CN108073782A - A kind of data assimilation method based on the equal weight particle filter of observation window - Google Patents

Abstract

The invention discloses a particle filter data assimilation method based on observation window average weight, which specifically includes the following steps: (1) acquiring the initial background field of model integration; (2) calculating the proposed density according to the observation information in the observation window; (3) At a given assimilation moment, use the average weight method to calculate the particle weight and adjust the particle state; (4) Use the resampling method to adjust the set of particles to maintain a stable number of particles; (5) Calculate the state posterior after the average weight particle filter estimated value. The present invention utilizes the observation information stored in the observation window, and adjusts the aggregate particle state by proposing the density before the assimilation time, and further improves the average weighted particle filter assimilation method. Using this method can effectively improve the quality of data assimilation in nonlinear mode, and can be better applied in the field of current data assimilation applications.

Description

A data assimilation method based on particle filter with average weight of observation window

technical field

The invention relates to the field of atmospheric and oceanic data assimilation, in particular to a method for assimilating atmospheric and oceanic data based on observation window average weight particle filtering.

Background technique

There are two ways to study ocean dynamics, one is to use numerical models for research, and the other is to conduct direct observations of the atmosphere and ocean. With the rapid development of atmospheric and ocean-related data and information research, the requirements for atmospheric and ocean data are also increasing, and traditional numerical models can approximately reflect ocean changes. Although the data obtained by direct observation is a reflection of the real state, due to the limitations of the equipment and the continuous changes of the observation points, the observation results inevitably have inevitable errors and random errors. The core of data assimilation is the continuous integration of new observational information in the dynamic model to achieve the purpose of improving the initial value of the model and the forecast effect. The data assimilation method used in the current research can effectively improve the effect of ocean simulation and reduce the initial value of ocean and climate forecast. Uncertainty of conditions, improve reanalysis data.

Data assimilation methods are mainly divided into two categories: variational method and sequential method. Variational method includes three-dimensional variation and four-dimensional variation. Its main feature is to use numerical optimization algorithm to solve the minimization problem of the objective function. For example, the patent application number 201510047795.6 applies for a direct assimilation method of MODIS satellite data. This patent uses a three-dimensional variational assimilation method to assimilate satellite observation data to improve the accuracy of numerical weather forecasting. The sequential method is a recursive method based on statistical estimation theory. Its advantage is that it does not need to develop the tangent and adjoint models required by the variational assimilation algorithm, and can explicitly provide the initial disturbance of the ensemble forecast. It has been widely used, such as the patent application number 201010561909.6 Kalman filter assimilation method for fast collection of real-time data of high-frequency observation data. This patent improves the problem of insufficient operation in the ensemble Kalman filter, but when the ensemble Kalman filter derives the posterior mean and variance of the mode state, it assumes that the prior distribution of the mode state is Gaussian. This assumption is for the linear mode. It is correct, but in practice, most of the atmospheric-ocean numerical models have strong nonlinearity. In recent years, the particle filter method featuring nonlinear Monte Carlo simulation has gradually become a hot spot in the research of data assimilation in nonlinear models. For example, the patent application No. 201110090879.X is a general data assimilation method based on Bayesian filtering. The patent proposes a general data assimilation method combining ensemble Kalman filtering and particle filtering. Since the Kalman filter has certain deviations when used in a non-Gaussian environment, nonlinear and non-Gaussian random patterns have more general significance in real life. The particle filter method has its unique characteristics. First, it can completely solve the problem of nonlinear data assimilation. Second, the particle filter uses the importance sampling method to ensure that the state of the particles remains unchanged, so that the dynamic balance of the model is not destroyed.

The main advantage of particle filter data assimilation is to sample according to the weight of the particle, to ensure that the state of the particle remains unchanged, and the observation information only changes the weight of the particle itself, so that the dynamic balance of the model is not destroyed. However, the particle filter data assimilation method also has shortcomings. Although the particles in the particle filter constantly adjust their own weights according to the observation information, a single particle will get a higher weight, and other particles will get a very low weight, resulting in particle degradation. For the problem of particle degradation in particle filter, the resampling method is usually used, and the single use of resampling method will cause the problem of particle degradation.

