is constructed, the phase estimate is calculated, the first-order time derivative is solved based on the phase estimate and defined as the reconstruction frequency, the reconstruction vector is constructed, and the residual vector between the reconstruction vector and the observation vector is solved by element-wise subtraction. The squared Euclidean norm of the residual vector is used to determine the feasibility of the preliminary phase coefficient vector.

[0016] As a preferred embodiment of the positioning method for a novel basic surveying and mapping equipment based on BeiDou technology described in this invention, wherein: the step of performing a correction operation to generate a final phase correction value vector based on feasible results refers to performing a dechirping operation on the baseband signal based on a feasible preliminary phase coefficient vector, generating a dechirped signal, performing phase unwrapping, obtaining unwrapped phase values, splicing them together, and generating a phase vector;

[0017] Using the timestamps of all instantaneous frequencies in the instantaneous frequency set, a new regression matrix is ​​reconstructed and combined with the phase vector to perform a quadratic regression, generating a correction vector. This correction vector is then summed with the initial phase coefficient vector to obtain the final phase correction value vector o.

[0018] Before performing the quadratic regression, the total number of instantaneous frequencies K in the instantaneous frequency set is counted, and the new regression matrix is ​​verified in combination with the total number of orders M of the polynomial phase function. When the total number K ≥ < +1, it means that the verification is satisfied and the quadratic regression can be performed. Otherwise, the total number of orders M of the polynomial phase function is adjusted to the total number K-1, and the initial phase coefficient vector is recalculated for verification again.

[0019] As a preferred embodiment of the positioning method for a novel basic surveying and mapping equipment based on BeiDou technology described in this invention, the step of constructing the maximum likelihood criterion function and combining it with a hybrid optimization algorithm to update the final phase correction value vector refers to extracting the final phase correction value based on the final phase correction value vector o, constructing the maximum likelihood criterion function, and then updating and iterating iteratively. After iterating to the maximum number of times, candidate phase correction values ​​are output and combined to generate a candidate phase correction value vector.

[0020] Based on the candidate phase correction value vector, after being treated as an individual particle, the initial velocity and position of the individual particle are randomly set in a uniformly distributed random manner, and a population is randomly generated for initialization.

[0021] The modulus of the maximum likelihood criterion function is defined as the fitness function. The fitness values ​​are calculated, and the maximum and minimum fitness values ​​in the fitness value calculation results are normalized using the maximum and minimum fitness values ​​as the weights for each individual particle.

[0022] After calculating the distance between any two individual particles using Euclidean distance, the gravitational force between any two individual particles is calculated using a gravity search algorithm in combination with the weights. A uniformly distributed random number is generated using a random number generator. After calculating the resultant force of each individual particle in combination with the gravity, the ratio between the resultant force and the weights is used as the acceleration value.

[0023] When using the gravity search algorithm to calculate the gravitational force between any two individual particles, the maximum distance is selected through a maximization operation, the initial value of the gravitational constant is calculated, and the initial value of the gravitational constant is updated through an exponential decay method.

[0024] Based on the acceleration value, the acceleration value is used as a perturbation term and added to the standard velocity update formula of the particle swarm optimization algorithm by summation. The standard memory and collaborative update mechanism is used to update and iterate the position of each individual particle. After the maximum number of iterations, the optimal correction vector is output.

[0025] As a preferred embodiment of the positioning method for a novel basic surveying and mapping equipment based on BeiDou technology described in this invention, the step of performing positioning calculation based on the optimal correction vector refers to extracting the optimal phase coefficient based on the optimal correction vector, recalculating the phase estimate using a polynomial phase function, recalculating the first-order time derivative based on the phase estimate, defining it as a new frequency, integrating the new frequency using the integral accumulation method, converting the carrier phase observation value, and generating pseudorange observation values ​​of BeiDou satellites.

[0026] Based on the position coordinates of BeiDou satellites and combined with pseudorange observations, positioning equations for all BeiDou satellites are generated, forming a set of positioning equations. The least squares method is used to iteratively solve the positioning equations to obtain the coordinate position and clock error of the surveying equipment as the positioning basis.

[0027] As a preferred embodiment of the novel basic surveying and mapping equipment positioning method based on BeiDou technology described in this invention, the method of receiving radio frequency signals and position coordinates from BeiDou satellites and preprocessing them to generate baseband signals indicates that the surveying and mapping equipment is equipped with a multi-frequency antenna and receiver.

[0028] The radio frequency signals from BeiDou satellites are received by a multi-frequency antenna, denoised, normalized, and down-converted to generate the baseband signals of BeiDou satellites. The broadcast ephemeris of BeiDou satellites is received by a receiver, and the position coordinates of BeiDou satellites are obtained from the broadcast ephemeris using the GNSS Kepler orbit propagation method.

