Pseudo-satellite spatial layout optimization method based on differential evolution algorithm

Abstract

The present invention provides a pseudolite space layout optimization method based on a differential evolution algorithm, comprising the following steps: Step 1: Modeling the actual problem to determine the specific size of the actual indoor space, including the length, width, and height of the indoor space; randomly generating multiple sets of different pseudolite space layouts as an initialization population based on the actual situation; and performing a boundary absorption operation based on the length, width, and height of the indoor space to constrain the pseudolite coordinates; Step 2: Setting initialization parameters of the differential evolution algorithm, including the length, width, and height of the indoor space, population size NP, individual dimension D, scaling factor F, crossover probability CR, maximum iteration number maxGen, and pseudolite coordinate limit settings for the boundary absorption operation; Step 3: Optimizing the optimal pseudolite space layout using the differential evolution algorithm with the set initialization parameters; and Step 4: Field deploying pseudolites according to the optimal pseudolite space layout optimized by the algorithm. This method applies the differential evolution algorithm to pseudolite space layout technology, effectively improving the pseudolite spatial geometric configuration.

Description

Technical Field

[0001] The present invention relates to the technical field of pseudolite space layout, and in particular to a pseudolite space layout optimization method based on a differential evolution algorithm. Background Art

[0002] Currently, Global Navigation Satellite System (GNSS) positioning can achieve high-precision real-time positioning in open areas outdoors. However, in areas with severe signal obstruction, the number of visible satellites is small, and especially in indoor environments, receivers cannot receive GNSS signals at all. To address these issues, various GNSS augmentation and assistance systems have been proposed and researched, with pseudolite systems being one effective solution. Pseudolites are "terrestrial satellites," equivalent to satellites placed in near-Earth space over 20,000 kilometers above the Earth's surface. They are devices capable of transmitting and receiving GNSS-like signals. Pseudolite systems not only enhance GNSS systems but also enable independent positioning in GNSS-denied environments. In situations where some GNSS navigation satellites are completely invisible, a sufficient number of pseudolites can be used to form a navigation constellation for independent navigation and positioning. A key advantage is that the geometric distribution of pseudolites can be pre-designed. Due to their advantages over GNSS systems, pseudolite systems have been widely researched and applied in the field of indoor positioning. To achieve optimal indoor pseudolite positioning results, the primary consideration is the spatial layout of pseudolites. A well-placed pseudolite layout can minimize the dop value, thereby reducing the amplification factor of the user ranging error (URE), resulting in more accurate positioning results. For GNSS satellites located over 20,000 kilometers away, their positions constantly change over time, and their spatial configurations also change accordingly, making them difficult to control. However, if a pseudolite's position is fixed, its spatial configuration remains unchanged. Human intervention is possible, allowing for adjustments to the pseudolite's position to achieve a better spatial configuration. Indoor pseudolite placement is a complex issue that requires consideration based on specific circumstances. The general approach is to maximize the volume of the spatial geometry formed by the intersection of each pseudolite and the lines connecting each pseudolite to the user receiver. Since the dop value is inversely proportional to the volume of the spatial geometry, a larger volume corresponds to a smaller dop value. However, in actual engineering practice, it is difficult to rely solely on human judgment to determine the optimal pseudolite placement, and the resulting spatial configuration is often suboptimal or even near-optimal. Several artificial intelligence optimization algorithms, such as genetic algorithms (GAs) and particle swarm optimization (PSOs), have been applied to this type of problem. Both algorithms can optimize the spatial layout of pseudolites to a certain extent, approaching the optimal spatial layout. However, GAs cannot utilize timely feedback from the network, resulting in slower search speeds and requiring more training time to obtain a more accurate solution. PSOs converge quickly, but their optimization results are less effective.The differential evolution algorithm (DE algorithm) is also an artificial intelligence optimization algorithm. Compared with the first two methods, the DE algorithm is more robust and converges faster. It combines the two major advantages of the genetic algorithm's good optimization effect and the particle swarm algorithm's fast convergence speed. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a pseudolite space layout optimization method based on a differential evolution algorithm, which applies the differential evolution algorithm to pseudolite space layout technology and effectively improves the pseudolite space geometric configuration.

