Error evaluation weight distribution method and system for range finder ranging data

Abstract

The present application relates to a kind of range finder range finding data error evaluation weight distribution method and system.In existing measurement error evaluation, weight distribution does not consider the covariance between errors.This method equivalent to the measurement path as a straight line, determines the measuring point;Obtain the observed distance between any two measuring points, combined with actual distance and measurement error correction number, establish linear relationship matrix;Obtain the error weight of observed distance, combined with linear relationship matrix, establish error equation;The result of error equation is obtained and fully differentiated, and the minimum value of variance function is obtained under the constraint condition;The error weight of observed distance is derived, and the function that weight is inversely proportional to variance is further transformed, and the correct weight distribution of measurement distance and measurement error is calculated.This method considers the influence of covariance, lists the error equation of observation value with weight, obtains the variance expression of parameter error by applying covariance propagation law, and the new formula includes the influence of covariance, and the error analysis is more rigorous.

Description

Technical Field

[0001] This invention relates to the field of railway surveying and mapping technology, specifically to a method and system for allocating error assessment weights for distance measurement data from a distance measuring instrument. Background Technology

[0002] Surveying for high-speed railways is an integral part of the entire construction process, including the survey and design phase, the construction phase, and the acceptance and maintenance phases after project completion. The appropriateness of the technologies used directly affects the quality of high-speed railway construction.

[0003] Distance measuring instruments are frequently used in high-speed railway engineering surveying, but the measured values ​​are generally not equally weighted observations. Traditional measurement error assessment uses variance as the basis for weight allocation; the ratio of the standard deviation to the variance of the observed error is the weight of the observed value. However, during the measurement process, errors are not strictly independent. Due to the repetition of measurement conditions, errors often exhibit correlation, meaning the covariance between errors is not zero. Current weight determination only considers variance, neglecting the influence of covariance. In the least squares equal weighting process, it is practically assumed that only variance has an effect, and the covariance is zero, which is clearly inaccurate.

[0004] Therefore, it is necessary to propose a new method for allocating error assessment weights for distance measurement data from rangefinders to overcome the shortcomings of the existing methods, which are not rigorous enough. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for weighting error assessment of distance measurement data from a distance measuring instrument, so as to solve the problem that the weighting of existing measurement error assessments does not consider the covariance between errors.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for allocating error assessment weights for distance measurement data from a rangefinder, the method comprising:

[0008] The measurement path is equivalent to a straight line, and the measurement points are determined on the measurement path;

[0009] The observed distance between any two measuring points is obtained by using a rangefinder. A linear relationship matrix between the observed distance and the actual distance is established by combining the actual distance and the measurement error correction.

[0010] Obtain the error weights of the observed distance, and establish the error equation by combining the linear relationship matrix between the observed distance and the actual distance;

[0011] The result of the error equation is obtained and the total differential is calculated to obtain the variance function. Under the constraints, the minimum value of the variance is found.

[0012] Differentiate the error weights of the observation distance and further transform them to obtain a function inversely proportional to the variance;

[0013] By using a function that is inversely proportional to the variance, the measured distance with the correct weight allocation and the measurement error can be obtained.

[0014] Furthermore, the measurement path is equated to a straight line, and measurement points are determined on the measurement path, including:

[0015] Determine the measurement points on the straight line as points A, B, C, and D;

[0016] Assume the actual distance between A and B is y1, the actual distance between B and C is y2, and the actual distance between C and D is y3.

[0017] Furthermore, by obtaining the observed distance between any two measuring points using a rangefinder, and combining the actual distance and measurement error correction, a linear relationship matrix between the observed distance and the actual distance is established, including:

[0018] The observed distance between any two measuring points is obtained using a rangefinder. Let x1 be the observed distance between A and B, x2 between AC, x3 between AD, x4 between BC, x5 between BD, and x6 between CD. Then:

[0019] x1+v1=y1;

[0020] x² + v² = y₁ + y₂;

[0021] x3+v3=y1+y2+y3;

[0022] x4 + v4 = y2;

[0023] x5 + v5 = y2 + y3;

[0024] x6 + v6 = y3;

[0025] in:

[0026] v i Let i be the measurement error correction number, i = 1, 2, 3, ..., 6;

[0027] Establish a linear relationship matrix between observed distance and actual distance:

[0028]

[0029] Right now:

[0030] V = BY - X;

[0031] Calculated using the least squares method:

[0032] Y = (B T PB) -1 B T PX;

[0033] in:

[0034] V is a sequence of measurement error corrections;

[0035] B is the coefficient matrix, with elements b. i ,i=1,2,3,…,n,n=6;

[0036] Y represents the actual distance sequence;

[0037] X represents the observation distance sequence;

[0038] P is the sequence of error weight variables for the observation distance.

