Laser ceilometer system error compensation method based on regression analysis

Abstract

The invention provides a laser ceilometer system error compensation method based on regression analysis, and belongs to the technical field of laser ceilometers. A measurement range is divided into four height intervals by constructing a layered height interval step regression equation set, and an independent nonlinear regression equation is established; designing a double-layer game optimization framework to realize collaborative optimization of global error minimization and local fitting precision maximization, executing historical data preprocessing and data set division, and implementing a double-layer game model collaborative optimization algorithm to determine a regression equation coefficient and a neural network parameter; a self-adaptive cloud height error correction model based on a Transform architecture is constructed to realize real-time error compensation, the optimal performance of the model is kept through sliding time window monitoring and automatic retraining, and the technical problem that the measurement precision of the laser ceilometer is affected by atmospheric environment parameters and equipment parameter changes, and consequently system errors are remarkable is solved.

Description

Technical Field

[0001] This invention belongs to the field of laser astronomy technology, and more specifically, relates to a system error compensation method for laser astronomy based on regression analysis. Background Technology

[0002] Laser cenotes, as core equipment for modern meteorological observation and aviation meteorological support, measure cloud base height by emitting laser beams and receiving reflected signals from clouds. They are widely used in airport meteorological observation, climate monitoring, and numerical weather prediction. Traditional laser cenote systems primarily use simple linear models or empirical formulas based on laser echo time ranging to calculate cloud base height, and then use fixed calibration coefficients to initially correct the measurement results. This method can provide relatively accurate measurement results under standard atmospheric conditions. However, traditional technology exhibits significant limitations when facing complex and variable atmospheric environments. In particular, when environmental parameters such as atmospheric temperature, humidity, and pressure change significantly, the laser beam propagation characteristics are affected to varying degrees. Furthermore, fluctuations in the laser's own emission power and changes in the response characteristics of the photodetector introduce additional systematic errors. In current laser cenote applications, due to the lack of comprehensive consideration of multi-dimensional influencing factors and dynamic compensation mechanisms, the measurement accuracy often fails to meet the stringent requirements of high-precision meteorological observation and aviation safety. In other words, existing technologies suffer from the technical problem of significant systematic errors caused by changes in atmospheric environmental parameters and the equipment's own parameters affecting the measurement accuracy of laser cenotes. Summary of the Invention

[0003] In view of this, the present invention provides a system error compensation method for laser astronomy height meters based on regression analysis, which can solve the technical problem in the prior art where the measurement accuracy of laser astronomy height meters is affected by changes in atmospheric environmental parameters and equipment parameters, resulting in significant system errors.

[0004] This invention is implemented as follows: It provides a system error compensation method for laser ceilometers based on regression analysis, comprising: collecting laser beam emission power data, laser echo signal intensity data, atmospheric temperature data, atmospheric humidity data, and atmospheric pressure data; and synchronously acquiring standard cloud base height measurements using a reference laser ceilometer as the dependent variable benchmark data for regression analysis; constructing a hierarchical height interval stepped regression equation system, dividing the cloud base height measurement range according to different height intervals, establishing an independent nonlinear regression equation for each height interval, the nonlinear regression equation including a linear term for laser parameters, a nonlinear term for atmospheric parameters, and an output term for an adaptive cloud height error correction model; and establishing a two-layer game optimization framework to minimize the cloud base height. An upper-level optimization model with the root mean square error of measurement as the objective function and a lower-level optimization model with the objective function of maximizing the goodness of fit of the regression equations for each altitude interval are implemented. A two-level game-theoretic collaborative optimization algorithm is implemented to determine the linear coefficients of the laser parameters and the nonlinear coefficients of the atmospheric parameters in the nonlinear regression equations for each altitude interval. At the same time, the network connection weight parameters and bias parameters of the adaptive cloud height error correction model are optimized. A real-time cloud base height error compensation algorithm is constructed. Based on the data obtained from the current measurement, the altitude interval category is determined by the altitude interval discrimination function. The nonlinear regression equation of the corresponding altitude interval is called to calculate the preliminary cloud base height prediction value. Then, the error compensation amount is calculated by the adaptive cloud height error correction model, and the final cloud base height measurement result is output.

[0005] Specifically, the step of constructing the hierarchical height interval step regression equation system involves dividing the cloud base height measurement range into a low cloud interval of 30 meters to 500 meters, a mid-low cloud interval of 500 meters to 2000 meters, a mid-high cloud interval of 2000 meters to 5000 meters, and a high cloud interval of 5000 meters to 7500 meters.

[0006] Specifically, the nonlinear regression equation for each altitude range is the logarithmic term of the ratio of laser beam emission power data to laser echo signal intensity data, plus the square root term of the product of atmospheric temperature data and atmospheric humidity data, minus the exponential decay term of atmospheric pressure data, plus the product term of the quadratic coefficient of laser beam emission power data and atmospheric temperature data, and finally the output term of the adaptive cloud height error correction model.

[0007] Specifically, the objective function of the upper-level optimization model is used to minimize the overall measurement error of the entire laser astronomy system. The inputs include the cloud base height measurement error sequence for each height interval, the coefficient vector of the nonlinear regression equation, the model structure complexity index, the L2 regularization penalty parameter, and the upper and lower layer coupling weight coefficients. The output is the optimal objective function value of the upper-level optimization model.

[0008] Specifically, the objective function of the lower-level optimization model is used to maximize the fitting accuracy of the nonlinear regression equations for each height interval to the historical training data. The inputs include the training dataset fitting residual vector, the determination coefficients of each regression equation, the k-fold cross-validation error, the degree of constraint violation, and the lower-upper-level coupling weight coefficients. The output is the optimal objective function value of the lower-level optimization model.

[0009] Before implementing the two-layer game model collaborative optimization algorithm, the process also includes a preprocessing procedure for historical cloud height measurement data. This involves detecting and removing outliers from the collected laser beam emission power data, laser echo signal intensity data, atmospheric temperature data, atmospheric humidity data, atmospheric pressure data, and standard cloud base height measurements. Anomalies are removed using a 3-times standard deviation criterion. The data after outlier removal is then normalized, and the dataset is divided into a 70% training set and a 30% validation set.

[0010] Specifically, the height interval discrimination function is used to automatically identify the height interval category to which the cloud base height belongs based on the current laser measurement parameters and atmospheric environment parameters. The inputs include laser beam emission power data, laser echo signal intensity data, atmospheric temperature data, and preliminary cloud base height estimation value. The output is the corresponding height interval category identifier.

[0011] The process includes designing a dynamic model parameter update mechanism after constructing the real-time cloud base height error compensation algorithm. This involves using a sliding time window method to continuously monitor the statistical indicators of cloud base height measurement errors. When the root mean square error of the continuous measurement error exceeds a preset error threshold, the model retraining process is automatically initiated, and the two-layer game model collaborative optimization algorithm is re-executed to update the parameters of the nonlinear regression equations for each height interval and the parameters of the adaptive cloud height error correction model.

[0012] Specifically, the adaptive cloud height error correction model adopts a sequence processing architecture based on a Transformer encoder. It includes an input feature embedding layer that maps five-dimensional parameters such as laser beam emission power, laser echo signal intensity, atmospheric temperature, humidity, and pressure to a unified feature space through linear transformation. The position encoding layer uses learned position embedding vectors to represent the importance weights of different parameters. The Transformer encoder captures the complex nonlinear relationships between the parameters through a self-attention mechanism.

