A method for judging spatial atmospheric density

Abstract

The invention discloses a method for judging spatial atmospheric density, which is specifically implemented according to the following steps: a user provides input parameters, which are recorded as in; in is normalized; a constant term 1 is added to the parameter sequence after normalization operation; a neural network input layer weight matrix is ​​multiplied by the input sequence, and the number of calculations of the neural network hidden layer is n=1; a constant term 1 is added to the input sequence, so that a(n)=[a(n);1], so that the transformed input parameter sequence a(n) is multiplied by LW(n), a(n)=LW(n)*a(n), and a hidden layer calculation is completed; step 6, n=n+1, if n>3, the hidden layer calculation is completed, and the next step is entered; otherwise, n=n+1 is set, and the previous step is repeated to complete the next hidden layer calculation; the output layer is calculated; the calculation result is reversely normalized to obtain the spatial atmospheric density, and the spatial atmospheric density judgment is completed. The atmospheric judgment accuracy of the traditional atmospheric model in the spatial range can be improved.

Description

Technical Field

[0001] The invention belongs to the technical field of earth atmosphere density judgment, and relates to a method for judging space atmosphere density. Background Art

[0002] In addition to the gravity of the earth, spacecraft are also affected by some other perturbations in space. The earth's gravity and these perturbations together constitute the mechanical environment of the spacecraft flying in space. If accurate modeling of these perturbations is achieved, according to a=F / m, the acceleration of the spacecraft at each position in the space environment can be accurately determined, and the speed of the spacecraft at that position can be accurately determined by integration, and then the spatial position of the spacecraft can be accurately calculated by integration, completing the calculation of the spacecraft's orbital dynamics.

[0003] For low-orbit satellites, atmospheric drag is one of the main perturbation factors, so the accuracy of determining the atmospheric density of low-Earth orbit directly affects the accuracy of determining the orbit of low-Earth satellites. To accurately determine the atmospheric drag experienced by a spacecraft at every location in space, the atmospheric density at every point in the spacecraft's location must be accurately known. Since the atmosphere in space is changing all the time, the atmospheric density data over a long period of time and over a large range cannot be obtained through measurement, but can only be obtained through analysis, induction and modeling of limited data.

[0004] Through the analysis of the existing mainstream multi-dimensional atmospheric models (including the Jacchia model, MSIS00 model, DTM2013 model, etc.), it can be determined that the factors affecting the atmospheric density at a certain point in space include time (day count in the year), longitude, latitude, altitude, F 10.7 (F 30 ) of the measurement value of the day before the measurement, F 10.7 (F 30 )81-day average K p Three-hour measurement value, K p Daily average Etc., the spatial atmospheric density is a function of the above parameters. 10.7 (F 30 ) and its 81-day average The value of the previous day is taken for calculation because the effect of solar radiation on atmospheric density is one day later due to propagation factors. Traditional models give different analytical expressions based on different understandings of the above parameters. However, the accuracy of these models is generally not high. When various influencing factors are very stable, the error is generally 10-15%. Under higher disturbances, the error can usually reach about 30%, and in some years it can even be as high as 100%. Summary of the invention

[0005] The purpose of the present invention is to provide a spatial atmospheric density judgment method for judging the atmospheric density in the range of 250km to 280km above the earth, latitude from 90° to -90°, and longitude from 0° to 360°, which can improve the atmospheric judgment accuracy of traditional atmospheric models in this spatial range.

[0006] The technical solution adopted by the present invention is a method for determining the spatial atmospheric density, which is specifically implemented according to the following steps:

[0007] Step 1: The user provides 8 input parameters and the above data is combined into a sequence, recorded as in;

[0008] Step 2: Normalize in;

[0009] Step 3: Add a constant term 1 to the parameter sequence that has undergone the normalization operation, and convert it into an input sequence consisting of 9 input parameters, that is, p = [in; 1];

[0010] Step 4: Multiply the input sequence by the weight matrix of the neural network input layer, and set the number of calculations of the neural network hidden layer to n = 1;

[0011] Step 5: Add a constant term 1 to the input sequence, so that a(n) = [a(n); 1], so that the transformed input parameter sequence a(n) is multiplied by LW(n), a(n) = LW(n)*a(n), and a hidden layer calculation is completed;

[0012] Step 6: Set n = n + 1. If n > 3, the hidden layer calculation is completed and the process goes to step 7. Otherwise, set n = n + 1 and repeat step 5 to complete the next hidden layer calculation.

[0013] Step 7: Calculate the output layer;

[0014] Step 8: Perform reverse normalization processing on the calculation result of step 7 to obtain the spatial atmospheric density and complete the spatial atmospheric density judgment.

[0015] The present invention is also characterized in that:

[0016] The eight input parameters in step 1 include the measurement time, the longitude, latitude, and altitude of the spatial point, the measurement value of the solar radiation index the day before, and the 81-day average value of the solar radiation index. Three-hour measurement values ​​of geomagnetic parameters and daily average values ​​of geomagnetic parameters

[0017] The time counting method for measurement is: calculate the day count of the current date in the year based on the year, month, and day information in the coordinated universal time of the current satellite operation. The calculation method is: the sum of the dates of the previous m-1 months plus the day count m is the current month, is the sum of the dates of all months before the current month, and d is the date of the current month.