Aiming at the problem of particle degradation in the current particle filter research field, British professor Van Leeuwen summarized the particle filter algorithm in high-dimensional model data assimilation in detail, and further proposed the average weight particle filter algorithm. The main idea of this method is to use the proposed density to achieve particle adjustment, so that The aggregate particles are close to the observation information, and the number of effective particles in the sampling process is increased, so that each particle contributes the maximum posterior probability density, thereby avoiding the occurrence of particle degradation and particle impoverishment. This method reasonably adjusts the particle state, that is, a small number of particles can meet the particle filter assimilation effect that traditional resampling particle filters need hundreds to thousands of particles to achieve. In particle filter data assimilation, observation information plays a leading role in the quality of assimilation results. It is of great application value to design a particle filter based on average weight particle filter and efficiently use observation information based on observation window average weight particle filter data assimilation method.

The invention proposes a particle filter data assimilation technology based on the average weight of the observation window. Compared with the traditional particle filter data assimilation technology, the remarkable feature of the present invention is that it not only calculates the proposed density according to the observation at the moment of assimilation, but also adjusts the particle position state. Instead, the available observation information obtained before the assimilation time is stored in the observation window, and according to the observation information stored in the window, the proposed density is calculated before the assimilation time, and the particle position is adjusted to be close to the observation information. At the time of assimilation, the particle state adjusted according to the proposed density can effectively increase the number of effective particles sampled, and then calculate the weight of the sampled particles, and select the optimal particle state according to the weight to complete data assimilation. The method proposed by the invention can overcome the problems of particle degeneration and particle impoverishment in the traditional particle filter method, and improves the problem that the average weight particle filter method adjusts the state at a single assimilation time, and the particle filter assimilation result fluctuates too much.

Contents of the invention

Summary of the invention of the present invention is as follows:

A method of data assimilation based on observation window average weight particle filter, characterized in that it specifically comprises the following steps:

(1) Obtain the initial background field of the model integral;

(2) Calculate the proposed density according to the observation information in the observation window;

(3) At a given assimilation moment, use the average weight method to calculate the particle weight and adjust the particle state;

(4) Use the resampling method to adjust the set of particles to maintain a stable number of particles;

(5) Calculating the state posterior estimation value after the average weighted particle filter.

Described step (1) specifically comprises:

The model equation product is input into the initial field of the model equation, so that the model variable reaches a chaotic state, and the model variable that reaches the chaotic state is used as the initial background field. Based on the model background field, the initial value of the particle filter ensemble particles is obtained through the model equation.

Described step (2) specifically comprises:

(2.1) Calculate particle probability density based on observation information:

Compute the probability density of an ensemble particle from the particle state at time n-1 using the mode equation Integrate, the probability density expression of the aggregated particles is:

Represents the probability density from the particle state at time n-1 to time n, Indicates the state of the i-th particle at time n, Indicates the integration result of the model equation at time n-1, and Q indicates the model error covariance expression is:

M represents the total number of aggregate particles, Indicates the mean value of aggregate particles;

(2.2) Find the particle proposal density through the probability density:

Based on the prior density calculated in (2.1) in the model equation, the proposed density in the average weight particle is obtained, and the proposed density expression obtained from the prior density is:

formula Indicates the proposed density with observation y as the target, K ⁿ indicates the relaxed stress matrix, its expression is K ⁿ ＝QHT ^T (HQHT+R) ^-1 , the expression of K ⁿ and model error covariance Q and observation error covariance R is :

Indicates the state of the i-th particle at time n, H indicates that the observation operator generally takes a value of 1, and y indicates the observation information; in the particle filter based on the average weight of the observation window, the calculation of the proposed density is not limited to the observation information at the time of assimilation, The proposed density can use the observation information stored in the observation window before the assimilation moment;

(2.3) Select the optimal proposal density and calculate the particle weight:

suppose The weight of each particle in the ensemble is expressed as:

where _ωi represents the weight of the i-th particle in the set, represents the state of the i-th particle at time n, y ⁿ represents the observation information at time n, represents the probability density, denotes the proposal density, Indicates the probability density of the particle state at n time for the particle at n time; according to the calculation, the weight of the particles in the set is obtained.