[0013] The number of layers in the Transformer encoder is dynamically adjusted according to the rate of change of data environment parameters. When the change of environment parameters is small (the similarity between adjacent input environment parameters is greater than or equal to 90%), a 3-layer encoder is used to reduce computational overhead. When the change of environment parameters is large (the similarity between adjacent input environment parameters is less than 90%), the number of layers is increased to 6 to improve the representation capability. Finally, the high-dimensional features are mapped to cloud bottom height error compensation values ​​through a multi-head fully connected output layer, and residual connections and layer normalization mechanisms are introduced to improve the training stability and generalization performance of the model.

[0014] The construction of the training dataset for the adaptive cloud height error correction model specifically involves collecting laser cloud height measurement sample data under different weather conditions, covering six typical atmospheric conditions: clear sky, partly cloudy, cloudy, overcast, precipitation, and haze. For each weather condition, at least 15,000 valid measurement samples are collected. Laser beam emission power data, laser echo signal intensity data, atmospheric temperature data, atmospheric humidity data, and atmospheric pressure data are used as network input features, and the corresponding cloud base height measurement error is used as the network output label. The construction of the training dataset involves expanding the original training dataset to 90,000 training samples using data augmentation techniques and noise injection methods. The dataset is then divided into three subsets—training set, validation set, and test set—in chronological order. The training process of the adaptive cloud height error correction model specifically employs the AdamW optimization algorithm for network parameter gradient updates, setting the initial learning rate to 0.0001, the batch size to 128, and the total number of training iterations to 300. A cosine annealing learning rate decay strategy is used to dynamically adjust the learning rate. The model performance is evaluated on the validation set every 20 rounds. The training process is terminated early when the validation set loss function value does not decrease for 15 consecutive rounds. The network parameters with the best performance on the validation set are selected as the final adaptive cloud height error correction model parameters.

[0015] Furthermore, the adaptive cloud height error correction model specifically includes an image block adjustment function, which is used to dynamically optimize the feature extraction granularity of the adaptive cloud height error correction model based on real-time atmospheric environmental conditions and laser measurement parameters. The image block adjustment function calculates the block adjustment factor based on three key environmental parameters: laser echo signal intensity data, atmospheric humidity data, and atmospheric pressure data.

[0016] Specifically, the image block adjustment function uses a larger image block size when the block adjustment factor is in a low sensitivity range to reduce computational complexity and improve processing efficiency; uses a medium image block size when the block adjustment factor is in a medium sensitivity range to balance feature extraction accuracy and computational efficiency; and uses a smaller image block size when the block adjustment factor is in a high sensitivity range to obtain more refined feature representation and higher error correction accuracy, thereby dynamically adjusting the image block parameters of the adaptive cloud height error correction model.

[0017] Furthermore, it also includes a multi-parameter synchronous data acquisition system for laser astronomy, specifically an integrated sensor network platform. Its core function is to coordinate and control multiple sensor modules to achieve precise synchronous acquisition of laser measurement parameters and environmental parameters. Through a high-precision clock synchronization mechanism, it ensures that the laser beam emission power data and laser echo signal intensity data are strictly consistent with environmental parameters such as atmospheric temperature, humidity, and pressure in the time dimension. At the same time, it integrates a reference laser astronomy device to obtain a standard cloud base height measurement benchmark value. It adopts a distributed data acquisition architecture, and each sensor node communicates with the central processing unit through a CAN bus or Ethernet protocol.

[0018] This invention effectively solves the technical problem of significant system errors in traditional laser astronomy meters by constructing a hierarchical set of step regression equations for different altitude ranges and a two-level game optimization framework, combined with an adaptive cloud height error correction model. This invention establishes independent nonlinear regression equations for different altitude ranges, fully considering the differentiated influence of laser and atmospheric parameters at different altitudes. The two-level game optimization model achieves synergistic optimization of minimizing global error and maximizing local fitting accuracy, overcoming the shortcomings of traditional methods that cannot simultaneously consider overall performance and local accuracy. Furthermore, it introduces an adaptive error correction model based on the Transformer architecture, which can dynamically capture the complex nonlinear relationships between parameters and adjust the compensation strategy in real time. This invention also designs a dynamic model parameter update mechanism, using a sliding time window monitoring and automatic retraining process to ensure that the compensation model can continuously adapt to environmental changes, fundamentally solving the problem of system errors fluctuating with environmental conditions. In summary, this invention solves the technical problem mentioned in the background art where the measurement accuracy of laser astronomy meters is affected by changes in atmospheric environmental parameters and the equipment's own parameters, leading to significant system errors. Attached Figure Description

[0019] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0021] like Figure 1 The diagram shown is a flowchart of a laser cemetery system error compensation method based on regression analysis provided by the present invention. This method includes the following steps: S01. Establish a multi-parameter synchronous data acquisition system for laser cloud height meter, synchronously acquire laser beam emission power data, laser echo signal intensity data, atmospheric temperature data, atmospheric humidity data, and atmospheric pressure data, and synchronously obtain standard cloud base height measurement values ​​as the dependent variable benchmark data for regression analysis by referring to the laser cloud height meter. S02. Construct a set of stepped regression equations for different height intervals. Divide the cloud base height measurement range into low cloud intervals of 30 meters to 500 meters, mid-low cloud intervals of 500 meters to 2000 meters, mid-high cloud intervals of 2000 meters to 5000 meters, and high cloud intervals of 5000 meters to 7500 meters. Establish an independent nonlinear regression equation for each height interval. The nonlinear regression equation includes a linear term for laser parameters, a nonlinear term for atmospheric parameters, and an output term for the adaptive cloud height error correction model. S03. Establish a two-layer game optimization framework, construct an upper-layer optimization model with the objective function of minimizing the root mean square error of cloud base height measurement and a lower-layer optimization model with the objective function of maximizing the goodness of fit of the regression equation in each height interval. The objective function of the upper-layer optimization model includes a measurement error sum of squares term, a regression coefficient regularization penalty term, a model complexity control term, and upper-lower layer coupling constraint term. The objective function of the lower-layer optimization model includes a fitting residual sum of squares term, a determination coefficient maximization term, a cross-validation error minimization term, and an upper-lower layer coupling constraint term. S04. Perform the historical cloud height measurement data preprocessing process, and perform outlier detection and removal on the collected laser beam emission power data, laser echo signal intensity data, atmospheric temperature data, atmospheric humidity data, atmospheric pressure data and standard cloud base height measurement values. Use the 3-times standard deviation criterion to remove outlier measurement data, normalize the data after removing outliers, and divide the dataset according to the ratio of 70% training set and 30% validation set. S05. Implement a two-layer game model collaborative optimization algorithm. Through the iterative solution process of the upper-layer optimization model and the lower-layer optimization model, determine the linear coefficients of the laser parameters and the nonlinear coefficients of the atmospheric parameters of the nonlinear regression equation for each altitude range. At the same time, optimize the network connection weight parameters and bias parameters of the adaptive cloud height error correction model. S06. Construct a real-time cloud base height error compensation algorithm. Based on the laser beam emission power data, laser echo signal intensity data, atmospheric temperature data, atmospheric humidity data, and atmospheric pressure data obtained from the current measurement, determine the category of the height interval through the height interval discrimination function, call the nonlinear regression equation of the corresponding height interval to calculate the preliminary cloud base height prediction value, and then calculate the error compensation amount through the adaptive cloud height error correction model to output the final cloud base height measurement result. S07. Design a dynamic model parameter update mechanism. Use the sliding time window method to continuously monitor the statistical indicators of cloud base height measurement error. When the root mean square error of the continuous measurement error exceeds the preset error threshold, automatically start the model retraining process, re-execute the two-layer game model collaborative optimization algorithm, and update the parameters of the nonlinear regression equation for each height interval and the parameters of the adaptive cloud height error correction model.