[0039] Furthermore, the error weights of the observed distance are obtained, and an error equation is established by combining the linear relationship matrix between the observed distance and the actual distance, including:

[0040] Considering the influence of weights, and combining the linear relationship matrix between observed and actual distances, an error equation is established:

[0041]

[0042] in:

[0043] x i Let i be the observation distance, i = 1, 2, 3, ..., 6;

[0044] V i That is, v i , is the measurement error correction number, i = 1, 2, 3, ..., 6;

[0045] P i Let i be the error weight variable for the observation distance, i = 1, 2, 3, ..., n, n = 6.

[0046] Furthermore, the result of the error equation is obtained and totally differentiald to obtain the variance function. Under the constraints, the minimum value of the variance is found, including:

[0047] Using the least squares method, the result of the error equation, i.e., the actual distance function y, is:

[0048]

[0049] make Taking the total differential of the actual distance function, we get:

[0050] Δy=P1b1Δx1+P2b2Δx2+…+P n b n Δxn =B T PΔX;

[0051] Using the covariance propagation law, the variance function is obtained:

[0052]

[0053] in:

[0054] Δy represents the actual distance error;

[0055] σ 2 (Δy) represents the variance of the actual distance error;

[0056] D(ΔX) is the variance-covariance matrix of the observation distance error;

[0057] ΔX is the observation distance error matrix, with elements Δx. i , i = 1, 2, 3, ..., n;

[0058] σ i 2 Let i be the variance of the observed distances, i = 1, 2, 3, ..., n

[0059] σ ij Let i = 1, 2, 3, ..., n, j = 1, 2, 3, ..., n.

[0060] When σ 2 When (Δy) reaches its minimum value, the measured quality of the actual distance is the best, under the constraints. Next, find σ. 2 The minimum value of (Δy) can be obtained using the Lagrange multiplier method.

[0061]

[0062] Furthermore, by differentiating the error weights of the observation distance, a function inversely proportional to the variance is obtained, including:

[0063] For P i Taking the derivative and setting it to 0, we get:

[0064]

[0065] in;

[0066] λ0 represents the Lagrange multiplier;

[0067] The transformation yields:

[0068]

[0069] p i Indicates that for P iThe assignment is a real number for the weight variable;

[0070]

[0071]

[0072] in:

[0073] y0 represents the optimal measured value;

[0074] Δy0 represents the error of the best measured value;

[0075] σ 2 (Δy0) represents the variance of the error of the best measured value;

[0076] Further transformation yields a function where the weights are inversely proportional to the variance:

[0077]

[0078] Furthermore, using a function where weights are inversely proportional to variance, the measured distance with correctly assigned weights and the measurement error are obtained, including:

[0079] The rangefinder has the following observation errors:

[0080]

[0081] in:

[0082] R is the proportional error;

[0083] c represents a constant error;

[0084] The variance-covariance calculation formula is as follows:

[0085] D ΔX =E[(ΔX)(ΔX)] T ];

[0086] in:

[0087] D ΔX This represents the variance-covariance matrix of the observation distance error;

[0088] E[(ΔX)(ΔX) T [] indicates the calculation of expectation;

[0089] The calculation yielded:

[0090]

[0091] in:

[0092] The variance represents the proportional error;

[0093] The variance represents the constant error;

[0094] Combination

[0095]

[0096] The weight of each observation distance is calculated;

[0097] according to

[0098] Y = (B T PB) -1 B T PX;

[0099] The optimal measured value Y can then be calculated.