Described step (3) specifically comprises:

(3.1) Calculate the weight of the particles based on the proposed density-adjusted set of particles:

According to the observation information in the assimilation window, the proposed density is calculated to adjust the position of the particles in the set, so that the particles are closer to the observed information at the time of assimilation; the proposed density makes each particle in the set close to the observed information, so that it can obtain almost the same weight; each particle’s The weight expression is:

in Indicates the prior weight of the i-th particle, which is the weight of each particle in the proposed density calculation process; y represents the observation vector; H represents the observation projection operator, and the projection operator in simple mode H=1; x Indicates the state vector; the superscript T indicates matrix transposition; Q indicates the model error covariance matrix; R indicates the observation error covariance matrix; assuming that the weight C _i of the particle target in the set is obtained, it is guaranteed that C _i satisfies the following expression:

For the state at time n Most of the particles in the set maintain the same weight, and some particles that do not reach the average weight are adjusted by the resampling method;

(3.2) Adjust the particle state according to the weight:

After obtaining the weight of the aggregated particles, adjust the particle state according to the weight, then the state at time n can be expressed as:

In the formula, y represents the observation vector; H represents the observation projection operator (H=1); x represents the state vector; K= ^QHT (HQHT+R) ^-1 , Q is the model error covariance, R is the observation error covariance, When the aggregate particle weights are approximately equal in the average weighted particle filter, the vector α _i can be expressed as:

in and In these two expressions C represents the selected target weight, Indicates the relative weight of the particle at the current moment; in order to ensure the random effect of the particle state in the set, random items are added to obtain the final analytical equation, where Represents the random error:

Described step (4) specifically comprises:

After the particle state is adjusted by the average weight particle filter, the final state adjustment is carried out by using the resampling method according to the particle weight to maintain the stability of the particle number.

Described step (5) specifically comprises:

Based on the state of the resampled ensemble particles, calculate the posterior estimated ensemble mean of the state:

The updated posterior estimated set mean is used as the initial value of the analysis model for the next step of prediction and assimilation, and the above steps are repeated to obtain the final analysis field within the assimilation time, which serves as the data field reflecting the current environmental state.

The advantages of the present invention are:

(1) Improve the traditional particle filter method, effectively improve the problem of particle degradation and particle impoverishment, and improve the problem that the average weight particle filter is only adjusted at the time of assimilation, so that the assimilation result fluctuates too much.

(2) Before the assimilation time, the observation information is allocated more reasonably, and the assimilation quality can be improved by proposing the density to bring the particles closer to the observation information. Compared with the assimilation at all observation times, the calculation pressure of particle state adjustment is significantly improved. decrease.

Description of drawings

Figure 1 is a flow chart of atmospheric ocean data assimilation;

Fig. 2 is a flow chart of data assimilation based on weighted particle filter based on improved observation information.

Detailed ways

The following will be described in conjunction with specific embodiments.

The present invention provides a particle filter data assimilation technology based on observation window average weight, which specifically includes the following steps:

Step 1: Obtain the initial background field of the model integral

The initial value of the numerical model integration is selected, and the model equation is integrated first, so that the model equation reaches a chaotic state and avoids the fluctuation of the model equation. The mode state at this time is taken as the initial background field of the assimilation experiment mode, and the background field is used as the integration starting point, and the mode state equation is used for integration.

Step 2: Calculate the proposed density according to the observation information in the observation window

According to the observation information stored in the window and the state of the aggregated particles, the proposed density is solved, and the corresponding optimal proposed density is selected to further determine the posterior probability density of the aggregated particles.