[0018] Step 2 is specifically implemented as follows: Use:

[0019] in=(xoutmax-xoutmin). / (xinmax-xinmin).*(in-xinmin)+xoutmin normalizes the input array.

[0020] In step 3, p is a matrix in 9*1 format.

[0021] Step 4 is specifically implemented as follows: Let a(0) = IW*p, where IW is a 10*9 matrix. After calculation, a(0) is a 10*1 matrix. By formula Transform a(0), where n=a(0), and add a constant term 1 to the input sequence so that a(1)=[tansig(a(1));1], where a(1) is a 11*1 format matrix.

[0022] In step 8, the calculation result of step 7 is reverse normalized as follows:

[0023] ym=(yinmax-yinmin). / (youtmax-youtmin).*(a(3)-youtmin)+yinmin performs reverse normalization processing on the calculation result obtained in step 7.

[0024] The beneficial effects of the present invention are as follows: a spatial atmospheric density judgment method of the present invention is used to judge the atmospheric density in the range of 250km to 280km above the earth, 90° to -90° in latitude, and 0° to 360° in longitude, and can improve the atmospheric judgment accuracy of the traditional atmospheric model in this spatial range. In the atmospheric density simulation of randomly sampled spatial positions in different years, the performance of the two neural network atmospheric models is significantly better than the two traditional atmospheric models DTM2013 and MSIS00, and the average error rate of the neural network atmospheric model is about 1 / 3-1 / 2 of the traditional atmospheric model; there is no need to use different expressions to judge the value of each influencing factor according to different influencing factors, and the atmospheric density judgment result can be obtained by using multiple matrix multiplications, which significantly simplifies the judgment method. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a flow chart of a method for determining spatial atmospheric density of the present invention;

[0026] Figure 2 It is a method for obtaining the solar radiation index in a method for judging the spatial atmospheric density of the present invention;

[0027] Figure 3 The invention relates to a method for obtaining geomagnetic parameters in a method for judging spatial atmospheric density. DETAILED DESCRIPTION

[0028] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0029] The present invention provides a method for determining the spatial atmospheric density. Figure 1 As shown, the specific implementation steps are as follows:

[0030] Step 1: The user provides 8 input parameters and the above data is combined into a sequence, recorded as in;

[0031] The eight input parameters in step 1 include the measurement time (day count in a year), the longitude, latitude, altitude of the spatial point, and the solar radiation index F 10.7 (F 30 ) measured the day before, solar radiation index F 10.7 (F 30 )81-day average Geomagnetic parameter K p Three-hour measurement value, geomagnetic parameter K p Daily average

[0032] The time counting method for measurement is: calculate the day count of the current date in the year based on the year, month, and day information in the coordinated universal time of the current satellite operation. The calculation method is: the sum of the dates of the previous m-1 months plus the day count m is the current month, is the sum of the dates of all months before the current month, and d is the date of the current month.

[0033] Step 2: Normalize in;

[0034] Step 2 is specifically implemented as follows: Use:

[0035] in=(xoutmax-xoutmin). / (xinmax-xinmin).*(in-xinmin)+xoutmin normalizes the input array.

[0036] Step 3: Add a constant term 1 to the parameter sequence that has undergone the normalization operation, and convert it into an input sequence consisting of 9 input parameters, that is, p = [in; 1];

[0037] In step 3, p is a matrix in 9*1 format.

[0038] Step 4: Multiply the input sequence by the weight matrix of the neural network input layer, and set the number of calculations of the neural network hidden layer to n = 1;

[0039] Step 4 is specifically implemented as follows: Let a(0) = IW*p, where IW is a 10*9 matrix. After calculation, a(0) is a 10*1 matrix. By formula Transform a(0), where n=a(0), and add a constant term 1 to the input sequence so that a(1)=[tansig(a(1));1], where a(1) is a 11*1 format matrix.

[0040] Step 5: Add a constant term 1 to the input sequence, so that a(n) = [a(n); 1], so that the transformed input parameter sequence a(n) is multiplied by LW(n), a(n) = LW(n)*a(n), and a hidden layer calculation is completed;

[0041] Specifically, let a(n) = LW(n)*a(n), n = 1, complete the calculation of the first hidden layer, where LW(1) is a 20*11 format matrix. After the calculation, a(1) is a 20*1 format matrix. Perform Tan-Sigmoid transformation on the result sequence and add a constant term 1, so that a(1) = [tansig(a(1)); 1], and a(1) is a 21*1 format matrix.

[0042] Step 6: Set n=n+1. If n>3, the hidden layer calculation is completed and go to step 7; otherwise, repeat step 5 to complete the next hidden layer calculation;

[0043] Step 7, calculating the output layer; since the output layer in the spatial atmospheric density judgment method of the present invention is a linear function, this step can be skipped;

[0044] Step 8: Perform reverse normalization processing on the calculation result of step 7 to obtain the spatial atmospheric density and complete the spatial atmospheric density judgment.

