Method and system for establishing a unified model of deep space solar wind plasma density based on Q-learning

Abstract

The present invention discloses a method and system for establishing a unified model of deep space solar wind plasma density based on Q learning, and the method comprises the following steps: S1, obtaining the electron density of the earth's ionosphere; S2, obtaining the electron density of solar wind plasma; S3, determining the boundary range between the earth's ionosphere and deep space and the sample points in the range, solving the optimal solution of the Gaussian kernel function parameter σ in the local weighted regression operation based on Q learning; S4, substituting the optimal solution of σ into the Gaussian kernel function, performing a local weighted regression operation on the samples in the boundary range, obtaining the predicted plasma density value at the sample point, and then obtaining the unified model of deep space solar wind plasma density. The present invention successfully solves the problem of the inconsistency of the solar wind plasma density model, and significantly improves the smoothness and accuracy of the electron density model at the boundary between the earth's ionosphere and deep space.

Description

Technical Field

[0001] The present invention belongs to the technical field of deep space exploration, and in particular relates to a method and system for establishing a unified model of deep space solar wind plasma density based on Q learning. Background Art

[0002] In deep space exploration, when the detector transmits signals back to the earth, it is inevitably affected by the solar wind plasma and the earth's ionosphere plasma, both of which are ionized media. Therefore, the effects of solar wind plasma and earth's ionosphere plasma on radio waves are basically the same, but there are differences in the degree of influence. This is the premise for the present invention to consider solar wind plasma and earth's ionosphere plasma uniformly.

[0003] At present, the research on the two ionized media, solar wind plasma and the earth's ionosphere, is relatively independent, and there is no unified model of plasma density. Therefore, it is difficult to derive the overall impact of these two ionized media on deep space wireless signals, which in turn affects the accuracy of deep space communication system design. In response to this challenge, the present invention regards the solar wind plasma density and the earth's ionosphere density as a whole, and uses a local weighted regression operation based on Q learning to obtain a unified model of deep space solar wind plasma density. The present invention uses a deterministic approach to deal with the uncertainty in system design, thereby improving the reliability of deep space communication system design. Summary of the invention

[0004] In view of the above-mentioned status quo, the present invention aims to construct a deep space solar wind plasma density model based on Q learning to solve the problem of the inconsistency of the solar wind plasma density model. The Q learning described in the present invention is a classic reinforcement learning algorithm, and deep space refers to the space far beyond the limit of the earth's atmosphere. The present invention adopts Q learning to solve the optimal solution of the Gaussian kernel function parameter σ in the local weighted regression operation, and solves the problem of the inconsistency of the solar wind plasma density model based on the local weighted regression operation of the improved Gaussian kernel function, so that the electron density model data at the junction of the earth's ionosphere and deep space is smoother and more accurate.

[0005] The specific technical solutions of the present invention are as follows:

[0006] A method for establishing a unified model of deep space solar wind plasma density based on Q learning, comprising the following steps:

[0007] S1, obtain the electron density of the Earth's ionosphere;

[0008] S2, obtain the electron density of solar wind plasma;

[0009] S3, determine the boundary range between the Earth's ionosphere and deep space and the sample points in this range, and solve the optimal solution of the Gaussian kernel function parameter σ in the local weighted regression operation based on Q learning;

[0010] S4, substitute the optimal solution of σ into the Gaussian kernel function, perform local weighted regression operation on the samples within the boundary range, obtain the predicted plasma density value at the sample point, and then obtain a unified model of deep space solar wind plasma density.

[0011] The present invention regards the solar wind plasma density and the Earth's ionosphere density as a whole, and uses a local weighted regression operation based on Q learning to obtain a unified model of deep space solar wind plasma density, so as to deal with the uncertainty in system design in a deterministic way and improve the reliability of deep space communication system design.

[0012] Preferably, in step S1, the electron density model of the Earth's ionosphere is obtained by using the NeQuick model to obtain the electron density of the Earth's ionosphere in a specific height, time, and region. The NeQuick model is a three-dimensional ionosphere electron density model jointly studied by an Italian laboratory and an Austrian institute.