Step 3: At a given assimilation moment, use the average weight method to calculate the particle weight and adjust the particle state

According to the observation information and the adjusted state, the weight of the particles in the set is calculated through the weight calculation formula to ensure that most particles in the particle set can achieve a better weight, and the particle state is adjusted according to the weight.

Step 4: Use the resampling method to adjust the set of particles to maintain a stable number of particles

Use the resampling method to adjust the particles with poor weight performance, eliminate the particles that do not meet the weight requirements, copy the particles with better performance, and maintain the stability of the number of aggregated particles.

Step 5: Calculate the state posterior estimation value after the average weighted particle filter

The resampled particles are reintroduced into the model equation, and the model integration process is updated during the assimilation process to form the final assimilation analysis result.

In order to more simply and clearly describe the specific implementation steps of the particle filter assimilation method based on the average weight of the observation window, a simple Lorenz-63 model is taken as an example for a brief description.

(1) Obtain the initial background field of the model integral

In the Lorenz-63 model, the initial field (0, 1, 0) is first input into the model equation to integrate 1 million steps, so that the model variables reach a chaotic state, avoiding the introduction of model fluctuation deviation in the process of assimilation and integration of the model, and the model that will reach the chaotic state The variable is used as the initial background field, and based on the model background field, the initial value of the particles in the particle filter set is obtained through the model equation. It can effectively improve the reliability of the collective particle state obtained by the mode equation.

(2) Calculate the proposed density according to the observation information in the observation window

In the particle filter data assimilation, adjust the position state of the collection particles and observation information during the assimilation process, adjust the particles in the collection to be closer to the observation information, increase the number of effective particles in the sampling process, and improve the particle degradation and particle filter data assimilation. For particle depletion problems, precomputation proposes density-adjusted particle states. The specific calculation method is as follows:

(2.1) Calculate particle probability density based on observation information

For the calculation of the proposed density, it is necessary to calculate the probability density of the aggregated particles first, using the Lorenz-63 model equation, from the particle state at time n-1 Integrate, the probability density expression of the aggregated particles is:

Represents the probability density from the particle state at time n-1 to time n, Indicates the state of the i-th particle at time n, Indicates the integration result of the Lorenz-63 model equation at time n-1, and Q indicates the model error covariance expression is:

M represents the total number of aggregate particles, Indicates the mean value of the set of particles. The probability density of particles is calculated by this formula.

(2.2) Calculate the particle proposal density through the probability density

In the Lorenz 63 model for example, based on the prior density calculated in the previous step, the proposed density in the weight-average particle can be further obtained, and the proposed density expression obtained from the prior density is:

formula Indicates the proposed density with the observation y as the target, K ⁿ indicates the relaxed stress matrix and its expression is K ⁿ ＝QH ^T (HQH ^T +R) ^-1 , the expression of K ⁿ and model error covariance Q and observation error covariance R for:

Indicates the state of the i-th particle at time n, H indicates that the observation operator generally takes a value of 1, and y indicates the observation information. In the particle filter based on the average weight of the observation window, the calculation of the proposed density is not limited to the observation information at the time of assimilation. The proposed density can use the observation information stored in the observation window before the time of assimilation. The purpose is to adjust the position of the aggregate particles before the time of assimilation. close to observation information.

(2.3) Select the optimal proposal density and calculate the particle weight

The selection of the proposed density is considered to be an important criterion for controlling the position of particles and observation information and the calculation of particle weights. Selecting an appropriate and optimal proposed density can ensure the number of effective particles in the sampling, and at the same time ensure the reliability of particle weights. The most important part of , finding the optimal proposed density assumption The weight of each particle in the ensemble is expressed as:

where _ωi represents the weight of the i-th particle in the set, represents the state of the i-th particle at time n, y ⁿ represents the observation information at time n, represents the probability density, denotes the proposal density, Indicates the probability density of the particle state at n time for the particle at n time. Calculates the weight of the particles in the collection.

