A Method for Attitude Correction of a Ceilometer Based on a Buoy

Abstract

The present invention relates to the technical field of monitoring and correction, and specifically relates to a method for correcting the attitude of a ceilometer based on a buoy. The method includes: Step 1: Collect the attitude data of the buoy multiple times, and for each collected attitude data of the buoy, construct a reference attitude quaternion; Step 2: Use the discrete Fourier transform to extract the wave main frequency component and the high-frequency residual component from the reference attitude quaternion sequence composed of all the reference attitude quaternions, and calculate the comprehensive attitude quaternion; Step 3: Based on the sea condition data obtained by real-time monitoring, use wave spectrum analysis to calculate the buoy wave perturbation variable; Step 4: Based on the buoy wave perturbation variable and the comprehensive attitude quaternion, perform attitude correction on the ceilometer measurement value. The present invention realizes the high-precision estimation of the buoy attitude under multi-band wave perturbations on the sea surface, and combines real-time sea condition analysis and ceilometer line-of-sight correction.

Description

Technical Field

[0001] The present invention belongs to the technical field of monitoring and correction, and particularly relates to a method for correcting the attitude of a ceilometer based on a buoy. Background Art

[0002] In recent years, with the continuous growth of the demand for ocean meteorological observations, various detection devices based on buoy platforms have become increasingly popular in practical applications. Among them, the ceilometer used to measure the cloud base height has important value in the fields of ocean meteorology, maritime traffic, and environmental monitoring. However, the buoy is affected by various factors such as waves, wind waves, and tides in the marine environment, and its motion state is extremely complex. If the attitude of the buoy cannot be effectively measured and compensated accurately, obvious measurement errors will occur during the actual observation of the ceilometer, resulting in fluctuations or even distortion of the measurement results with the large swing of the buoy. Therefore, how to improve the measurement accuracy of the ceilometer based on the buoy platform in a wave environment has always been an important technical problem in the field of ocean meteorological observations.

[0003] Currently, there have been some public technical attempts to correct the attitude of the offshore buoy platform to solve similar problems. For example, some researchers have integrated multiple sensors (such as accelerometers, gyroscopes, and magnetometers) on the buoy, estimated the real-time attitude of the buoy through a fusion algorithm, and then used this attitude information to correct the measurement direction of the mounted device. However, most of the existing attitude solution methods focus on fusing the data of accelerometers and gyroscopes, and the use of magnetometers is often limited to the correction of the heading angle, and only good results can be obtained in relatively calm sea conditions. Once the sea conditions become severe, or there are multi-directional mixed waves, the attitude estimation of the system often becomes unstable, resulting in the correction result deviating significantly from the real situation. In addition, for the wave disturbance received by the buoy, many existing technologies simply regard it as random noise or small fluctuations, and use means such as low-pass filtering or moving average to "smooth" the attitude data. However, actual ocean waves often contain both long-period main waves and several high-frequency swells or wind waves. In some cases, the influence of the high-frequency vibration component on the buoy attitude cannot be ignored. Simple filtering methods not only easily lose key information, but may also lag or distort in severely changing sea conditions, resulting in insufficient accuracy of attitude correction. Summary of the Invention

[0004] The main object of the present invention is to provide a method for correcting the attitude of a ceilometer based on a buoy, which realizes high-precision estimation of the buoy attitude under multi-band wave disturbances on the sea surface, and combines real-time sea condition analysis and ceilometer line-of-sight correction, so that the measurement results can effectively offset the attitude errors caused by the main waves and high-frequency jitters, and significantly improve the measurement accuracy and stability of the ceilometer in complex sea conditions.

[0005] The technical solution of the present invention is realized as follows:

[0006] A method for attitude correction of a ceilometer based on a buoy, the method comprising:

[0007] Step 1: Collect the attitude data of the buoy multiple times. For the attitude data of the buoy collected each time, construct a reference attitude quaternion;

[0008] Step 2: Use the discrete Fourier transform to extract the main wave frequency component and the high-frequency residual component from the reference attitude quaternion sequence composed of all the reference attitude quaternions, and then perform the inverse discrete Fourier transform to reconstruct the main wave attitude and the high-frequency attitude. Based on the main wave attitude, the high-frequency attitude and the reference attitude quaternion sequence, calculate the comprehensive attitude quaternion;

[0009] Step 3: Based on the sea condition data obtained by real-time monitoring, use wave spectrum analysis to calculate the buoy wave disturbance variable;

[0010] Step 4: Based on the buoy wave disturbance variable and the comprehensive attitude quaternion, perform attitude correction on the ceilometer measurement value.