[0022] The mathematical form of the nonlinear regression equation for each altitude range is the logarithmic term of the ratio of laser beam emission power data to laser echo signal intensity data, plus the square root term of the product of atmospheric temperature data and atmospheric humidity data, minus the exponential decay term of atmospheric pressure data, plus the product term of the quadratic coefficient of laser beam emission power data and atmospheric temperature data, and finally the output term of the adaptive cloud height error correction model.

[0023] The objective function of the upper-level optimization model is used to minimize the overall measurement error of the entire laser astronomy system. The inputs include the cloud base height measurement error sequence for each height interval, the coefficient vector of the nonlinear regression equation, the model structure complexity index, the L2 regularization penalty parameter, and the upper and lower layer coupling weight coefficients. The output is the optimal objective function value of the upper-level optimization model.

[0024] The objective function of the lower-level optimization model is used to maximize the fitting accuracy of the nonlinear regression equations for each height interval to the historical training data. The inputs include the training dataset fitting residual vector, the determination coefficients of each regression equation, the k-fold cross-validation error, the degree of constraint violation, and the lower-upper-level coupling weight coefficients. The output is the optimal objective function value of the lower-level optimization model.

[0025] The height interval discrimination function is used to automatically identify the height interval category to which the cloud base height belongs based on the current laser measurement parameters and atmospheric environment parameters. The inputs include laser beam emission power data, laser echo signal intensity data, atmospheric temperature data, and preliminary cloud base height estimate. The output is the corresponding height interval category identifier.

[0026] The adaptive cloud height error correction model adopts a sequence processing architecture based on a Transformer encoder to replace the original visual processing mode. This network structure includes an input feature embedding layer that maps five-dimensional parameters—laser beam emission power, laser echo signal intensity, atmospheric temperature, humidity, and pressure—to a unified feature space through linear transformation. A position encoding layer uses learnable position embedding vectors to represent the importance weights of different parameters. The number of Transformer encoder layers is dynamically adjusted according to the rate of change of the data environment parameters. When the environmental parameters change little (the similarity between adjacent input environmental parameters is greater than or equal to 90%), a 3-layer encoder is used to reduce computational overhead. When the environmental parameters change significantly (the similarity between adjacent input environmental parameters is less than 90%), the number of layers is increased to 6 to improve representation capabilities. Finally, a multi-head fully connected output layer maps high-dimensional features to cloud bottom height error compensation values, and residual connections and layer normalization mechanisms are introduced to improve the model's training stability and generalization performance.

[0027] The construction of the training dataset for the adaptive cloud height error correction model includes collecting laser cloud height measurement sample data under different weather conditions, covering six typical atmospheric conditions: clear sky, partly cloudy, cloudy, overcast, precipitation, and haze. For each weather condition, no less than 15,000 sets of valid measurement samples are collected. Laser beam emission power data, laser echo signal intensity data, atmospheric temperature data, atmospheric humidity data, and atmospheric pressure data are used as network input features, and the corresponding cloud base height measurement error is used as the network output label. The original training dataset is expanded to 90,000 sets of training samples through data augmentation technology and noise injection method. The dataset is divided into three subsets: training set, validation set, and test set according to the time series order.

[0028] The training process of the adaptive cloud height error correction model includes using the AdamW optimization algorithm for network parameter gradient updates, setting the initial learning rate to 0.0001, the batch size to 128, and the total number of training iterations to 300. A cosine annealing learning rate decay strategy is used to dynamically adjust the learning rate. The model performance index is evaluated on the validation set every 20 rounds. The training process is terminated early when the validation set loss function value does not decrease for 15 consecutive rounds. The network parameters with the best performance on the validation set are selected as the final adaptive cloud height error correction model parameters.

[0029] The image block adjustment function is used to dynamically optimize the feature extraction granularity of the adaptive cloud height error correction model based on real-time atmospheric environmental conditions and laser measurement parameters. The image block adjustment function calculates the block adjustment factor based on three key environmental parameters: laser echo signal intensity data, atmospheric humidity data, and atmospheric pressure data. When the block adjustment factor is in a low sensitivity range, a larger image block size is used to reduce computational complexity and improve processing efficiency. When the block adjustment factor is in a medium sensitivity range, a medium image block size is used to balance feature extraction accuracy and computational efficiency. When the block adjustment factor is in a high sensitivity range, a smaller image block size is used to obtain more refined feature representation and higher error correction accuracy, thereby dynamically adjusting the image block parameters of the adaptive cloud height error correction model.

[0030] The laser cenote multi-parameter synchronous data acquisition system is an integrated sensor network platform. Its core function is to coordinate and control multiple sensor modules to achieve precise synchronous acquisition of laser measurement parameters and environmental parameters. The system uses a high-precision clock synchronization mechanism to ensure that laser beam emission power data and laser echo signal intensity data remain strictly consistent with environmental parameters such as atmospheric temperature, humidity, and pressure in the time dimension. It also integrates a reference laser cenote device to obtain standard cloud base height measurement benchmark values. The system adopts a distributed data acquisition architecture, with each sensor node communicating with the central processing unit via CAN bus or Ethernet protocol to ensure real-time and reliable data transmission. It also includes modules for data preprocessing, storage management, and quality control, providing high-quality, multi-dimensional input data for subsequent regression analysis and error compensation algorithms.

[0031] The specific implementation methods of the above steps are described in detail below.

[0032] The specific implementation of step S01 involves first building a hardware synchronization control platform, using a high-precision GPS clock chip as the main timing generator to ensure that the data acquisition timestamp error of each sensor module is controlled within 1 millisecond. The laser emission power sensor monitors the laser output power in real time through a photodiode array, with a sampling frequency set to 1 kHz and a measurement accuracy of 0.1 watts. The laser echo signal intensity detection module uses avalanche photodiode technology, combined with a low-noise preamplifier circuit, to achieve high-sensitivity detection of weak echo signals. The atmospheric temperature sensor uses a platinum resistance thermometer, with a measurement range covering -40℃ to 60℃ and an accuracy of 0.1℃. The atmospheric humidity sensor is based on the capacitive humidity detection principle, with a relative humidity measurement range of 0% to 100% and an accuracy of 2%. The atmospheric pressure sensor uses silicon piezoresistive pressure detection technology, with a measurement range of 80 kPa to 110 kPa and an accuracy of 0.1 kPa. All sensors are connected to the data acquisition controller via a controller area network bus to achieve distributed real-time data transmission. The reference laser ceilometer provides a baseline cloud base height measurement via a standard serial communication interface, with a data update frequency of 10 times per second.

[0033] The specific implementation of step S02 involves dividing the measurement range into four altitude intervals based on cloud height distribution characteristics and atmospheric physical properties. The low cloud interval is set at 30 to 500 meters, primarily targeting the measurement needs of stratus and hazy clouds. The mid-low cloud interval is set at 500 to 2000 meters, covering typical cloud types such as stratocumulus and nimbostratus. The mid-high cloud interval is set at 2000 to 5000 meters, corresponding to mid-altitude clouds such as altocumulus and altostratus. The high cloud interval is set at 5000 to 7500 meters, mainly handling high-altitude clouds such as cirrus and cirrocumulus. An independent nonlinear regression equation is established for each altitude interval. The equation structure includes a natural logarithm term representing the ratio of laser beam emission power to echo signal intensity, reflecting the attenuation law of the laser in the atmosphere. The square root term of the product of atmospheric temperature and humidity reflects the influence of water vapor condensation on optical propagation. The exponential decay term of atmospheric pressure describes the influence of altitude changes on atmospheric density. The product of the second-order term of laser emission power and atmospheric temperature characterizes the nonlinear effect of temperature on the laser's operating state. The output term of the adaptive error correction model is used to compensate for systematic errors under complex environmental conditions.

