阅读说明：本技术 一种考虑微波链路高差的近地面三维立体雨量场反演方法 (Near-ground three-dimensional rainfall field inversion method considering microwave link height difference ) 是由 宋�莹 杨涛 李振亚 洪岱 陈志远 师鹏飞 秦友伟 于 2021-09-09 设计创作，主要内容包括：本发明公开了一种考虑微波链路高差的近地面三维立体雨量场反演方法,包括如下步骤：获取研究区在研究时段内多条超高频无线微波链路数据；采用ITU-R雨衰公式反演每条链路的线平均雨强；考虑微波链路两端基站的高差,将微波链路离散成多个特征空间点,通过拉格朗日算子推求满足微波衰减量线约束条件的特征空间点雨强估计值；迭代求解特征空间点雨强的三维空间分布；构建高时空分辨率的近地面三维立体雨量场。本发明创新性地提出了近地面空间三维雨量场的构建方法,可实现三维空间任意点的雨量过程反演,生成高时空分辨率的三维雨量场数据。由于结合了高密度的微波通信基站,可节约大量人力、物力和基础设施成本,且大幅提高降雨监测的密度和精度。(The invention discloses a near-ground three-dimensional rainfall field inversion method considering microwave link elevation difference, which comprises the following steps of: acquiring data of a plurality of ultrahigh frequency wireless microwave links in a research period in a research area; inverting the line average rain intensity of each link by adopting an ITU-R rain attenuation formula; considering the height difference of base stations at two ends of a microwave link, dispersing the microwave link into a plurality of characteristic space points, and calculating a characteristic space point rain intensity estimated value meeting the constraint condition of a microwave attenuation line through a Lagrange operator; iteratively solving three-dimensional spatial distribution of the rain intensity of the characteristic spatial points; and constructing a near-ground three-dimensional rainfall field with high space-time resolution. The invention innovatively provides a method for constructing a three-dimensional rainfall field in a near-ground space, can realize rainfall process inversion of any point in the three-dimensional space, and generates three-dimensional rainfall field data with high space-time resolution. Due to the combination of the high-density microwave communication base station, a large amount of manpower, material resources and infrastructure cost can be saved, and the density and the precision of rainfall monitoring are greatly improved.)

1. A near-ground three-dimensional rainfall field inversion method considering microwave link elevation difference is characterized by comprising the following steps: the method comprises the following steps:

s1, acquiring data of a plurality of ultrahigh frequency wireless microwave links in a research period in a research area, wherein the data comprises link signal attenuation intensity, base station elevation, longitude and latitude and link length;

s2, inverting the line average rain intensity of each link by adopting an ITU-R rain attenuation formula;

s3, taking into account the height difference of base stations at two ends of the microwave link, dispersing the microwave link into a plurality of characteristic space points, and calculating the characteristic space point rain intensity estimated value meeting the constraint condition of the microwave attenuation line through a Lagrange operator;

s4, circularly and iteratively updating the raininess estimation value of the characteristic space point until the raininess estimation value is converged;

and S5, constructing a high-space-time resolution near-ground three-dimensional rainfall field.

2. The method for inverting the near-ground three-dimensional stereoscopic rainfall field considering the height difference of the microwave link according to claim 1, wherein in the step S2, the step of inverting the line average rainfall intensity of each link by using an ITU-R rainfall attenuation formula comprises:

assuming that the rainfall rate is uniformly distributed on the whole link, establishing an ITU-R rainfall attenuation model:

wherein A is_iThe microwave attenuation value of the ith link, i is 1,2, …, N, a_i、b_iITU-R model parameter values corresponding to the ith microwave link, which are related to link frequency, polarization mode and rainfall particle morphology, can be obtained according to the ITU-R recommendation_iLine average rain strength, L, for the ith link_iThe link length of the ith link;

and (3) according to the obtained link microwave signal attenuation intensity, base station elevation, longitude and latitude and link length information, calculating the line average rain intensity of each link through a formula (1).