[0011] Further, in Step 1, a three-axis accelerometer and a three-axis magnetometer are used to respectively obtain the measured acceleration of the buoy and the measured geomagnetic field ; based on the components of the measured acceleration on the X-axis, Y-axis and Z-axis respectively , and , calculate the pitch angle and the roll angle ; based on the components of the measured geomagnetic field on the X-axis, Y-axis and Z-axis respectively , and calculate the heading angle .

[0012] Further, define the reference attitude quaternion as , and each of its elements is defined by the following formula:

[0013] ;

[0014] ;

[0015] ;

[0016] .

[0017] Further, in Step 2, define the main wave frequency as ; the number of times of collecting the attitude data of the buoy is times, and a set of reference attitude quaternion sequences varying with time is obtained:

[0018] ;

[0019] is an integer index; each component in the reference attitude quaternion sequence is processed using discrete Fourier transform to obtain Corresponding results 、 Corresponding results 、 Corresponding results and Corresponding results ; is a frequency domain variable; defines the main frequency change threshold ;for , extract the wave main frequency components corresponding to each component in the reference attitude quaternion sequence respectively 、 、 and .

[0020] Furthermore, in step 2, the high-frequency residual component corresponding to each component in the reference attitude quaternion sequence is extracted using the following formula:

[0021] ;

[0022] ;

[0023] ;

[0024] ;

[0025] in, 、 and and They are 、 、 and The corresponding high-frequency residual component.

[0026] Furthermore, in step 2, the main wave posture for:

[0027] ;

[0028] in, 、 、 and They are 、 、 and The result of the inverse discrete Fourier transform; high-frequency posture sequence is:

[0029] ;

[0030] Among them, , , and are respectively , and and results of the inverse discrete Fourier transform of.

[0031] Furthermore, in step 2, the combined attitude quaternion is calculated through the following formula :

[0032] ;

[0033] Among them, represents the F norm; is quaternion multiplication.

[0034] Furthermore, in step 3, based on the sea state data obtained from real-time monitoring, the buoy wave perturbation variable is calculated using wave spectrum analysis :

[0035] ;

[0036] Among them, represents the significant wave height of the wave; represents the wave angular frequency; is the wave peak frequency; represents the wave direction angle; represents the main wave direction of the wave; is a preset kurtosis parameter; is the direction spread parameter, which is a set value; is the frequency weight parameter, which is a set value.

[0037] Furthermore, in step 4, attitude correction is performed based on the buoy wave perturbation variable and the combined attitude quaternion:

[0038] ;

[0039] Among them, is the empirical correction coefficient, which is a set value; is the ceilometer measurement value; is the ceilometer correction value; is the ideal line of sight of the ceilometer.

[0040] A method for attitude correction of a ceilometer based on a buoy according to the present invention has the following beneficial effects:

[0041] Through a multi-scale decomposition and fusion strategy, the present invention realizes high-precision correction of the buoy attitude in complex motions in the marine environment. As a result, the ceilometer can still obtain reliable measurement results on a dynamic platform, which has significant beneficial effects.

[0042] First of all, the present invention proposes an attitude representation method based on quaternions, which can avoid the gimbal lock problem faced by traditional Euler angle methods and is more concise and efficient in numerical calculations. By decomposing the buoy attitude into the main wave attitude and the high-frequency residual component respectively, the present invention finely extracts the large-period and short-period motion characteristics of the buoy in the frequency domain, enabling the system to respectively correct these two different frequency-level motions, and improving the compatibility ability for instantaneous disturbances and periodic swings. Compared with the existing solutions that only use a single filter or a simple time-domain method, the present invention can better capture the multi-dimensional attitude changes of the buoy in severe sea conditions and greatly reduce the attitude estimation error. During the discrete Fourier transform and inverse transform, the present invention adaptively extracts the energy within the main frequency range through bandwidth setting and threshold screening and regards the remaining frequencies as high-frequency residuals. It can not only accurately describe the dominant influence of the main period of the sea waves, but also independently separate the fast disturbance components such as wind waves, swells and buoy structure vibrations, so as to be considered separately during attitude reconstruction. This separated attitude reconstruction method enables the system to flexibly superimpose the main wave swings with low frequency and large amplitude and the short but high-frequency small disturbances during further fusion, avoiding both the blind smoothing of high-frequency components and the problem of insufficient fineness caused by relying only on large-period data.