[0034] The specific implementation of step S03 involves constructing a hierarchical optimization solution architecture. The upper-level optimization model aims to minimize the overall measurement error. The objective function includes a quadratic summation of the cloud base height measurement error, reflecting the overall accuracy level of the system. An L2 regularization penalty term for the regression coefficients prevents overfitting, with the regularization coefficient set to 0.01. A model complexity control term evaluates the rationality of the model structure using the Akaike Information Criterion. Upper-lower coupling constraints ensure the consistency between the two optimization problems, with a coupling weight coefficient set to 0.5. The lower-level optimization model focuses on improving the fitting accuracy of the regression equations for each height interval. The sum of squared residuals measures how closely the regression equations approximate the training data. The coefficient of determination maximization term requires that the explanatory power of each regression equation reach at least 0.85. The k-fold cross-validation error minimization term uses a 5-fold cross-validation strategy to evaluate the model's generalization performance. The upper-lower coupling constraints maintain parameter consistency with the upper-level model. The two-layer game structure achieves the coordination and unification of the upper-lower optimization objectives through Nash equilibrium theory.

[0035] The specific implementation of step S04 involves establishing a complete data quality control process. First, outlier identification and removal are performed on the raw measurement data. The laser power data is detected using a 3-standard-deviation criterion; any measurement value exceeding the range of the average plus or minus 3 standard deviations is identified as an outlier and removed. For laser echo signal intensity data, the box plot interquartile range method is used to identify outliers; data points exceeding the first quartile minus 1.5 interquartile range or the third quartile plus 1.5 interquartile range are marked as outliers. Atmospheric parameter data is smoothed using a sliding window median filtering method, with the window length set to 5 sampling points. After outlier removal, the remaining data is normalized. For laser parameters, the maximum-minimum normalization method maps the values ​​to the 0-1 interval. For atmospheric parameters, the zero-mean unit variance normalization method ensures the comparability of parameters with different dimensions. The dataset is divided using a time-series split; the first 70% of the time-series data is used as the training set for model parameter learning, and the last 30% is used as the validation set to evaluate model performance, ensuring temporal continuity and avoiding data leakage.

[0036] The specific implementation of step S05 involves implementing an iterative solution algorithm for the two-layer game model, using a genetic algorithm to solve the upper-level optimization problem. The population size is set to 100 individuals, and the chromosome encoding uses real-number encoding to represent the regression coefficient vector. The selection operation employs a tournament selection strategy with a tournament size of 3. The crossover operation uses a simulated binary crossover method with a crossover probability of 0.8. The mutation operation uses a polynomial mutation strategy with a mutation probability of 0.1. The lower-level optimization problem is solved using a particle swarm optimization algorithm with a particle swarm size of 50 particles. The inertia weight uses a linear decreasing strategy, with an initial value of 0.9 and a final value of 0.4. Acceleration factor... and All values ​​are set to 2.0. The iterative solution process between upper and lower layers achieves parameter coordination through bidirectional information exchange. The optimization results of the upper layer serve as constraints for the optimization of the lower layer, and the optimization results of the lower layer are fed back to the upper layer model to adjust the search direction. The iteration termination condition is set to the improvement of the optimal solution for 20 consecutive generations being less than [a certain value]. It can reach a maximum of 500 iterations. The adaptive error correction model parameters are optimized synchronously through the backpropagation algorithm, and the learning rate is dynamically adjusted according to gradient changes using an adaptive adjustment strategy.

[0037] The specific implementation of step S06 involves establishing a real-time cloud base height compensation calculation process. First, the height interval category corresponding to the current measurement conditions is determined using a height interval discriminant function. This discriminant function is based on fuzzy logic inference, with input parameters including laser beam emission power, laser echo signal intensity, atmospheric temperature, and a preliminary height estimate. The fuzzification process converts continuous input variables into fuzzy set membership degrees, using triangular and trapezoidal membership functions to describe the fuzzy intervals of each parameter. The inference rule base contains 24 if-then rules describing the correspondence between different parameter combinations and height intervals. The defuzzification process uses the centroid method to calculate the final height interval category probability distribution. Based on the discriminant results, the corresponding nonlinear regression equation for the height interval is called to calculate the preliminary cloud base height prediction value. The equation solution uses the Newton-Raphson iterative method to ensure numerical stability. The adaptive error correction model calculates the error compensation amount through forward propagation. The currently measured five-dimensional environmental parameters are input into a Transformer encoder network, undergoing multiple nonlinear transformations to obtain a high-dimensional feature representation. Finally, this is mapped to the cloud base height error compensation value through a fully connected layer. The compensation value is added to the preliminary prediction value to obtain the final cloud base height measurement result.

[0038] The specific implementation of step S07 involves establishing a dynamic model update monitoring mechanism, employing a sliding time window method to continuously monitor measurement error statistics. The time window length is set to 1 hour, and the root mean square error, mean absolute error, and maximum absolute error of the measurement error within the window are calculated every 10 minutes. When the root mean square error exceeds a preset threshold of 20 meters for three consecutive calculation cycles, the system automatically triggers the model retraining process. The retraining process first collects measurement data from the most recent 72 hours as new training samples, mixing them with historical training data at a 3:7 ratio to form an updated training set. Model retraining uses an incremental learning strategy, fine-tuning the original parameters rather than completely retraining to maintain the model's historical knowledge and accelerate convergence. Parameter updates use an exponential moving average method, with the fusion weight of new and old parameters set to 0.2:0.8 to ensure model stability. After retraining, the performance metrics of the updated model are evaluated using an independent validation set. When the performance improvement exceeds 5%, the new model parameters are officially deployed; otherwise, the original model continues to run. The model update history is stored in a database for easy tracking and analysis of model evolution trends.

[0039] The adaptive cloud height error correction model employs a deep learning architecture based on a Transformer encoder, possessing powerful sequence modeling and feature learning capabilities. The network structure first includes an input feature embedding layer, which maps five input parameters—laser beam emission power, laser echo signal intensity, atmospheric temperature, atmospheric humidity, and atmospheric pressure—to a unified 128-dimensional feature space through linear transformation. Each input parameter corresponds to a learnable embedding matrix with dimensions 1×128, and a fully connected layer achieves the linear mapping from parameter vectors to high-dimensional feature vectors. The position encoding layer uses learnable position embedding vectors to assign a 128-dimensional position code to each input parameter, representing the importance weights of different parameters in the error correction process. The position codes and feature embeddings are added to form the final input representation, which is then fed into the subsequent Transformer encoder module.

[0040] The Transformer encoder module is the core computational unit of the network, consisting of a stacked structure of multiple encoder layers. Each encoder layer comprises two sub-modules: a multi-head self-attention mechanism and a feedforward neural network. The multi-head self-attention mechanism uses eight attention heads, each with a query and key-value vector dimension of 16. The attention weight distribution is obtained by calculating the dot product of the query vector and the key vector. After softmax normalization, the weight distribution is multiplied by the value vector to obtain a weighted feature representation. The outputs of the multi-head attention are merged into a 128-dimensional feature vector through concatenation operations. The feedforward neural network contains two fully connected layers. The first layer expands the 128-dimensional input to 512 dimensions and uses the ReLU activation function. The second layer compresses the 512-dimensional features back to 128 dimensions. Residual connections and layer normalization operations are added after each sub-module. Residual connections alleviate the gradient vanishing problem through skip connections, and layer normalization accelerates training convergence by standardizing the feature distribution. The number of encoder layers is dynamically adjusted according to the complexity of environmental conditions. When the atmospheric parameters change by less than 10%, a 3-layer encoder is used to reduce computational complexity. When environmental conditions change drastically, the number of encoder layers is increased to 6 to improve the model's representational ability.