[0100] On the other hand, an error assessment weighting system for distance measurement data from a rangefinder is provided, the system being used to implement the method, including:

[0101] The equivalent module is used to convert the measurement path into a straight line and determine the measurement points on the measurement path;

[0102] The matrix building module is used to obtain the observed distance between any two measuring points through a rangefinder, and to establish a linear relationship matrix between the observed distance and the actual distance by combining the actual distance and the measurement error correction.

[0103] The error equation establishment module is used to obtain the error weights of the observed distance and establish the error equation by combining the linear relationship matrix between the observed distance and the actual distance.

[0104] The variance function calculation module is used to obtain the result of the error equation and perform total differential to obtain the variance function, and to find the minimum value of the variance under the constraints.

[0105] The module for obtaining the weight and variance function is used to differentiate the error weights of the observation distance and further transform them to obtain a function inversely proportional to the weight and variance.

[0106] The results calculation module is used to obtain the measurement distance with correct weight allocation and the measurement error by using a function inversely proportional to the weight and variance.

[0107] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0108] The error assessment weighting method and system for distance measurement data provided by this invention starts from the influencing factors of weighting, considers the influence of covariance, lists the weighted observation error equation, and expresses the parameter results in a weighted manner according to the adjustment method. It performs total differential and applies the covariance propagation law to obtain the variance expression of the parameter error. Under certain constraints, the variance expression of the parameter error is minimized by the Lagrange multiplier method. In the process, after parameter transformation, a strict mathematical formula inversely proportional to the weight and variance can be obtained, and the new formula includes the influence of covariance.

[0109] Traditional methods assume that measured values ​​are independent and do not consider their correlation, thus leading to problems in determining weights. This method, compared to traditional calculations, fully considers the correlation between measured values. Based on the number of observations, it derives the relationship between the weights and variances of the measured values, proving that the weights are not independent but correlated, and related to the coefficient matrix and the variance of the observation error. This results in a more accurate weight calculation method, leading to more precise measurement results and providing more accurate guidance for subsequent construction. Attached Figure Description

[0110] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other embodiments can be obtained from these drawings without creative effort.

[0111] Figure 1 This is a flowchart of the method of the present invention.

[0112] Figure 2 This is a system composition diagram of the present invention.

[0113] Figure 3 This is a schematic diagram of the observation distance between any two measuring points. Detailed Implementation

[0114] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Preferred embodiments of the invention are shown in the drawings. However, the invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a thorough and complete understanding of the disclosure of the invention.

[0115] It should be noted that similar reference numerals and letters indicate similar items; therefore, once an item is defined in one embodiment, it does not need to be further defined and explained in subsequent embodiments. Furthermore, the terms "comprising" and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, system, product, or apparatus that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0116] It should also be noted that although the order of steps is mentioned in the method description, in some cases, steps may be performed in a different order than that described here, and this should not be interpreted as a restriction on the order of steps.

[0117] Example 1:

[0118] This embodiment provides a method for weighting error assessment of distance measurement data from a rangefinder. When assigning weights based on measurement error theory, only variance is considered, while the influence of covariance is ignored. Through rigorous derivation using regression mathematics, a logically sound method for weighting error assessment is provided.

[0119] Before processing the adjustment data, this method often requires weighting the observations. In this embodiment, the weighted observation error equation is listed, and the parameter results are expressed in a weighted manner according to the adjustment method. The total differential is applied and the covariance propagation law is applied to obtain the variance expression of the parameter error. Under certain constraints, the Lagrange multiplier method is used to find the minimum value of the variance expression of the parameter error. In the process, after parameter transformation, a strict mathematical formula inversely proportional to the weight and variance can be obtained, and the new formula includes the influence of covariance.

[0120] like Figure 1 The method includes:

[0121] S1: The measurement path is represented as a straight line, and measurement points are determined along the path. This includes:

[0122] S101: Determine the measuring points on the straight line, namely points A, B, C, and D, as follows: Figure 3 The number of measuring points can be increased or decreased depending on the actual situation.

[0123] S102: Assume the actual distance between AB is y1, the actual distance between BC is y2, and the actual distance between CD is y3.

