A method for evaluating the uncertainty of laser interferometer measurement results of unknown distribution
The uncertainty of laser interferometer measurement results is evaluated by using beta distribution and particle filtering methods, which solves the problem of uncertainty assessment under unknown distribution types and achieves more efficient and accurate uncertainty assessment.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HEFEI UNIV OF TECH
- Filing Date
- 2023-07-14
- Publication Date
- 2026-06-09
Smart Images
Figure CN116907336B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of measurement uncertainty assessment technology, and relates to a method for assessing the uncertainty of laser interferometer measurement results with unknown distribution. Background Technology
[0002] Laser interferometers are commonly used precision measuring instruments with wide-ranging significance and application value in scientific research, engineering applications, and industrial fields. Uncertainty is an important parameter in interferometer measurement results, used to characterize the degree of dispersion of the measurement results and reflect the quality of the measurement results. Currently, the internationally recognized standard for assessing uncertainty is the "Guide to the Expression of Measurement Uncertainty (GUM)" published by the Joint Committee on Metrology. The GUM includes two methods for uncertainty assessment, known as Type A and Type B assessments. Type A methods are based on statistical analysis theory and typically assume that the data follows a Gaussian distribution or a known distribution type. This assumption simplifies various uncertainty factors in the actual measurement process and can introduce errors in the true uncertainty estimation. Type B methods evaluate uncertainties through other methods, such as experimental design, expert judgment, historical data, or literature. These methods usually require knowledge of the data distribution type and interval half-width. This method is highly subjective and may lead to inconsistencies between different evaluators. Monte Carlo simulation uncertainty assessment is a statistical method based on random sampling. This method can overcome some assumptions and simplifications in traditional methods. However, it usually requires convergence judgment and adjustment strategies to ensure the accuracy and efficiency of the guess sampling. As laser interferometry systems and measurement environments become increasingly complex, the problem of uncertainty assessment for non-Gaussian or nonlinear distribution measurement data becomes increasingly prominent, at which point traditional uncertainty assessment methods may fail. Summary of the Invention
[0003] To address the shortcomings or deficiencies of existing technologies, this invention proposes a method for evaluating the uncertainty of laser interferometer measurement results with unknown distributions. The aim is to characterize various distribution types of laser interferometer measurement results through the beta distribution, thereby solving the problem of optimal estimation and uncertainty evaluation of measurement results with unknown distribution types, and improving estimation accuracy.
[0004] To achieve its objectives, the present invention proposes the following technical solution:
[0005] The present invention provides a method for evaluating the uncertainty of laser interferometer measurement results of unknown distribution type, characterized by comprising the following steps:
[0006] Step 1: Use a laser interferometer to measure the object under test for K time steps to obtain a dataset Y = {y} of measurement results with an unknown distribution type. k |k=1,2,…,K}, where yk This represents the measurement result at the k-th time step;
[0007] The measurement result dataset Y is preprocessed by removing and normalizing data to obtain the effective measurement result sequence Z = {z}. k |k=1,2,…,K} is represented using the beta distribution method, where z k Let z represent the valid measurement value at time k, and z k ~β(α) k ,β k ); β(·) represents a beta distribution, ~ indicates that it follows a certain pattern, α k Let β represent the first distribution parameter at time k. k Let represent the second distribution parameter at time k, and we have:
[0008]
[0009] In equation (1), Δα k The first distribution parameter α at time k k-1 The noise variable, Δβ k Let α be the second distribution parameter at time k. k-1 The noise variable, when k=1, let α1=β1=1;
[0010] Step 2: Let the state parameter vector to be estimated at time k be... T represents transpose, and we have:
[0011]
[0012] In equation (2), x k-1 Let p(x) be the state parameter vector at time k-1. k |x k-1 Let x be the state parameter vector at time k. k The transition probability density, p(z) k |x k Let x be the state parameter vector at time k. k The likelihood probability density;
[0013] Step 3: Construct the state parameter value vector x before time k using equation (3). 1:k The posterior probability density p(x) 1:k |z 1:k ):
[0014]