[0004] To solve the above technical problems, the technical solution adopted by the present invention is: a pseudolite spatial layout optimization method based on a differential evolution algorithm, comprising the following steps:

[0005] Step 1: Model the actual problem and determine the specific size of the actual indoor space, including the length, width, and height of the indoor space. Based on the actual situation, design multiple sets of different pseudolite spatial layouts as the initialization population. Perform boundary absorption operations based on the length, width, and height of the indoor space to constrain the pseudolite coordinates (X, Y, Z);

[0006] Step 2: Set the initialization parameters of the differential evolution algorithm, including the length, width and height of the indoor space, the population size NP, the individual dimension D, the scaling factor F, the crossover probability CR, the maximum iteration number maxGen, and the boundary absorption operation pseudo-satellite coordinate limit setting;

[0007] Step 3: Using the differential evolution algorithm with set initialization parameters to obtain the optimized optimal pseudolite spatial layout;

[0008] Step 4: Deploy pseudolites on-site according to the optimal pseudolite spatial layout optimized by the algorithm.

[0009] In the preferred solution, in step 2, the length, width and height of the indoor space are determined according to the actual spatial dimensions; the population size NP is the number of spatial layout types in the initialized population; each pseudo-satellite spatial layout represents an individual, and the individual dimension D is equal to three times the pseudo-satellite position parameters contained in each individual.

[0010] In a preferred embodiment, the step three includes the following steps:

[0011] S301. Calculate the objective function value of the individual to be optimized: Take the average of the sum of the pdop values of the ground grid points in the positioning area of interest under a certain pseudolite spatial layout as the objective function, traverse the ground grid points in the positioning area of interest to calculate their pdop values, then calculate the sum of the pdop values of all the ground grid points in the positioning area of interest, and finally divide the sum by the number of ground grid points in the positioning area of interest to obtain the objective function value. The smaller the objective function value, the more superior the pseudolite spatial layout individual vector. The objective function calculation formula is as follows:

[0012]

[0013] Where M is the number of ground grid points in the positioning area of interest, (pdop) i is the pdop value of the i-th ground grid point under a certain pseudolite spatial layout;

[0014] S302, mutation operation: the population to be optimized is mutated in one of the following five ways:

[0015] (a) “DE / rand / 1”:

[0016] (b) “DE / best / 1”:

[0017] (c) “DE / rand-to-best / 1”:

[0018] (d) “DE / best / 2”:

[0019] (e) “DE / rand / 2”:

[0020] Where X is the initial population individual vector; V is the population individual vector after mutation; G represents the number of cycles; index are mutually exclusive integers randomly generated in the range [1, NP]. For the strategy "DE / rand / 1", NP is at least greater than or equal to 3. For the strategies "DE / best / 1", "DE / rand-to-best / 1", "DE / best / 2", and "DE / rand / 2", NP is at least greater than or equal to 2, 2, 4, and 5, respectively. The scaling factor F is a positive control parameter used to scale the difference vector. X best,G is the best individual vector with the best fitness value in a generation population;

[0021] S303, crossover operation: select between the initial individual vector X and the mutated individual vector V to generate a crossover individual vector U, and use binomial crossover to generate the crossover individual vector. The specific formula is as follows:

[0022]

[0023] Where, j rand is an integer randomly selected in the range [1, D]; the above formula shows that when the random number generated in [0, 1] is less than or equal to the crossover probability CR or j = j rand When , the mutant individual vector V is selected as the cross individual vector U from the initial individual vector X and the mutant individual vector V, otherwise, the initial individual vector X is selected as the cross individual vector U;

[0024] S304, boundary absorption operation, performing boundary absorption operation on individuals in the cross-individual vector U. When an element in the cross-individual vector U exceeds the set limit, the value is reset to the upper or lower limit closest to the value, or a random value between the upper and lower limits is selected to replace it;

[0025] S305, select operation, calculate the objective function value f(U) of each individual of the cross individual vector U after cross and boundary absorption operation i,G ), and the objective function value f(X i,G ) is compared. If the initial population individual vector X is better, then the individual vector in X remains unchanged. If the crossover individual vector U after the boundary absorption operation is better, then the initial population individual vector X is replaced by the crossover individual vector U, and the new X obtained in the current generation is cycled for the next generation. The above operation is expressed as follows:

[0026]

[0027] S306. Repeat steps S302 to S305. When the number of iterations reaches maxGen, stop the iteration.