[0124] S2: Obtain the observed distance between any two measuring points using a rangefinder, and establish a linear relationship matrix between the observed distance and the actual distance by combining the actual distance and the measurement error correction. This includes:

[0125] S201: Obtain the observed distance between any two measuring points using a rangefinder. Let x1 be the observed distance between AB, x2 between AC, x3 between AD, x4 between BC, x5 between BD, and x6 between CD. Then:

[0126] x1+v1=y1;

[0127] x2+v2=y1+y2;

[0128] x3+v3=y1+y2+y3;

[0129] x4 + v4 = y2;

[0130] x5 + v5 = y2 + y3;

[0131] x6 + v6 = y3;

[0132] in:

[0133] v i Let i be the measurement error correction number, i = 1, 2, 3, ..., 6.

[0134] S202: Establish a linear relationship matrix between observed distance and actual distance:

[0135]

[0136] Right now:

[0137] V = BY - X;

[0138] Calculated using the least squares method:

[0139] Y = (B T PB) -1 B T PX;

[0140] in:

[0141] V is a sequence of measurement error corrections;

[0142] B is the coefficient matrix, with elements b. i ,i=1,2,3,…,n,n=6;

[0143] Y represents the actual distance sequence;

[0144] X represents the observation distance sequence;

[0145] P is the sequence of error weight variables for the observation distance.

[0146] S3: Obtain the error weights for the observed distance, and establish the error equation by combining the linear relationship matrix between the observed and actual distances. This includes:

[0147] S301: Considering the influence of weights, and combining the linear relationship matrix between observed and actual distances, establish the error equation:

[0148]

[0149] in:

[0150] x i Let i be the observation distance, i = 1, 2, 3, ..., 6;

[0151] V i That is, v i , is the measurement error correction number, i = 1, 2, 3, ..., 6;

[0152] P i Let i be the error weight variable for the observation distance, i = 1, 2, 3, ..., n, n = 6.

[0153] S4: Obtain the result of the error equation and perform total differential to obtain the variance function. Find the minimum value of the variance under the constraints. This includes:

[0154] S401: Using the least squares method, the result of the error equation, i.e., the actual distance function y, is:

[0155]

[0156] S402: Order Taking the total differential of the actual distance function, we get:

[0157] Δy=P1b1Δx1+P2b2Δx2+…+P n b n Δx n =B T PΔX;

[0158] in:

[0159] Δy represents the actual distance error.

[0160] S403: Obtain the variance function using the covariance propagation law:

[0161]

[0162] in:

[0163] σ 2 (Δy) represents the variance of the actual distance error;

[0164] D(ΔX) is the variance-covariance matrix of the observation distance error;

[0165] ΔX is the observation distance error matrix, with elements Δx.i , i = 1, 2, 3, ..., n;

[0166] σ i 2 Let i be the variance of the observed distances, i = 1, 2, 3, ..., n

[0167] σ ij Let i = 1, 2, 3, ..., n, j = 1, 2, 3, ..., n.

[0168] Existing weights The premise for this to hold is σ. ij =0, meaning the covariance is not zero in this method. p i Indicates that for P i The assignment is a real number for the weight variable.

[0169] S404: When σ 2 When (Δy) reaches its minimum value, the measured quality of the actual distance is the best, under the constraints. Next, find σ. 2 The minimum value of (Δy) can be obtained using the Lagrange multiplier method.

[0170]

[0171] S5: Differentiate the error weights of the observation distance, and further transform to obtain a function where the weights are inversely proportional to the variance. This includes:

[0172] S501: For P i Taking the derivative and setting it to 0, we get:

[0173]

[0174] in;

[0175] λ0 represents the Lagrange multiplier.

[0176] S502: Transformation yields:

[0177]

[0178] p i Indicates that for P i The assignment is a real number for the weight variable;

[0179]

[0180]

[0181] in:

[0182] y0 represents the optimal measured value;

[0183] Δy0 represents the error of the best measured value;

[0184] σ 2 (Δy0) represents the variance of the error of the best measured value;

[0185] S503: Further transformation yields a function where the weights are inversely proportional to the variance:

[0186]

[0187] S6: Using a function where weights are inversely proportional to variance, obtain the measured distance with correctly assigned weights and the measurement error. This includes:

[0188] The rangefinder has the following observation errors:

[0189]

[0190] in:

[0191] R is the proportional error;