[0043] On the other hand, the present invention also proposes a wave disturbance variable obtained by combining wave spectrum analysis, and uses multiple indicators such as significant wave height, peak frequency, wave direction and its spreading parameter to comprehensively describe the driving force characteristics that the buoy may face in real sea conditions. By introducing this disturbance variable into the attitude correction and measurement compensation links, the system can immediately sense and make dynamic adjustments when the wind waves or swells are significantly enhanced, avoiding the lag and error accumulation of traditional pure geometric attitude correction in severe sea conditions. This strategy based on comprehensive modeling in the frequency domain and direction domain enables the ceilometer to have stronger adaptability to multi-directional wave superposition, kurtosis change or extreme sea conditions. Description of the Drawings

[0044] Figure 1 It is a schematic flow chart of a method for attitude correction of a ceilometer based on a buoy provided by an embodiment of the present invention. Detailed Embodiments

[0045] In the following description, specific details such as specific system structures, interfaces, technologies, etc. are presented for the purpose of illustration rather than limitation, so as to thoroughly understand the embodiments of the present invention. However, those skilled in the art should clearly understand that the embodiments of the present invention can also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known devices, circuits, and methods are omitted to avoid unnecessary details from interfering with the description of the embodiments of the present invention.

[0046] Embodiment 1, refer to Figure 1 : A method for attitude correction of a ceilometer based on a buoy, the method comprising:

[0047] Step 1: Collect the attitude data of the buoy multiple times. For the attitude data of the buoy collected each time, construct a reference attitude quaternion;

[0048] The collection of attitude data usually relies on a high-precision inertial measurement unit (IMU). The IMU includes sensors such as accelerometers, gyroscopes, and magnetometers. These sensors work together to be able to sense the motion state of the buoy in three-dimensional space in real time. During the data collection process, the system will perform multiple samplings at a certain time interval. Each time a sample is taken, the IMU records the angular velocity, linear acceleration, and geomagnetic information of the buoy. After processing these data, they can be used to calculate the attitude of the buoy at a specific moment. Since there are many ways to represent attitudes, such as Euler angles, direction cosine matrices, and quaternions, etc., and the present invention adopts the quaternion form because the quaternion has no gimbal lock problem compared with Euler angles, and has a smaller computational amount and is more suitable for real-time attitude tracking compared with the direction cosine matrix. After obtaining the instantaneous attitude data of the buoy, it is necessary to convert it into a quaternion representation to form a reference attitude quaternion. A quaternion is a hypercomplex number composed of a real part and three imaginary parts, and can describe the three-dimensional rotation state in a compact form. The calculation of quaternions involves the rotation axis and rotation angle. By numerically integrating the angular velocity measured by the IMU and combining the initial attitude, the quaternion representation of the buoy at different time points can be obtained. In the actual calculation process, in order to reduce the error accumulation effect, data filtering algorithms such as Kalman filtering or complementary filtering are usually combined to optimize the accuracy of attitude estimation.

[0049] The core purpose of constructing the reference attitude quaternion is to provide a reference for subsequent attitude decomposition and correction. Since the movement of the buoy has periodic characteristics, for example, when driven by waves, its attitude usually oscillates periodically around a certain equilibrium point. Therefore, the data sampled once often contains certain instantaneous perturbations. By collecting data multiple times and establishing a sequence of reference attitude quaternions, the law of the attitude evolution of the buoy can be effectively captured. This sequence not only contains the attitude information of the buoy at different time points but also provides a data basis for subsequent Fourier transform analysis, enabling the further extraction of the main wave frequency component and the high-frequency residual component to achieve more refined attitude correction. In addition, the construction of the reference attitude quaternion also needs to consider the dynamic changes in the ocean environment. For example, factors such as tides, storms, and ocean currents may cause long-term attitude drift of the buoy. Therefore, during the data collection process, an appropriate time window needs to be set to ensure that the collected data can reflect the short-term attitude change characteristics and is not affected by long-term drift. In this process, an adaptive data selection strategy, such as a method based on weighted average, can also be introduced to enhance the representativeness of the reference attitude quaternion.