[0013] Preferably, in step S2, the acquisition of the electron density of solar wind plasma is based on the detection results of deep space detectors, and the following empirical model of the electron density of solar wind plasma is established by fitting:

[0014]

[0015] Among them, N e is the solar wind plasma density, r is the solar radius R Θ (R Θ ≈6.96×10 8 The values ​​of parameters A, b, c and d vary with the solar activity cycle, but can be considered as constants within a specific period.

[0016] Preferably, in step S3, the boundary range between the Earth's ionosphere and deep space and the sample points in the range are determined, and a local weighted regression operation is performed on the samples within the boundary range between the Earth's ionosphere plasma density and the deep space solar wind plasma density. The specific steps are as follows: First, determine the interval size and the number of samples in the interval, and divide it into 5 intervals according to the boundary range, each interval containing 5 samples. Secondly, perform polynomial fitting on the samples in each interval. By repeatedly executing this process (the specific number of executions can be set), weighted regression curves in different intervals are obtained. Finally, the centers of these regression curves are connected together to form a complete regression curve.

[0017] The Gaussian kernel function formula in the local weighted regression operation is:

[0018]

[0019] Where exp(·) is the exponential function, x i is the horizontal coordinate of the i-th sample in the interval, and x is the horizontal coordinate of the center sample in the interval. The σ parameter controls the range of the Gaussian kernel function and determines the shape and width of the Gaussian curve. The larger σ is, the wider the local influence range of the Gaussian kernel function is.

[0020] The polynomial fitting formula of the interval is expressed as:

[0021]

[0022] in, is the column matrix composed of the ordinates of the new predicted samples in the interval, X is the column matrix composed of the abscissas of all samples in the interval, X T is the transposed matrix of the X matrix, and W is the matrix of all W i The diagonal matrix is ​​composed of , and Y is the column matrix composed of the vertical coordinates of all samples in the interval.

[0023] In order to find the optimal solution of parameter σ, the present invention adopts Q learning method to solve it. According to the core formula of Q learning, Bellman formula, the parameters are set to obtain the iterative formula. Bellman formula is:

[0024] Q(s,a)←Q(s,a)+α[r+γmaxQ(s',a')-Q(s,a)]

[0025] Among them, Q(s,a) is the Q function composed of state s and action a. α is the learning rate, r is the reward value, γ is the discount rate, and maxQ(s',a') is the maximum Q function value of the next state.

[0026] Update the Q table according to the iterative formula, the iterative formula is:

[0027] Q(1,action)=r+γ×Q(1,next_action)

[0028] Among them, Q(1,action) is the Q function of the current state, the initial reward r is 1000, the reward r is superimposed by 4 after each action, the discount rate γ is 0.9, and Q(1,next_action) is the Q function after the action.

[0029] Initialize the Q table. Update the Q table according to the iterative formula, and use the sum of squared errors as the criterion for judging the direction of the action. When the sum of squared errors reaches the threshold, stop the iteration and find the optimal σ parameter value corresponding to the Q table.

[0030] In step S4, the optimal σ parameter value obtained by Q learning is applied to the Gaussian kernel function of the local weighted regression operation, and the local weighted regression operation is performed on the samples within the boundary range to obtain the predicted plasma density value at the sample point, and then obtain the unified model of deep space solar wind plasma density.

[0031] In step S4, the steps of performing local weighted regression operation on samples within the boundary between the Earth's ionosphere and deep space are as follows: determine the interval size and the number of samples within the interval, perform polynomial fitting on the samples in each interval, repeat this process to obtain weighted regression curves in different intervals (the number of repetitions can be set); finally, connect the centers of these regression curves together to form a complete regression curve; the Gaussian kernel function formula in the local weighted regression operation is:

[0032]

[0033] Among them, W i is the weight assigned according to the distance between the i-th sample and the central sample point in the interval; x i is the abscissa of the ith sample in the interval, and x is the abscissa of the center sample in the interval;

[0034] The polynomial fitting formula for the interval is:

[0035]

[0036] in, is the column matrix composed of the ordinates of the newly predicted samples in the interval, X is the column matrix composed of the abscissas of all samples in the interval, X T is the transposed matrix of the X matrix, and W is the matrix of all W i The diagonal matrix is ​​composed of , and Y is the column matrix composed of the ordinates of all samples in the interval.