[0192] c represents a constant error;

[0193] S601: Calculated using the following variance-covariance formula:

[0194] D ΔX =E[(ΔX)(ΔX)] r ];

[0195] in:

[0196] D ΔX This represents the variance-covariance matrix of the observation distance error;

[0197] E[(ΔX)(ΔX) T [] indicates the calculation of expectation;

[0198] S602: Calculated result:

[0199]

[0200] in:

[0201] The variance represents the proportional error;

[0202] The variance represents the constant error;

[0203] S603: Combination

[0204]

[0205] The weight of each observation distance is calculated;

[0206] S604: According to

[0207] Y = (B T PB) -1 B T PX;

[0208] The optimal measured value Y can then be calculated.

[0209] The method in this embodiment starts with variance and covariance to analyze the correlation between errors. For the current weight allocation, which only considers the variance, the covariance is incorporated into the weight allocation, thereby re-deriving a rigorous mathematical function inversely proportional to the variance.

[0210] Example 2:

[0211] This embodiment provides an error assessment weighting system for distance measurement data from a rangefinder, used to implement the method described in Embodiment 1, including:

[0212] The equivalent module is used to convert the measurement path into a straight line and determine the measurement point on the measurement path, corresponding to S1 in Embodiment 1;

[0213] The matrix establishment module is used to obtain the observed distance between any two measuring points through the rangefinder, and to establish a linear relationship matrix between the observed distance and the actual distance by combining the actual distance and the measurement error correction, which corresponds to S2 in Example 1.

[0214] The error equation establishment module is used to obtain the error weights of the observed distance, and establish the error equation by combining the linear relationship matrix between the observed distance and the actual distance, which corresponds to S3 in Example 1;

[0215] The variance function calculation module is used to obtain the result of the error equation and perform total differential to obtain the variance function. Under the constraint conditions, it finds the minimum value of the variance, corresponding to S4 in Example 1.

[0216] The weight and variance function acquisition module is used to differentiate the error weights of the observation distance and further transform them to obtain a function inversely proportional to the weights and variances, corresponding to S5 in Example 1;

[0217] The result calculation module is used to obtain the measurement distance and measurement error with correct weight allocation by using a function that is inversely proportional to the weight and variance, corresponding to S6 in Example 1.

[0218] Those skilled in the art will understand that all or part of the functions of the embodiments of the present invention can be implemented by hardware or by computer program. When all or part of the functions in the above embodiments are implemented by computer program, the program can be stored in a computer-readable storage medium, which may include: read-only memory, random access memory, disk, optical disk, hard disk, etc., and the program is executed by a computer to achieve the above functions. For example, the program can be stored in the memory of a device, and when the program in the memory is executed by the processor, all or part of the above functions can be achieved. In addition, when all or part of the functions in the above embodiments are implemented by computer program, the program can also be stored in a storage medium such as a server, another computer, disk, optical disk, flash drive, or portable hard drive, and can be downloaded or copied to the memory of a local device, or the system of the local device can be updated. When the program in the memory is executed by the processor, all or part of the functions in the above embodiments can be achieved.

[0219] The above examples illustrate the present invention only to aid in understanding it and are not intended to limit the scope of the invention. Those skilled in the art can make various simple deductions, modifications, or substitutions based on the principles of this invention.

Claims

1. A method for allocating error weights for distance measurement data from a rangefinder, characterized in that: The method includes: The measurement path is equivalent to a straight line, and the measurement points are determined on the measurement path; The observed distance between any two measuring points is obtained by using a rangefinder. A linear relationship matrix between the observed distance and the actual distance is established by combining the actual distance and the measurement error correction. Obtain the error weights for the observed distance, and establish the error equation by combining the linear relationship matrix between the observed and actual distances, including: Considering the influence of error weights, and combining the linear relationship matrix between observed and actual distances, an error equation is established: ； in: For observation distance, ; That is , is the measurement error correction value. ; The error weight variable is the observation distance. ; This is a coefficient matrix with elements . , ; Y represents the actual distance sequence; The result of the error equation is obtained and the total differential is calculated to obtain the variance function. Under the constraints, the minimum value of the variance is found. Differentiating the error weights of the observation distance and further transforming them, we obtain a function inversely proportional to the variance; By using a function that is inversely proportional to the variance, the measurement distance with the correct weight allocation and the measurement error can be obtained.