[0029] Secondly, this invention provides a novel positioning system for basic surveying and mapping equipment based on BeiDou technology, comprising:

[0030] The processing and verification module is used to receive the radio frequency signals and position coordinates of Beidou satellites for preprocessing, generate baseband signals for demodulation and decoding, calculate the signal-to-noise ratio, and perform validity detection and sampling verification.

[0031] The generation and judgment module is used to extract the instantaneous frequency set and combine the polynomial phase function and residual judgment mechanism to make a feasible-infeasible judgment.

[0032] The update solution module is used to perform correction operations, construct the maximum likelihood criterion function, and combine it with a hybrid optimization algorithm to update and perform localization solutions.

[0033] Thirdly, the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, wherein when the computer program is executed by the processor, it implements any step of the novel basic surveying and mapping equipment positioning method based on BeiDou technology as described in the first aspect of the present invention.

[0034] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein: when the computer program is executed by a processor, it implements any step of the novel basic surveying and mapping equipment positioning method based on BeiDou technology as described in the first aspect of the present invention.

[0035] The beneficial effects of this invention are as follows: By extracting instantaneous frequency, constructing polynomial phase functions, determining and correcting residuals, and further combining the maximum likelihood criterion and hybrid optimization algorithm, this invention achieves robust recovery and high-precision positioning calculation of incomplete signals, significantly improving the stability and accuracy of positioning of surveying equipment in complex environments. Attached Figure Description

[0036] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This is a flowchart of the new basic surveying and mapping equipment positioning method based on Beidou technology in Example 1.

[0038] Figure 2 This is a structural diagram of the new basic surveying and mapping equipment positioning system based on BeiDou technology in Example 1.

[0039] Figure 3 This is a flowchart of the localization calculation performed based on the optimal correction vector in Example 1. Detailed Implementation

[0040] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0041] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0042] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0043] Example 1, referring to Figures 1-3 This is the first embodiment of the present invention, which provides a novel positioning method for basic surveying and mapping equipment based on BeiDou technology, including the following steps:

[0044] S1. Receive the radio frequency signals and position coordinates of BeiDou satellites, preprocess them, and generate baseband signals;

[0045] Specifically, the radio frequency signals and position coordinates received from BeiDou satellites are preprocessed to generate baseband signals for the mapping equipment equipped with multi-frequency antennas and receivers;

[0046] The radio frequency signals from BeiDou satellites are received by a multi-frequency antenna, and then denoised, normalized, and down-converted to generate the baseband signals of BeiDou satellites.

[0047] The receiver receives the broadcast ephemeris of the BeiDou satellites and uses the GNSS Kepler orbit propagation method to obtain the position coordinates of the BeiDou satellites from the broadcast ephemeris.

[0048] The system acquires signals from BeiDou satellites using a multi-frequency antenna and a high-performance receiver. This effectively increases the number of available satellites in complex environments. The multi-frequency antenna refers to an antenna system capable of simultaneously receiving signals from multiple BeiDou frequencies, such as B1I, B2a, and B3I. Furthermore, denoising and digital normalization preprocessing effectively suppress signal amplitude fluctuations, improving demodulation success rates under weak signal conditions. Secondly, satellite coordinates are obtained using the Kepler orbital propagation method, providing data support for subsequent positioning calculations.

[0049] S2. Based on the baseband signal, demodulate and decompute to generate the complex form observation signal, and calculate the signal-to-noise ratio for validity detection and sampling verification to obtain the verification result;

[0050] Specifically, based on the baseband signal, demodulation and decoding are performed to generate a complex form observation signal. The signal-to-noise ratio (SNR) is then calculated for validity detection and sampling verification. The verification result is obtained by performing envelope demodulation and phase decoding on the baseband signal to generate the amplitude and phase of the baseband signal. The amplitude and phase are used as the observation signal, and a timestamp is added. All observation signals are uniformly modeled to generate complex form observation signals at different times. The SNR of the complex form observation signal is then obtained using the standard SNR formula. Validity detection is then performed to generate the detection result, and sampling verification is performed based on the detection result.

[0051] The formula for generating complex-form observation signals at different times is:

[0052] x(n)=A·exp(jφ(n))

[0053] In the formula, x(n) represents the complex form of the observed signal at time n, A represents the signal amplitude, exp(·) represents the exponential function, φ(n) represents the signal phase at time n, and j represents the imaginary unit (j 2 =-1);

[0054] The next step is to perform an effectiveness test and generate a test result. This involves setting a test threshold based on relevant book knowledge and experiments. If the signal-to-noise ratio is less than the test threshold, the current signal is considered an invalid sample and is removed. Otherwise, the current signal is considered a valid sample and is retained.