3. The method according to claim 1, wherein in step S3, the microwave link is discretized into a plurality of feature space points in consideration of the height difference between the two ends of the microwave link, and the step of estimating the raininess estimate of the feature space points satisfying the constraint condition of the microwave attenuation line by using a lagrange operator comprises:

s3-1, characteristic space point sampling and rain intensity initial value setting on space link

Splitting the ith link into K_iConsidering the rainfall rate on each short link as a constant and taking the midpoint of each short link as a feature space point, each link is discretized into K_iM characteristic space points are taken from N microwave links at equal intervals,the spatial position and the elevation information of the characteristic space points can be known according to the microwave link information, and the initial value of the rain intensity of each characteristic space point is set as the line average rain intensity of the link where the point is located;

s3-2, establishing a characteristic space point rain intensity reestimation model considering the measurement error based on the height difference of two ends of the microwave link,

rainfall intensity inverse calculation according to microwave attenuation amount has quantization error n_iThe error is related to microwave attenuation and link length:

wherein n is_iThe quantization error of the i (i-1, 2, …, N) th link microwave attenuation quantity is subject to uniform distribution, delta A_iThe error range of the ith link can be 1dB,

therefore, the line average rain intensity of the ith link under the quantization error condition is considered as:

R_i＝R_i(A_i+n_i)＝R_i(A_i)+ΔR_i(A_i+n_i) (3)

taylor first order expansion according to equation (1), R_iCan be expressed as:

the second term on the right of equation (4) is approximately equal to the rain intensity quantization error, so the measurement error m_iCan be expressed as:

the variance is:

if the sequence of the rain intensity estimated values of M discrete characteristic space points of the N links is [ gamma ]₁,γ_M]Considering that the height difference exists between two ends of the microwave link and the microwave link is distributed in a three-dimensional space, the rain intensity estimated value of any point (x, y, z) in the space is theta:

wherein, W_jAs an inverse distance squared weight function, gamma_jIs the raininess estimate for the jth feature space point,

wherein l_jIs the distance between the point (x, y, z) to be solved in space and the jth feature space point, Γ_iIn order to influence the radius, the raininess estimation values of the points to be solved and the M characteristic space points have the following relationship:

wherein the content of the first and second substances,γ＝(γ₁ γ₂ … γ_M)^T，υis an error vector that follows a gaussian distribution,υ～N(0，Λ)，

Λ^-1the rainfall intensity estimated value of the point to be solved is determined by the space positions of the point to be solved and the characteristic space points and is obtained by combining the formulas (7) to (10):

θ＝(1Λ^-1 1)^-1 1Λ^-1 γ (11)

wherein the content of the first and second substances,1is a unit vector;

in addition, in consideration of measurement errors, equations (9) and (10) can be expressed as:

wherein the content of the first and second substances,m＝(m₁ m₂ … m_M)^Tfor measurement error, ζ is a proportionality constant related to the properties of the raincell, for the same microwave link, there isIf not, then,

in conjunction with equations (12) through (14), equation (11) is rewritten as:

wherein

S3-3, establishing line constraint condition by considering microwave signal attenuation

According to the formula (1), the raininess value of the feature space point on the ith link further needs to satisfy the following constraint:

wherein A is_ijIs the microwave attenuation value of the jth short link on the ith link; r is_ijIs the actual value of the rain intensity of the jth feature space point on the ith link,

a penalty function is defined which is a function of,

wherein the content of the first and second substances,when the constraint condition (18) is not considered, the rainfall intensity estimated value of the jth characteristic space point on the ith link obtained by the formula (15) is used for calculating the minimum value of the formula (19) by adopting a Lagrange multiplier method according to the constraint formula (18), and the jth link on the ith link can be obtainedThe characteristic space point considers the raininess estimated value of the line constraint condition (18):

when r is_ij<When 0, let r_ij＝0。

4. The method for inverting the near-ground three-dimensional stereoscopic rainfall field considering the height difference of the microwave link according to claim 1, wherein the step S4 of iteratively updating the raininess estimation value of the feature space point in a loop until the raininess estimation value converges includes:

s4-1, setting initial value of spatial characteristic point rain intensity

According to formula 1, initializing the raininess estimation values of the characteristic space points on the N links to the line average raininess when the quantization errors of the corresponding links are not considered, wherein the total number of the characteristic space points is M, whereinObtaining the sequence [ gamma ] of the raininess estimation value₁₀,γ_M0]；

S4-2, updating the raininess estimation value of each spatial feature point by considering the line constraint condition;

updating K on link 1₁The rain intensity estimated value of each characteristic space point, the rain intensity estimated value sequence of other links is known, and K under the line constraint condition is considered according to the formula (15) and the formula (20)₁Rain intensity estimation value sequence [ gamma ] of characteristic space point₁₁,γ_K11]，

By analogy, the raininess estimation values of the characteristic space points on the 2 nd, 3 rd, … th and N th links are sequentially calculated to obtain a raininess estimation value sequence [ gamma ] of M data points₁₁,γ_M1]；

S4-3, setting iteration termination conditions

After iteration is carried out for T times, the raininess estimation error epsilon is calculated as:

when epsilon<0.1, stopping iteration to obtain the rain intensity sequence [ gamma ] of M characteristic space points of N links_1T,γ_MT](ii) a If epsilon>0.1, return to S4-2 to continue the iterative process.