[0028] In a preferred solution, in step 3, in S301, the method for calculating the pdop value of the ground grid point under a certain pseudolite spatial layout is as follows: when a certain pseudolite spatial layout is fixed, the design matrix B in the error equation is as follows:

[0029]

[0030] Among them, l i 、m i 、n i (i=1,2,…,n) is the direction cosine from the ground user receiver to each pseudo-satellite, which is calculated as follows:

[0031]

[0032] Among them, (X i,Y i ,Z i ) is the coordinate of the ith pseudo-satellite, (X 0 ,Y 0 ,Z 0 ) is the approximate coordinate of the ground user receiver, ρ 0 is the approximate distance to the i-th pseudo-satellite calculated from the approximate coordinates of the ground user receiver, ρ 0 The expression is as follows:

[0033]

[0034] The cofactor matrix Q obtained after single point positioning:

[0035]

[0036] The pdop value is calculated by tracing the cofactor matrix Q, and the calculation formula is as follows:

[0037]

[0038] The present invention provides a pseudolite spatial layout optimization method based on a differential evolution algorithm, which has the following beneficial effects:

[0039] 1. The present invention proposes a pseudolite spatial layout optimization method based on the differential evolution algorithm (DE). The artificial intelligence optimization algorithm is applied to the pseudolite spatial layout technology. The advantages of the DE algorithm are strong robustness and fast convergence speed. The mean of the ground position precision dilution (PDOP) is used as the objective function. By setting the positioning focus area to meet the user positioning requirements in different environments, the optimal solution of the pseudolite layout is searched within a certain space, which effectively improves the pseudolite spatial geometric configuration.

[0040] 2. The spatial configuration obtained by the pseudo-satellite spatial layout optimization method based on the differential evolution algorithm has the characteristics of a wider and more uniform distribution of low pdop values, which indicates that the positioning results obtained by positioning users under this spatial configuration are more likely to meet the accuracy requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The present invention will be further described below with reference to the accompanying drawings and examples:

[0042] Figure 1 Flow chart of the implementation of the present invention;

[0043] Figure 2 This is the flow chart of the pseudolite spatial layout optimization algorithm based on differential evolution method;

[0044] Figure 3 For simulation scenarios;

[0045] Figure 4 The conventional spatial layout of pseudolites in the embodiment;

[0046] Figure 5 This is the ground pdop value distribution map under the conventional layout;

[0047] Figure 6 Optimize the spatial layout of pseudolites of the present invention in the embodiment;

[0048] Figure 7 This is the ground pdop value distribution map under the optimized layout; DETAILED DESCRIPTION

[0049] Combine Figures 1 to 7 The specific embodiments of the present invention are described in further detail.

[0050] A pseudolite spatial layout optimization method based on a differential evolution algorithm comprises the following steps:

[0051] Step 1: Model the actual problem and determine the specific size of the actual indoor space, including the length, width, and height of the indoor space. Based on the actual situation, design multiple sets of different pseudolite spatial layouts as the initial population. The number of these different pseudolite spatial layouts is the population size NP. Each pseudolite spatial layout is equivalent to an individual in the population. Boundary absorption operations are performed according to the length, width, and height of the indoor space to constrain the pseudolite coordinates (X, Y, Z).

[0052] Step 2: Set the initialization parameters of the differential evolution algorithm, including the length, width and height of the indoor space, the population size NP, the individual dimension D, the scaling factor F, the crossover probability CR, the maximum iteration number maxGen, and the boundary absorption operation pseudo-satellite coordinate limit setting.

[0053] The length, width, and height of the indoor space are determined based on the actual spatial dimensions. The population size NP and individual dimension D are derived from the initialized pseudolite spatial layout population. The population size NP is the number of spatial layout options in the initialized population. Each pseudolite spatial layout represents an individual, and the individual dimension D is equal to three times the pseudolite position parameters contained in each individual. For example, within a 20m*20m*4m indoor space, there are ten pseudolite spatial layout options, each requiring six pseudolites. Therefore, the population size NP = 10 and the individual dimension D = 6*3 = 18.

[0054] Different mutation strategies have different requirements for NP, because they need to generate mutually exclusive integers r in the range [1, NP] iAs an index, where i is at least greater than or equal to 2, NP is at least greater than or equal to 2. In fact, NP should take a larger value, because the larger the population size, the greater the diversity of the population, and the greater the possibility that the good genes of each individual in the population will be retained after mutation, crossover and selection in each generation.