(3) At a given assimilation moment, use the average weight method to calculate the particle weight and adjust the particle state

(3.1) Calculate the weight of the particles based on the proposed density-adjusted set of particles

According to the observation information in the assimilation window, the proposed density is calculated to adjust the position of the particles in the set, so that the particles are closer to the observation information at the time of assimilation, and ensure that most of the particles get equal weights in the posterior probability density function at the time of assimilation. The proposal density makes each particle in the collection close to the observation information, so that it gets nearly the same weight. The weight expression of each particle is:

in Indicates the prior weight of the i-th particle, which is the weight of each particle in the proposed density calculation process; y represents the observation vector; H represents the observation projection operator, and the projection operator in simple mode H=1; x Indicates the state vector; the superscript T indicates the matrix transpose; Q indicates the model error covariance matrix; R indicates the observation error covariance matrix. Assuming that the target weight C _i of the particles in the set is obtained, in order to ensure that 80% of the particles in the particle set can reach the calculated weight and avoid the occurrence of particle degradation and impoverishment problems:

Thus it can be found that for the state at time n Most of the particles in the set can maintain the same weight, and some particles that do not reach the average weight can be adjusted by resampling.

(3.2) Adjust particle state according to weight

After obtaining the weight of the aggregated particles, adjust the particle state according to the weight, then the state at time n can be expressed as:

In the formula, y represents the observation vector; H represents the observation projection operator (H=1); x represents the state vector; K=QH ^T (HQH ^T +R) ^-1 , Q is the model error covariance, R is the observation error covariance , when the aggregate particle weights are approximately equal in the weighted particle filter, the vector α _i can be expressed as:

middle and In these two expressions C represents the selected target weight, Indicates the relative weight of the particle at the current moment. In order to ensure that the random effect of the particle state in the set is added to the random item, the final analytical equation is obtained, where Represents the random error:

(4) Use the resampling method to adjust the set of particles to maintain a stable number of particles

The basic idea of the resampling algorithm is to remove the particles with small weight and copy the particles with large weight. In order to prevent that a very small number of particles do not meet the requirements of equal weight during the weight equalization process, after the particle state is adjusted by the weight equalization particle filter, the final state adjustment is performed using the resampling method according to the particle weight.

(5) Calculating the state posterior estimated value after the average weighted particle filter

Based on the state of the resampled ensemble particles, calculate the posterior estimated ensemble mean of the state: The updated posterior estimated set mean is used as the initial value of the analysis model for the next step of prediction and assimilation, and the above steps are repeated to obtain the final analysis field within the assimilation time, which serves as the data field reflecting the current environmental state.

Claims (6)