[0041] The output layer employs a multi-head fully connected structure to map high-dimensional features to cloud base height error compensation values. The first fully connected layer maps the 128-dimensional encoder output to 64-dimensional intermediate features, using Dropout regularization to prevent overfitting, with the Dropout probability set to 0.1. The second fully connected layer maps the 64-dimensional features to 32 dimensions, also using Dropout regularization. The final output layer is a single neuron, using a linear activation function to output the cloud base height error compensation value. The compensation value ranges from -100 meters to 100 meters, covering most error correction needs.

[0042] The training dataset creation process includes comprehensive data acquisition and preprocessing. During the data acquisition phase, long-term continuous observations were conducted under different geographical locations and climatic conditions, covering six typical weather types: clear sky, partly cloudy, cloudy, overcast, precipitation, and haze. 15,000 samples were collected under clear sky conditions, characterized by visibility greater than 20 km and cloud cover less than 10%. 15,000 samples were collected under partly cloudy conditions, with cloud cover between 10% and 30% and a uniform cloud base height distribution. 15,000 samples were collected under cloudy conditions, with cloud cover between 30% and 70% and the presence of multi-layered cloud structures. 15,000 samples were collected under overcast conditions, with cloud cover greater than 70% and a relatively stable cloud base height. 15,000 samples were collected under precipitation conditions, including measurements under both rainfall and snowfall conditions. 15,000 samples were collected under haze conditions, with atmospheric visibility less than 5 km and the presence of aerosol particles.

[0043] Data augmentation techniques expand the number of training samples through various methods. Time-series data augmentation employs a sliding window sampling strategy, dividing continuous measurement data into new training samples according to different time steps. Noise injection adds Gaussian white noise to the original data, with the noise intensity set to 5% of the signal standard deviation to simulate random errors in actual measurements. Parameter perturbation applies small random perturbations to laser power and atmospheric parameters, with the perturbation amplitude controlled within 2% of the original values, enhancing the model's robustness to parameter fluctuations. Interpolation generation uses cubic spline interpolation to generate new data points among existing samples, maintaining the continuity and smoothness of the data distribution. After data augmentation, the original 90,000 training samples are expanded to 270,000, providing ample learning samples for model training.

[0044] The dataset was partitioned using a stratified sampling strategy to ensure a consistent proportion of samples for various weather conditions across the training, validation, and test sets. The training set comprised 60% of the total samples for model parameter learning, the validation set 20% for hyperparameter tuning and early stopping strategies, and the test set 20% for final performance evaluation. Sample labeling involved comparing the cloud base height error between laser ceilometer measurements and standard values ​​from a reference device. This error value was smoothed and filtered to eliminate high-frequency noise, serving as a supervisory signal for model training. Data preprocessing also included outlier detection and missing value imputation to ensure the quality and completeness of the training data.

[0045] Analysis of key technical ideas reveals four core innovations of this invention. First, the layered altitude interval stepped regression equation technique establishes a regression model based on the differences in the physical characteristics of clouds at different altitudes. Compared to traditional single regression equations, this significantly improves the model's adaptability to complex atmospheric environments. Segmented modeling effectively captures the nonlinear characteristics of laser-atmosphere interactions at different altitudes, avoiding the loss of fitting accuracy and insufficient generalization ability caused by global modeling. Second, the two-layer game theory optimization framework achieves a balance between minimizing global error and maximizing local fitting accuracy through collaborative optimization between upper and lower layers. Compared to traditional single-objective optimization methods, it better balances the relationship between model complexity and prediction accuracy. The game theory mechanism ensures the consistency of regression equations across different altitude intervals, avoiding the problem of local optimization falling into suboptimal solutions. Third, the adaptive error correction model technique based on a Transformer encoder utilizes a self-attention mechanism to deeply mine the nonlinear correlations between multidimensional environmental parameters. Compared to traditional neural networks, it has stronger feature learning and pattern recognition capabilities, automatically discovering the complex mapping patterns between laser measurement errors and environmental factors, achieving intelligent and adaptive error compensation. The dynamic model parameter update mechanism technology, by monitoring system performance indicators in real time and automatically triggering the retraining process, has stronger environmental adaptability and long-term stability compared to static models, effectively solving the problem of model performance degradation caused by changes in the atmospheric environment.

[0046] The synergistic effect of four key technological approaches forms a complete intelligent error compensation technology system. Hierarchical regression modeling provides basic predictive capabilities for different cloud environments; two-layer game optimization ensures the global coordination of each hierarchical model; the Transformer error correction network provides refined compensation capabilities; and the dynamic update mechanism guarantees long-term system performance stability. Compared to the single linear regression or simple neural network methods commonly used in existing technologies, the collaborative technology architecture of this invention achieves a leapfrog improvement from coarse approximation to accurate prediction, maintaining stable high-precision measurement performance even in complex and variable atmospheric environments. This provides a solid technical foundation for the widespread application of laser ceilometer systems in meteorological observation, aviation safety, environmental monitoring, and other fields.

[0047] It should be noted that this invention also solves the following technical problem: existing laser ceilometer systems lack a compensation mechanism for differences in cloud characteristics at different altitudes, leading to inconsistent measurement accuracy across different altitude ranges. Traditional laser ceilometers use a uniform measurement model and calibration parameters to process cloud base height measurements across the entire altitude range, neglecting the significant differences in atmospheric density, humidity distribution, temperature gradient, and cloud droplet size distribution at different altitudes, such as low clouds, low-middle clouds, mid-high clouds, and high clouds. These differences in physical characteristics directly affect the scattering characteristics and attenuation patterns of the laser beam, resulting in significant differences in the applicability of the same set of measurement parameters across different altitude ranges. This invention constructs a stepped regression equation system for different altitude ranges, establishing independent nonlinear regression equations for four different altitude ranges: 30m to 500m, 500m to 2000m, 2000m to 5000m, and 5000m to 7500m. Each equation fully considers the unique physical laws of laser propagation and cloud scattering within the corresponding altitude range. By using a two-layer game optimization framework, the regression coefficients of each range are optimized, enabling measurement compensation to accurately adapt to the differences in cloud characteristics at different altitude ranges. This solves the problem of inconsistent measurement accuracy in traditional methods at different altitude ranges.

[0048] Existing laser astronomy systems suffer from limited error compensation effectiveness due to the lack of multi-parameter collaborative modeling in complex atmospheric environments. Traditional compensation methods typically consider only a single or a few influencing factors, such as temperature correction or simple humidity compensation. These methods fail to comprehensively characterize the complex coupling relationships and nonlinear interactions between multidimensional parameters such as laser power, echo intensity, temperature, humidity, and pressure. This is especially true under extreme weather conditions such as haze, precipitation, and rapid changes in temperature and humidity, where the interactions between parameters become even more complex, making it difficult for traditional linear or simple nonlinear models to accurately model these multidimensional nonlinear relationships. This invention designs an adaptive cloud height error correction model based on a Transformer encoder architecture. It utilizes a self-attention mechanism to simultaneously process five-dimensional parameters, including laser beam emission power, laser echo signal intensity, atmospheric temperature, humidity, and pressure. This model can automatically learn and model the complex nonlinear coupling relationships between these parameters. Through a multi-layer encoder structure, it gradually extracts deep feature representations and dynamically adjusts the network depth according to environmental complexity. In simple environments, a 3-layer encoder is used to improve computational efficiency, while in complex environments, it is extended to a 6-layer encoder to enhance representation capabilities. At the same time, residual connections and layer normalization mechanisms are combined to improve model stability and generalization performance, thereby achieving high-precision error compensation under multi-parameter collaborative modeling.