5. The method for inverting the near-surface three-dimensional rainfall field considering the height difference of the microwave link according to claim 1, wherein the step of constructing the near-surface three-dimensional rainfall field with high space-time resolution in the step S5 comprises the steps of:

knowing the rain intensity sequence [ gamma ] of M characteristic space points_1T,γ_MT]The rainfall intensity of any point in the three-dimensional space can be obtained by solving according to the formula (11), and the rainfall intensity values at different times and any position can be solved according to the microwave attenuation signals at different times, so that the high-space-time-resolution near-ground three-dimensional rainfall field is constructed.

Technical Field

The invention relates to the field of application of new-generation communication technology, in particular to a near-ground three-dimensional rainfall field inversion method considering microwave link elevation difference.

Background

Rainfall is an important driving element of hydrologic cycle of a drainage basin or a region and is one of the most important basic data for water resource management and scheduling, and accurate rainfall monitoring has important significance on the aspects of human production and life such as agricultural production, water conservancy development, river flood control, engineering management and the like.

In recent years, researchers have proposed a two-dimensional rainfall field construction technique based on microwave link signal attenuation, which can provide rainfall field data with high space-time resolution by projecting the linear rainfall of microwave inversion onto a two-dimensional plane. However, in mountainous areas or urban areas where building forests stand, the height difference between microwave base stations can reach dozens or even hundreds of meters, and under the conditions of strong wind disturbance, barrier blockage, local wind field change and the like, the distribution of near-ground rain fields at different heights often has great difference. In the prior art, the difference of rainfall fields with different heights is not considered, the rainfall field inverted by microwaves is projected to a certain plane, and a larger error exists between the rainfall field and a real three-dimensional rainfall field. Therefore, the invention considers the height difference of base stations at two ends of a link, realizes the construction of a three-dimensional rainfall field based on microwave signal attenuation, innovating a rainfall monitoring method and has important significance for improving the space-time resolution of rainfall monitoring.

Disclosure of Invention

The purpose of the invention is as follows: in order to solve the problem that a two-dimensional rainfall field inverted by using a microwave signal attenuation principle in the prior art cannot reflect the difference of rainfall fields with different heights, the invention provides a near-ground three-dimensional rainfall field inversion method considering the height difference of a microwave link.

The technical scheme is as follows: in order to achieve the purpose, the invention provides a method for monitoring dew intensity by wireless microwaves based on wet antenna cause judgment, which comprises the following steps:

s1, acquiring data of a plurality of ultrahigh frequency wireless microwave links in a research period in a research area, wherein the data comprises link signal attenuation intensity, base station elevation, longitude and latitude, link length and the like;

s2, inverting the line average rain intensity of each link by adopting an ITU-R rain attenuation formula;

s3, taking into account the height difference of base stations at two ends of the microwave link, dispersing the microwave link into a plurality of characteristic space points, and calculating the characteristic space point rain intensity estimated value meeting the constraint condition of the microwave attenuation line through a Lagrange operator;

s4, circularly and iteratively updating the raininess estimation value of the characteristic space point until the raininess estimation value is converged;

and S5, constructing a high-space-time resolution near-ground three-dimensional rainfall field.

Further, in step S2, the step of inverting the line average rain intensity of each link by using the ITU-R rain attenuation formula includes:

assuming that the rainfall rate is uniformly distributed on the whole link, establishing an ITU-R rainfall attenuation model:

wherein A is_iIs the microwave attenuation value of the ith link, i is 1,2_i、b_iITU-R model parameter values corresponding to the ith microwave link, which are related to link frequency, polarization mode and rainfall particle morphology, a_iAs attenuation coefficient, b_iFor the attenuation index, the ITU-R recommendation can be found, R_iLine average rain strength, L, for the ith link_iThe link length of the ith link;

according to the obtained information of the microwave signal attenuation intensity of the links, the elevation of the base station, the longitude and latitude, the length of the links and the like, the line average rain intensity of each link can be obtained through a formula (1).

Further, in step S3, the step of discretizing the microwave link into a plurality of characteristic space points by considering the height difference between the two ends of the microwave link, and calculating the rain intensity estimation value of the characteristic space point satisfying the constraint condition of the microwave attenuation line by using a lagrange operator includes:

s3-1, characteristic space point sampling and rain intensity initial value setting on the space link.