[0055] The scaling factor F = 0.5, the crossover probability CR = 0.3, and the maximum iteration number maxGen can be set to terminate the iteration or set to a larger value. Otherwise, the iteration will stop before convergence to the optimal value. In this embodiment, maxGen = 2000. The X, Y, and Z limits of the boundary absorption operation can be set to the maximum and minimum length, width, and height values, or they can be set according to actual needs. For example, if only a spatial layout with a large pseudolite elevation angle is desired, the lower limit of the Z value constraint can be increased.

[0056] Step 3: Use the differential evolution algorithm with the initialization parameters to obtain the optimized optimal pseudolite spatial layout. Specifically, the following steps are included:

[0057] S301. Calculate the objective function value of the individual to be optimized: take the average of the sum of the pdop (position dilution of precision) values of the ground grid points in the positioning area of interest under a certain pseudolite spatial layout as the objective function, traverse the ground grid points in the positioning area of interest to calculate their pdop values, then calculate the sum of the pdop values of all the ground grid points in the positioning area of interest, and finally divide the sum by the number of ground grid points in the positioning area of interest to obtain the objective function value. The smaller the objective function value, the more superior the pseudolite spatial layout individual vector. The objective function calculation formula is as follows:

[0058]

[0059] Where M is the number of ground grid points in the positioning area of interest, (pdop) i is the pdop value of the i-th ground grid point under a certain pseudolite spatial layout.

[0060] The calculation method of the pdop value of the ground grid point under a certain pseudolite spatial layout is as follows: When a certain pseudolite spatial layout is fixed, the design matrix B in the error equation is as follows:

[0061]

[0062] Among them, l i 、m i 、n i (i=1,2,…,n) is the direction cosine from the ground user receiver to each pseudo-satellite, which is calculated as follows:

[0063]

[0064] Among them, (X i ,Y i ,Z i ) is the coordinate of the ith pseudo-satellite, (X 0 ,Y 0 ,Z 0 ) is the approximate coordinate of the ground user receiver, ρ 0 is the approximate distance to the i-th pseudo-satellite calculated from the approximate coordinates of the ground user receiver, ρ 0 The expression is as follows:

[0065]

[0066] The cofactor matrix Q obtained after single point positioning:

[0067]

[0068] The pdop value is calculated by tracing the cofactor matrix Q, and the calculation formula is as follows:

[0069]

[0070] The above analysis shows that the design matrix B and the cofactor matrix Q are entirely dependent on the number of pseudolites and their geometric distribution relative to the ground user receiver, and are unrelated to the signal strength or the quality of the receiver. Therefore, the pdop value calculated from the diagonal elements of the cofactor matrix Q is also related only to the spatial layout of pseudolites. The relationship between the standard deviation of positioning error and the standard deviation of measurement error shows that, given the same user measurement error, the smaller the pdop value, the smaller the multiple of the measurement error that is magnified into positioning error, and the higher the spatial positioning accuracy. Therefore, it is very appropriate to use the average of the sum of the ground pdop values under the spatial layout as the objective function to evaluate the quality of a particular pseudolite spatial layout.

[0071] S302, mutation operation: the population to be optimized is mutated in one of the following five ways:

[0072] (a) “DE / rand / 1”:

[0073] (b) “DE / best / 1”:

[0074] (c) “DE / rand-to-best / 1”:

[0075] (d) “DE / best / 2”:

[0076] (e) “DE / rand / 2”:

[0077] Where X is the individual vector of the initial population or a certain pseudo-satellite spatial layout in the initial population; V is the individual vector of the mutated population or the pseudo-satellite spatial layout after mutation; G represents the number of cycles; index are mutually exclusive integers randomly generated in the range [1, NP]. For the strategy "DE / rand / 1", NP is at least greater than or equal to 3. For the strategies "DE / best / 1", "DE / rand-to-best / 1", "DE / best / 2", and "DE / rand / 2", NP is at least greater than or equal to 2, 2, 4, and 5, respectively. The scaling factor F is a positive control parameter used to scale the difference vector. X best,G is the best individual vector with the best fitness value in a generation population.