[0037] The present invention also discloses a system for establishing a unified model of deep space solar wind plasma density based on Q learning, which includes the following modules based on the above method:

[0038] Earth ionosphere electron density acquisition module: obtain the earth ionosphere electron density;

[0039] Solar wind plasma electron density acquisition module: obtain the solar wind plasma electron density;

[0040] The module for finding the optimal solution of the parameter σ: determines the boundary between the Earth's ionosphere and deep space and the sample points in this range, and finds the optimal solution of the Gaussian kernel function parameter σ in the local weighted regression operation based on Q learning;

[0041] Model acquisition module: Substitute the optimal solution of σ into the Gaussian kernel function, perform local weighted regression operation on the samples within the boundary range, obtain the predicted plasma density value at the sample point, and then obtain a unified model of deep space solar wind plasma density.

[0042] The present invention solves the problem of inconsistent solar wind plasma density models and significantly improves the smoothness and accuracy of the electron density model at the interface between the Earth's ionosphere and deep space. The present invention handles the uncertainty in system design in a deterministic way, further enhancing the reliability of deep space communication system design. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a flow chart of a method for establishing a unified model of deep space solar wind plasma density based on Q learning in a preferred embodiment of the present invention;

[0044] Figure 2 This is a flowchart for solving the optimal solution of the Gaussian kernel function parameter σ in the local weighted regression operation based on Q learning;

[0045] Figure 3 A system block diagram for establishing a unified model of deep space solar wind plasma density based on Q learning according to a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0046] In order to enable those skilled in the art to better understand the present invention, the technical solutions of the preferred embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings.

[0047] The present invention regards the solar wind plasma density and the Earth's ionosphere density as a whole, and uses a local weighted regression operation based on Q learning to obtain a unified model of deep space solar wind plasma density.

[0048] See also Figure 1 In this embodiment, the method for establishing a unified model of deep space solar wind plasma density based on Q learning has the following specific steps:

[0049] Step 1: Obtaining the electron density of the Earth's ionosphere.

[0050] This step specifically uses the NeQuick model to obtain the electron density of the Earth's ionosphere at a specific altitude, time, and region.

[0051] Step 2: Obtaining the electron density of solar wind plasma.

[0052] Based on the detection results of deep space probes, the following empirical model of solar wind plasma electron density is established by fitting:

[0053]

[0054] Among them, Ne is the solar wind plasma density. r is the solar radius R Θ (R Θ ≈6.96×10 8 The values ​​of parameters A, b, c and d vary with the solar activity cycle, but can be considered as constants within a specific period.

[0055] Using the above model, in the solar low latitude and equatorial regions, the fitting range is When , the solar wind plasma density model can be expressed by the following formula:

[0056]

[0057] Step 3: Determine the boundary between the Earth’s ionosphere and deep space, select sample points, perform local weighted regression operations, and find the optimal solution for the Gaussian kernel function parameter σ.

[0058] The solar wind plasma electron density model and the earth's ionosphere electron density model are considered in a unified way, so that the two density models can reflect their electron density change characteristics in one diagram. The independent variable is unified, and the solar diameter distance of the heliocentric-geocentric line is used as the independent variable.

[0059] The present invention determines the boundary range between the earth's ionosphere and deep space and the sample points in the range, and performs local weighted regression operation on the samples within the boundary range between the earth's ionosphere and deep space. The steps are as follows: First, determine the interval size and the number of samples in the interval, and divide it into 5 intervals according to the boundary range, each interval containing 5 samples. Secondly, perform polynomial fitting on the samples in each interval respectively to obtain weighted regression curves in different intervals. Finally, connect the centers of these regression curves together to form a complete regression curve.

[0060] The Gaussian kernel function formula in the local weighted regression operation is:

[0061]

[0062] Where exp(·) is the exponential function, x i is the horizontal coordinate of the i-th sample in the interval, and x is the horizontal coordinate of the center sample in the interval. The σ parameter controls the range of the Gaussian kernel function and determines the shape and width of the Gaussian curve. The larger σ is, the wider the local influence range of the Gaussian kernel function is.

[0063] The polynomial fitting formula for the interval is:

[0064]

[0065]

[0066] Where W is all Wi The diagonal matrix is ​​composed of X, the column matrix composed of the horizontal coordinates of all samples in the interval, and Y is the column matrix composed of the vertical coordinates of all samples in the interval. is the column matrix composed of the ordinates of the new predicted samples in the interval, X T is the transposed matrix of the X matrix.