[0015] In equation (3), z 1:k Let z be the measurement value before time k. 1:k-1 p(z) represents the measurement value before time k-1. 1:k |x1:k ) indicates that the measured value is z k The likelihood probability density at time p(x) 1:k |z 1:k-1 Let ) be the prior probability density at time k;
[0016] The posterior filtering probability density p(x) at time k is obtained using equation (4). k |z 1:k ):
[0017] p(x k |z 1:k )=∫∫...∫p(x 1:k |z 1:k )dx0dx1...dx k-1 (4)
[0018] Step 4: Let the state parameter vector x at time k-1 be... k-1 The posterior filtering probability density is p(x) k-1 |z 1:k-1 Then, using equation (5), we can obtain the state parameter vector x at time k. k The prior probability p(x) k |z 1:k-1 ):
[0019] p(x k |z 1:k-1 )=∫p(x k |x k-1 )p(x k-1 |z 1:k-1 )dx k-1 (5)
[0020] In equation (5), p(x) k |x k-1 ) represents the state parameter vector x at time k. k The transition probability density;
[0021] Based on the measured value z at time k k The state parameter vector x at time k is obtained using equation (6). k The posterior probability density p(x) k |z 1:k ):
[0022]
[0023] In equation (6), p(z) k |x k ) is the state parameter vector x at time k. k The likelihood probability density, p(z) k |z 1:k-1 () represents the measured value z at time k.k The probability distribution of p(z) is given, and p(z) is given. k |z 1:k-1 )=∫p(z k |x k )p(x k |z 1:k-1 )dx k ;
[0024] Step 5: From the posterior probability density p(x) at time k k |z 1:k N is generated in ) S Independent and identically distributed samples in, N represents the particle vector with the i-th state parameter at time k. S This represents the total number of particles generated by a single state parameter, and we have:
[0025]
[0026] In equation (7), g(x) k ) is x k Any function; E(g(x) k )) represents g(x k The mathematical expectation of ).
[0027] Step 6: Initialize k=1, and use equation (8) to generate the particle vector of the i-th state parameter at time k-1. i = 1, 2, ..., N s Thus, N is obtained. s Particle vectors with state parameters:
[0028]
[0029] In equation (8), p(x) k-1 Let x be the state parameter vector at time k-1. k-1 The prior distribution is given, and when the prior distribution is unknown, a uniform distribution is taken; and let the particle vector of the i-th state parameter at time k-1 be... The weight vector is All of its element values are 1 / N s ;
[0030] Step 7: From a known importance probability density distribution q(x) k |z 1:k Generate the particle vector with the i-th state parameter at time k in the process. Therefore, the i-th weighted particle vector at time k can be obtained using equation (9).
[0031]
[0032] In equation (9), Let α represent the first distribution parameter at time k. k The i-th state parameter particle The weights, β represents the second distribution parameter at time k. k The i-th state parameter particle The weights;
[0033] right After normalization, the normalized weight vector is obtained. Thus, the state parameter vector x at time k can be obtained using equation (10). k The posterior filtering probability distribution p(x) k |z 1:k ):
[0034]
[0035] In equation (10), δ(·) represents the Dirac-delta function.
[0036] Step 8: Calculate the state parameter x at time k using equations (11) and (12) respectively. k The estimated value and variance
[0037]
[0038]
[0039] In equation (11), This represents the estimated value of the first distribution parameter at time k. This represents the estimated value of the second distribution parameter at time k;
[0040] In equation (12), This represents the variance of the first distribution parameter at time k. Let represent the variance of the second distribution parameter at time k;
[0041] Step 9: Use equation (13) to generate the i-th state parameter particle vector at time k+1.
[0042]
[0043] In equation (13), Let represent the noise value of the particle vector for the i-th state parameter at time k, and in, Indicates the interval Uniform distribution on Let $k$ be the mean of the $n$ standard deviations prior to time $k$.
[0044] Step 10: After assigning k+1 to k, if k > K, then the state parameter vector at time K is obtained. Otherwise, return to step 7 and execute sequentially;
[0045] Step 11: Calculate the estimated value of the normalized measurement result using equation (14).
[0046]
[0047] Step 12: Let the confidence probability be p, and use equation (16) to obtain the left quantile d of the uncertainty of the laser interferometer measurement result. left Right quantile d right :
[0048]
[0049] In equation (15), F(·) represents the cumulative distribution function of the beta distribution, and B(·) represents the beta function;
[0050] Step 13: Use equation (16) to obtain the normalized uncertainty of the interferometer measurement results at time K.
[0051]
[0052] Step 14: Use equations (17) and (18) to obtain the actual estimated values of the interferometer measurement results at time K. and uncertainty
[0053]
[0054]
[0055] In equations (17) and (18), y max y min This represents the maximum and minimum values of the measurement results in the measurement result dataset Y.
