A gravity value extraction method based on minimizing orthogonal distance

Abstract

A gravity value extraction method based on orthogonal distance minimization relates to the field of design of gravity value extraction methods using gravimeter interference fringe fitting. It addresses the numerous difficulties faced in extracting the phase of interference fringes during interference fringe fitting in the prior art, which in turn limits the measurement efficiency and accuracy of atomic gravimeters. The method of the present invention is implemented by initializing interference fringe-related parameters; setting the minimum sum of the orthogonal distances from data points to the curve as the optimization objective function; fitting the interference fringes using an adaptive cuckoo search algorithm; and calculating the gravity value based on the phase obtained after fitting. When optimizing the objective function, the method uses an adaptive cuckoo search algorithm that introduces multiple optimization strategies, improving the algorithm's global search capability and enabling better application in gravity value extraction scenarios. The method of the present invention can improve the accuracy of gravity value extraction to a certain extent.

Description

Technical Field

[0001] The present invention relates to the field of design of methods for extracting gravity values ​​by fitting interference fringes of gravimeters, and in particular to a method for extracting gravity values ​​based on minimizing orthogonal distances. Background Art

[0002] In an atomic gravimeter, atoms are cooled to near absolute zero and trapped in a specific optical potential trap. A series of precise laser pulses are then used to manipulate the atoms to form interference paths in the gravitational field. The phase difference between these interference paths is proportional to the acceleration due to gravity. By measuring the phase shift of the interference fringes, the value of gravitational acceleration can be accurately inferred.

[0003] When fitting interference fringes, how to more efficiently and accurately fit the fringe phase and thus extract gravitational acceleration has always been a focus of scientific research. Due to the presence of environmental and system noise, phase extraction of interference fringes faces many challenges, which to some extent limits the measurement efficiency and accuracy of atomic gravimeters. Therefore, efficient and stable interference fringe fitting methods are of great significance for improving the performance of atomic gravimeters.

[0004] In view of this, the present invention proposes a gravity value extraction method based on orthogonal distance minimization, aiming to improve the fitting accuracy through optimization algorithm, and provide a new and effective method for the accurate measurement of gravitational acceleration of atomic gravimeter. Summary of the Invention

[0005] The present invention aims to solve the problems faced by the phase extraction of interference fringes when performing interference fringe fitting in the prior art, which in turn limits the measurement efficiency and accuracy of atomic gravimeters. A gravity value extraction method based on orthogonal distance minimization is provided.

[0006] A gravity value extraction method based on orthogonal distance minimization specifically includes the following steps:

[0007] Step S1: Initialize interference fringe data;

[0008] Step S2: setting the minimum sum of the orthogonal distances from the interference fringe data points to the fitting curve as the optimization objective function;

[0009] Step S3: fitting the interference fringe data using an adaptive cuckoo search algorithm;

[0010] Step S4: Calculate the gravity value according to the phase obtained after fitting.

[0011] Beneficial effects of the present invention: The method of the present invention optimizes parameters to find the best fitting curve by minimizing the sum of the orthogonal distances between the interference fringe data points and the fitting curve as the objective function of the adaptive cuckoo search algorithm during interference fringe fitting.

[0012] In the method described in the present invention, the minimum sum of the orthogonal distances from the data points to the fitted curve is used as the optimization objective function. The advantage of using orthogonal distance is that it considers the measurement errors of the independent variable x and the dependent variable y at the same time, which is suitable for scenarios where errors exist in both. In addition, when the data distribution is uneven or the noise is heteroscedastic, the orthogonal distance can provide more robust results by balancing the errors in the x and y directions, avoiding the situation where the error in a single direction dominates the fitting process.

[0013] The method described in this paper uses an adaptive cuckoo search algorithm to fit interference fringe data. A dynamic step-size scaling factor adjustment strategy and mixed Levy flight distribution parameters are optimized. Dual threshold constraints, using the maximum and minimum values ​​of the step-size scaling factor, are used to prevent parameter drift. This strategy achieves a dynamic balance in step-size adjustment: when the algorithm stagnates, the search step size is increased to enhance global exploration capabilities; when a more optimal solution is found, the step size is gradually reduced to refine local exploration.

[0014] The heavy-tail characteristics of Levy flight are controlled by adjusting the Levy distribution parameters: using smaller distribution parameters increases the probability of long-distance jumps and improves global exploration capabilities; using standard distribution parameters maintains local fine search.

[0015] The method proposed in this paper also proposes an elite perturbation replacement strategy combined with a nest reset mechanism to avoid local stagnation. The Gaussian perturbation standard deviation is positively correlated with the current step length scaling factor, enabling adaptive matching of perturbation intensity and search step length. This composite perturbation combines the advantages of long jumps and fine-tuning, significantly enhancing local escape capabilities. The nest reset mechanism effectively breaks the homogeneity of the population, thereby strengthening global search capabilities, while preserving elite individuals and preventing loss of historical search experience.