[0050] Step 2: Use the discrete Fourier transform to extract the main wave frequency component and the high-frequency residual component from the sequence of reference attitude quaternions composed of all reference attitude quaternions, and then perform the inverse discrete Fourier transform to reconstruct the main wave attitude and the high-frequency attitude. Based on the main wave attitude, the high-frequency attitude, and the sequence of reference attitude quaternions, calculate the comprehensive attitude quaternion;

[0051] First, in the previous stage, a sequence of reference attitude quaternions has been constructed. This sequence contains the attitude information of the buoy at multiple moments and can completely describe the law of the attitude evolution of the buoy under the action of ocean waves. However, since the movement of the buoy is driven by multiple factors jointly, its attitude change often shows complex time-domain fluctuation characteristics. Therefore, directly using the reference attitude quaternion for correction may lead to error accumulation, especially in the case where the influence of the main wave frequency is large or the high-frequency perturbation is significant. To deeply understand the change pattern of the buoy attitude, it is necessary to perform frequency-domain analysis on the sequence of reference attitude quaternions to extract the main fluctuation components for more refined attitude correction. The discrete Fourier transform is a powerful frequency-domain analysis tool that can convert the original time-domain data into a superposition of different frequency components, thereby revealing the attitude change patterns at different scales in the movement of the buoy. In the method of the present invention, the discrete Fourier transform is applied to the sequence of reference attitude quaternions to decompose the main wave frequency component and the high-frequency residual component. The main wave frequency component mainly reflects the low-frequency swing mode formed by the buoy being periodically driven by ocean waves, while the high-frequency residual component is mainly contributed by instantaneous perturbations, swells, and the high-frequency response of the buoy. Through this frequency-domain decomposition process, the attitude changes at different scales can be effectively distinguished, and a more refined calculation basis can be provided for subsequent attitude correction.

[0052] After the frequency-domain decomposition is completed, the inverse Fourier transforms of the dominant wave frequency component and the high-frequency residual component need to be performed separately to reconstruct the corresponding attitude components. Among them, the main wave attitude is determined by the dominant wave frequency component, which reflects the overall motion trend of the buoy under the dominant action of the waves and usually has a long time period and a large amplitude. In contrast, the high-frequency attitude is determined by the high-frequency residual component, which describes the rapid perturbation changes of the buoy on a short time scale and usually has a short period and a small amplitude. Since the high-frequency attitude often contains more random components, in some cases, the influence of high-frequency noise can be reduced through appropriate filtering or smoothing processing to improve the stability of attitude correction. After obtaining the main wave attitude and the high-frequency attitude, it is necessary to further calculate the combined attitude quaternion to construct a reference coordinate system that can comprehensively describe the attitude changes of the buoy. The calculation of the combined attitude quaternion is based on the joint processing of the main wave attitude, the high-frequency attitude, and the reference attitude quaternion sequence. It performs corresponding mathematical operations in the quaternion space to ensure that the obtained combined attitude can accurately reflect the periodic motion of the buoy and reasonably compensate for the influence of high-frequency perturbations on attitude correction. The calculation process of the combined attitude quaternion involves the weighted combination, normalization, and corresponding interpolation processing of quaternions to ensure that the final attitude estimation has high accuracy and stability.

[0053] It should be emphasized that the buoy is usually affected by multiple factors in the marine environment, such as wind waves, tides, and ocean currents. The superposition of these factors may cause the buoy attitude to exhibit different characteristics on different time scales. Therefore, when calculating the combined attitude quaternion, it is necessary to adaptively adjust the dominant wave frequency and the high-frequency component according to the sea conditions. For example, in the case of large wind waves, the influence of high-frequency perturbations is more significant. Therefore, a higher weight can be given to the high-frequency attitude in the process of calculating the combined attitude to ensure that the corrected attitude can better match the actual motion of the buoy. On the contrary, in the case of relatively calm sea conditions, the influence of the main wave attitude dominates, so the contribution of the high-frequency component can be reduced to avoid unnecessary attitude fluctuations. In addition, in practical applications, to improve the calculation efficiency, the calculation of the combined attitude quaternion can be combined with the fast Fourier transform (FFT) technology to accelerate the frequency-domain decomposition and reconstruction process. FFT is an optimized Fourier transform algorithm that can greatly reduce the computational complexity, enabling the system to complete attitude analysis and correction in a short time and meet the real-time requirements. At the same time, when calculating the combined attitude quaternion, an adaptive filtering algorithm, such as the Kalman filter, can also be introduced to further improve the stability and noise resistance of attitude estimation.