[0045] In step 8, the calculation result of step 7 is reverse normalized as follows:

[0046] ym=(yinmax-yinmin). / (youtmax-youtmin).*(a(3)-youtmin)+yinmin performs reverse normalization processing on the calculation result obtained in step 7.

[0047] The parameters involved in the spatial atmospheric density judgment method of the present invention, such as the network input layer weight matrix IW, the neural network hidden layer weight matrix LW, xinmin, xinmax, xoutmin, xoutmax, etc., are shown in Appendix 1 and Appendix 2.

[0048] like Figure 2 As shown, a method for obtaining the solar radiation index in a method for determining the spatial atmospheric density of the present invention is as follows:

[0049] Step 101: According to the current operating time (year, month, day, hour, minute, second) and position (corresponding to the longitude, latitude and altitude of the earth) of the satellite, the year, month and day data in the satellite operating time are converted into Coordinated Universal Time (UTC), and then go to step 102;

[0050] Step 102: Query and download the F data of the day before the satellite operation time from the China National Science Data Center. 10.7 or F 30 and or

[0051] It should be noted that F 10.7 or F 30 The value and its 81-day average or Published by the National Oceanic and Atmospheric Administration, obtained from other sources 10.7 or F 30 The value and its 81-day average or It does not affect the essential content of the present invention.

[0052] like Figure 3 As shown, the steps of the method for obtaining geomagnetic parameters in a method for determining spatial atmospheric density of the present invention are as follows:

[0053] Step 201: According to the current satellite operation time (year, month, day, hour, minute, second) and position (corresponding to the earth's longitude, latitude, and altitude), the year, month, and day data in the satellite operation time are converted into Coordinated Universal Time (UTC), and the current date and geomagnetic segment are calculated according to the year, month, day, hour, minute, and second (UTC). The geomagnetic segment is 1 segment of 3 hours, 0-3 hours is the first segment, 3-6 hours is the second segment, and so on, 21-24 hours is the eighth segment. Go to step 202;

[0054] Step 202: Query the corresponding geomagnetic index and its average value according to the date and geomagnetic zone.

[0055] It should be noted that those skilled in the art can obtain the geomagnetic three-hour index value K from other channels. p and daily average The data does not affect the essence of the present invention;

[0056] The steps to calculate the day count within a year based on the current date are as follows:

[0057] Calculate the day count of the current date based on the year, month, and day information in the current satellite coordinated universal time (UTC). The calculation method is: the sum of the dates of the previous m-1 months plus the day count m is the current month, is the sum of the dates of all months before the current month, and d is the date of the current month.

[0058] The principle of the method for determining the spatial atmospheric density of the present invention is that, for a satellite, the atmospheric resistance perturbation acceleration of the satellite body is:

[0059]

[0060] In the above formula, C D is the atmospheric drag coefficient, ρ is the atmospheric density at the satellite’s location, is the ratio of the satellite reference cross-sectional area to the satellite mass, is the velocity vector of the satellite relative to the atmosphere. The atmospheric drag perturbation acceleration of the satellite solar sail is:

[0061]

[0062] C DP is the atmospheric drag coefficient of the solar panel, A p is the area of ​​the solar panel, cosψ is the direction cosine of the satellite's velocity relative to the atmosphere, is the solar panel normal The unit vector of .

[0063] From the above formula, we can know that the key to judging the atmospheric drag on the satellite in space is to obtain the density of the atmosphere at the spatial position of the satellite at that moment. This is the key problem to be solved by various atmospheric models. Traditional atmospheric models can be divided into two categories: the first category only considers the change of atmospheric density with the altitude, such as exponential model, improved Harris-Priester model, etc.; the second category not only considers the change of atmospheric density with altitude, but also considers the change of atmospheric density with longitude, latitude and different time periods, such as Jacchia series models, DTM series models and MSIS series models, etc. This type of multi-dimensional model is the mainstream model used in aerospace engineering judgment.

[0064] Through the analysis of the existing mainstream multi-dimensional atmospheric models (including the Jacchia model, MSIS00 model, DTM2013 model, etc.), it can be determined that the factors affecting the atmospheric density at a certain point in space include time (day count in the year), longitude, latitude, altitude, F 10.7 (F 30 ) of the measurement value of the day before the measurement, F 10.7 (F 30 )81-day average K p Three-hour measurement value, K p Daily average Etc., the spatial atmospheric density is a function of the above parameters. 10.7 (F30 ) and its 81-day average The value of the previous day is taken for judgment because the effect of solar radiation on atmospheric density is one day later due to propagation factors. Traditional models give different analytical expressions based on different understandings of the above parameters. However, the accuracy of these models is generally not high. When various influencing factors are very stable, the error is generally 10-15%. Under higher disturbances, the error can usually reach about 30%, and in some years it can even be as high as 100%. The present invention provides a spatial atmospheric density judgment method based on a neural network, and provides an atmospheric density neural network model based on a large amount of measurement data, which has higher accuracy than the traditional atmospheric model.

