RU2697433C1 - Method for automatic determination of ionospheric layers parameters by ionograms - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: invention relates to ionosphere studies and can be used to determine parameters of ionospheric layers. Summary: ionograms-pattern adjustment, determined by required parameters, is performed for experimentally obtained ionogram by searching for maximum overlapping of said two ionograms. Template used is an ionogram obtained by solving a direct problem of propagation of radio waves in an ionospheric plasma. Maximum overlap is found using the Nelder-Mead optimization algorithm. Note here that pattern adjustment may be performed step-by-step for different parts of ionogram and ionospheric layers. Experimentally obtained ionogram is pre-modified to facilitate search in order to eliminate sharp edges of trace, and area of parameters is divided into parts, in each of which adjustment is performed in parallel in order to find global maximum.

EFFECT: operational monitoring of ionosphere parameters round-the-clock without operator intervention.

1 cl, 2 dwg

Description

It can be used for automatic (without operator intervention) processing of ionograms of vertical and inclined sensing to determine the parameters of the ionosphere, primarily the critical frequencies and heights of layers F2, F1 and E.

1. General description

The ionospheric layers above a given point on the earth's surface are traditionally described by a set of parameters that are necessary for solving the problems of short-wave communication, satellite navigation and other areas related to the ionosphere. As these parameters, the maximum values of the densities (or plasma frequencies) of each layer, the heights at which these maximum values and thicknesses (or half thicknesses) of the layers are reached [1] are used. To monitor the state of the ionosphere, various types of short-wave ionosondes are used - ground-based vertical and inclined sounding, as well as satellite ones. The output information of ionosondes are ionograms, that is, images in the coordinate space “frequency - time of radar delay”. The ionospheric parameters are determined by the ionogram either by the processing operator or by software that recognizes the characteristic features of the ionogram and determines the numerical characteristics that describe the ionospheric layers.

The following describes a new method for the automatic processing of ionograms for determining parameters, based on the optimization approach [2], which is widely used to solve pattern recognition problems. An ideal ionosphere, consisting of distinct layers of a mathematically defined form, is uniquely described by a set of numerical parameters. Therefore, these same parameters uniquely determine the ionogram that would be obtained by radio sounding of such an ideal ionosphere. Recognition of the ionogram consists in fitting the ionospheric parameters so that the model ionogram calculated from them matches the experimentally obtained on the ionosonde. In addition to the maximum frequencies, heights and half-thicknesses of the ionospheric layers E, F1, F2, for a more realistic description of the ionosphere, other parameters can be added to the set, for example, the height and maximum frequency of the layer of the sporadic layer E and frequency broadening during F scattering.

To solve the optimization problem, the Nelder-Mead algorithm (simplex method) is used [3]. If you want to find a set of n parameters that most accurately describe the ionogram, n + 1 initial sets of these parameters are specified to enter the algorithm. From a mathematical point of view, these sets of parameters represent an n + 1 point in the n-dimensional space of parameters. These points represent the vertices of the simplex (tetrahedron in n-dimensional space). During the execution of the algorithm, the initial vertices approach in such a way that the simplex is compressed to the point where the result of comparing the model and real ionograms is the best (the optimization function reaches its maximum). When the distance between the vertices on all axes becomes less than the specified accuracy of determining the parameters, the algorithm exits the cycle.

The Nelder-Mead algorithm tends to erroneously converge to local minima instead of global ones. For the sets of parameters obtained in this way, the coincidence of the model and real ionograms will be bad, however, any small change in any of the parameters leads to even greater deterioration of the match. To solve this problem, the entire area in which the optimal set of parameters is sought is divided into subdomains, in each of which an initial simplex is created. For each of these simplexes (their number can be hundreds or more), the entire sequence of the algorithm should be performed. The results are compared with each other, and the largest of the maxima found is considered global. It is he who is issued as the final result.

This approach is very reliable, but requires significant processing power. For the algorithm to work effectively, parallel computing is required on modern multiprocessor servers or on video processors.

For more efficient operation of the algorithm, it is possible to perform ionogram recognition in parts. For example, at the first stage, the parameters of the F2 layer are determined by the high-frequency part, at the second - the presence of trace broadening due to F scattering is checked, at the third - the presence of the F1 layer is determined and its parameters are determined in the mid-frequency region, at the fourth - the parameters of the E layers are determined and Es at the bottom of the ionogram. This approach allows you to save processing time, if, for example, it is known in advance that the layers E and F1 are absent.

2. Modification of the ionogram

When using the Nelder-Mead algorithm, the correct choice of the optimization function, in this case, a numerical estimate of the degree of coincidence of ionograms, is of paramount importance. You can choose as such a function the intersection area of the traces of the real and model ionograms, but the problem arises of assessing the coincidence of ionograms with disjoint traces. Even a closely spaced, but disjoint with the real pattern, will give the same zero match as the remote one.