[0056] The present invention provides an electronic device, comprising a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the method for evaluating the uncertainty of the measurement results of the laser interferometer, and the processor is configured to execute the program stored in the memory.
[0057] The present invention discloses a computer-readable storage medium on which a computer program is stored, wherein the computer program, when executed by a processor, performs the steps of the method for evaluating the uncertainty of the measurement results of the laser interferometer.
[0058] Compared with existing technologies, the beneficial effects of this invention are reflected in:
[0059] 1. This invention proposes a novel uncertainty estimation method based on particle filters and beta distribution. The measurement data is represented by the beta distribution representation method, and its distribution parameters are used as state variables. The particle filtering method is used for recursive estimation, which solves the problem of unknown error distribution type. This method can estimate the uncertainty of laser interferometer measurement data with unknown distribution type, and can estimate the uncertainty of measurement results more accurately, thereby improving the reliability of evaluation.
[0060] 2. This invention uses the beta distribution representation method to represent measurement data, overcoming the problem that traditional uncertainty assessment requires prior assumptions about the distribution type. The probability distribution of the beta distribution has wide applicability and can be applied to the distribution types of various uncertainty factors, such as normal distribution, uniform distribution, bell-shaped distribution, U-shaped distribution, etc. This method has good flexibility and applicability when dealing with different types of measurement result distributions.
[0061] 3. This invention uses a probability density function and a weight vector to express the posterior distribution of the measurement results, and uses Monte Carlo sampling and particle filtering to calculate the posterior probability density, which is applicable to complex measurement systems and has an efficient calculation process; finally, the uncertainty interval is represented by calculating quantiles, thereby improving the accuracy of uncertainty assessment. Attached Figure Description
[0062] Figure 1 This is a flowchart of the uncertainty algorithm based on the drift measurement results of a Michelson laser interferometer in an embodiment of the present invention;
[0063] Figure 2 The graph shows the probability density function of the beta distribution for different values of the distribution parameter.
[0064] Figure 3 This is a histogram showing the distribution of Michelson interferometer drift measurement data in an embodiment of the present invention.
[0065] Figure 4 This is a comparison chart of uncertainty assessment results and measurement data in an embodiment of the present invention;
[0066] Figure 5This is a comparison chart of the final results of the uncertainty evaluation method for laser interferometer measurement data with unknown distribution in this embodiment of the invention and the standard method. Detailed Implementation
[0067] In this embodiment, a method for evaluating the uncertainty of laser interferometer measurement results with unknown distribution is proposed. This method assesses the uncertainty of laser interferometer measurement data with unknown distribution and uses the flexible probability distribution beta distribution as the distribution type of the measurement results. The distribution parameters of the beta distribution are used as state parameters to establish a state-space model. Based on the measurement result sequence of the interferometer, the particle filtering method is used to recursively solve for the estimated value of the beta distribution parameters. Finally, the obtained distribution parameters are used to calculate the best estimate of the measurement results and its uncertainty magnitude.
[0068] When the distribution type of measurement data is unknown, it is impossible to rely on traditional statistical methods to assess uncertainty. When conducting the assessment, it is also necessary to consider how to combine prior information to improve the estimation accuracy. Therefore, a method is needed to estimate the uncertainty of measurement data with unknown distribution to assess the uncertainty of laser interferometer measurement data.
[0069] Specifically, such as Figure 1 As shown, the method includes the following steps:
[0070] Step 1: Use a laser interferometer to measure the object under test for K time steps to obtain a dataset Y = {y} of measurement results with an unknown distribution type. k |k=1,2,…,K}, where y k This represents the measurement result at the k-th time step, where the maximum and minimum values of the dataset are y and y, respectively. max =0.028, y min = -0.006.