[0065] The Error Back Propagation (BP) algorithm in the neural network algorithm was first proposed by Rumelhart, McClelland and others from the Parallel Distributed Processing (PDP) group. The BP neural network uses the error back propagation algorithm to adjust the network weights, solving the learning problem of multi-layer neural networks and greatly promoting the development of neural networks. In the BP network, there are input layers, hidden layers and output layers. The layers of the multi-layer network are fully connected, and there is no connection between neurons in the same layer. Its main principles are:

[0066] In the BP network, there are input layers, hidden layers and output layers. The layers are fully connected, and the neurons in the same layer are not connected. Assume that the number of input neurons is M, the number of hidden layer neurons is I, the number of output layer neurons is J, and the mth neuron in the input layer is denoted by x. m , the i-th neuron in the hidden layer is denoted as k i , the jth neuron in the output layer is denoted as y j . From x m to k i The connection weight is ω mi , from k i to y j The hidden layer connection weight is ω ij . By ω mi The input layer transfer matrix composed of is denoted as IW, which is composed of ω ij The N hidden layer transfer matrices are recorded as LW(n) (n=1, 2, ..., N). In the iterative calculation process of the neural network, the initial values ​​of IW and LW(n) (n=1, 2, ..., N) can start with random numbers. For the p-th neural network input layer transfer matrix IW is recorded as IW p (p>0, p=1,2,3,…), the p-th neural network hidden layer transfer matrix LW(n) is denoted as LW(n) p(p>0,p=1,2,3,…), there exists an equation

[0067] and Where H is the Hessian matrix of the error performance function and g is the gradient. For a binary differentiable function f(x, y), its Hessian matrix is

[0068]

[0069] BP neural network generally uses Tan-Sigmoid function or linear function as transfer function. This method uses linear function in the output layer and Tan-Sigmoid transfer function in the network hidden layer. The calculation formula of Tan-Sigmoid is:

[0070]

[0071] The neural network atmospheric model based on n hidden layers includes an input layer weight matrix IW and three hidden layer transfer matrices LW(n) (n=1, 2...n). Let its input parameter sequence be in and its output parameter be ym.

[0072] The invention discloses a method for determining the spatial atmospheric density, which is used to calculate the atmospheric density in the range of 250km to 280km above the earth, 90° to -90° in latitude, and 0° to 360° in longitude. The method for determining the spatial atmospheric density can improve the atmospheric determination accuracy of traditional atmospheric models such as the DTM2013 model and the MSIS00 model in the spatial range, and the determination method is simple and has good engineering application value.

[0073] The present invention provides a spatial atmospheric density judgment method, which is based on a neural network with n hidden layers, including an input layer weight matrix IW and three hidden layer transfer matrices LW(n) (n=1, 2...n), assuming that its input parameter sequence is in and its output parameter is ym, specifically:

[0074] The user provides 8 input parameters, including the measurement time (day count in a year), the longitude, latitude, altitude, F 10.7 (F 30 ) of the measurement value of the day before the measurement, F 10.7 (F 30 )81-day average K p Three-hour measurement value, K p Daily average Among them, F 10.7 (F 30 ) of the measurement value of the day before the measurement, F 10.7 (F 30)81-day average, K p Three-hour measurement value, K p The daily average value can be obtained by querying the historical data of solar radiation flux released by the National Oceanic and Atmospheric Administration and other institutions and the historical geomagnetic data released by the National Geophysical Data Center (NGDC). The above data are combined into a sequence and recorded as in;

[0075] Normalize in. The specific operation algorithm is as follows:

[0076] in=(xoutmax-xoutmin). / (xinmax-xinmin).*(in-xinmin)+xoutmin, where the parameters xinmin, xinmax, xoutmin, xoutmax, etc. are shown in Appendix 1 of this article;

[0077] Add a constant term 1 to the parameter sequence that has completed the normalization operation, and turn it into an input sequence consisting of 9 input parameters, that is, p = [in; 1];

[0078] Multiply the input sequence by the weight matrix of the neural network input layer, the algorithm is a(0)=IW*p, perform Tan-Sigmoid transmission change on the input parameter sequence, that is, a(n)=tansig(a(n-1)) to complete the input layer calculation, Tan-Sigmoid transmission change is shown above. The weight matrix IW of the neural network input layer is shown in Appendix 1 and Appendix 2 of this article, and the number of calculations of the neural network hidden layer is n=1;

[0079] Add a constant term 1 to the input sequence, so that a(n) = [a(n); 1], so that the transformed input parameter sequence a(n) is multiplied by LW(n), a(n) = LW(n)*a(n), completing a hidden layer calculation;

[0080] Let n = n + 1. If n > 3, the hidden layer calculation ends and goes to step 7) to complete the output layer calculation. Otherwise, repeat step 5) to complete the next hidden layer calculation.

[0081] Calculate the output layer. Since the output layer is a linear function in this method, this step can be skipped.

[0082] The calculated results are reverse normalized to obtain the spatial atmospheric density, that is,

[0083] ym=(yinmax-yinmin). / (youtmax-youtmin).*(a(n)-youtmin)+yinmin.