[0055] The sampling verification refers to setting the number of samples using the Nyquist sampling theorem, counting the total number of valid samples, and then using a ratio formula to obtain the ratio between the total number of valid samples and the number of samples, which is defined as the sampling ratio. An empirical rule is used to set a judgment threshold. If the sampling ratio is less than the judgment threshold, the current sample is considered to be undersampled; otherwise, the current sample is considered to be complete, and the localization calculation is performed directly.

[0056] By combining the generation of signals in complex form with signal-to-noise ratio (SNR) detection and sampling verification, a dual-guarantee mechanism is formed. Amplitude and phase exist uniformly under complex modeling, allowing the intrinsic characteristics of the signal to be fully expressed. SNR detection provides point-by-point validity screening, and sampling verification ensures temporal integrity. Furthermore, this dual-guarantee mechanism guarantees that the observed data meets the prerequisites for positioning calculation in both quality and quantity. Undersampling and noise interference are common problems in surveying equipment. This invention effectively avoids data anomalies through residual judgment and threshold determination, preventing calculation divergence and enabling adaptive selection of subsequent phase coefficients, greatly enhancing the robustness of positioning under undersampling conditions.

[0057] S3. When the current sample is undersampled, extract the instantaneous frequency set based on the baseband signal and generate a preliminary phase coefficient vector. Combine the polynomial phase function and residual judgment mechanism to make a feasible-infeasible judgment on the preliminary phase coefficient vector.

[0058] Specifically, the instantaneous frequency set is extracted based on the baseband signal, and a preliminary phase coefficient vector is generated. The feasibility-infeasibility judgment of the preliminary phase coefficient vector is performed by combining the polynomial phase function and the residual judgment mechanism. When the current sample is undersampled, the baseband signal is divided into frames using a sliding window. In each frame, the baseband signal is converted to time and frequency using short-time Fourier transform (STFT) to obtain the frequency variable of each frame signal. Then, the frequency variable is maximized to generate the instantaneous frequency of each frame signal at different times and the timestamp is recorded.

[0059] The time-frequency conversion of the baseband signal using Short-Time Fourier Transform (STFT) is described by the following formula:

[0060] STFT(n,w)=T{x(n i )exp(-jw(n i -n))}

[0061]

[0062] In the formula, STFT(n,w) represents the frequency variable obtained by short-time Fourier transform within a window of time n, T{·} represents the robust operator, and x(n) i ) represents the i-th baseband signal within the window of time n, exp(·) represents the exponential function, and j represents the imaginary unit (i.e., the direction of phase rotation is negative, j 2 =-1), w represents the frequency variable, (n i -n) represents the relative time difference, h represents the length of the time window, and ∈ indicates belonging to;

[0063] The robust operator can be set as the alpha-trimmed mean algorithm, and the specific calculation formula is as follows:

[0064] T{x(n i )}=median(real(x(n i )))+j·median(imag(x(n i )))

[0065] In the formula, median(·) represents the median function, real(·) represents the function that takes the real part of the complex number, and imag(·) represents the function that takes the imaginary part of the complex number;

[0066] The formula for further maximization is:

[0067] w'(n) = arg max w ||STFT h (n,w)||

[0068] In the formula, w'(n) represents the instantaneous frequency at time n, and arg max w This indicates the operation of taking the maximum value based on the frequency variable, and ||·|| indicates the modulus operation.

[0069] Integrate the instantaneous frequencies at different times to form a set of instantaneous frequencies of the current baseband signal. Use a uniformly distributed random number generator to generate random numbers, and randomly select non-repeating instantaneous frequencies from the set of instantaneous frequencies based on the random numbers to generate the observation vector of the current baseband signal.

[0070] Based on the selected instantaneous frequency, the timestamps corresponding to the instantaneous frequency are integrated into a regression matrix;

[0071] The observation vector and the regression matrix are fitted using the least squares method to generate a preliminary phase coefficient vector;

[0072] The least squares method is used to fit the observation vector and the regression matrix, and the formula is as follows:

[0073]

[0074] In the formula, Let Γ represent the coefficients of the m-th initial phase of the polynomial phase function at the λ-th iteration, Γ represent the regression matrix, and T represent the transpose operation. Represents the observation vector;

[0075] Extract the initial phase coefficients from the initial phase coefficient vector, construct a polynomial phase function, calculate the phase estimate, and solve for the first-order time derivative based on the phase estimate, which is defined as the reconstructed frequency.