[0049] Specifically, the principle of this invention is as follows: The core principle that enables this invention to solve the significant error problem of laser cloud height measurement systems lies in establishing a multi-dimensional parameter coupling hierarchical error compensation mechanism and an intelligent dynamic optimization framework. First, this invention constructs a hierarchical set of step regression equations for different cloud base height ranges, addressing the differences in physical characteristics across these ranges. Each height range independently establishes a regression equation containing linear terms for laser parameters and nonlinear terms for atmospheric parameters. This hierarchical modeling strategy can accurately characterize the differentiated performance of laser propagation characteristics and atmospheric scattering patterns within different height ranges, avoiding the problem of insufficient fitting accuracy of traditional single models across the entire height range. Second, the design of the two-layer game-theoretic optimization framework is based on multi-objective optimization theory. The upper-layer model aims to minimize the global measurement error, while the lower-layer model aims to maximize the local fitting accuracy. The two models achieve collaborative optimization through coupling constraint terms. This game-theoretic mechanism can optimize the local accuracy of each sub-range while ensuring overall system performance, resolving the contradiction that traditional optimization methods struggle to balance global and local optima. Furthermore, the adaptive cloud height error correction model based on the Transformer architecture captures the complex nonlinear relationships between multidimensional parameters such as laser power, echo intensity, temperature, humidity, and pressure through a self-attention mechanism. Compared to traditional linear or simple nonlinear models, it can more accurately model the coupling effects and interactions between parameters, thereby achieving more precise error prediction and compensation. Finally, the dynamic model parameter update mechanism is based on statistical process control theory. It monitors the statistical characteristics of errors in real time through a sliding time window. When the error exceeds a preset threshold, it automatically triggers a retraining process. This adaptive mechanism ensures that the compensation model can continuously track environmental changes and maintain optimal compensation performance, thus completely solving the problem of system errors accumulating with changes in time and environmental conditions.

[0050] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0051] In this embodiment, the specific implementation of step S01 is the same as described above, and will not be repeated in detail here.

[0052] The specific implementation of step S02 is to establish nonlinear regression equations for each altitude interval, as shown below: ; In the formula, For the first Predicted cloud base height for each altitude range, in meters; This data represents the laser beam emission power, expressed in watts. This is data on laser echo signal intensity, in watts per square meter. These are atmospheric temperature data, in Kelvin. This is atmospheric humidity data, expressed as a percentage. This is atmospheric pressure data, in Pascals; The standard atmospheric pressure is taken as 101325 Pascals; For the first Regression coefficients for each height interval; This is the output term of the adaptive cloud height error correction model, in meters; This represents a random error term, measured in meters. The height interval is divided into... Corresponding to 30 meters to 500 meters, Corresponding to 500 meters to 2000 meters, Corresponding to 2000 meters to 5000 meters, Corresponding to 5000 meters to 7500 meters.

[0053] The parameter acquisition method is as follows: The laser output power is acquired in real time by using a photodiode array with a sampling frequency of 1 kHz. The avalanche photodiode technology is used in conjunction with a low-noise preamplifier circuit. The temperature was measured using a platinum resistance thermometer with an accuracy of 0.1 Kelvin. The humidity is obtained using the capacitive humidity detection principle, with an accuracy of 2%. The pressure is obtained using silicon piezoresistive pressure detection technology with an accuracy of 0.1 kPa. Obtained through calculation using an adaptive cloud height error correction model; The range is from -5 meters to 5 meters.

[0054] The specific implementation of step S03 is to construct the objective function of the two-layer game optimization framework. The objective function of the upper-layer optimization model is specifically expressed as follows: ; In the formula, The objective function value of the upper-level optimization model; This represents the total number of measurement samples; For the first The cloud base height measured in this measurement is in meters. For the first The standard cloud base height reference value for this measurement is in meters; This is the L2 regularization penalty parameter, with a value of 0.01; This is a parameter for controlling model complexity, with a value of 0.05. This is the coupling weight coefficient between the upper and lower layers, with a value of 0.5. This is the value of the Akaike Information Criterion; The upper and lower layer coupling constraint terms are calculated using the following formula: ,in and The upper and lower layer models are respectively in the first and second layers. The local objective function values ​​for each height interval.

[0055] The objective function of the lower-level optimization model is specifically expressed as follows: ; In the formula, To optimize the objective function value of the lower-level model; For the first The number of training samples in each height range; For the first The height range The predicted value for each sample, in meters; For the first The height range The observations for each sample are in meters. The weight parameters for the lower layer are optimized with values ​​of 1.0, 0.8, 0.3, and 0.5 respectively. For the first The determining factor for each height range; For the first Cross-validation error for each height interval; The formula for calculating the degree of constraint violation is as follows: ,in The minimum threshold for the coefficient of determination is set to 0.85.

[0056] The parameter acquisition method is as follows: and Acquired through synchronous measurement using a laser astronomy caliper and a reference device; Using formula Calculation and acquisition, where The number of model parameters. The value is the likelihood function value. Using formula Calculation and acquisition, where For the first Sum of squared residuals for each interval For the first The sum of squares of each interval; Obtained through 5-fold cross-validation; and The objective functions of the upper and lower layers are respectively at the th... The components of each height range; This is the lower limit of the determination coefficient constraint.

[0057] The specific implementation of step S04 is the same as described above, and will not be repeated in detail here.

[0058] The specific implementation of step S05 is to implement a two-layer game model collaborative optimization algorithm. The upper-layer optimization adopts a genetic algorithm, and the individual fitness function is specifically expressed as follows: ; In the formula, This represents the individual fitness value. This represents the objective function value of the upper layer. The lower layer optimization uses the particle swarm optimization algorithm, and the particle position update formula is expressed as follows: ; ; In the formula, For the first The particle velocity vector of the next iteration; For the first The particle velocity vector of the next iteration; As an inertial weight, a linear decreasing strategy is adopted to decrease it from 0.9 to 0.4; The acceleration factor is 2.0. A random number between 0 and 1; This is the optimal position vector in the particle's history. The global optimal position vector; For the first The particle position vector of the next iteration; For the first The particle position vector of the next iteration.

[0059] The parameter acquisition method is as follows: and Obtained by comparing historical fitness values; The numbers are obtained using a pseudo-random number generator; the iteration termination condition is that the improvement of the optimal solution for 20 consecutive generations is less than [a certain value]. Or it can reach the maximum number of iterations, 500 generations.

[0060] The specific implementation of step S06 is to construct a height interval discrimination function, which is specifically expressed as follows: ; in, ; In the formula, The height range category identifier for determination; For the first Membership function for each height interval; This is a preliminary estimate of the cloud base height, in meters. For the first The interval is the first The weighting coefficients of each parameter; For the first Input parameters In the Membership function values ​​for each interval; The final formula for calculating the cloud base height measurement result is as follows: ; In the formula, The final cloud base height measurement result is in meters; The results of the regression equation calculation for the corresponding height range; This is the output value of the adaptive error correction model for the corresponding height range.

[0061] The parameter acquisition method is as follows: Based on the basic principles of laser ranging Calculation and acquisition, where At the speed of light, This refers to the round-trip time of the laser. Determined through expert experience and historical data analysis; The calculation is performed using triangular and trapezoidal membership functions.