[0084] To compare F 10.7 、F 30The accuracy of the two neural network atmospheric models and the two traditional atmospheric models DTM2013 and MSIS00 were compared. GOCE measurement data were randomly selected from 2009 to 2012, and simulation calculations were performed using the four atmospheric models. The comparison results of the input parameters and the atmospheric density measured by the four models with GOCE are as follows:

[0085] Table 1 Randomly sampled GOCE orbit atmospheric density input data

[0086]

[0087]

[0088] Table 2 Atmospheric density results measured by GOCE and simulated by four models

[0089]

[0090] Table 3 Statistics of absolute error rates of atmospheric density simulations of four models

[0091]

[0092]

[0093] Compared with the existing atmospheric models, the accuracy of the spatial atmospheric density judgment method of the present invention is significantly improved. In the atmospheric density simulation of randomly sampled spatial positions in different years, the performance of the two neural network atmospheric models is significantly better than that of the two traditional atmospheric models DTM2013 and MSIS00. The average error rate of the neural network atmospheric model is about 1 / 3-1 / 2 of that of the traditional atmospheric model.

[0094] Compared with the existing atmospheric models, the spatial atmospheric density judgment method of the present invention does not need to use different expressions to judge the value of each influencing factor according to different influencing factors. It only needs to use multiple matrix multiplications to obtain the atmospheric density judgment result, which significantly simplifies the judgment method.

[0095] Appendix 1

[0096] When the solar radiation index is F 10.7 When , the weight matrix and normalization parameters are as follows:

[0097] IW=[-2.616794 -0.545390 0.002589 0.023241 -0.155807 -0.1532650.084614 0.024183 2.827008;-0.943743 0.219746 0.002215 -0.157282 0.1509401.013049 0.016286 0.181446 -0.508654;0.355593 0.348025 0.002156 -0.1995030.236831 0.487658 0.034799 0.126388 0.511955;-0.047784 0.336996 -0.002046 -0.037515 -0.235262 -0.261375 -0.004072 -0.159350 -0.649836;-3.814662 0.5060250.003041 0.138453 -0.274796 0.540789 0.037088 -0.150098 2.315829;-3.1605240.595374 0.001867 0.111715 -0.091412 1.317847 0.011001 -0.045527 1.392140;0.160456 0.978652 -0.003656 1.549382 -0.015287 -0.177179 0.038659 0.0622370.254357;3.426514 -0.124265 0.002369 0.194377 -0.092807 -1.025843 -0.048656 -0.340893 0.552356;-0.173058 0.241054 0.000812 -0.031857 0.030697 -1.500813 -0.013840 0.037667 -1.258546;0.121937 -0.161028 -0.013389 0.193027 -1.0672850.574960 0.691277 -0.000116 2.230767];

[0098] LW(1)=[2.139509 0.322103 -2.088099 -0.806936 -0.679019 0.7214651.146181 0.628451 0.532523 -1.221859 -2.818649;-0.886199 0.500647 -0.2546150.640856 2.145411 -3.831047 -0.099154 0.235048 -0.392087 0.976616 1.375280;1.733166 -1.369631 -0.841082 -0.537111 0.667299 -1.152895 -0.663124 -0.9440134.322746 0.495377 -1.395760;0.968971 -0.313212 0.241563 0.542926 1.3466091.533891 -0.666920 0.609197 -1.393919 -0.965379 -3.378395;-1.030343 -1.869460-1.189202 -1.784085 0.415868 -0.268837 -1.236713 0.047773 -0.183367 0.082494-0.621462;-1.426568 -1.927746 -0.977701 -1.637063 1.656299 -0.064401 0.839494-0.781838 -3.083426 -1.866219 -2.578923;0.534198 -0.256586 -1.073620 -1.545232 -0.358081 0.326531 0.255732 -0.138158 -0.212176 1.174118 -1.788279;-0.189394 0.384169 1.393699 -0.132588 0.593180 -0.327706 -0.417015 1.333879 -2.156396 0.241020 -0.539580;0.692626 0.150743 1.061327 0.383650 -0.9098620.057930 1.090887 0.237649 2.021781 0.148827 -0.055484;-0.468643 -0.4504500.074459 -0.225713 -1.543177 1.388383 -0.530593 1.215340 -0.287394 2.135439 -1.453621；-1.334531 0.411473 1.889914 1.440956 -0.575117 -0.190529 0.1352670.821277 -2.627912 -1.007042 -0.792733；-2.138145 0.804739 0.097838 -0.716458-1.014860 0.060279 0.198331 0.118312 -0.215687 -0.998025 0.371920；0.2479501.022063 -0.788178 1.442612 -0.753803 -0.220657 0.681695 -0.354005 -0.254191-0.813762 -0.261808；1.288585 2.381788 1.208464 4.364791 0.413474 -0.4331721.471952 -0.542267 2.311497 -1.635836 1.479236；1.059487 0.294570 0.2878190.314133 -0.772389 -0.208704 0.630015 -1.048409 -1.694912 -1.420733 -0.643735；0.761009 -1.052729 0.600402 -0.754672 0.111862 -0.314360 -1.278458 -0.065159 -1.704098 -0.113060 -2.282499；-1.283489 0.089441 -1.038639 -2.329550-1.434672 1.342574 -1.100788 1.415836 -2.651629 1.103136 -2.433887；-0.8854160.542206 -0.747501 -0.196422 -0.723185 0.410348 -0.680399 -0.116439 0.062172-1.035097 -2.089334；-0.128712 1.210447 0.171519 -0.061216 0.852945 -0.039373-1.114574 1.087548 0.483474 -0.840410 -1.990672；-0.688091 -0.158441 1.4188130.392104 1.726500 -1.289272 1.196700 0.441385 1.807171 0.880358 -1.817444]；.