[0076] The polynomial phase function is constructed using the following formula:

[0077]

[0078] In the formula, φ'(n) represents the initial phase coefficient at time n, a0 represents the coefficient of the initial phase, M represents the total number of orders, and a m The coefficients representing the initial phase of the m-th order are... This represents the m-th power at time n;

[0079] The formula for calculating the first-order time derivative based on the phase estimate is as follows:

[0080]

[0081] In the formula, c(n) represents the reconstruction frequency at time n;

[0082] Based on the reconstruction frequency, a reconstruction vector is constructed, and the residual vector between the reconstruction vector and the observation vector is solved by element-wise subtraction. The squared Euclidean norm of the residual vector is used to make a feasibility-infeasibility judgment on the initial phase coefficient vector.

[0083] The feasibility-infeasibility judgment of the preliminary phase coefficient vector by taking the square of the Euclidean norm of the residual vector refers to setting a judgment threshold based on standard industry knowledge and experiments. When the square of the Euclidean norm is less than the judgment threshold, the preliminary phase coefficient vector is considered feasible; otherwise, the preliminary phase coefficient vector is discarded and resampling is performed (i.e., random selection of non-repeating instantaneous frequencies from the instantaneous frequency set).

[0084] By extracting local frequencies using a sliding window and STFT, and then applying robust operators for noise reduction, the results remain stable even in low signal-to-noise ratio environments. Furthermore, the formation of the observation vector utilizes a uniformly distributed random number generator for non-repeating sampling, avoiding matrix singularity issues caused by high correlation of sample points. This ensures the reversibility and robustness of the least-squares fitting process. Using a conventional fixed-point selection strategy would easily lead to ill-conditioned regression matrices and non-convergence. The residual judgment mechanism compares the reconstructed frequencies with the observation vector point-by-point and calculates the squared Euclidean norm, establishing a judgment index directly related to the physical characteristics of the signal. This avoids the uncertainty of relying solely on statistical filtering or empirical thresholds, providing a rigorous mathematical basis for the "feasibility-infeasibility" judgment. Therefore, this step ensures that even with lost sampling points and severe noise interference, the invention can still generate a stable set of instantaneous frequencies, maintaining the effectiveness of the overall solution chain.

[0085] S4. Based on the feasible results, perform correction operations to generate the final phase correction value vector, construct the maximum likelihood criterion function and combine it with the hybrid optimization algorithm to update the final phase correction value vector, output the optimal correction vector, and perform positioning calculation based on the optimal correction vector to obtain the coordinate position and clock difference of the surveying equipment as the positioning basis.

[0086] Hybrid optimization algorithms refer to a combination of particle swarm optimization and gravity search algorithms;

[0087] Specifically, based on feasible results, performing correction operations to generate the final phase correction value vector refers to performing a dechirping operation on the baseband signal based on feasible preliminary phase coefficient vectors, generating a dechirped signal, performing phase unwrapping, obtaining unwrapped phase values, splicing them together, and generating a phase vector.

[0088] Using the timestamps of all instantaneous frequencies in the instantaneous frequency set, a new regression matrix is ​​reconstructed and combined with the phase vector to perform a quadratic regression, generating a correction vector. This correction vector is then summed with the initial phase coefficient vector to obtain the final phase correction value vector o.

[0089] Before performing the quadratic regression, the total number of instantaneous frequencies K in the instantaneous frequency set is counted, and the new regression matrix is ​​verified in combination with the total number of orders M of the polynomial phase function. When the total number K ≥ < +1, it means that the verification is satisfied and the quadratic regression can be performed. Otherwise, the total number of orders M of the polynomial phase function is adjusted to the total number K-1, and the initial phase coefficient vector is recalculated for verification again.

[0090] The formula for performing the dechirping operation on the baseband signal is as follows:

[0091]

[0092] In the formula, b(n) represents the dechirped signal at time n;

[0093] The reconstructed regression matrix, combined with the phase vector, is used to perform quadratic regression, as follows:

[0094] k=(Ξ T Ξ) -1 ΞΨ

[0095] In the formula, k represents the correction vector, Ξ represents the new regression matrix, T represents the transpose operation, and Ψ represents the phase vector.