2. The error weighting method for distance measurement data of a rangefinder according to claim 1, characterized in that: The measurement path is equivalent to a straight line, and the measurement points are determined on the measurement path, including: Determine the measurement points on the straight line as points A, B, C, and D; Assume the actual distance between A and B is y1, the actual distance between B and C is y2, and the actual distance between C and D is y3.

3. The error weighting method for distance measurement data of a rangefinder according to claim 2, characterized in that: By obtaining the observed distance between any two measuring points using a rangefinder, and combining this with the actual distance and measurement error correction, a linear relationship matrix between the observed distance and the actual distance is established, including: The observed distance between any two measuring points is obtained using a rangefinder. Let x1 be the observed distance between AB, x2 between AC, x3 between AD, x4 between BC, x5 between BD, and x6 between CD. Then: ； ； ； ； ； ； in: This is the measurement error correction value. ; Establish a linear relationship matrix between observed distance and actual distance: - ； Right now: ； Calculated using the least squares method: ； in: This is a sequence of measurement error corrections; This is an observation distance sequence; P is the sequence of error weight variables for the observation distance.

4. The error weighting method for distance measurement data of a rangefinder according to claim 3, characterized in that: Obtain the result of the error equation and perform total differential to obtain the variance function. Under constraints, find the minimum value of the variance, including: Using the least squares method, the result of the error equation, i.e., the actual distance function y, is: ； make Taking the total differential of the actual distance function, we get: ； Using the covariance propagation law, the variance function is obtained: ； in: This represents the actual distance error. This represents the variance of the actual distance error; The variance-covariance matrix of the observation distance error; △X is the observation distance error matrix, with elements △x i , ; The variance of the observed distance, ; The covariance between observation distances, , ; when When the minimum value is taken, the quality of the actual distance measurement is the best, under the constraints. Next, please The minimum value of can be obtained using the Lagrange multiplier method. ； in, It represents the Lagrange multiplier.

5. The error weighting method for distance measurement data of a rangefinder according to claim 4, characterized in that: Differentiating the error weights of the observation distance and further transforming them, we obtain a function inversely proportional to the variance, including: right Taking the derivative and setting it to 0, we get: ； The transformation yields: ； Indicates to The value is assigned as a real number to the error weight variable; ； ； in: This indicates the best measured value; This indicates the error of the best measured value; The variance represents the error of the best measured value; Further transformation yields a function where the error weights are inversely proportional to the variance: 。 6. The error weighting method for distance measurement data of a rangefinder according to claim 5, characterized in that: By using a function where error weights are inversely proportional to variance, the correctly weighted measurement distance and measurement error are obtained, including: The rangefinder has the following observation errors: ； in: R is the proportional error; c represents a constant error; The variance-covariance calculation formula is as follows: ； in: This represents the variance-covariance matrix of the observation distance error; This indicates the calculation of the expectation; The calculation yielded: ； in: The variance represents the proportional error; The variance represents the constant error; Combination ； The error weight for each observation distance is calculated; according to ； The optimal measured value Y can then be calculated.

7. An error weighting system for distance measurement data from a rangefinder, characterized in that: The system is used to implement the method according to any one of claims 1-6, comprising: The equivalent module is used to convert the measurement path into a straight line and determine the measurement points on the measurement path; The matrix building module is used to obtain the observed distance between any two measuring points through a rangefinder, and to establish a linear relationship matrix between the observed distance and the actual distance by combining the actual distance and the measurement error correction. The error equation establishment module is used to obtain the error weights of the observed distance and establish the error equation by combining the linear relationship matrix between the observed distance and the actual distance. The variance function calculation module is used to obtain the result of the error equation and perform total differential to obtain the variance function, and to find the minimum value of the variance under the constraints. The error weight and variance function acquisition module is used to differentiate the error weight of the observation distance and further transform it to obtain a function inversely proportional to the error weight and variance. The results calculation module is used to obtain the measurement distance with correct weight allocation and the measurement error by using a function that is inversely proportional to the error weight and the variance.

Images