[0071] Gross errors in the measurement result dataset Y are removed using the 3σ criterion, and normalization preprocessing is performed to obtain the effective measurement result sequence Z = {z...} k |k=1,2,…,K}, see the distribution histogram of the drift dataset. Figure 3 The probability density function of the beta distribution is represented using the beta distribution method. The beta distribution probability density functions with different parameters are as follows: Figure 2 As shown, where z k Let z represent the valid measurement value at time k, and z k ~β(α) k ,β k ), β(·) represents the beta distribution, ~ indicates that it follows a certain pattern, α k Let β represent the first distribution parameter at time k. k Let represent the second distribution parameter at time k, and we have:
[0072]
[0073] In equation (1), Δα k The first distribution parameter α at time k k-1 The noise variable, Δβ k Let α be the second distribution parameter at time k. k-1 The noise variable, when k=1, let α1=β1=1;
[0074] Step 2: Treat the distribution parameters to be estimated as random state variables following a certain probability distribution. The parameter estimation model can be represented by the observation probability density and the state transition probability density. Let the state parameter vector to be estimated at time k be... T represents transpose, and we have:
[0075]
[0076] In equation (2), x k-1 Let p(x) be the state parameter vector at time k-1. k |x k-1 Let x be the state parameter vector at time k. k The transition probability density, p(z) k |x k Let x be the state parameter vector at time k. k The likelihood probability density;
[0077] Step 3: Based on the principle of Bayesian estimation, construct the state parameter value vector x before time k using equation (3). 1:k The posterior probability density p(x) 1:k |z 1:k ):
[0078]
[0079] In equation (3), z 1:k Let z be the measurement value before time k. 1:k-1 p(z) represents the measurement value before time k-1. 1:k |x 1:k ) indicates that the measured value is z k The likelihood probability density at time p(x) 1:k |z 1:k-1 Let be the prior probability density at time k. The prior probability density represents the summarization of all information about the unknown state parameter variable before the arrival of new measurement data. The likelihood probability density expresses the probability of the unknown state parameter variable appearing given that the actual measurement data is known. It reflects the logical connection between the observed data and the unknown variable.
[0080] The posterior filtering problem is to calculate the posterior edge probability density p(x).k |z 1:k ), that is, p(x 1:k |z 1:k The marginal probability density of x is obtained by using equation (4), and the posterior filtered probability density p(x) at time k is obtained by using equation (4). k |z 1:k ):
[0081] p(x k |z 1:k )=∫∫...∫p(x 1:k |z 1:k )dx0dx1...dx k-1 (4)
[0082] Step 4: Let the state parameter vector x at time k-1 be... k-1 The posterior filtering probability density is p(x) k-1 |z 1:k-1 Then, using equation (5), we can obtain the state parameter vector x at time k. k The prior probability p(x) k |z 1:k-1 ):
[0083] p(x k |z 1:k-1 )=∫p(x k |x k-1 )p(x k-1 |z 1:k-1 )dx k-1 (5)
[0084] In equation (5), p(x) k |x k-1 ) represents the state parameter vector x at time k. k The transition probability density;
[0085] Based on the measured value z at time k k The state parameter vector x at time k is obtained using equation (6). k The posterior probability density p(x) k |z 1:k ):
[0086]
[0087] In equation (6), p(z) k |x k ) is the state parameter vector x at time k. k The likelihood probability density, p(z) k |z 1:k-1 () represents the measured value z at time k. k The probability distribution of z is a normalized constant, and p(z) k|z 1:k-1 )=∫p(z k |x k )p(x k |z 1:k-1 )dx k ;
[0088] Step 5: See Figure 3 The distribution of the measurement result dataset obviously does not satisfy a Gaussian distribution, so conventional methods cannot solve equation (6). Therefore, the particle filter method is chosen to recursively solve the posterior probability density of the state parameter vector, starting from the posterior probability density p(x) at time k. k |z 1:k N is generated in ) S Independent and identically distributed samples in, N represents the particle vector with the i-th state parameter at time k. S This represents the total number of particles generated by a single state parameter, and we have:
[0089]
[0090] In equation (7), g(x) k ) is x k Any function; E(g(x) k )) represents g(x k The mathematical expectation of ).
[0091] Step 6: Initialize k=1, and use equation (8) to generate the particle vector of the i-th state parameter at time k-1. i = 1, 2, ..., N s Thus, N is obtained. s Particle vectors with state parameters:
[0092]
[0093] In equation (8), p(x) k-1 Let x be the state parameter vector at time k-1. k-1 The prior distribution is given, and when the prior distribution is unknown, a uniform distribution is taken; and let the particle vector of the i-th state parameter at time k-1 be... The weight vector is All of its element values are 1 / N s ;
[0094] Step 7: In practical problems, it is often difficult, or even impossible, to obtain the posterior probability density p(x) from the actual probability density function. 1:k |z 1:k Sampling is performed from a known importance probability density distribution q(x) k |z 1:kGenerate the particle vector with the i-th state parameter at time k in the process. Therefore, the i-th weighted particle vector at time k can be obtained using equation (9).