[0062] The specific implementation of step S07 is to establish a dynamic model parameter update monitoring mechanism. The formula for calculating the root mean square error of the sliding window is as follows: ; In the formula, The root mean square error of the sliding window is expressed in meters. This is the length of the time window, with a value of 360 sampling points corresponding to 1 hour; This refers to the current time point; For the first The final measurement result of the time; For the first The standard baseline value at time 1. The specific formula for updating the model parameters is as follows: ; In the formula, This is the updated model parameter vector; This is the original model parameter vector; The model parameter vector obtained through retraining; The parameter is the fusion weight, with a value of 0.2.

[0063] The parameter acquisition method is as follows: Real-time data is obtained by referencing a laser astrometry device; when Retraining is triggered when the distance exceeds the threshold of 20 meters for three consecutive calculation cycles. This is obtained by re-executing the two-level game optimization algorithm.

[0064] The objective function of the upper-level optimization model is specifically expressed as follows: ; The meanings of the parameters are the same as those defined in step S03. The objective function optimizes system performance by minimizing the overall measurement error, the regularization term prevents overfitting, the complexity control term maintains model simplicity, and the coupling constraint term ensures consistency between upper and lower layers.

[0065] The objective function of the lower-level optimization model is specifically expressed as follows: ; The meanings of the parameters are the same as those defined in step S03. The objective function optimizes the local modeling effect by maximizing the fitting accuracy of each height interval, the determination coefficient term ensures interpretability, the cross-validation term improves generalization performance, and the constraint term maintains the feasibility of the solution.

[0066] The height interval discrimination function is specifically expressed as follows: ; The meanings of each parameter are the same as those defined in step S06. This discriminant function automatically identifies the interval to which the cloud base height belongs through fuzzy logic reasoning, avoiding the instability at the boundaries of traditional hard classification methods and improving the accuracy and robustness of interval division.

[0067] The adaptive cloud altitude error correction model employs a Transformer encoder architecture to map multi-dimensional environmental parameters into error compensation values. It leverages a self-attention mechanism to uncover nonlinear correlations between parameters, achieving intelligent error correction. The model outputs... It is directly used as a compensation term in the regression equation to dynamically adjust the prediction results to adapt to complex environmental changes.

[0068] It should be noted that the nonlinear regression equations for each altitude range establish predictive models for different cloud physical characteristics using a piecewise modeling strategy, and for several terms... Lambert-Beer Law, which reflects atmospheric attenuation of laser light. ,in The intensity of light after attenuation. The initial light intensity, Atmospheric attenuation coefficient, The square root term represents the distance light travels. The exponential decay term reflects the nonlinear effect of water vapor condensation. Describes the distribution pattern of atmospheric pressure at altitude, quadratic product term The nonlinear modulation effect of temperature on laser performance is captured. Compared to traditional single linear models, this hierarchical regression equation significantly improves prediction accuracy and adaptability in complex atmospheric environments, avoiding the accumulation of fitting errors in global modeling. A two-layer game-theoretic optimization framework achieves a balance between minimizing global error and maximizing local accuracy through a collaborative mechanism between upper and lower layers. Game equilibrium ensures parameter coordination across different intervals, effectively avoiding local optimum traps and parameter conflicts compared to independent optimization methods. The altitude interval discriminant function, based on a fuzzy logic-based soft classification mechanism, overcomes the instability of traditional hard classification in boundary regions, improving the accuracy and continuity of interval identification through multi-parameter comprehensive judgment. A sliding window dynamic monitoring mechanism provides real-time performance evaluation. and adaptive parameter update It maintains the stability and accuracy of the model in long-term operation, and significantly improves the system's adaptability and robustness to environmental changes compared to static models.

[0069] To better understand and implement this invention, Example 2, a specific application scenario, is provided below: A technical team received a task to build a high-precision laser cloud height measurement system for a meteorological observation station. This station faces complex atmospheric environmental conditions, including large diurnal temperature variations, drastic humidity changes, and low air pressure. Traditional laser cloud height instruments exhibit significant measurement errors under these conditions. The technical team decided to use a laser cloud height instrument system error compensation method based on regression analysis to solve this technical challenge.

[0070] The technical team first established a multi-parameter synchronous data acquisition system for the laser ceilometer. The core of the system uses a 905-nanometer wavelength semiconductor laser, with laser emission power monitored in real time via a high-precision photodiode array and a sampling frequency set to 1 kHz. Laser echo signal intensity detection employs avalanche photodiode technology, coupled with a gain-adjustable low-noise preamplifier. Atmospheric environmental parameter monitoring includes atmospheric temperature measurement using a platinum resistance thermometer, relative humidity measurement using a capacitive sensor, and atmospheric pressure measurement using a silicon piezoresistive sensor. All sensors are connected to the data acquisition controller via a controller area network bus, achieving microsecond-level time synchronization. The reference laser ceilometer uses imported equipment to provide a standard cloud base height benchmark, with a data update frequency of 10 times per second.

[0071] During the 30-day continuous observation period, the technical team collected measurement data under different weather conditions. As shown in Table 1, the effective measurement samples cover six typical atmospheric conditions in the plateau region.

[0072] Table 1. Statistical table of measurement samples under different weather conditions

[0073] Based on cloud distribution characteristics, the technical team divided the measurement range into four altitude intervals and established hierarchical regression equations. The low cloud interval (30-500 meters) mainly corresponds to orographic clouds and radiation fog; the mid-low cloud interval (500-2000 meters) covers plateau stratocumulus clouds; the mid-high cloud interval (2000-5000 meters) corresponds to altocumulus clouds; and the high cloud interval (5000-7500 meters) includes cirrus cloud systems. Through a two-level game-theoretic optimization algorithm, the team determined the coefficients of the nonlinear regression equations for each altitude interval. As shown in Table 2, the regression coefficients for different altitude intervals reflect the differences in laser-atmosphere interaction at various altitude levels.

[0074] Table 2. Coefficients of Nonlinear Regression Equations for Each Height Range

[0075] The technical team constructed an adaptive cloud height error correction model based on a Transformer encoder. The network architecture includes a 128-dimensional feature embedding layer, an 8-head self-attention mechanism, and a 3-layer encoder structure. The training process employed the AdamW optimization algorithm, with an initial learning rate of 0.0001, a batch size of 128, and 300 training epochs. The model achieved its best performance on the validation set in epoch 187, at which point the root mean square error (RMSE) reached a minimum of 6.8 meters. The team implemented dynamic interval recognition using a height interval discriminant function, and the fuzzy logic reasoning rule base contained 24 if-then rules. The membership function adopted a hybrid form of triangles and trapezoids.

[0076] During the real-time measurement phase, the technical team conducted continuous performance testing on the system for seven days. The testing period encountered various complex weather conditions, including sandstorms, snowfall, and strong winds. As shown in Table 3, the system's measurement accuracy remained stable under different weather conditions.

[0077] Table 3 Real-time Measurement Performance Statistics

[0078] The technical team established a dynamic model parameter update mechanism and used a sliding time window method to monitor system performance. The window length was set to 1 hour, and the root mean square error (RMSE) was calculated every 10 minutes. When the RMS error exceeded a preset threshold of 20 m for three consecutive calculation cycles, the system automatically triggered a model retraining process. A total of four retraining sessions were triggered during the test, each lasting approximately 45 minutes. System performance was effectively restored after each retraining. Parameter updates employed an exponential moving average strategy, with the weighting of the new and old parameters set to 0.2:0.8 to ensure model stability.