[0096] By dechirping, the rapidly changing high-order phase terms in the original signal are weakened, and the residual signal exhibits low-order phase characteristics. This simplified component reduces complexity and makes subsequent unwrapping and regression calculations more stable, effectively avoiding interference from high-frequency noise in phase modeling. Phase unwrapping transforms the original phase folded curve into a continuous curve, and the resulting phase vector encompasses complete time-domain information, thus restoring the true physical phase evolution of the signal. Furthermore, by constructing a new regression matrix using the timestamps of all sample points in the instantaneous frequency set, all available information can be fully utilized. Quadratic regression introduces the phase vector as an observation and directly solves for the correction vector, thereby improving the global robustness of phase estimation. Compared to preliminary regression that relies only on a subset of sampling points, this step significantly reduces the error caused by undersampling. Secondly, the correction vector is added to the preliminary phase coefficient as compensation to obtain the final phase correction value vector. This step combines the robustness of random sampling estimation with the high precision of full-sample regression, achieving complementary advantages and avoiding biases or divergences that may occur with a single method. Furthermore, before the quadratic regression, the number of instantaneous frequencies and the order of the polynomial phase function are matched and verified to ensure matrix invertibility and computational stability. When data is insufficient, the order is automatically reduced to ensure the invention can still operate under low-sampling conditions. This enhances the adaptability of the invention.

[0097] Furthermore, the maximum likelihood criterion function is constructed and combined with the hybrid optimization algorithm to update the final phase correction value vector. Based on the final phase correction value vector o, the final phase correction value is extracted, the maximum likelihood criterion function is constructed, and then the update is iterated. After the maximum number of iterations, the candidate phase correction values ​​are output and combined to generate the candidate phase correction value vector.

[0098] The maximum likelihood criterion function is constructed as follows:

[0099]

[0100] In the formula, J represents the maximum likelihood criterion function value, K represents the total number of baseband signals, and o m The coefficients representing the m-th order initial phase of the final phase correction value vector;

[0101] Based on the candidate phase correction value vector, after being treated as an individual particle, the initial velocity and position of the individual particle are randomly set in a uniformly distributed random manner, and a population is randomly generated for initialization.

[0102] The modulus of the maximum likelihood criterion function is defined as the fitness function. The fitness values ​​are calculated, and the maximum and minimum fitness values ​​in the fitness value calculation results are normalized using the maximum and minimum fitness values ​​as the weights for each individual particle.

[0103] The modulus of the maximum likelihood criterion function is defined as the fitness function, and the formula is:

[0104]

[0105] In the formula, fit u This represents the fitness function value of the u-th particle.

[0106] After calculating the distance between any two individual particles using Euclidean distance, the gravitational force between any two individual particles is calculated using a gravity search algorithm in combination with the weights. A uniformly distributed random number is generated using a random number generator. After calculating the resultant force of each individual particle in combination with the gravity, the ratio between the resultant force and the weights is used as the acceleration value.

[0107] When using the gravity search algorithm to calculate the gravitational force between any two individual particles, the maximum distance is selected through a maximization operation, the initial value of the gravitational constant is calculated, and the initial value of the gravitational constant is updated through an exponential decay method.

[0108] The gravity search algorithm is used to calculate the gravitational force between any two particles, and the formula is as follows:

[0109]

[0110] In the formula, F ur G(t) represents the gravitational force between particle u and r at the t-th iteration, G(t) represents the gravitational constant at the t-th iteration, and H(t) represents the gravitational constant. u H(t) represents the weight of particle u at the t-th iteration. r (t) represents the weight of particle r at the t-th iteration, R ur (t) represents the Euclidean distance between particle u and r at the t-th iteration, l u (t) represents the position of particle u at the t-th iteration, l r (t) represents the position of particle r at the t-th iteration, and β represents a constant (which can be set by expert experience and experimental data, or taken as a fixed constant value of 10). -6 );

[0111] The formula for calculating the resultant force of each individual particle is as follows:

[0112]

[0113] In the formula, F u (t) represents the resultant force of particle u at the t-th iteration, D represents the total number of particles, and rand represents a random number;

[0114] The formula for calculating the initial value of the gravitational constant is as follows:

[0115]

[0116] In the formula, G1 represents the initial value of the gravitational constant, and R max Indicates the maximum distance;

[0117] The initial value of the gravitational constant is updated using an exponential decay method, as shown in the following formula:

[0118]

[0119] In the formula, G1 represents the initial value of the gravitational constant, exp(·) is the exponential function, μ represents the control parameter (which can be set through experiments and domain knowledge), and t max Indicates the maximum number of iterations;

[0120] Based on the acceleration value, the acceleration value is used as a perturbation term and added to the standard velocity update formula of the particle swarm optimization algorithm by summation. The standard memory and collaborative update mechanism is used to update and iterate the position of each individual particle. After the maximum number of iterations, the optimal correction vector is output.