1. A data assimilation method based on observation window average weight particle filter, is characterized in that, specifically comprises the following steps: (1) Obtain the initial background field of the model integral; (2) Calculate the proposed density according to the observation information in the observation window; (3) At a given assimilation moment, use the average weight method to calculate the particle weight and adjust the particle state; (4) Use the resampling method to adjust the set of particles to maintain a stable number of particles; (5) Calculating the state posterior estimation value after the average weighted particle filter. 2. a kind of data assimilation method based on observation window average weight particle filter, it is characterized in that, described step (1) specifically comprises: The model equation product is input into the initial field of the model equation, so that the model variable reaches a chaotic state, and the model variable that reaches the chaotic state is used as the initial background field. Based on the model background field, the initial value of the particle filter ensemble particles is obtained through the model equation. 3. A data assimilation method based on observation window average weight particle filter, it is characterized in that, described step (2) specifically comprises: (2.1) Calculate particle probability density based on observation information: Compute the probability density of an ensemble particle from the particle state at time n-1 using the mode equation Integrate, the probability density expression of the aggregated particles is: Represents the probability density from the particle state at time n-1 to time n, Indicates the state of the i-th particle at time n, Indicates the integration result of the model equation at time n-1, and Q indicates the model error covariance expression is: <mrow><mi>Q</mi><mo>=</mo><mi>cov</mi><mo>{</mo><msub><mi>x</mi><mi>i</mi></msub><mo>,</mo><mover><mi>x</mi><mo>&amp;OverBar;</mo></mover><mo>}</mo><mo>=</mo><mfrac><mn>1</mn><mi>M</mi></mfrac><munderover><mo>&amp;Sigma;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>M</mi></munderover><msup><mrow><mo>(</mo><msub><mi>x</mi><mi>i</mi></msub><mo>-</mo><mover><mi>x</mi><mo>&amp;OverBar;</mo></mover><mo>)</mo></mrow><mn>2</mn></msup><mo>;</mo></mrow> M represents the total number of aggregate particles, Indicates the mean value of aggregate particles; (2.2) Find the particle proposal density through the probability density: Based on the prior density calculated in (2.1) in the model equation, the proposed density in the average weight particle is obtained, and the proposed density expression obtained from the prior density is: <mrow><mi>q</mi><mrow><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mi>n</mi></msubsup><mo>|</mo><msubsup><mi>x</mi><mi>i</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mi>y</mi><mo>)</mo></mrow><mo>&amp;Proportional;</mo><mi>exp</mi><mo>&amp;lsqb;</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mrow><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mi>n</mi></msubsup><mo>-</mo><mi>f</mi><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mo>)</mo><mo>)</mo></mrow><mo>-</mo><msup><mi>K</mi><mi>n</mi></msup><msup><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mi>H</mi><mo>(</mo><msup><mi>x</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo><mo>)</mo></mrow><mi>T</mi></msup><msup><mi>Q</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mi>n</mi></msubsup><mo>-</mo><mi>f</mi><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mo>)</mo><mo>-</mo><msup><mi>K</mi><mi>n</mi></msup><mo>(</mo><mi>y</mi><mo>-</mo><mi>H</mi><mo>(</mo><msup><mi>x</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo><mo>)</mo></mrow><mo>&amp;rsqb;</mo><mo>;</mo></mrow> formula Indicates the proposed density with the observation y as the target, K ⁿ indicates the relaxed stress matrix and its expression is K ⁿ ＝QH ^T (HQH ^T +R) ^-1 , the expression of K ⁿ and model error covariance Q and observation error covariance R for: <mrow><mi>R</mi><mo>=</mo><mi>cov</mi><mo>{</mo><msub><mi>x</mi><mi>i</mi></msub><mo>,</mo><mi>y</mi><mo>}</mo><mo>=</mo><mfrac><mn>1</mn><mi>M</mi></mfrac><munderover><mo>&amp;Sigma;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>M</mi></munderover><msup><mrow><mo>(</mo><msub><mi>x</mi><mi>i</mi></msub><mo>-</mo><mi>y</mi><mo>)</mo></mrow><mn>2</mn></msup><mo>;</mo></mrow> Indicates the state of the i-th particle at time n, H indicates