[0079] The technical team compared and analyzed the performance differences between the traditional method and the method of this invention. As shown in Table 4, the present invention is significantly superior to the traditional method in terms of measurement accuracy, adaptability, and stability.

[0080] Table 4 Performance Comparison of Traditional Methods and the Method of This Invention

[0081] The technical team further analyzed the distribution characteristics of the error compensation effect. The adaptive error correction model showed varying compensation capabilities across different altitude ranges, with the best compensation effect in the low cloud range (average compensation of -3.2 meters), followed by the mid-to-low cloud range (average compensation of -4.7 meters), the mid-to-high cloud range (average compensation of -6.1 meters), and the high cloud range (average compensation of -8.5 meters). The increasing trend of compensation with altitude is consistent with the atmospheric physical characteristics of the plateau, reflecting the model's adaptive learning ability to environmental conditions.

[0082] In long-term operational tests across different seasons, the technical team found that the system performance remained stable. The average root mean square error (RMSE) was 8.9 meters during spring testing, 9.2 meters in summer, 10.1 meters in autumn, and 11.4 meters in winter. The seasonal differences mainly stemmed from variations in atmospheric stability in the plateau region throughout the year, but the system effectively adapted to these changes through a dynamic parameter update mechanism. The model retraining frequency was once a week in spring, twice a week in summer, three times a week in autumn, and four times a week in winter, demonstrating its adaptive adjustment capabilities.

[0083] It should be noted that the variables involved in this invention are explained in detail in Tables 5 and 6 below.

[0084] Table 5. Variable Explanation Table (Part 1)

[0085] Table 6. Variable Explanation Table (Part Two)

[0086] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for error compensation in a laser astronomy pylon meter system based on regression analysis, characterized in that, include: Data on laser beam emission power, laser echo signal intensity, atmospheric temperature, atmospheric humidity, and atmospheric pressure were collected. Standard cloud base height measurements were simultaneously acquired using a reference laser ceilometer as the dependent variable benchmark data for regression analysis. A hierarchical set of step regression equations was constructed, dividing the cloud base height measurement range into different height intervals. An independent nonlinear regression equation was established for each height interval, including linear terms for laser parameters, nonlinear terms for atmospheric parameters, and an output term from an adaptive cloud height error correction model. A two-layer game-theoretic optimization framework was established, constructing an upper-level optimization model with the objective function of minimizing the root mean square error of cloud base height measurement. A lower-level optimization model is constructed with the objective function of maximizing the goodness of fit of the regression equations for each altitude interval. A two-level game-theoretic collaborative optimization algorithm is implemented to determine the linear coefficients of the laser parameters and the nonlinear coefficients of the atmospheric parameters in the nonlinear regression equations for each altitude interval. At the same time, the network connection weight parameters and bias parameters of the adaptive cloud height error correction model are optimized. A real-time cloud base height error compensation algorithm is constructed. Based on the data obtained from the current measurement, the altitude interval category is determined by the altitude interval discrimination function. The nonlinear regression equation of the corresponding altitude interval is called to calculate the preliminary cloud base height prediction value. Then, the error compensation amount is calculated by the adaptive cloud height error correction model, and the final cloud base height measurement result is output.

2. The error compensation method for a laser astronomy gaiter system based on regression analysis according to claim 1, characterized in that, The step of constructing the hierarchical height interval step regression equation system specifically involves dividing the cloud base height measurement range into a low cloud interval of 30 meters to 500 meters, a mid-low cloud interval of 500 meters to 2000 meters, a mid-high cloud interval of 2000 meters to 5000 meters, and a high cloud interval of 5000 meters to 7500 meters.

3. The error compensation method for a laser astronomy gaiter system based on regression analysis according to claim 2, characterized in that, The nonlinear regression equations for each altitude range are specifically: the logarithmic term of the ratio of laser beam emission power data to laser echo signal intensity data, plus the square root term of the product of atmospheric temperature data and atmospheric humidity data, minus the exponential decay term of atmospheric pressure data, plus the product term of the quadratic coefficient of laser beam emission power data and atmospheric temperature data, and finally the output term of the adaptive cloud height error correction model.

4. The error compensation method for a laser astronomy gaiter system based on regression analysis according to claim 3, characterized in that, The objective function of the upper-level optimization model is specifically used to minimize the overall measurement error of the entire laser astronomy system. The inputs include the cloud base height measurement error sequence for each height interval, the coefficient vector of the nonlinear regression equation, the model structure complexity index, the L2 regularization penalty parameter, and the upper and lower layer coupling weight coefficients. The output is the optimal objective function value of the upper-level optimization model.

5. The error compensation method for a laser astronomy caliper system based on regression analysis according to claim 4, characterized in that, The objective function of the lower-level optimization model is specifically used to maximize the fitting accuracy of the nonlinear regression equations for each height interval to the historical training data. The inputs include the training dataset fitting residual vector, the determination coefficients of each regression equation, the k-fold cross-validation error, the degree of constraint violation, and the lower and upper layer coupling weight coefficients. The output is the optimal objective function value of the lower-level optimization model.

6. The error compensation method for a laser astronomy gaiter system based on regression analysis according to claim 5, characterized in that, Before implementing the two-layer game model collaborative optimization algorithm, the process also includes a preprocessing procedure for historical cloud height measurement data. This involves detecting and removing outliers from the collected laser beam emission power data, laser echo signal intensity data, atmospheric temperature data, atmospheric humidity data, atmospheric pressure data, and standard cloud base height measurements. Anomalies are removed using a 3-times standard deviation criterion. The data after outlier removal is then normalized, and the dataset is divided into a 70% training set and a 30% validation set.

7. The error compensation method for a laser astronomy gaiter system based on regression analysis according to claim 6, characterized in that, The height interval discrimination function is specifically used to automatically identify the height interval category to which the cloud base height belongs based on the current laser measurement parameters and atmospheric environment parameters. The inputs include laser beam emission power data, laser echo signal intensity data, atmospheric temperature data, and preliminary cloud base height estimation value. The output is the corresponding height interval category identifier.

8. The error compensation method for a laser astronomy gaiter system based on regression analysis according to claim 7, characterized in that, After constructing the real-time cloud base height error compensation algorithm, the algorithm also includes designing a dynamic model parameter update mechanism. The sliding time window method is used to continuously monitor the statistical indicators of cloud base height measurement error. When the root mean square error of the continuous measurement error exceeds the preset error threshold, the model retraining process is automatically started, the two-layer game model collaborative optimization algorithm is re-executed, and the parameters of the nonlinear regression equation and the adaptive cloud height error correction model parameters for each height interval are updated.

9. The error compensation method for a laser astronomy gaiter system based on regression analysis according to claim 8, characterized in that, The adaptive cloud height error correction model specifically adopts a sequence processing architecture based on a Transformer encoder. It includes an input feature embedding layer that maps the laser beam emission power, laser echo signal intensity, atmospheric temperature, humidity, and pressure to a unified feature space through linear transformation. The position encoding layer uses learned position embedding vectors to represent the importance weights of different parameters. The Transformer encoder captures the complex nonlinear relationships between the parameters through a self-attention mechanism.

10. The error compensation method for a laser astronomy gaiter system based on regression analysis according to claim 9, characterized in that, The number of layers in the Transformer encoder is dynamically adjusted according to the rate of change of data environment parameters. Finally, the high-dimensional features are mapped to cloud bottom height error compensation values ​​through a multi-head fully connected output layer. Residual connections and layer normalization mechanisms are introduced to improve the training stability and generalization performance of the model.

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