[0095]
[0096] In equation (9), Let α represent the first distribution parameter at time k. k The i-th state parameter particle The weights, β represents the second distribution parameter at time k. k The i-th state parameter particle The weights;
[0097] right After normalization, the normalized weight vector is obtained. Thus, the state parameter vector x at time k can be obtained using equation (10). k The posterior filtering probability distribution p(x) k |z 1:k ):
[0098]
[0099] In equation (10), δ(·) represents the Dirac-delta function.
[0100] Step 8: Calculate the state parameter x at time k using equations (11) and (12) respectively. k The estimated value and variance
[0101]
[0102]
[0103] In equation (11), This represents the estimated value of the first distribution parameter at time k. This represents the estimated value of the second distribution parameter at time k;
[0104] In equation (12), This represents the variance of the first distribution parameter at time k. Let represent the variance of the second distribution parameter at time k;
[0105] Step 9: Use equation (13) to generate the i-th state parameter particle vector at time k+1.
[0106]
[0107] In equation (13), Let represent the noise value of the particle vector for the i-th state parameter at time k, and in, Indicates the interval Uniform distribution on Let $k$ be the mean of the $n$ standard deviations prior to time $k$.
[0108] Step 10: After assigning k+1 to k, if k > K, then the state parameter vector at time K is obtained. Otherwise, return to step 7 and execute sequentially; the final estimated value of the beta distribution parameter is...
[0109] Step 11: Calculate the normalized estimated value of the measurement result using equation (14).
[0110]
[0111] Step 12: Since the distribution of the measurement result error is non-Gaussian, the uncertainty cannot be calculated using statistical methods. Therefore, it is necessary to calculate the left and right quantiles of the uncertainty separately. Let the confidence probability p = 0.95, and use equation (16) to obtain the left quantile d of the uncertainty of the laser interferometer measurement result. left Right quantile d right :
[0112]
[0113] In equation (15), F(·) represents the cumulative distribution function of the beta distribution, and B(·) represents the beta function;
[0114] Step 13: Use equation (16) to obtain the normalized uncertainty of the interferometer measurement results at time K=1800.
[0115]
[0116] Step 14: Using equations (17) and (18), obtain the actual estimated values of the interferometer measurement results at time K = 1800. and uncertainty
[0117]
[0118]
[0119] In equations (17) and (18), y max y minThis represents the maximum and minimum values of the measurement results in the measurement results dataset Y. The final uncertainty assessment result is as follows: Figure 4 As shown, the uncertainty results evaluated using the proposed method and the standard Monte Carlo method are as follows: Figure 5 As shown, the evaluation results of the two are consistent, verifying the effectiveness of the method of the present invention.
[0120] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.
[0121] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.
Claims
1. A method for evaluating the uncertainty of laser interferometer measurement results with unknown distribution type, characterized in that, Includes the following steps: Step 1: Use a laser interferometer to measure the object under test for K time steps to obtain a dataset Y = {y} of measurement results with an unknown distribution type. k |k=1,2,,K}, where y k This represents the measurement result at the k-th time step; The measurement result dataset Y is preprocessed by removing and normalizing data to obtain the effective measurement result sequence Z = {z}. k |k=1,2,,K} is represented using the beta distribution method, where z k Let z represent the valid measurement value at time k, and z k ~β(α) k ,β k ); β(·) represents a beta distribution, ~ indicates that it follows a certain pattern, α k Let β represent the first distribution parameter at time k. k Let represent the second distribution parameter at time k, and we have: In equation (1), Δα k The first distribution parameter α at time k k-1 The noise variable, Δβ k Let α be the second distribution parameter at time k. k-1 The noise variable, when k=1, let α1=β1=1; Step 2: Let the state parameter vector to be estimated at time k be... T represents transpose, and we have: In equation (2), x k-1 Let p(x) be the state parameter vector at time k-1. k |x k-1 Let x be the state parameter vector at time k. k The transition probability density, p(z) k |x k Let x be the state parameter vector at time k. k The likelihood probability density; Step 3: Construct the state parameter value vector x before time k using equation (3). 1:k The posterior probability density p(x) 1:k |z 1:k ): In equation (3), z 1:k Let z be the measurement value before time k. 1:k-1 p(z) is the measurement value before time k-1. 