To solve this problem, a real ionogram is modified. When an ionogram is modified, the track is artificially broadened, first in frequency, then in height, due to the addition of wide wings of low intensity in frequency and height, decreasing with distance from the track. An example of a modified ionogram (only an ordinary trace) is shown in Figure 1. Color shades show additional broadening, red - the highest intensity, blue - the lowest.

3. Initialization of the simplex

To initialize the initial set of simplexes, one can use climatic ionospheric models, which make it possible to give a preliminary estimate of the critical frequencies, heights, and half-thicknesses of tracks. The search area for the optimization maximum is constructed on the basis of these preliminary estimates, starting from values several times smaller than model averages, to values several times larger. Then the search area is divided into cells into which the original simplexes fit. The limits of the search area, the number of cells and initial simplexes should be selected for a specific implementation of the algorithm, depending on the solved and available computing power.

4. Modeling the plasma frequency profile

The vertical profile of the plasma frequency in the ionosphere is calculated based on the given parameters as the overlay of several layers in the form of a parabola, cosine or any other mathematical function with a pronounced maximum. For example, in the case of cosine layers, each of the layers will be described by a function

плазменная частота, зависящая от высоты h, и ионосферные параметры, задающие слой:

- плазменная частота в максимуме данного слоя,

высота максимума электронной концентрации слоя,

полутолщина слоя.Here

plasma frequency, depending on the height h, and ionospheric parameters defining the layer:

- plasma frequency at the maximum of this layer,

the height of the maximum electron concentration of the layer,

half thickness of the layer.

5. Modeling an ionogram

At the next stage, an ionogram is calculated according to a given profile. For each of the given frequencies of the ionogram, stepwise integration of the effective height is performed, which is the propagation time of the radio wave pulse t through the plasma medium, multiplied by the speed of light c [4]:

. (6)

. (6)

раз, где

 – групповой показатель преломления. Поэтому действующую высоту можно определить как:A pulse propagates in a plasma at a slower rate than

times where

- group refractive index. Therefore, the effective height can be defined as:

(7)

(7)

, (8)

, (eight)

истинная высота,

групповая скорость. При численном интегрировании шаг по времени и действующей высоте является равномерным, а по истинной высоте - неравномерным (меньшим в областях меньшей групповой скорости).Where

true height

group speed. In numerical integration, the time step and the effective height are uniform, and the true step is uneven (smaller in areas of lower group velocity).

плазменной частоты, определенного в предыдущем параграфе, требуются данные о магнитном поле, которые рассчитываются по модели геомагнитного поля, такой как IGRF.To calculate the refractive index, except for the profile

the plasma frequency defined in the previous paragraph, magnetic field data are required, which are calculated using a geomagnetic field model such as IGRF.

для обыкновенной волны и

для необыкновенной:First, the phase refractive index is determined

for an ordinary wave and

for extraordinary:

, (9)

, (9)

, (10)

, (ten)

, (11)

, (eleven)

– квадрат отношения плазменной частоты к частоте радиоволны,

– отношение гирочастоты геомагнитного поля к частоте радиоволны,

,

, θ – наклонение геомагнитного поля.Where

- the square of the ratio of the plasma frequency to the frequency of the radio wave,

- the ratio of the gyrofrequency of the geomagnetic field to the frequency of the radio wave,

,

, θ is the inclination of the geomagnetic field.

с помощью следующей формулы:Then the group refractive index is determined

using the following formula:

, (12)

, (12)

- фазовый показатель преломления.Where

- phase refractive index.

Now you can determine the group velocity of the radio pulse

(13)

(13)

, определить приращения действующей высоты

и истинной высоты

.and based on the time step

determine the increments of the effective height

and true height

.

не станет мнимым, т.е., не выполнится условие отражения

, что дает истинную и действующую высоту отражения радиоволны от ионосферы.Having added the value of the increment of the true height to the current value, we get the opportunity to determine the plasma frequency value at the new height from the ionospheric profile, calculate the group velocity and repeat the cycle again. Integration occurs until the phase refractive index

does not become imaginary, i.e., the reflection condition is not satisfied

, which gives the true and effective height of the reflection of the radio wave from the ionosphere.

All actions are performed twice, for ordinary and extraordinary waves. Knowing the reflection heights, it is possible to fill in the matrix of ionograms containing zeros and ones for the ordinary and extraordinary components. The unit fills the trace located at the current reflection height and having a thickness that is determined by the specified duration of the radar pulse of the ionosonde.

6. Comparison of real and model ionograms

To successfully find the model ionogram closest to the real one, it is necessary to select the appropriate comparison function, which will play the role of the optimization function in the Nelder-Mead algorithm. Since the selection of ionograms is carried out in several stages, it is possible to increase the efficiency of the algorithm by choosing different comparison functions for different stages. Depending on the recognition stage, either a fill metric or a cross metric is used.

The filling metric is defined as the fraction of filling the model trace (template) with real.

The cross-metric determines the fraction of filling the model trace with real, and then vice versa - the fraction of filling the real ionogram with model traces, after which the obtained values are multiplied.