[0121] By replacing the traditional error minimization method with the maximum likelihood criterion, this invention maintains stable and reliable computational performance even under non-Gaussian noise and incomplete sampling conditions. Unlike traditional methods that use the minimization of mean square error or residuals as optimization objectives, this invention uses the magnitude of the maximum likelihood criterion function as the core indicator. This allows for stable convergence and the output of a reliable phase correction vector even under extreme environments such as undersampling, signal fading, and strong noise interference, providing a solid foundation for subsequent positioning calculations. Furthermore, the introduction of a hybrid optimization algorithm combining gravity search and particle swarm optimization, along with the physical definition of the acceleration perturbation term, endows the population evolution process with the dual characteristics of "dynamic convergence" and "random jumps." This design avoids the limitation of premature convergence that traditional particle swarm optimization is prone to in the later stages of iteration, ensuring that the population maintains necessary diversity during the convergence process and effectively preventing the positioning parameter calculation from being trapped in local optima.

[0122] Furthermore, by introducing the normalized weights of the maximum likelihood function's magnitude into the calculation of gravity between particles, the calculation not only reflects the spatial relationships between individuals but also incorporates the matching degree between the observed signal and the correction vector, forming a deep fusion of statistical evaluation and physical search. Moreover, the use of an exponential decay function to obtain the gravitational constant gives the hybrid optimization algorithm strong global exploratory capabilities in the early stages of the search, while gradually focusing on local refinement in the later stages, greatly improving convergence efficiency and stability. Through this gravitational constant, the hybrid optimization algorithm can find the optimal phase correction vector within a limited number of iterations without relying on external redundant compensation methods, thus significantly improving the efficiency and accuracy of the localization solution.

[0123] Secondly, the matching relationship between the "observed signal and correction vector" is directly characterized by the maximum likelihood criterion function. Combined with a hybrid optimization algorithm, this achieves stable updates to the candidate phase correction vector, enabling high-precision phase correction results even in complex environments such as BeiDou satellite signal obstruction, multipath interference, and incomplete sampling. This result can be directly used to solve the positioning equations of surveying equipment, ensuring higher accuracy and robustness in coordinate calculations for surveying equipment in dynamic environments. This improves the reliability of surveying equipment positioning and ensures the consistency of positioning results.

[0124] Furthermore, the positioning solution is performed based on the optimal correction vector. After extracting the optimal phase coefficient based on the optimal correction vector, the phase estimate is recalculated using a polynomial phase function, and the first-order time derivative is recalculated based on the phase estimate, which is defined as the new frequency.

[0125] Based on the new frequency, the new frequency is integrated using the integral accumulation method to obtain carrier phase observations. These observations are then converted to generate pseudorange observations for the BeiDou satellites. The formula is as follows:

[0126]

[0127] In the formula, P e Φ(n) represents the pseudorange observation value of the e-th Beidou satellite at time n, Φ(n) represents the carrier phase observation value at time n, and ζ represents the carrier wavelength (set according to the specific Beidou frequency used, for example, the wavelength of B1I signal is about 19.2cm).

[0128] Based on the position coordinates of BeiDou satellites and combined with pseudorange observations, positioning equations for all BeiDou satellites are generated, forming a set of positioning equations. The formula is as follows:

[0129]

[0130] In the formula, P e (n) represents the pseudorange observation value of the e-th Beidou satellite at time n, δ represents the error term (which can be set through domain knowledge and experiments), Δt represents the clock error to be solved, (g,y,z) represents the coordinate position of the mapping equipment to be solved, d represents the speed of light (using standard physical constants, i.e., 299,792,458 m / s), (g e ,y e ,z e () represents the position coordinates of the e-th Beidou satellite;

[0131] The least squares method is used to iteratively solve the positioning equations to obtain the coordinate position and clock difference of the surveying equipment as the positioning basis.

[0132] By employing a phase reconstruction and high-precision frequency integration strategy driven by the optimal correction vector, coupled with robust solution of multi-satellite equations and least squares method, the surveying equipment can still perform positioning with high stability, high accuracy and high reliability in complex environments.

[0133] This embodiment also provides a new basic surveying and mapping equipment positioning system based on BeiDou technology, including:

[0134] The processing and verification module is used to receive the radio frequency signals and position coordinates of Beidou satellites for preprocessing, generate baseband signals for demodulation and decoding, calculate the signal-to-noise ratio, and perform validity detection and sampling verification.

[0135] The generation and judgment module is used to extract the instantaneous frequency set and combine the polynomial phase function and residual judgment mechanism to make a feasible-infeasible judgment.

[0136] The update solution module is used to perform correction operations, construct the maximum likelihood criterion function, and combine it with a hybrid optimization algorithm to update and perform localization solutions.

[0137] This embodiment also provides a computer device applicable to the positioning method of a new basic surveying and mapping equipment based on BeiDou technology, including: a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to realize the positioning method of a new basic surveying and mapping equipment based on BeiDou technology as proposed in the above embodiment.