Splitting the ith link into K_iConsidering the rainfall rate on each short link as a constant and taking the midpoint of each short link as a feature space point, each link is discretized into K_iSpaced equally apart feature space points. Co-fetching on N microwave linksAnd knowing the spatial position and the elevation information of each characteristic space point according to the microwave link information, and setting the initial value of the rain intensity of each characteristic space point as the line average rain intensity of the link where the point is located.

S3-2, establishing a characteristic space point rain intensity re-estimation model considering the measurement error based on the height difference of two ends of the microwave link.

Rainfall intensity inverse calculation according to microwave attenuation amount has quantization error n_iThe error is related to microwave attenuation and link length:

wherein n is_iA quantization error of the i (i ═ 1, 2.., N) th link microwave attenuation, obeying a uniform distribution, Δ a_iThe error range of the ith link can be 1 dB.

Therefore, the line average rain intensity of the ith link under the quantization error condition is considered as:

R_i＝R_i(A_i+n_i)＝R_i(A_i)+ΔR_i(A_i+n_i) (3)

taylor first order expansion according to equation (1), R_iCan be expressed as:

the second term on the right of equation (4) is approximately equal to the rain intensity quantization error, so the measurement error m_iCan be expressed as:

the variance is:

if the sequence of the rain intensity estimated values of M discrete characteristic space points of the N links is [ gamma ]₁，γ_M]Considering that the height difference exists between two ends of the microwave link and the microwave link is distributed in a three-dimensional space, the rain intensity estimated value of any point (x, y, z) in the space is theta:

wherein, W_jAs an inverse distance squared weight function, gamma_jIs the raininess estimate of the jth feature space point.

Wherein l_jIs the distance between the point (x, y, z) to be solved in space and the jth feature space point, Γ_iTo influence the radius. The rain intensity estimated values of the point to be solved and the M characteristic space points have the following relationship:

wherein the content of the first and second substances,γ＝(γ₁ γ₂ ... γ_M)^T，υis an error vector that follows a gaussian distribution,υ～N(0，Λ)。

Λ^-1the spatial position of the spatial candidate point and the characteristic spatial point is determined. Combining the formulas (7) to (9), the rain intensity estimation value of the point to be solved is obtained as follows:

θ＝(1Λ^-1 1)^-1 1Λ^-1 γ (11)

wherein the content of the first and second substances,1is a unit vector.

In addition, in consideration of measurement errors, equations (9) and (10) can be expressed as:

wherein the content of the first and second substances,m＝(m₁ m₂...m_M)^Tto measure error, ζ is a proportionality constant related to the raincell characteristics. For the same microwave link, there areIf not, then,

in conjunction with equations (12) through (14), equation (11) is rewritten as:

wherein

And S3-3, establishing a line constraint condition by considering the microwave signal attenuation amount.

According to the formula (1), the raininess value of the feature space point on the ith link further needs to satisfy the following constraint:

wherein A is_ijIs the microwave attenuation (dB) of the jth short link on the ith link; r is_ijIs the actual value of the rain intensity of the jth feature space point on the ith link.

A penalty function is defined which is a function of,

wherein the content of the first and second substances,when the constraint condition (18) is not considered, the rainfall intensity estimated value of the jth characteristic space point on the ith link is obtained through the formula (15). According to the constraint formula (18), the Lagrange multiplier method is adopted to calculate the minimum value of the formula (19), and the rain intensity estimation of the jth characteristic space point on the ith link considering the line constraint condition (18) can be obtainedAnd (3) evaluating:

when r is_ijWhen < 0, let r_ij＝0。

Further, in step S4, iteratively updating the rain intensity estimated value of the feature space point until the rain intensity estimated value converges includes:

and S4-1, setting an initial value of the rain intensity of the spatial characteristic point.

The characteristic space points on N links (total M, whereinInitializing the raininess estimation value to the line average raininess when the quantization error of the corresponding link is not considered (formula (1)), and obtaining the raininess estimation value sequence [ gamma ]₁₀，γ_M0]。

And S4-2, updating the raininess estimation value of each spatial feature point by considering the line constraint condition.