that the observation operator generally takes a value of 1, and y indicates the observation information; in the particle filter based on the average weight of the observation window, the calculation of the proposed density is not limited to the observation information at the time of assimilation, The proposed density can use the observation information stored in the observation window before the assimilation moment; (2.3) Select the optimal proposal density and calculate the particle weight: suppose The weight of each particle in the ensemble is expressed as: <mrow><mtable><mtr><mtd><mrow><msub><mi>&amp;omega;</mi><mi>i</mi></msub><mo>=</mo><mi>p</mi><mrow><mo>(</mo><msup><mi>y</mi><mi>n</mi></msup><mo>|</mo><msubsup><mi>x</mi><mi>i</mi><mi>n</mi></msubsup><mo>)</mo></mrow><mfrac><mrow><mi>p</mi><mrow><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mi>n</mi></msubsup><mo>|</mo><msubsup><mi>x</mi><mi>i</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mo>)</mo></mrow></mrow><mrow><mi>q</mi><mrow><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mi>n</mi></msubsup><mo>|</mo><msubsup><mi>x</mi><mi>i</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mo>,</mo><msup><mi>y</mi><mi>n</mi></msup><mo>)</mo></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mi>p</mi><mrow><mo>(</mo><msup><mi>y</mi><mi>n</mi></msup><mo>|</mo><msubsup><mi>x</mi><mi>i</mi><mi>n</mi></msubsup><mo>)</mo></mrow><mfrac><mrow><mi>p</mi><mrow><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mi>n</mi></msubsup><mo>|</mo><msubsup><mi>x</mi><mi>i</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mo>)</mo></mrow></mrow><mrow><mi>p</mi><mrow><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mi>n</mi></msubsup><mo>|</mo><msubsup><mi>x</mi><mi>i</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mo>,</mo><msup><mi>y</mi><mi>n</mi></msup><mo>)</mo></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mi>p</mi><mrow><mo>(</mo><msup><mi>y</mi><mi>n</mi></msup><mo>|</mo>mo><msubsup><mi>x</mi><mi>i</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mo>)</mo></mrow></mrow></mtd></mtr></mtable><mo>;</mo></mrow> where _ωi represents the weight of the i-th particle in the set, represents the state of the i-th particle at time n, y ⁿ represents the observation information at time n, represents the probability density, denotes the proposal density, Indicates the probability density of the particle state at n time for the particle at n time; according to the calculation, the weight of the particles in the set is obtained. 4. a kind of data assimilation method based on observation window average weight particle filter, it is characterized in that, described step (3) specifically comprises: (3.1) Calculate the weight of the particles based on the proposed density-adjusted set of particles: According to the observation information in the assimilation window, the proposed density is calculated to adjust the position of the particles in the set, so that the particles are closer to the observed information at the time of assimilation; the proposed density makes each particle in the set close to the observed information, so that it can obtain almost the same weight; each particle’s The weight expression is: <mrow><msub><mi>&amp;omega;</mi><mi>i</mi></msub><mo>&amp;Proportional;</mo><msubsup><mi>&amp;omega;</mi><mi>i</mi><mrow><mi>r</mi><mi>e</mi><mi>s</mi><mi>t</mi></mrow></msubsup><mi>exp</mi><mo>{</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mrow><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mi>n</mi></msubsup><mo>-</mo><mi>f</mi><mo>(</mo><msup><mi>x</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo><mo>)</mo></mrow><mi>T</mi></msup><msup><mi>Q</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mi>n</mi></msubsup><mo>-</mo><mi>f</mi><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mo>)</mo><mo>)</mo></mrow><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mrow><mo>(</mo><msup><mi>y</mi><mi>n</mi></msup><mo>-</mo><mi>H</mi><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mi>n</mi></msubsup><mo>)</mo><mo>)</mo></mrow><mi>T</mi></msup><msup><mi>R</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><msup><mi>y</mi><mi>n</mi></msup><mo>-</mo><mi>H</mi><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mi>n</mi></mo>msubsup><mo>)</mo><mo>)</mo></mrow><mo>}</mo><mo>;</mo></mrow> in Indicates the prior weight of the i-th particle, which is the weight of each particle in the proposed density calculation process; y represents the