[0099] LW(2)=[0.838203 0.053291 0.743290 -0.134469 0.369262 0.1588611.006794 0.073847 0.559335 -0.172343 -0.233033 0.194050 0.539651 -0.3325380.345820 0.228055 0.188345 -0.051355 0.905023 1.016831 -2.066606;-1.576014 -0.095125 -1.997617 -2.047279 2.262519 1.416746 0.596954 -0.806695 0.8153100.656865 0.283497 0.723870 -1.975048 2.755429 0.557862 1.090138 0.5311970.247651 -0.630888 -0.885171 1.286706;0.862309 -1.819828 -1.054906 -0.1071800.638288 1.063795 2.433368 0.272228 -1.295934 2.408630 2.339203 -0.497327 -1.533148 -0.717121 1.544770 1.306420 -1.773514 1.713846 0.389719 -0.823198 -2.292501;0.324730 -0.239933 -0.652329 -0.858472 -0.217311 -0.808172 0.761055-0.602175 -0.967272 1.077954 -1.353793 -1.021338 -0.517255 -0.225403 0.782477-1.024640 1.491147 1.647579 1.626408 0.931376 -0.878472;0.995326 -0.800964 -0.620626 -0.816822 1.539107 -1.177823 -1.608216 -0.393950 -1.616591 0.350094-0.682163 -1.100930 1.377853 0.444989 2.934491 -0.890349 0.710757 -1.577143 -0.665421 0.517388 1.066820;-0.071304 1.276296 -1.340264 -0.492594 -0.279262 -1.188064 0.148135 -0.176278 0.110702 1.797650 -0.859275 -0.311068 -0.0435021.049550 -0.275547 -0.250611 0.235176 -0.221723 -0.408895 0.866856 0.023445；-0.514264 -0.404341 1.180224 -0.424279 0.498719 1.058482 0.010603 1.372646 -0.330654 0.730560 -1.046435 -0.011290 3.231599 -1.408663 0.993711 -0.2460650.577448 -0.029715 -0.664007 -0.548829 -0.124043；0.946303 1.350477 -0.6244551.100934 -0.963757 0.912285 1.776893 -0.784007 -0.020521 -2.222460 0.4232190.735499 1.148800 -2.257466 -1.905923 -0.616635 0.778168 -0.183465 -0.1861780.663508 0.018536；0.321837 -0.710126 1.347513 1.716795 0.547547 -0.419921 -0.198914 -0.107046 0.251711 1.139767 -1.241182 0.075868 1.200943 -0.649651 -2.302962 -1.210695 0.135326 -0.232382 -1.034142 1.140584 -0.373855；-0.1073500.135148 0.769675 -0.312323 -0.418832 0.491868 -0.029269 0.745598 -0.095823 -0.041231 -1.054055 0.275260 -0.767410 -0.733767 -0.191525 -0.046500 0.2922660.221351 0.402254 -0.787645 -1.600745]；.

[0100] LW(3)=[-0.867085 0.408333 1.351278 2.443695 -0.610150 -0.323569 -1.480836 -0.555783 -0.225262 1.097846 1.274749];

[0101] xinmin = [1.000000; 180838.320000; 0.000000; -83.449000; 67.900000; 70.400000; -1.000000; 0.000000];

[0102] xinmax=[365.000000; 294500.700000; 359.999000; 83.448000; 190.500000; 146.800000; 243.000000; 138.000000];

[0103] xoutmin = -1.000000;

[0104] xoutmax = 1.000000;

[0105] yinmin=0.500102;

[0106] yinmax=9.194016;

[0107] youtmin=-1.000000;

[0108] youtmax=1.000000;

[0109] Appendix 2

[0110] When the solar radiation index is F 30 When , the weight matrix and normalization parameters are as follows:

[0111] IW=[-0.172321 0.839804 1.339939 -0.031856 0.085698 -0.4002620.459607 -0.365143 3.743635;-2.881733 0.399339 -0.003825 0.005593 -0.048045 -1.436791 0.049981 0.217019 1.495403;0.603195 0.270602 0.009008 0.1296891.647595 1.170529 -0.108471 -0.570662 -2.112497;1.334401 0.385205 0.0015560.686239 0.129083 0.000626 0.042546 -0.022302 0.204888;0.490799 0.756258 -0.000501 0.265068 0.110554 0.160208 -0.015589 -0.036637 -0.360307;0.448294 -0.306459 0.009341 0.054553 0.958209 3.193791 -0.053498 0.156810 -0.816268;0.771797 -0.143364 -0.004877 -0.847939 -0.096613 -0.024779 -0.028717 -0.115201 0.095425;-0.028644 0.027778 -0.012094 -0.387827 -0.871046 -0.534304-0.049905 -0.280930 -0.504926;-1.691627 -1.032830 0.003150 -0.001370 -0.091685 -0.226643 -0.037287 0.028274 -0.966100;-0.369312 -0.020666 -0.009874-0.580317 0.054776 -0.352784 0.077774 0.100698 -1.901011];