1:k |x 1:k ) indicates that the measured value is z k The likelihood probability density at time p(x) 1:k |z 1:k-1 Let ) be the prior probability density at time k; The posterior filtering probability density p(x) at time k is obtained using equation (4). k |z 1:k ): p(x k |z 1:k )=∫∫...∫p(x 1:k |z 1:k )dx0dx1...dx k-1 (4) Step 4: Let the state parameter vector x at time k-1 be... k-1 The posterior filtering probability density is p(x) k-1 |z 1:k-1 Then, using equation (5), we can obtain the state parameter vector x at time k. k The prior probability p(x) k |z 1:k-1 ): p(x k |z 1:k-1 )=∫p(x k |x k-1 )p(x k-1 |z 1:k-1 )dx k-1 (5) In equation (5), p(x) k |x k-1 ) represents the state parameter vector x at time k. k The transition probability density; Based on the measured value z at time k k The state parameter vector x at time k is obtained using equation (6). k The posterior probability density p(x) k |z 1:k ): In equation (6), p(z) k |x k ) is the state parameter vector x at time k. k The likelihood probability density, p(z) k |z 1:k-1 () represents the measured value z at time k. k The probability distribution of p(z) is given, and p(z) is given. k |z 1:k-1 )=∫p(z k |x k )p(x k |z 1:k-1 )dx k ; Step 5: From the posterior probability density p(x) at time k k |z 1:k N is generated in ) S Independent and identically distributed samples in, N represents the particle vector with the i-th state parameter at time k. S This represents the total number of particles generated by a single state parameter, and we have: In equation (7), g(x) k ) is x k Any function; E(g(x) k )) represents g(x k The mathematical expectation of ). Step 6: Initialize k=1, and use equation (8) to generate the particle vector of the i-th state parameter at time k-1. Thus, N is obtained. s Particle vectors with state parameters: In equation (8), p(x) k-1 Let x be the state parameter vector at time k-1. k-1 The prior distribution is given, and when the prior distribution is unknown, a uniform distribution is taken; and let the particle vector of the i-th state parameter at time k-1 be... The weight vector is All of its element values are 1 / N s ; Step 7: From a known importance probability density distribution q(x) k |z 1:k Generate the particle vector with the i-th state parameter at time k in the process. Therefore, the i-th weighted particle vector at time k can be obtained using equation (9). In equation (9), Let α represent the first distribution parameter at time k. k The i-th state parameter particle The weights, β represents the second distribution parameter at time k. k The i-th state parameter particle The weights; right After normalization, the normalized weight vector is obtained. Thus, the state parameter vector x at time k can be obtained using equation (10). k The posterior filtering probability distribution p(x) k |z 1:k ): In equation (10), δ(·) represents the Dirac-delta function; Step 8: Calculate the state parameter x at time k using equations (11) and (12) respectively. k The estimated value and variance In equation (11), This represents the estimated value of the first distribution parameter at time k. This represents the estimated value of the second distribution parameter at time k; In equation (12), This represents the variance of the first distribution parameter at time k. Let represent the variance of the second distribution parameter at time k; Step 9: Use equation (13) to generate the i-th state parameter particle vector at time k+1. In equation (13), Let represent the noise value of the particle vector for the i-th state parameter at time k, and in, Indicates the interval Uniform distribution on Let $k$ be the mean of the $n$ standard deviations prior to time $k$. Step 10: After assigning k+1 to k, if k > K, then the state parameter vector at time K is obtained. Otherwise, return to step 7 and execute sequentially; Step 11: Calculate the estimated value of the normalized measurement result using equation (14). Step 12: Let the confidence probability be p, and use equation (16) to obtain the left quantile d of the uncertainty of the laser interferometer measurement result. left Right quantile d right : In equation (15), F(·) represents the cumulative distribution function of the beta distribution, and B(·) represents the beta function; Step 13: Use equation (16) to obtain the normalized uncertainty of the interferometer measurement results at time K. Step 14: Use equations (17) and (18) to obtain the actual estimated values of the interferometer measurement results at time K. and uncertainty In equations (17) and (18), y max y min This represents the maximum and minimum values of the measurement results in the measurement result dataset Y.
2. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing the laser interferometer measurement result uncertainty assessment method of claim 1, and the processor is configured to execute the program stored in the memory.
3. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is run by the processor, it executes the steps of the method for evaluating the uncertainty of laser interferometer measurement results as described in claim 1.