At different stages it is advisable to use different metrics. For example, the complement metric can be used to determine the exact value of the critical frequency of layer F from the high-frequency part of the ionogram. In all other cases, i.e. in determining the frequency scattering and the parameters of the F1 layer, a cross-metric is used. When determining the critical frequencies, a weight factor is introduced that increases with increasing height for a more exact match of the asymptotic tail tail with the template.

7. Nelder-Mead Algorithm

To find the minimum of the comparison function, the Nelder-Mead method was chosen primarily because of its efficiency and ease of implementation, and also because of the lack of the need to consider the gradients of the optimization function, which saves machine time.

точка

в заданной области поиска. Эти точки являются вершинами симплекса в n-мерном пространстве. В этих точках вычисляются значения функции:As described above, select

point

in the given search area. These points are the vertices of the simplex in n-dimensional space. At these points, the function values are calculated:

.

.

After that, the Nelder-Mead algorithm is applied in the following form:

. Выбираются три вершины: наихудшая

с наименьшим значением функции

,

со следующим по величине значением

и наилучшая

с наибольшим значением функции

.1) Vertices are sorted by function values

. Three peaks are chosen: the worst

with the smallest function value

,

with the next largest value

and the best

with the highest function value

.

всех вершин симплекса, за исключением вершины

:

2) The center of gravity is calculated

all vertices of the simplex, except for the vertex

:

отражается относительно

с коэффициентом α=1 в точку

, в которой вычисляется функция:

. Координаты новой точки вычисляются по формуле

.3) Point

reflected relatively

 with coefficient α = 1 per point

in which the function is calculated:

. The coordinates of the new point are calculated by the formula

.

со значениями

,

,

:4) Next, the value is compared

with values

,

,

:

, то производится растяжение. Новая точка

и значение функции

.a) If

then stretching is performed. New point

and function value

.

, то точка

заменяется на

, итерация заканчивается.b) If

then point

replaced by

, the iteration ends.

, то точка

заменяется на

, итерация заканчивается.c) If

then point

replaced by

, the iteration ends.

, то точка

заменяется на

, итерация заканчивается.d) If

then point

replaced by

, the iteration ends.

, то обозначения

,

(и соответствующие значения функции) меняются местами, и производится сжатие (шаг 5).e) If

, then the notation

,

(and the corresponding function values) are interchanged, and compression is performed (step 5).

, то производится сжатие (шаг 5).f) If

, then compression is performed (step 5).

, в которой вычисляется значение

.5) Compression is performed: the point is built

in which the value is calculated

.

, то точка

заменяется на

, итерация заканчивается.6) If

then point

replaced by

, the iteration ends.

, то производится гомотетическое равномерное сжатие к точке с наименьшим значением

для всех требуемых точек

.7) If

, then homothetic uniform compression to the point with the smallest value is performed

for all required points

.

8) Checking the conditions for exit from the loop, exit or transition to a new iteration.

The exit from the Nelder-Mead algorithm is carried out in three cases:

1) if more than a given maximum number of iterations is completed, but the result is not found;

2) if the difference in metrics at the best and worst point is less than the specified;

3) if the specified accuracy of determination of all parameters is achieved, i.e. the difference in parameters for the vertices of the simplex Δ does not exceed the specified.

In the case of a successful search, the output is performed according to condition 3. The remaining conditions are needed for a more rapid termination of calculations for poorly selected simplexes that take up processor time.

If no model ionogram matches the real one or doesn’t match exactly (with low values of the comparison metrics), then the real ionogram is marked as unrecognized.

To illustrate, Figure 2 shows an intermediate step of fitting a template. Red is the experimentally obtained trace of the ordinary component, green is the unusual component, blue transparent is the template ionogram, a thin blue line is the vertical plasma frequency profile, based on which the ionogram is calculated.

Literature

1. URSI Guide to the interpretation and processing of ionograms / M.: Science, 1978. - 342 ° C.

2. R.O. Duda, P.E. Hart, and D.G. Stork. Pattern Classification. John Wiley & Sons, second edition, 1999.

3. Nelder J.A. and Mead R. A Simplex Method for Function Minimization. Computer Journal, 1965, V. 7, p. 308-313.

4. Davies K. Ionospheric radio waves. Blaisdell Publishing Company, 1969.

Claims (1)

The method of determining the parameters of ionospheric layers from ionograms of satellite, ground-based vertical and ground-based oblique sounding, which consists in fitting the template ionogram determined by these parameters to the experimentally obtained ionogram by searching for the maximum overlap of these two ionograms, characterized in that the ionogram obtained by solving the direct problems of radio wave propagation in the ionospheric plasma, the maximum overlap is found using the optimization algorithm Nelder – Mead, moreover, the template can be adjusted step by step for different parts of the ionogram and ionosphere layers, the experimentally obtained ionogram is preliminarily modified to facilitate the search in order to eliminate the sharp edges of the trace, and the parameter region is divided into parts, in each of which the adjustment is made in parallel with the aim of finding global high.

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