[0054] Step 3: Based on the sea condition data obtained from real-time monitoring, use wave spectrum analysis to calculate the wave perturbation variables of the buoy;

[0055] In the actual ocean environment, waves are usually composed of multiple frequency components, including both dominant periodic components, high-frequency swells, and low-frequency tidal effects. To accurately describe the energy distribution and evolution law of waves, it is necessary to use wave spectrum analysis methods for calculation. The wave spectrum is a mathematical model used to characterize the distribution of wave energy at different frequencies, and it can provide information on key parameters such as wave height, period, and direction. In the method of the present invention, the calculation of the wave spectrum is mainly based on real-time monitored sea condition data, such as wave height, wavelength, wave speed, and wave direction data collected by accelerometers, gyroscopes, pressure sensors, or other environmental monitoring devices on buoys. Based on these raw data, power spectrum estimation methods, such as the fast Fourier transform (FFT) or Welch method, can be used to analyze the frequency characteristics of waves, thereby obtaining the wave energy spectrum. After obtaining the wave energy spectrum, it is necessary to further calculate the wave perturbation variables of the buoy to describe the actual impact of waves on the buoy attitude. Since the buoy floats on the water surface, its motion state is affected by waves in a relatively complex manner, including both up-and-down motion affected by wave crests and troughs, and rolling and pitching motions affected by horizontal hydrodynamic forces. Therefore, the wave perturbation variables usually include multiple physical parameters, such as the vertical displacement of the buoy, the lateral tilt angle, the longitudinal tilt angle, the rolling angular velocity, and the pitching angular velocity. These variables can be calculated by analyzing the characteristic parameters of the wave spectrum. For example, by solving the response function at a specific wave frequency, the attitude change pattern of the buoy under different wave conditions can be obtained. In addition, due to the randomness of the wave action, the calculation of the wave perturbation variables can also be combined with statistical analysis methods, such as extreme value analysis or probability density function estimation, to obtain a more stable perturbation model.

[0056] It should be noted that when calculating the wave perturbation variables of the buoy, the nonlinear effects of waves need to be considered. In an ideal situation, waves are usually assumed to be sinusoidal waves with linear superposition. However, in the actual ocean environment, waves often exhibit nonlinear characteristics, such as crest skewness caused by wind wave growth and breaking, and nonlinear interactions between waves. Therefore, in order to improve the calculation accuracy, the method of the present invention can adopt an improved nonlinear wave spectrum model, such as the JONSWAP spectrum or the PM spectrum, to more accurately describe the distribution of wave energy. In addition, during the actual calculation process, ocean hydrodynamic simulation methods can also be combined, such as using a numerical wave tank or the finite element method, to simulate the dynamic response of the buoy under the action of waves, so as to optimize the calculation results of the wave perturbation variables. After the calculation of the wave perturbation variables is completed, it can be further combined with the comprehensive attitude quaternion to provide more accurate attitude correction parameters. In this process, the role of the wave perturbation variables is to compensate for the attitude offsets caused by short-period waves or instantaneous fluctuations, ensuring that the final attitude correction results not only consider the overall movement trend of the buoy but also can reflect the subtle perturbation effects of waves. Through this strategy, the measurement accuracy of the ceilometer in complex sea conditions can be significantly improved, and the accumulation of measurement errors caused by the irregular movement of the buoy can be avoided.

[0057] Step 4: Based on the buoy wave perturbation variables and the comprehensive attitude quaternion, perform attitude correction on the ceilometer measurement values.

[0058] The basic idea of attitude correction is to adjust the measurement direction of the ceilometer in real time based on the wave disturbance variables of the buoy and the integrated attitude quaternion. First, during the measurement process, the original measurement data of the ceilometer is obtained based on the measurement direction determined by the current attitude of the buoy. However, since the buoy is always in a dynamic motion state, there is a certain deviation between its attitude and the true vertical direction. To eliminate this deviation, it is necessary to introduce the real-time attitude information of the buoy into the calculation to correct the measurement direction of the ceilometer. Specifically, the measurement direction of the ceilometer can be represented by a vector, which is fixed in the buoy coordinate system but will be continuously adjusted in the geographic coordinate system as the attitude of the buoy changes. Therefore, the key to attitude correction lies in using the integrated attitude quaternion to transform the measurement vector in the buoy coordinate system to the geographic coordinate system, so as to obtain the measurement direction of the ceilometer in the standard attitude. In this process, the rotation operation of the quaternion plays a core role. The quaternion is an efficient tool for describing rotation. It can avoid the gimbal lock problem in the traditional Euler angle representation method, and at the same time has a relatively small amount of calculation, which is suitable for real-time applications. Through the quaternion rotation transformation, the influence of the current attitude of the buoy on the measurement direction of the ceilometer can be accurately calculated, and a high numerical stability can be maintained during the calculation process. In addition, in order to further improve the correction accuracy, real-time filtering algorithms such as the extended Kalman filter (EKF) or the unscented Kalman filter (UKF) can be introduced to smooth the attitude data and reduce the influence of high-frequency noise in a short period of time. After completing the correction of the measurement direction, it is also necessary to consider the influence of the wave disturbance variables of the buoy on the measurement value of the ceilometer. Since the buoy will generate periodic up and down movements under the action of waves, this movement will directly affect the measurement result of the ceilometer for the cloud height. For example, when the buoy is at the wave crest, the measured height of the ceilometer will be relatively smaller than the true value, and when the buoy is at the wave trough, the measured height will be relatively larger than the true value. Therefore, while correcting the attitude, it is also necessary to dynamically compensate the measured height based on the wave disturbance variables. The calculation of the wave disturbance variables is based on the wave spectrum analysis in the previous stage, which can provide the vertical movement information of the buoy at different time points. By introducing this variable, the measurement result of the ceilometer can be adjusted in real time so that it always corresponds to a fixed reference plane, thereby eliminating the measurement error caused by the vertical movement of the buoy.