Updating K on link 1₁The rain intensity estimation value of each characteristic space point. Knowing the rain intensity estimation value sequences of other links, according to the formula (15) and the formula (20), K can be obtained under the condition of considering line constraint₁Rain intensity estimation value sequence of characteristic space points

By analogy, the raininess estimation values of the characteristic space points on the 2 nd, 3 rd, … th and N th links are sequentially calculated to obtain a raininess estimation value sequence [ gamma ] of M data points₁₁，γ_M1]。

And S4-3, setting an iteration termination condition.

After iteration is carried out for T times, the raininess estimation error epsilon is calculated as:

when the epsilon is less than 0.1,stopping iteration to obtain the rain intensity sequence [ gamma ] of M characteristic space points of N links_1T，γ_MT](ii) a If epsilon is more than 0.1, returning to S4-2 to continue the iterative process.

Further, the step of constructing a high-spatial-temporal-resolution near-ground three-dimensional rainfall field in step S5 includes:

knowing the rain intensity sequence [ gamma ] of M characteristic space points_1T，γ_MT]And solving according to the formula (11) to obtain the rain intensity of any point in the three-dimensional space. According to the microwave attenuation signals at different moments, the rainfall intensity values at different moments and at any position can be solved, and a high-space-time-resolution near-ground three-dimensional rainfall field is constructed.

Has the advantages that: the invention provides a near-ground three-dimensional rainfall field inversion method considering microwave link elevation difference, which has the following advantages compared with the prior art:

1. the method utilizes the ultrahigh frequency wireless microwave link to dynamically monitor the rain intensity, adopts the existing wireless base station communication facilities, saves the investment of disposable infrastructure and a large amount of operation and personnel maintenance cost, and has the remarkable advantages of quick construction, small investment, convenient maintenance, flexible encryption observation and the like.

2. The height difference of base stations at two ends of a link is considered, the three-dimensional rainfall field is constructed based on microwave signal attenuation, the rainfall fields with different heights can be monitored, and the time-space resolution of rainfall monitoring can be improved.

3. And the rainfall intensity estimated value of the characteristic space point is updated through multiple loop iterations, so that the error of the rainfall intensity inversion is greatly reduced, the monitoring precision is improved, and the high-spatial-temporal-resolution near-ground three-dimensional rainfall field can be constructed.

Drawings

FIG. 1 is a flow chart of the method of the present invention.

Detailed Description

The invention is further elucidated with reference to the drawings and the embodiments.

As shown in fig. 1, the present invention provides a near-ground three-dimensional rainfall field inversion method considering microwave link elevation difference, which includes the following steps:

s1, acquiring data of a plurality of ultrahigh frequency wireless microwave links in a research period in a research area, wherein the data comprises link signal attenuation intensity, base station elevation, longitude and latitude, link length and the like;

s2, inverting the line average rain intensity of each link by adopting an ITU-R rain attenuation formula;

assuming that the rainfall rate is uniformly distributed on the whole link, establishing an ITU-R rainfall attenuation model:

wherein A is_iIs the microwave attenuation value of the ith link, i is 1,2_i、b_iITU-R model parameter values corresponding to the ith microwave link, which are related to link frequency, polarization mode and rainfall particle morphology, can be obtained according to the ITU-R recommendation_iLine average rain strength, L, for the ith link_iThe link length of the ith link;

according to the obtained information of the microwave signal attenuation intensity of the links, the elevation of the base station, the longitude and latitude, the length of the links and the like, the line average rain intensity of each link can be obtained through a formula (1).

S3, taking into account the height difference of base stations at two ends of the microwave link, dispersing the microwave link into a plurality of characteristic space points, and calculating the characteristic space point rain intensity estimated value meeting the constraint condition of the microwave attenuation line through a Lagrange operator, wherein the method specifically comprises the following steps:

s3-1, characteristic space point sampling and rain intensity initial value setting on the space link.

Splitting the ith link into K_iConsidering the rainfall rate on each short link as a constant and taking the midpoint of each short link as a feature space point, each link is discretized into K_iSpaced equally apart feature space points. Co-fetching on N microwave linksThe space position and elevation information of each characteristic space point can be known according to the microwave link information, and the rain intensity of each characteristic space point is determinedThe starting value is set to the line average rain intensity of the link where the point is located.

S3-2, establishing a characteristic space point rain intensity re-estimation model considering the measurement error based on the height difference of two ends of the microwave link.

Rainfall intensity inverse calculation according to microwave attenuation amount has quantization error n_iThe error is related to microwave attenuation and link length:

wherein n is_iA quantization error of the i (i ═ 1, 2.., N) th link microwave attenuation, obeying a uniform distribution, Δ a_iThe error range of the ith link can be 1 dB.