[0138] The computer device can be a terminal, comprising a processor, memory, communication interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0139] This embodiment also provides a storage medium storing a computer program. When executed by a processor, the program implements the positioning method for a new type of basic surveying and mapping equipment based on BeiDou technology as proposed in the above embodiments. The storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read Only Memory (EPROM), Programmable Red-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk.

[0140] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A novel positioning method for basic surveying and mapping equipment based on BeiDou technology, characterized in that: include, The radio frequency signals and position coordinates received from BeiDou satellites are preprocessed to generate baseband signals; Based on the baseband signal, demodulation and decomposition are performed to generate the complex form of the observation signal. The signal-to-noise ratio is calculated for validity detection and sampling verification to obtain the verification results, including whether the current sample is undersampled or complete. Based on the baseband signal, envelope demodulation and phase calculation are performed separately to generate the amplitude and phase of the baseband signal. The amplitude and phase are used as the observation signal and a timestamp is added. All observation signals are uniformly modeled to generate complex form observation signals at different times. The signal-to-noise ratio of the complex form observation signal is obtained using the standard signal-to-noise ratio formula. Then, the validity is detected to generate the detection result. Sampling verification is performed based on the detection result. The next step is to perform an effectiveness test and generate a test result. This involves setting a test threshold based on relevant book knowledge and experiments. If the signal-to-noise ratio is less than the test threshold, the current signal is considered an invalid sample and is removed. Otherwise, the current signal is considered a valid sample and is retained. The sampling verification refers to setting the number of samples using the Nyquist sampling theorem, counting the total number of valid samples, using a ratio formula to obtain the ratio between the total number of valid samples and the number of samples, which is defined as the sampling ratio. An empirical rule is used to set a judgment threshold. If the sampling ratio is less than the judgment threshold, the current sample is considered to be undersampled; otherwise, the current sample is considered to be complete, and the localization calculation is performed directly. When the current sample is undersampled, the instantaneous frequency set is extracted based on the baseband signal, and a preliminary phase coefficient vector is generated. The preliminary phase coefficient vector is then judged as feasible or infeasible by combining the polynomial phase function and the residual judgment mechanism. Based on the feasible results, a correction operation is performed to generate the final phase correction value vector. The maximum likelihood criterion function is constructed and combined with a hybrid optimization algorithm to update the final phase correction value vector, and the optimal correction vector is output. The positioning solution is performed based on the optimal correction vector to obtain the coordinate position and clock difference of the surveying equipment as the positioning basis. The hybrid optimization algorithm refers to a combination of particle swarm optimization algorithm and gravity search algorithm.

2. The positioning method for novel basic surveying and mapping equipment based on BeiDou technology as described in claim 1, characterized in that: The process of extracting an instantaneous frequency set based on the baseband signal and generating a preliminary phase coefficient vector, and then using a polynomial phase function and residual judgment mechanism to perform a feasibility-infeasibility judgment on the preliminary phase coefficient vector, refers to using a sliding window to divide the baseband signal into frames when the current sample is undersampled, and using a short-time Fourier transform to perform time-frequency conversion on the baseband signal in each frame to obtain the frequency variable of the signal in each frame, and then maximizing it to generate the instantaneous frequency of the signal in each frame at different times, and recording the timestamp; Instantaneous frequencies from different times are integrated to form a set of instantaneous frequencies for the current baseband signal. Random numbers are generated using a uniformly distributed random number generator, and non-repeating instantaneous frequencies are randomly selected from the set of instantaneous frequencies based on the random numbers to generate the observation vector of the current baseband signal. Based on the selected instantaneous frequencies, the timestamps corresponding to the instantaneous frequencies are integrated into a regression matrix. The observation vector and the regression matrix are fitted using the least squares method to generate a preliminary phase coefficient vector. The preliminary phase coefficients are extracted from the preliminary phase coefficient vector, a polynomial phase function is constructed, the phase estimate is calculated, the first-order time derivative is solved based on the phase estimate and defined as the reconstruction frequency, the reconstruction vector is constructed, and the residual vector between the reconstruction vector and the observation vector is solved by element-wise subtraction. The squared Euclidean norm of the residual vector is used to determine the feasibility of the preliminary phase coefficient vector.