[0016] The method described in this paper incorporates multiple optimization strategies into the adaptive cuckoo search algorithm used to optimize the objective function, improving the algorithm's global search capabilities and enabling better application in gravity extraction scenarios. This method can provide researchers with a new approach and method for extracting gravity values ​​using interference fringe fitting. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a flow chart of a gravity value extraction method based on orthogonal distance minimization according to the present invention;

[0018] Figure 2 Flowchart of the adaptive cuckoo search algorithm;

[0019] Figure 3This is a comparison chart of the simulation data fitting effect. In the figure, method 1 is the least squares method (LS); method 2 is the extended Kalman filter (EKF); this method is the adaptive cuckoo search algorithm (ACS);

[0020] Figure 4 The following is a comparison chart of the fitting results of the three methods and the set values. DETAILED DESCRIPTION

[0021] Combine Figures 1 to 4 To illustrate this embodiment, a gravity value extraction method based on minimizing the orthogonal distance is described. Figure 1 As shown, the method specifically includes the following steps:

[0022] Step S1: Initialize interference fringe related parameters (interference fringe data);

[0023] In this embodiment, the interference fringe data is used as the algorithm parameters for extracting the gravity value in this embodiment, including the number of interference fringe data points, the phase range of the interference fringe, the effective wave vector value k eff , interference time T, etc.

[0024] In this embodiment, the number of data points (simulation data) of the interference fringes used is 40 data points, and the phase range of the interference fringes is 、k eff = 1.61×10 7 , T = 250ms.

[0025] Step S2: setting the minimum sum of the orthogonal distances from the data points to the fitting curve as the optimization objective function;

[0026] The designed objective function is to transform the interference fringe data points into the fitting curve The sum of the orthogonal distances is the smallest, which can be expressed as:

[0027] ;

[0028] Where A is the fringe offset, B is the phase value, and C is the fringe contrast. A, B, and C are all parameters to be fitted; x and P are the horizontal and vertical coordinate data respectively; and is the horizontal and vertical coordinate point of the i-th data point; is the i-th data point The corresponding phase variable (internal optimization variable) projected onto the curve; for each data point, the solution is required Make Euclidean distance Minimum, among which .

[0029] In this embodiment, the advantage of using orthogonal distance is that it considers the measurement errors of the independent variable x and the dependent variable y at the same time, which is suitable for scenarios where errors exist in both. In addition, when the data distribution is uneven or the noise is heteroscedastic, the orthogonal distance can provide more robust results by balancing the errors in the x and y directions, avoiding the situation where the error in a single direction dominates the fitting process.

[0030] Step S3: fitting the interference fringe data using an adaptive cuckoo search algorithm;

[0031] In this embodiment, the adaptive cuckoo search algorithm is used to fit the interference fringe data. By continuously iteratively searching for the optimal parameters A, B, and C that minimize the sum of the orthogonal distances from the data points to the fitting curve, a specific interference fringe function is obtained, namely: the fitting curve .like Figure 2 As shown in Figure 2, the specific process of iterative optimization using the adaptive cuckoo search algorithm is as follows:

[0032] Step A: Initialize the parameters of the adaptive cuckoo search algorithm, including the number of solutions, problem dimension, maximum number of iterations, and discovery probability;

[0033] Step B: setting the boundaries of the parameters to be optimized;

[0034] Step C, initializing the bird's nest position;

[0035] Step D: Determine whether the maximum number of iterations has been reached. If so, output the optimal result; that is, obtain the optimal nest position (optimal parameters A, B, C), which is also the fitting result, and end; otherwise, execute step E;

[0036] Step E: Using dynamic step-size scaling factor adjustment strategy and hybrid Levy flight distribution parameter fusion to generate a new nest location;

[0037] In this embodiment, a dynamic step-size scaling factor adjustment strategy and a hybrid Levy flight distribution parameter fusion are used to generate a new nest location. The formula for generating a random solution using Levy flight is as follows:

[0038] ;

[0039] Where α is the step size scaling factor, is a Lévy random path, is the dot product operation; where The Mantegna method is used to generate random step sizes that obey the Levy distribution. The formula is as follows:

[0040] ;

[0041] Among them, μ~N(0,σ2 ), v~N(0,1), that is, both obey the normal distribution, and:

[0042] ;

[0043] Where, For the gamma function, α and β are usually taken as fixed parameters (such as , ). In order to make the method have better convergence ability and global search ability, this method proposes to optimize α and β using a dynamic step-size scaling factor adjustment strategy and mixed Levy flight distribution parameters:

[0044] The dynamic step size scaling factor adjustment strategy is:

[0045] A fixed step-size scaling factor α is difficult to balance global exploration and local development, so the step-size scaling factor α is improved to an adaptive parameter, and its update rule is:

[0046] If the fitness is not updated for n consecutive generations: ;

[0047] If the fitness is updated: ;

[0048] Where, and are the maximum and minimum values ​​of the step scaling factor α respectively; by setting and , double threshold constraints are implemented to prevent parameter drift. This strategy achieves a dynamic balance in step size adjustment: when the algorithm stagnates, the global exploration capability is enhanced by enlarging the search step size; when a better solution is found, the step size is gradually reduced to perform refined local development.