Therefore, the line average rain intensity of the ith link under the quantization error condition is considered as:

R_i＝R_i(A_i+n_i)＝R_i(A_i)+ΔR_i(A_i+n_i) (3)

taylor first order expansion according to equation (1), R_iCan be expressed as:

the second term on the right of equation (4) is approximately equal to the rain intensity quantization error, so the measurement error m_iCan be expressed as:

the variance is:

if the sequence of the rain intensity estimated values of M discrete characteristic space points of the N links is [ gamma ]₁，γ_M]Considering that the height difference exists between two ends of the microwave link and the microwave link is distributed in a three-dimensional space, the rain intensity estimated value of any point (x, y, z) in the space is theta:

wherein, W_jAs an inverse distance squared weight function, gamma_jIs the raininess estimate of the jth feature space point.

Wherein l_jIs the distance between the point (x, y, z) to be solved in space and the jth feature space point, Γ_iTo influence the radius. The rain intensity estimated values of the point to be solved and the M characteristic space points have the following relationship:

wherein the content of the first and second substances,γ＝(γ₁ γ₂...γ_M)^T，υis an error vector that follows a gaussian distribution,υ～N(0，Λ)。

Λ^-1the spatial position of the spatial candidate point and the characteristic spatial point is determined. Combining the formulas (7) to (9), the rain intensity estimation value of the point to be solved is obtained as follows:

θ＝(1Λ^-1 1)^-1 1Λ^-1 γ (11)

wherein the content of the first and second substances,1is a unit vector.

In addition, in consideration of measurement errors, equations (9) and (10) can be expressed as:

wherein the content of the first and second substances,m＝(m₁ m₂...m_M)^Tto measure error, ζ is a proportionality constant related to the raincell characteristics. For the same microwave link, there areIf not, then,

in conjunction with equations (12) through (14), equation (11) is rewritten as:

wherein

And S3-3, establishing a line constraint condition by considering the microwave signal attenuation amount.

According to the formula (1), the raininess value of the feature space point on the ith link further needs to satisfy the following constraint:

wherein A is_ijIs the microwave attenuation (dB) of the jth short link on the ith link; r is_ijIs the actual value of the rain intensity of the jth feature space point on the ith link.

A penalty function is defined which is a function of,

wherein the content of the first and second substances,when the constraint condition (18) is not considered, the rainfall intensity estimated value of the jth characteristic space point on the ith link is obtained through the formula (15). According to the constraint formula (18), a Lagrange multiplier method is adopted to calculate the minimum value of the formula (19), and the raininess estimation value of the jth characteristic space point on the ith link considering the line constraint condition (18) can be obtained:

when r is_ijWhen < 0, let r_ij＝0。

S4, iteratively updating the raininess estimation values of the feature space points until the raininess estimation values converge, which specifically includes:

and S4-1, setting an initial value of the rain intensity of the spatial characteristic point.

The characteristic space points on N links (total M, wherein) Initializing the raininess estimation value to the line average raininess when the quantization error of the corresponding link is not considered (formula (1)), and obtaining the raininess estimation value sequence [ gamma ]₁₀，γ_M0]。

And S4-2, updating the raininess estimation value of each spatial feature point by considering the line constraint condition.

Updating K on link 1₁The rain intensity estimation value of each characteristic space point. Knowing the rain intensity estimation value sequences of other links, according to the formula (15) and the formula (20), K can be obtained under the condition of considering line constraint₁Rain intensity estimation value sequence of characteristic space points

By analogy, the raininess estimation values of the characteristic space points on the 2 nd, 3 rd, … th and N th links are sequentially calculated to obtain a raininess estimation value sequence [ gamma ] of M data points₁₁，γ_M1]。

And S4-3, setting an iteration termination condition.

After iteration is carried out for T times, the raininess estimation error epsilon is calculated as:

when epsilon is less than 0.1, stopping iteration to obtain N chains of M characteristic space points in total [ gamma ] sequence_1T，γ_MT](ii) a If epsilon is more than 0.1, returning to S4-2 to continue the iterative process.

And S5, constructing a high-space-time resolution near-ground three-dimensional rainfall field.

Knowing the rain intensity sequence [ gamma ] of M characteristic space points_1T，γ_MT]And solving according to the formula (11) to obtain the rain intensity of any point in the three-dimensional space. According to the microwave attenuation signals at different moments, the rainfall intensity values at different moments and at any position can be solved, and a high-space-time-resolution near-ground three-dimensional rainfall field is constructed.