[0067] See also Figure 2 In this embodiment, the following steps are used to achieve the optimal solution of the Gaussian kernel function parameter σ in the local weighted regression operation based on Q learning.

[0068] Set relevant parameters according to the Q-learning core formula Bellman formula, which is:

[0069] Q(s,a)←Q(s,a)+α[r+γmaxQ(s',a')-Q(s,a)]

[0070] (1) Initialize the Q table (set all Q table elements to 0), as shown in Table 1.

[0071] Table 1: Q function value table

[0072]

[0073] The present invention uses the diagonal matrix W in the polynomial fitting formula of the above interval to find the upper and lower limits of σ. In this embodiment, when σ reaches the maximum value of 0.01, the diagonal matrix W can be expressed as:

[0074]

[0075] When σ reaches the minimum value of 0.00001, the diagonal matrix W can be expressed as:

[0076]

[0077] A pseudo Q table is established to correspond to the Q table, as shown in Table 2.

[0078] Table 2: σ parameter table

[0079]

[0080] The fitting criterion is the sum of squared errors (SSE) which can be expressed as:

[0081]

[0082] Among them, y i is the actual value of the ith sample, is the predicted value of the i-th sample. The smaller the sum of squared errors is, the smaller the error between the predicted result of the local weighted regression operation and the actual result is, and the better the prediction performance is.

[0083] (2) This embodiment substitutes the upper and lower limits of σ and several randomly sampled σ values ​​into the Gaussian kernel function to perform a local weighted regression operation. The data shows that the smaller the σ value, the smaller the sum of squared errors.

[0084] In order to further verify this conclusion and avoid the problem that the minimum value of the error sum of squares calculated by substituting the σ lower limit is a minimum value, the present invention adopts the following processing method: start iterating from the rightmost side of the pseudo-Q number table, that is, start from the position where the σ parameter value is the largest. First, substitute the σ parameter value at the current pseudo-Q table into the Gaussian kernel function, perform the local weighted regression operation in step three of the above specific implementation method, and then substitute the result of the local weighted regression operation into the error sum of squares formula under the above Table 2. Next, substitute the σ parameters corresponding to the left and right positions of the current pseudo-Q table into the Gaussian kernel function respectively, perform the local weighted regression operation in step three of the above specific implementation method, and substitute the operation results on the left and right sides into the error sum of squares formula under the above Table 2 respectively. (If the current position is at the leftmost (right) end of the table, it is only necessary to substitute the σ parameter corresponding to the pseudo-Q table on the right (left) side into the Gaussian kernel function, perform the local weighted regression operation in step three of the above specific implementation method, and then substitute the result of the local weighted regression operation into the error sum of squares formula under the above Table 2).

[0085] (3) Compare the results of substituting the current position and the σ parameters on the left and right sides of the pseudo Q table into the error square sum formula in Table 2 above. Then, determine the action direction of the pseudo Q table so that it moves in the direction with a smaller error square sum. After determining the action direction, apply the action to the iteration formula, calculate the Q function value after the action according to the iteration formula, and update the Q table. The iteration formula is:

[0086] Q(1,action)=r+γ×Q(1,next_action)

[0087] Among them, the initial reward r is 1000, the reward r is superimposed by 4 after each action, the discount rate γ is 0.9, Q(1,action) is the Q function value of the current state, and Q(1,next_action) is the Q function value after the action.

[0088] (4) Termination condition of iteration: SSE ≤ 17.76586. 17.76586 is obtained by substituting σ = 0.00001 into the Gaussian kernel function, performing the same local weighted regression operation as in step 3 of the above specific implementation method, and then substituting the result of the local weighted regression operation into the SSE formula in Table 2 above.

[0089] After the iteration ends, the Q table function value is checked and it is found that the maximum value is obtained in the second column. The corresponding index is the value of the second column of the pseudo Q table, that is, σ = 0.00003.

[0090] Step 4: Substitute the optimal σ parameter into the Gaussian kernel function, and then perform the local weighted regression operation in step 3 of the above specific implementation method to obtain the predicted plasma density value at the sample point, and finally obtain a unified model of deep space solar wind plasma density.