[0112] LW(1)=[1.230786 1.121243 -0.157773 1.386367 1.819932 1.1784090.839584 1.530223 3.821693 -2.428207 -1.802739;0.549089 -0.469134 0.173453 -1.671184 -1.786060 0.617323 1.284957 0.040122 0.188343 0.444539 -1.781291;-1.210349 0.781719 -0.851828 2.298186 3.317180 0.287504 1.487728 0.602940 -0.914457 1.820384 -2.564481;0.315525 -0.430359 0.475137 -1.427080 -1.983891 -0.627344 1.780493 -0.716360 -0.425090 -0.472810 -1.813626;-0.328322 -1.0044490.045667 -1.461494 -0.431727 -0.620581 0.634304 -0.712051 -0.469799 1.1801641.723050;2.725034 -6.816112 0.501906 -0.639884 1.757610 -0.656766 -0.4689420.414776 -1.468007 -1.248682 2.063761;-1.075637 1.569914 0.516986 -0.1344390.545014 -0.437058 0.062764 -0.092890 -2.598033 -0.081121 -0.161857;-1.464699-0.077589 0.697152 0.426438 -0.697668 1.015330 -0.259469 1.477581 -2.288394 -0.135036 -0.026964;0.257861 0.485358 -0.515442 0.488191 -3.091613 0.209215 -0.784001 -1.170124 -0.516916 -0.057585 0.229271;-0.314272 0.362331 -0.407989-1.044094 1.656835 0.597795 0.763042 1.871669 -2.353332 -0.427150 -0.456951；0.748339 0.314499 -0.197079 1.300330 0.662203 0.429838 -1.471832 0.7345300.829893 -0.168073 -0.531902；-0.137052 0.187464 -0.281115 -1.675700 2.041889-0.003722 1.312725 0.599425 -1.341316 -0.033047 -0.012509；0.845699 0.3646830.129925 -0.368277 -0.960124 -0.494041 -0.149705 1.880190 -0.787014 -1.4236470.583750；-0.519933 0.790382 1.238527 1.530100 -1.029396 -3.162609 0.0006210.865885 -0.069174 2.389132 -1.057240；0.802311 0.916372 0.111358 3.829863 -3.537083 2.938236 2.719590 -0.909240 -0.883644 -2.003081 1.708627；0.1377610.402330 -0.507095 -0.203877 1.314661 0.614725 0.362889 0.342088 0.619685 -0.374487 -1.294374；1.905352 -0.776859 -0.465488 -0.242342 1.667663 -0.154403-0.663731 1.479279 -0.155983 0.349914 0.887872；0.416773 0.052471 0.0650530.292078 1.455111 0.092036 1.043797 1.538603 1.541063 -0.018564 1.817295；-0.695536 -0.458959 0.534181 -0.721107 0.339110 -0.618425 -0.267204 0.8396520.351672 1.082092 -1.895567；1.248093 -0.292222 0.455202 -1.541207 1.7922231.248218 1.190762 -0.693425 1.147964 -0.595884 3.019275]；.

[0113] LW(2)=[1.352873 -0.455497 0.077271 0.926761 -0.074577 -0.9935160.311538 3.135029 0.348609 0.508084 -0.012867 -0.231455 0.090814 0.1949730.224022 0.945286 -0.509750 -0.508095 0.131784 0.021894 -1.561599;1.320960 -0.147022 -0.705907 0.106748 -0.457946 -0.868837 -1.208192 -0.810425 -0.714872-0.893555 -0.154792 0.943955 -0.151740 -0.973507 0.383294 -1.631544 0.314331-0.032486 -0.081053 -0.880823 1.242477;0.004012 0.211689 0.108915 0.411275 -0.338818 0.330624 -0.095548 -0.062705 -0.134293 -0.485617 0.703135 0.8308240.406426 0.476805 0.019982 0.322941 -0.502856 0.243464 -0.851295 0.296474 -0.013281;-0.941230 -1.488910 1.637998 0.857883 -0.543040 -0.932981 -2.1422051.310770 0.401298 1.476433 -0.204092 -0.846364 0.733694 0.788979 -0.323747 -0.012353 1.052656 -0.622587 0.076257 -0.501184 -0.518351;3.649570 0.0680860.733007 -1.788286 -1.363180 -0.159966 2.861877 -1.732704 1.039458 -0.065194-0.797622 0.163147 -1.629964 0.923661 1.232250 1.991853 2.017353 0.759923 -1.262709 0.879148 0.669010;0.558207 -0.305150 -0.922191 1.631327 -2.862529 -2.979279 -0.420125 0.211451 -0.381078 0.092460 -1.371552 -1.209577 2.553368 -3.413477 -3.053347 -0.936099 -0.768264 1.492506 -0.126350 -0.5878730.273396；-0.774176 -1.929136 0.122858 -0.921888 1.147870 -1.095321 1.3016791.150665 -0.267309 1.097210 -0.743349 -1.937988 0.383600 -1.793246 -1.3358810.479877 -1.200222 0.053379 0.495890 -1.395135 0.320818；0.537758 1.3350100.021760 0.730043 -0.862194 -1.119970 -0.407957 -0.193616 0.461204 0.432088 -0.892703 -1.564478 -0.135585 -1.282667 1.159274 -0.378457 -1.122415 0.7067350.083263 0.781280 0.888003；0.466491 0.554104 0.208552 -0.889259 0.1565231.710811 -1.631964 -0.763996 -0.104743 0.921169 -0.486425 0.136366 -0.128691-0.129332 -1.060114 0.262002 1.566705 -2.480603 -0.114151 0.934707 -1.599172；-0.271694 1.009769 1.602559 0.087188 -2.125329 -1.293366 -1.0702241.014058 0.966880 -1.072676 -0.233230 0.484244 0.962137 -1.169235 1.430400 -3.529494 0.776723 1.107747 0.634226 0.004827 -2.673374]；.