3. The positioning method for novel basic surveying and mapping equipment based on BeiDou technology as described in claim 2, characterized in that: The step of performing a correction operation to generate the final phase correction value vector based on feasible results refers to performing a dechirping operation on the baseband signal based on feasible preliminary phase coefficient vectors, generating a dechirped signal, performing phase unwrapping, obtaining unwrapped phase values, splicing them together, and generating a phase vector. Using the timestamps of all instantaneous frequencies in the instantaneous frequency set, a new regression matrix is ​​reconstructed and combined with the phase vector to perform quadratic regression, generating a correction vector. This correction vector is then summed with the initial phase coefficient vector to obtain the final phase correction value vector. ; Before performing the quadratic regression, the total number of instantaneous frequencies in the instantaneous frequency set is counted. And combined with the total number of orders of the polynomial phase function The new regression matrix is ​​validated when the total number If the condition is met, the verification is satisfied and quadratic regression can be performed; otherwise, the total order of the polynomial phase function will be reduced. Adjust to total Then, the initial phase coefficient vector was recalculated for further verification.

4. The positioning method for novel basic surveying and mapping equipment based on BeiDou technology as described in claim 3, characterized in that: The construction of the maximum likelihood criterion function combined with the hybrid optimization algorithm to update the final phase correction value vector refers to the update of the final phase correction value vector. Extract the final phase correction value, construct the maximum likelihood criterion function, perform update iteration, and after iterating to the maximum number of times, output the candidate phase correction values ​​and combine them to generate a candidate phase correction value vector. Based on the candidate phase correction value vector, after being treated as an individual particle, the initial velocity and position of the individual particle are randomly set in a uniformly distributed random manner, and a population is randomly generated for initialization. The modulus of the maximum likelihood criterion function is defined as the fitness function. The fitness values ​​are calculated, and the maximum and minimum fitness values ​​in the fitness value calculation results are normalized using the maximum and minimum fitness values ​​as the weights for each individual particle. After calculating the distance between any two individual particles using Euclidean distance, the gravitational force between any two individual particles is calculated using a gravity search algorithm in combination with the weights. A uniformly distributed random number is generated using a random number generator. After calculating the resultant force of each individual particle in combination with the gravity, the ratio between the resultant force and the weights is used as the acceleration value. When using the gravity search algorithm to calculate the gravitational force between any two individual particles, the maximum distance is selected through a maximization operation, the initial value of the gravitational constant is calculated, and the initial value of the gravitational constant is updated through an exponential decay method. Based on the acceleration value, the acceleration value is used as a perturbation term and added to the standard velocity update formula of the particle swarm optimization algorithm by summation. The standard memory and collaborative update mechanism is used to update and iterate the position of each individual particle. After the maximum number of iterations, the optimal correction vector is output.

5. The positioning method for novel basic surveying and mapping equipment based on BeiDou technology as described in claim 4, characterized in that: The step of performing positioning calculation based on the optimal correction vector refers to extracting the optimal phase coefficient based on the optimal correction vector, recalculating the phase estimate using a polynomial phase function, recalculating the first-order time derivative based on the phase estimate, defining it as a new frequency, integrating the new frequency using the integral accumulation method, converting the carrier phase observation value, and generating pseudorange observation values ​​for the BeiDou satellite. Based on the position coordinates of BeiDou satellites and combined with pseudorange observations, positioning equations for all BeiDou satellites are generated, forming a set of positioning equations. The least squares method is used to iteratively solve the positioning equations to obtain the coordinate position and clock error of the surveying equipment as the positioning basis.

6. The positioning method for novel basic surveying and mapping equipment based on BeiDou technology as described in claim 5, characterized in that: The radio frequency signals and position coordinates received from the BeiDou satellites are preprocessed to generate baseband signals for the mapping equipment equipped with multi-frequency antennas and receivers; The radio frequency signals from BeiDou satellites are received by a multi-frequency antenna, denoised, normalized, and down-converted to generate the baseband signals of BeiDou satellites. The broadcast ephemeris of BeiDou satellites is received by a receiver, and the position coordinates of BeiDou satellites are obtained from the broadcast ephemeris using the GNSS Kepler orbit propagation method.

7. A novel basic surveying and mapping equipment positioning system based on BeiDou technology, based on the novel basic surveying and mapping equipment positioning method based on BeiDou technology as described in any one of claims 1 to 6, characterized in that: include, The processing and verification module is used to receive the radio frequency signals and position coordinates of Beidou satellites for preprocessing, generate baseband signals for demodulation and decoding, calculate the signal-to-noise ratio, and perform validity detection and sampling verification. The generation and judgment module is used to extract the instantaneous frequency set and combine the polynomial phase function and residual judgment mechanism to make a feasible-infeasible judgment. The update solution module is used to perform correction operations, construct the maximum likelihood criterion function, and combine it with a hybrid optimization algorithm to update and perform localization solutions.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the steps of the positioning method for a novel basic surveying and mapping equipment based on BeiDou technology as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the steps of the positioning method for a novel basic surveying and mapping equipment based on BeiDou technology as described in any one of claims 1 to 6.

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