[0078] S303, crossover operation: Select between the initial individual vector X and the mutated individual vector V to generate a crossover individual vector U. Binomial crossover or exponential crossover can be used. In this embodiment, binomial crossover is used to generate the crossover individual vector. The specific formula is as follows:

[0079]

[0080] Where, j rand is a randomly selected integer in the range [1,D].

[0081] The above formula shows that when the random number generated in [0, 1] is less than or equal to the crossover probability CR or j=j rand When , the mutant individual vector V is selected as the cross individual vector U from the initial individual vector X and the mutant individual vector V; otherwise, the initial individual vector X is selected as the cross individual vector U.

[0082] S304, boundary absorption operation, boundary absorption operation is performed on the individuals in the cross-individual vector U. When the elements in the cross-individual vector U exceed the set limit, the value is reset to the upper or lower limit closest to the value, or a random value between the upper and lower limits is selected to replace it.

[0083] For the specific problem of optimizing pseudolite indoor spatial layout, pseudolites must be placed on walls or wall tops within a certain spatial range. After the crossover operation, the coordinates of each pseudolite in the crossover individual vector U must be constrained within the maximum and minimum coordinate limits of X, Y, and Z to ensure that the newly obtained pseudolite coordinates are within the feasible spatial domain. If the boundary absorption operation is not performed, the optimal solution will likely not conform to the actual situation.

[0084] S305, select operation, calculate the objective function value f(U) of each individual of the cross individual vector U after cross and boundary absorption operation i,G ), and the objective function value f(X i,G ) is compared. If the initial population individual vector X is better, then the individual vector in X remains unchanged. If the crossover individual vector U after the boundary absorption operation is better, then the initial population individual vector X is replaced by the crossover individual vector U, and the new X obtained in the current generation is cycled for the next generation. The above operation is expressed as follows:

[0085]

[0086] S306. Repeat steps S302 to S305. When the number of iterations reaches maxGen, stop the iteration.

[0087] Step 4: Deploy pseudolites on-site according to the optimal pseudolite spatial layout optimized by the algorithm.

[0088] By using the pseudolite spatial layout optimization method based on the differential evolution algorithm (DE), we can obtain an optimal spatial layout that is better than the initial optimal spatial layout, with a smaller ground pdop mean and a smaller error amplification factor. Pseudolites are then deployed according to the optimized optimal spatial layout to achieve better subsequent positioning results.

[0089] Taking the simplest scenario of four pseudo-satellites and an empty hall as an example, the simulation is as follows Figure 3 The empty hall shown has no obstructions on the ground, and the positioning focus area is the entire floor of the hall. The conventional layout is to lay out at the four corners of the ceiling, such as Figure 4 As shown, the corresponding ground pdop value distribution is as follows Figure 5 This algorithm optimizes the layout as shown. Figure 6 As shown, the corresponding ground pdop value distribution is as follows Figure 7 As shown in the figure. The average ground Pdop value for the conventional layout is 1.9473, while the average ground Pdop value for the optimized layout using this method is 1.8288, a decrease of 6.09%. The ground Pdop value distribution diagram shows that the ground Pdop values for the conventional layout are low at the corners and high in the center, while the ground Pdop values for the optimized layout using this method are low in the center and high at the edges. Overall, the low Pdop values for the layout derived by the algorithm are more evenly distributed and distributed over a wider range than those for the conventional layout. This indicates that positioning results obtained by users using this layout are more likely to meet accuracy requirements compared to those obtained using the conventional layout.