[0049] The mixed Levy flight distribution parameters are specifically:

[0050] Since a single Levy distribution parameter β cannot adapt to the needs of different search stages, the Levy distribution parameter β is dynamically selected according to the current step size scaling factor α:

[0051] ;

[0052] The heavy-tail characteristics of Levy flight are controlled by adjusting the value of the Levy distribution parameter β: a smaller β (β=1.2) increases the probability of long-distance jumps and improves global exploration capabilities; a standard β (β=1.5) maintains local fine search.

[0053] Step F, calculating and comparing the fitness values ​​of the two generations of bird's nests, and updating the better bird's nest;

[0054] Step G: Abandon or retain the bird's nest according to the elite disturbance replacement strategy and nest reset mechanism;

[0055] In this implementation, an elite disturbance replacement strategy is designed to cooperate with a nest reset mechanism to discard or retain bird nests:

[0056] The elite perturbation replacement strategy is specifically:

[0057] In order to solve the problem that the direct worst solution replacement strategy is prone to falling into a steady state, when replacing the worst solution in proportion to the discovery probability, the current step size scaling factor is used. Add Gaussian noise to the benchmark to avoid local stagnation:

[0058] ;

[0059] Where N(0,1) is the normal distribution (i.e. Gaussian distribution), is the location of the bird's nest with the worst fitness at t+1 iterations (worst solution); is the nest location with the best fitness at t iterations (optimal solution); is the step size scaling factor at the tth iteration, σ= The last term in the formula is N(0,1) is calculated. N(0,1) is a normal distribution with a standard deviation of 1, so the standard deviation of the Gaussian perturbation is .

[0060] In this embodiment, the Gaussian disturbance standard deviation σ is The value is positively correlated, allowing the perturbation intensity to be adaptively matched to the search step size. This composite perturbation combines the advantages of long jumps and fine adjustment, significantly enhancing the ability to escape locally.

[0061] In this embodiment, the nest reset mechanism is specifically as follows:

[0062] Define the population stagnation generation threshold Ts. When the global optimal solution is not improved for Ts consecutive iterations, the nest reset operation is triggered:

[0063] First, select the bottom 20% of inferior solutions by fitness ranking;

[0064] Then, a new solution is randomly generated and ensured to be within the allowed range of the parameters (b min , b max )Inside:

[0065] ;

[0066] Where, is the lower limit of the parameter, is the upper limit of the parameter, and U(0,1) represents uniform distribution.

[0067] In this implementation, a nest reset mechanism is used to effectively break the homogeneity of the population, thereby enhancing the global search capability, while retaining elite individuals to avoid losing historical search experience.

[0068] Step H: Update the optimal nest location (optimal solution), increase the number of iterations by 1, and return to step D.

[0069] The adaptive cuckoo search algorithm described in this embodiment forms a closed-loop optimization mechanism of "exploration-exploitation-escape" through the synergistic effect of strategies such as dynamic parameter adjustment, mixed perturbation and population reset, thereby enhancing the search capability of the algorithm.

[0070] like Figure 3 and Figure 4 As shown in FIG, in order to reflect the effect of the method described in this embodiment, in this embodiment, the phase value B=0.6 is set as the real value, and three methods are used, namely, the least square method (method 1), the extended Kalman filter (method 2) and the method described in the present invention (this method) to fit the interference fringe data obtained by simulation. The fitting effect diagram is shown in FIG. Figure 3 As shown, the comparison between the extracted phase and the true value is shown in Figure 4 As shown in the accompanying drawings, it can be seen that the phase value B obtained by fitting using the method described in the present invention is closer to the actual value set in this embodiment.

[0071] Step S4: Calculate the gravity value based on the phase value obtained after fitting. The formula is as follows:

[0072] ;

[0073] In this embodiment, if the horizontal coordinate of the interference fringe data point is the chirp rate, then B obtained after fitting is used as the chirp rate, which can be calculated using the formula Calculate the gravity value.