[0091] In this step 4, the steps of performing local weighted regression operation on samples within the boundary between the Earth's ionosphere and deep space are as follows: determine the interval size and the number of samples in the interval, perform polynomial fitting on the samples in each interval respectively, and obtain weighted regression curves in different intervals; finally, connect the centers of these regression curves together to form a complete regression curve; the formula of the Gaussian kernel function in the local weighted regression operation is:

[0092]

[0093] Among them, W i is the weight assigned according to the distance between the i-th sample and the central sample point in the interval; x i is the horizontal coordinate of the i-th sample in the interval, x is the horizontal coordinate of the center sample in the interval, and σ is the optimal solution determined by Q learning;

[0094] The polynomial fitting formula for the interval is:

[0095]

[0096] in, is the column matrix composed of the ordinates of the newly predicted samples in the interval, X is the column matrix composed of the abscissas of all samples in the interval, X T is the transposed matrix of the X matrix, and W is the matrix of all W i The diagonal matrix is ​​composed of , and Y is the column matrix composed of the ordinates of all samples in the interval.

[0097] like Figure 3 As shown, this embodiment discloses a system for establishing a unified model of deep space solar wind plasma density based on Q learning, which includes the following modules based on the above method embodiment:

[0098] Earth ionosphere electron density acquisition module: obtain the earth ionosphere electron density;

[0099] Solar wind plasma electron density acquisition module: obtain the solar wind plasma electron density;

[0100] The module for finding the optimal solution of the parameter σ: determines the boundary between the Earth's ionosphere and deep space and the sample points in this range, and finds the optimal solution of the Gaussian kernel function parameter σ in the local weighted regression operation based on Q learning;

[0101] Model acquisition module: Substitute the optimal solution of σ into the Gaussian kernel function, perform local weighted regression operation on the samples within the boundary range, obtain the predicted plasma density value at the sample point, and then obtain a unified model of deep space solar wind plasma density.

[0102] For other contents of this embodiment, please refer to the above method embodiment.

[0103] In summary, the present invention aims at the problem of the inconsistency of solar wind plasma density model, and proposes a method and system for establishing a unified model of deep space solar wind plasma density based on Q learning. The present invention analyzes the influence of different σ parameters on the fitting degree of local weighted regression operation, and adopts Q learning to solve the optimal solution of the parameter σ of the Gaussian kernel function in the local weighted regression operation, so that the electron density model data at the junction of the earth's ionosphere and deep space is smoother and more accurate. The present invention uses a certain way to deal with the uncertainty in system design, thereby improving the reliability of deep space communication system design.

[0104] The above description is only a detailed description of the preferred embodiments and principles of the present invention. For ordinary technicians in this field, according to the ideas provided by the present invention, there will be changes in the specific implementation methods, and these changes should also be regarded as the protection scope of the present invention.

Claims

1. A method for establishing a unified model of deep space solar wind plasma density based on Q learning, characterized in that The following steps are involved: S1, obtain the electron density of the Earth's ionosphere; S2, obtain the electron density of solar wind plasma; S3, determine the boundary range between the Earth's ionosphere and deep space and the sample points in this range, and solve the optimal solution of the Gaussian kernel function parameter σ in the local weighted regression operation based on Q learning; S4, substitute the optimal solution of σ into the Gaussian kernel function, perform local weighted regression operation on the samples within the boundary range, obtain the predicted plasma density value at the sample point, and then obtain the unified model of deep space solar wind plasma density; In step S3, the reward calculation is performed within the σ parameter range through the Bellman formula of Q learning, and the sum of squared errors is used as the criterion for judging the direction of the action. When the sum of squared errors reaches the threshold, the iteration is stopped to find the optimal σ parameter value corresponding to the Q table; The optimal solution of parameter σ is achieved by the following steps: The Bellman formula is as follows: Q(s,a)←Q(s,a)+α[r+γmaxQ(s',a')-Q(s,a)] (1) Initialize the Q table and set all the elements in the Q table to 0; Use the diagonal matrix W in the polynomial fitting formula of the interval to find the upper and lower limits of σ; Establish a pseudo Q table corresponding to the Q table; The fitting criterion is the sum of squared errors SSE, expressed as: Among them, y i is the actual value of the ith sample, is the predicted value of the i-th sample; (2) Substitute the upper and lower limits of σ and several randomly sampled σ values ​​into the Gaussian kernel function and perform local weighted regression operation; (3) Compare the current position and the σ parameters on the left and right sides of the pseudo Q table, and substitute them into the calculation of the sum of squared errors; then, determine the action direction of the pseudo Q table so that it moves in the direction with a smaller sum of squared errors; after determining the action direction, apply the action to the iterative formula to calculate the Q function value after the action; update the Q table according to the iterative formula, which is: Q(1,action)=r+γ×Q(1,next_action) Among them, Q(s,a) is the Q function composed of state s and action a, α is the learning rate, r is the reward value, γ is the discount rate, maxQ(s',a') is the maximum Q function value of the next state; in the iterative formula, Q(1,action) is the Q function of the current state, and Q(1,next_action) is the Q function after the action; (4) When the sum of squared errors (SSE) is less than or equal to the threshold, the iteration terminates.