Claims

1. A pseudolite spatial layout optimization method based on differential evolution algorithm, characterized in that: The following steps are involved: Step 1: Model the actual problem and determine the specific size of the actual indoor space, including the length, width, and height of the indoor space. According to the actual situation, randomly generate multiple sets of different pseudo-satellite space layouts as the initialization population, and perform boundary absorption operations on the pseudo-satellite coordinates according to the length, width, and height of the indoor space. To impose restraints; Step 2: Set the initialization parameters of the differential evolution algorithm, including the length, width and height of the indoor space, the population size NP, the individual dimension D, the scaling factor F, the crossover probability CR, the maximum iteration number maxGen, and the boundary absorption operation pseudo-satellite coordinate limit setting; Step 3: Using the differential evolution algorithm with set initialization parameters to obtain the optimized optimal pseudolite spatial layout; The following steps are involved: S301, calculate the objective function value of the individual to be optimized: the ground grid points under a certain pseudo-satellite spatial layout are pdop The average value of the sum of the values is used as the objective function, and the ground grid points of the positioning area are traversed to find their pdop value, and then calculate the ground grid points of all positioning areas of interest pdop The sum of the values is finally divided by the number of ground grid points in the positioning area of interest to obtain the objective function value. The smaller the objective function value, the better the individual vector of the pseudolite spatial layout. The objective function calculation formula is as follows: ； in, M To locate the ground grid points in the area of interest, For a pseudo-satellite space layout i Ground grid points in the area of interest pdop value; S302, mutation operation: the population to be optimized is mutated in one of the following five ways: (a) "DE / row / 1": ; (b)"DE / best / 1”: ; (c)"DE / rand-to-best / 1”: ; (d)"DE / best / 2”: ; (e) "DE / row / 2": ; Where, X is the individual vector of the initial population; V is the individual vector of the population after mutation; G Algebraic representation of loops; indexing are mutually exclusive integers randomly generated in the range [1, NP]. For the strategy "DE / rand / 1", NP is at least greater than or equal to 3. For the strategies "DE / best / 1", "DE / rand-to-best / 1", "DE / best / 2", and "DE / rand / 2", NP is at least greater than or equal to 2, 2, 4, and 5, respectively. Scaling factor F is a positive control parameter used to scale the difference vector; is the best individual vector with the best fitness value in a generation population; S303, crossover operation: in the initial individual vector X and mutation individual vector V Select between to generate crossover individual vectors U , binomial crossover is used to generate crossover individual vectors. The specific formula is as follows: ； Where, is an integer randomly selected in the range [1, D]; the above formula shows that when the random number generated in [0, 1] Less than or equal to the crossover probability CR When or When the initial individual vector X and mutation individual vector V Select the mutation individual vector V As the cross-individual vector U , otherwise, select the initial individual vector X As the cross-individual vector U ; S304, boundary absorption operation, cross individual vector U The individuals in the cross-individual vector U perform boundary absorption operation. When the elements in the cross-individual vector U exceed the set limit, the elements in the cross-individual vector U are reset to the upper or lower limit closest to the elements in the cross-individual vector U, or randomly replace them with values between the upper and lower limits, so that the coordinates of each pseudo-satellite in the cross-individual vector U must be constrained within the range of the maximum and minimum coordinate limits of X, Y, and Z. S305, select operation, calculate the cross individual vector after cross and boundary absorption operation U The objective function value of each individual , and the initial population individual vector X The objective function value of each individual Compare, if the initial population individual vector X is better, then the individual vector in X remains unchanged, if the crossover and boundary absorption operation after the crossover individual vector U Better, then replace the initial population individual vector X with the crossover individual vector U , the newly obtained X of the current generation is cycled to the next generation. The above operation is expressed as follows: ； S306, repeat steps S302 to S305, and stop iterating when the number of iterations reaches maxGen; Step 4: Deploy pseudolites on-site according to the optimal pseudolite spatial layout optimized by the algorithm.

2. The pseudolite spatial layout optimization method based on differential evolution algorithm according to claim 1, characterized in that: In step 2, the length, width, and height of the indoor space are determined according to the actual spatial dimensions; the population size NP is the number of spatial layout types in the initialized population; each pseudolite spatial layout represents an individual, and the individual dimension D is equal to three times the pseudolite position parameters contained in each individual.

3. The pseudolite spatial layout optimization method based on differential evolution algorithm according to claim 1, characterized in that: In the step 3, in the step S301, the ground grid points under a certain pseudo-satellite spatial layout pdop The value is calculated as follows: When a certain pseudolite spatial layout is fixed, the design matrix B in the error equation is as follows: ； in, 、 、 ( i =1,2,…,n) are the direction cosines from the ground user receiver to each pseudo-satellite, which are calculated as follows: ， ， ； in, For the i Coordinates of pseudo-satellites, is the approximate coordinate of the ground user receiver, is the approximate coordinates calculated by the ground user receiver to the i The approximate distances of the pseudolites, The expression is as follows: ； The cofactor matrix obtained after single point positioning : ； pdop The value is calculated by taking the trace of the cofactor matrix Q, and the calculation formula is as follows: 。

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