[0074] From the calculation formula, we can see that the phase value B obtained by fitting is proportional to the extracted gravity value g. The more accurate the phase value B is, the more accurate the extracted gravity value g is. Figure 3 and Figure 4 It can be seen that the phase value B (ie, the gravity value g) obtained by fitting using this method is closer to the actual value set in this embodiment.

[0075] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0076] The above-described embodiments merely illustrate several implementations of the present invention, and while their descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the patent for this invention shall be determined by the appended claims.

Claims

1. A gravity value extraction method based on orthogonal distance minimization, characterized by: The method is implemented by the following steps: Step S1: Initialize interference fringe data; Step S2: Set the minimum sum of the orthogonal distances from the interference fringe data points to the fitting curve as the optimization objective function; specifically: The design objective function is to transform the interference fringe data points into the fitting curve The sum of the orthogonal distances is the smallest: ； Where A is the fringe offset, B is the phase value, and C is the fringe contrast; A, B, and C are the parameters to be fitted, and x and P are the horizontal and vertical coordinate data respectively; and is the horizontal and vertical coordinate point of the i-th data point; The phase variable corresponding to the projection of the data point onto the curve; solve for each data point Make Euclidean distance The smallest, among which ; Step S3: fitting the interference fringe data using an adaptive cuckoo search algorithm; Step S4: Calculate the gravity value according to the phase value B obtained after fitting.

2. The method for extracting gravity values ​​based on orthogonal distance minimization according to claim 1, characterized in that: In step S1, the interference fringe data includes the number of interference fringe data points, the phase range of the interference fringe, the effective wave vector value k eff and interference time T; and using the interference fringe data as parameters for extracting gravity values.

3. The gravity value extraction method based on orthogonal distance minimization according to claim 1, characterized in that: In step S3, the adaptive cuckoo search algorithm is used to fit the interference fringe data. The specific process is as follows: Step S31, initializing the adaptive cuckoo search algorithm parameters; Step S32: setting the boundaries of the parameters to be optimized; Step S33, initializing the bird's nest position; Step S34: Determine whether the maximum number of iterations has been reached. If so, output the optimization result and end; otherwise, execute step S35; Step S35: adopting the dynamic step-size scaling factor adjustment strategy and the hybrid Levy flight distribution parameter fusion to generate a new nest location; Step S36: Calculate and compare the fitness values ​​of the two generations of bird's nests, and update the better bird's nest position; Step S37: Abandon or retain the bird's nest according to the elite disturbance replacement strategy and the nest reset mechanism; Step S38: Update the optimal nest position and the optimal solution, increase the number of iterations by 1, and return to step D.

4. The method for extracting gravity values ​​based on minimizing orthogonal distance according to claim 3, characterized in that: In step S35, the step size scaling factor α is set as an adaptive parameter, and the update rule is: If the fitness is not updated for n consecutive generations: ; If the fitness is updated: ; Where, and are the maximum and minimum values ​​of the step scaling factor α, is the step size scaling factor at the tth iteration; Scale factor based on current step size Dynamically select the Levy distribution parameter β: ； The heavy-tail characteristics of Levy flight are controlled by adjusting the value of Levy distribution parameter β.

5. The method for extracting gravity values ​​based on minimizing orthogonal distance according to claim 3, characterized in that: In step S37, the elite perturbation replacement strategy is specifically: when replacing the worst solution in proportion to the probability of discovery, the current step size scaling factor is used. Add Gaussian noise to the reference to avoid local stagnation; it can be expressed as follows: ； Where N(0,1) is the normal distribution, is the nest location with the worst fitness at t+1 iteration; is the nest location with the best fitness at t iterations; is the step size scaling factor at the tth iteration; the Gaussian perturbation standard deviation σ is proportional to the current step size scaling factor The value is positively correlated, that is: σ = .

6. The method for extracting gravity values ​​based on minimizing orthogonal distance according to claim 3, characterized in that: In step S37, the nest reset mechanism is specifically as follows: Set the population stagnation generation threshold Ts. When the global optimal solution is not improved for Ts consecutive iterations, the nest reset operation is triggered: Sort by fitness and select the bottom 20% of inferior solutions; Randomly generate new solutions and ensure that it is within the allowed range of the parameter (b min , b max )Inside: ； Where, is the lower limit of the parameter, is the upper limit of the parameter, and U(0,1) represents uniform distribution.

7. The method for extracting gravity values ​​based on orthogonal distance minimization according to claim 1, characterized in that: In step S4, the gravity value is calculated based on the phase value B obtained after fitting, which is expressed as follows: ； Where k eff is the effective wave vector value, and T is the interference time.

8. The method for extracting gravity values ​​based on minimizing orthogonal distance according to claim 7, characterized in that: In step S4, if the horizontal coordinate of the interference fringe data is the chirp rate, then the B obtained after fitting is used as the chirp rate, using the formula Calculate the gravity value.

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