observation vector; H represents the observation projection operator, and the projection operator in simple mode H=1; x Indicates the state vector; the superscript T indicates matrix transposition; Q indicates the model error covariance matrix; R indicates the observation error covariance matrix; assuming that the weight C _i of the particle target in the set is obtained, it is guaranteed that C _i satisfies the following expression: <mrow><msub><mi>C</mi><mi>i</mi></msub><mo>=</mo><mo>-</mo><msubsup><mi>log&amp;omega;</mi><mi>i</mi><mrow><mi>r</mi><mi>e</mi><mi>s</mi><mi>t</mi></mrow></msubsup><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mrow><mo>(</mo><msup><mi>y</mi><mi>n</mi></msup><mo>-</mo><mi>H</mi><mi>f</mi><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mo>)</mo><mo>)</mo></mrow><mi>T</mi></msup><msup><mrow><mo>(</mo><msup><mi>HQH</mi><mi>T</mi></msup><mo>+</mo><mi>R</mi><mo>)</mo></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><msup><mi>y</mi><mi>n</mi></msup><mo>-</mo><mi>H</mi><mi>f</mi><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mo>)</mo><mo>)</mo></mrow><mo>;</mo></mrow> For the state at time n Most of the particles in the set maintain the same weight, and some particles that do not reach the average weight are adjusted by the resampling method; (3.2) Adjust the particle state according to the weight: After obtaining the weight of the aggregated particles, adjust the particle state according to the weight, then the state at time n can be expressed as: <mrow><msubsup><mi>x</mi><mi>i</mi><mi>n</mi></msubsup><mo>=</mo><mi>f</mi><mrow><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mo>)</mo></mrow><mo>+</mo><msub><mi>&amp;alpha;</mi><mi>i</mi></msub><mi>K</mi><mrow><mo>(</mo><msup><mi>y</mi><mi>n</mi></msup><mo>-</mo><mi>H</mi><mi>f</mi><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mo>)</mo><mo>)</mo></mrow><mo>;</mo></mrow> In the formula, y represents the observation vector; H represents the observation projection operator (H=1); x represents the state vector; K=QH ^T (HQH ^T +R) ^-1 , Q is the model error covariance, R is the observation error covariance , when the aggregate particle weights are approximately equal in the weighted particle filter, the vector α _i can be expressed as: <mrow><mi>&amp;alpha;</mi><mo>=</mo><mn>1</mn><mo>-</mo><msqrt><mrow><mn>1</mn><mo>-</mo><msub><mi>b</mi><mi>i</mi></msub><mo>/</mo><msub><mi>a</mi><mi>i</mi></msub></mrow></msqrt><mo>;</mo></mrow> in and In these two expressions C represents the selected target weight, Indicates the relative weight of the particle at the current moment; in order to ensure the random effect of the particle state in the set, random items are added to obtain the final analytical equation, where Represents the random error: <mrow><msubsup><mi>x</mi><mi>i</mi><mi>n</mi></msubsup><mo>=</mo><mi>f</mi><mrow><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mo>)</mo></mrow><mo>+</mo><msub><mi>&amp;alpha;</mi><mi>i</mi></msub><mi>K</mi><mrow><mo>(</mo><msup><mi>y</mi><mi>n</mi></msup><mo>-</mo><mi>H</mi><mi>f</mi><mo>(</mo><msubsup><mi>x</mi><mi>i</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mo>)</mo><mo>)</mo></mrow><mo>+</mo><msubsup><mi>&amp;beta;</mi><mi>i</mi><mi>n</mi></msubsup><mo>.</mo></mrow> 5. a kind of data assimilation method based on observation window average weight particle filter, it is characterized in that, described step (4) specifically comprises: After the particle state is adjusted by the average weight particle filter, the final state adjustment is carried out by using the resampling method according to the particle weight to maintain the stability of the particle number. 6. A data assimilation method based on observation window average weight particle filter, it is characterized in that, described step (5) specifically comprises: Based on the state of the resampled ensemble particles, calculate the posterior estimated ensemble mean of the state: <mrow><mover><mi>x</mi><mo>&amp;OverBar;</mo></mover><mo>=</mo><mfrac><mn>1</mn><mi>M</mi></mfrac><munderover><mo>&amp;Sigma;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>M</mi></munderover><msub><mi>x</mi><mi>i</mi></msub><mo>;</mo></mrow> The updated posterior estimated set mean is used as the initial value of the analysis model for the next step of prediction and assimilation, and the above steps are repeated to obtain the final analysis field within the assimilation time, which serves as the data field reflecting the current environmental state.