[0114] LW(3)=[-1.169689 -1.236662 -2.042856 -1.086024 -0.729860 1.207969 -0.442816 -1.747024 0.718393 0.338499 0.092824];

[0115] xinmin = [1.000000; 180836.480000; 0.000000; -83.449000; 46.000000; 46.400000; -1.000000; 0.000000];

[0116] xinmax=[365.000000; 294500.700000; 360.000000; 83.448000; 127.000000; 102.100000; 243.000000; 138.000000];

[0117] xoutmin = -1.000000;

[0118] xoutmax = 1.000000;

[0119] yinmin=0.500065;

[0120] yinmax=9.526194;

[0121] youtmin=-1.000000;

[0122] youtmax=1.000000.

[0123] The present invention discloses a spatial atmospheric density judgment method, which is used to judge the atmospheric density in the range of 250km to 280km above the earth, 90° to -90° in latitude, and 0° to 360° in longitude, and can improve the atmospheric judgment accuracy of the traditional atmospheric model in the spatial range. In the atmospheric density simulation of randomly sampled spatial positions in different years, the performance of the two neural network atmospheric models is significantly better than that of the two traditional atmospheric models DTM2013 and MSIS00, and the average error rate of the neural network atmospheric model is about 1 / 3-1 / 2 of that of the traditional atmospheric model; it is not necessary to use different expressions to judge the value of each influencing factor according to different influencing factors, and it is only necessary to use multiple matrix multiplications to obtain the atmospheric density judgment result, which significantly simplifies the judgment method.

Claims

1. A method for determining spatial atmospheric density, characterized in that: Follow the steps below to implement it: Step 1: The user provides 8 input parameters and the above data is combined into a sequence, recorded as ; Step 2: Perform normalization processing; Step 3: Add the constant term 1 to the parameter sequence that has completed the normalization operation, turning it into an input sequence consisting of 9 input parameters, that is, ; Step 4: Multiply the input sequence by the weight matrix of the neural network input layer, and let the hidden layer of the neural network calculate the number of times ; Step 5: Add a constant term 1 to the input sequence so that , so that the transformed input parameter sequence and Multiply, , complete a hidden layer calculation, LW(n) is the transfer matrix of the nth hidden layer; Step 6: ,like , then the hidden layer calculation ends and goes to step 7; otherwise, let , repeat step 5 to complete the next hidden layer calculation; Step 7: Calculate the output layer; Step 8: Perform reverse normalization processing on the calculation result of step 7 to obtain the spatial atmospheric density and complete the spatial atmospheric density judgment.

2. A method for determining spatial atmospheric density according to claim 1, characterized in that: The eight input parameters in step 1 include the measurement time, the longitude, latitude, and altitude of the spatial point, the measurement value of the solar radiation index the day before the measurement, and the 81-day average value of the solar radiation index. ( ), three-hour measurement value of geomagnetic parameters, daily average value of geomagnetic parameters .

3. A method for determining spatial atmospheric density according to claim 2, characterized in that: The time counting method of the measurement is: calculate the day count of the current date in the year according to the year, month and day information in the coordinated universal time of the current satellite operation, and the calculation method is: the sum of the dates of the previous m-1 months plus the day count , is the current month, is the sum of all the dates of the months before the current month. The date of the month.

4. A method for determining spatial atmospheric density according to claim 1, characterized in that: The step 2 is specifically implemented as follows: Normalize the input array.

5. A method for determining spatial atmospheric density according to claim 1, characterized in that: In step 3 It is a matrix of 9*1 format.

6. A method for determining spatial atmospheric density according to claim 1, characterized in that: The step 4 is specifically implemented as follows: ,in It is a 10*9 matrix. After calculation For a 10*1 matrix, the formula right Transform, where , and add a constant term 1 to the input sequence so that ,at this time It is a 11*1 format matrix.

7. A method for determining spatial atmospheric density according to claim 1, characterized in that: In step 8, the calculation result of step 7 is reverse normalized as follows: ， The calculation result obtained in step 7 is reverse normalized.

Images