2. According to claim 1, a method for establishing a unified model of deep space solar wind plasma density based on Q learning is characterized in that: In step S1, the NeQuick model is used to obtain the electron density of the Earth's ionosphere in a set altitude, time, and region.

3. A method for establishing a unified model of deep space solar wind plasma density based on Q learning according to claim 1 or 2, characterized in that: In step S2, based on the detection results of the deep space detector, the following solar wind plasma electron density empirical model is established by fitting: Among them, N e is the solar wind plasma density, r is the solar radius R Θ The daily distance in units.

4. According to claim 3, a method for establishing a unified model of deep space solar wind plasma density based on Q learning is characterized in that: In step S3, first, the interval size and the number of samples in the interval are determined, and the interval is divided into several intervals according to the boundary range, and each interval contains several samples; secondly, polynomial fitting is performed on the samples in each interval; the number of repeated executions reaches a threshold, and weighted regression curves in different intervals are obtained; finally, the centers of the regression curves are connected together to form a complete regression curve; In the local weighted regression operation, the Gaussian kernel function formula is: Where exp(·) is the exponential function, x i is the abscissa of the ith sample in the interval, and x is the abscissa of the center sample in the interval; The polynomial fitting formula of the interval is expressed as: in, is the column matrix composed of the ordinates of the new predicted samples in the interval, X is the column matrix composed of the abscissas of all samples in the interval, X T is the transposed matrix of the X matrix, and W is the matrix of all W i The diagonal matrix is ​​composed of , and Y is the column matrix composed of the vertical coordinates of all samples in the interval.

5. According to claim 4, a method for establishing a unified model of deep space solar wind plasma density based on Q learning is characterized in that: In step S4, the steps of performing local weighted regression operation on samples within the boundary between the Earth's ionosphere and deep space are as follows: determine the interval size and the number of samples within the interval, perform polynomial fitting on the samples in each interval respectively, and obtain weighted regression curves in different intervals; finally, connect the centers of these regression curves together to form a complete regression curve; the Gaussian kernel function formula in the local weighted regression operation is: Among them, W i is the weight assigned according to the distance between the i-th sample and the central sample point in the interval; x i is the abscissa of the ith sample in the interval, and x is the abscissa of the center sample in the interval; The polynomial fitting formula for the interval is: in, is the column matrix consisting of the ordinates of the newly predicted samples in the interval, X is the column matrix consisting of the abscissas of all samples in the interval, X T is the transposed matrix of the X matrix, and W is the matrix of all W i The diagonal matrix is ​​composed of , and Y is the column matrix composed of the ordinates of all samples in the interval.

6. A system for establishing a unified model of deep space solar wind plasma density based on Q learning, based on the method according to any one of claims 1 to 5, characterized in that Includes the following modules: Earth ionosphere electron density acquisition module: obtain the earth ionosphere electron density; Solar wind plasma electron density acquisition module: obtain the solar wind plasma electron density; The module for finding the optimal solution of the parameter σ: determines the boundary between the Earth's ionosphere and deep space and the sample points in this range, and finds the optimal solution of the Gaussian kernel function parameter σ in the local weighted regression operation based on Q learning; Model acquisition module: Substitute the optimal solution of σ into the Gaussian kernel function, perform local weighted regression operation on the samples within the boundary range, obtain the predicted plasma density value at the sample point, and then obtain a unified model of deep space solar wind plasma density.

Images