[0059] Embodiment 2: In step 1, a three-axis accelerometer and a three-axis magnetometer are used to obtain the measured acceleration of the buoy respectively and the measured geomagnetic field ; based on the components of the measured acceleration on the X-axis, Y-axis, and Z-axis respectively , and , the pitch angle and the roll angle are calculated; based on the components of the measured geomagnetic field on the X-axis, Y-axis, and Z-axis respectively , and Calculate the heading angle .

[0060] Specifically, the pitch and roll angles of the buoy are calculated based on accelerometer data. The role of the accelerometer is to measure the acceleration components of the buoy in three axes. In a stationary or quasi-stationary state, these acceleration data are mainly determined by the projection of the earth's gravitational acceleration. Since the direction of the gravitational acceleration always points to the center of the earth, and the measured values of the accelerometer are the components in the buoy's own coordinate system, the pitch and roll angles of the buoy can be derived using these acceleration components. The calculation method of the pitch angle takes into account the inclination of the buoy in the front-back direction and is calculated using the components of the accelerometer in the vertical axis and the plane; while the roll angle represents the inclination of the buoy in the left-right direction and is also calculated through the projection of the gravitational acceleration on different axes. The advantage of this calculation method is that it does not require additional gyroscope data and can obtain relatively stable attitude estimation results only relying on the accelerometer, thereby reducing the power consumption of the system and improving the long-term reliability of the measurement. After obtaining the pitch and roll angles, it is also necessary to calculate the heading angle, that is, the direction of the buoy relative to the geomagnetic north pole. The calculation of the heading angle is based on magnetometer data. The magnetometer measures the vector information of the ambient geomagnetic field. Since the direction of the geomagnetic field is relatively stable, the heading angle of the buoy can be derived using the magnetometer data. However, since the attitude of the buoy changes continuously in three-dimensional space, the geomagnetic field components measured by the magnetometer will also be affected by the pitch and roll angles of the buoy. Therefore, coordinate transformation is required when calculating the heading angle to eliminate the influence of the buoy attitude change on the magnetometer data. By performing a rotation transformation on the magnetometer measurement values, the corrected geomagnetic field components can be obtained and the heading angle can be further calculated. It should be noted that the calculation of the heading angle depends on the pitch and roll angles of the buoy. Therefore, in practical applications, it is necessary to ensure the stability of the accelerometer data to improve the accuracy of the heading angle estimation. During the calculation of the attitude angles, multiple non-linear mathematical transformations are involved. Therefore, in practical applications, filtering algorithms can be combined to improve the measurement accuracy. For example, the Extended Kalman Filter (EKF) or complementary filtering method can be used to fuse the data of the accelerometer and the magnetometer to reduce the errors caused by instantaneous acceleration interference or magnetic field anomalies. Especially in the ocean environment, the buoy may be affected by violent fluctuations in a short period of time, resulting in large noise in the measurement data. Therefore, using filtering methods to smooth the measurement data can improve the stability and accuracy of the attitude measurement.

[0061] Example 3: Define the reference attitude quaternion as , and each of its elements is defined by the following formula:

[0062] ;

[0063] ;

[0064] ;

[0065] 。

[0066] Specifically, in the buoy-based ceilometer attitude correction method of the present invention, accurately describing the buoy attitude is crucial for subsequent attitude decomposition and correction. In Embodiment 3, by constructing a reference attitude quaternion , the conversion from the traditional Euler angle representation (i.e., pitch angle , roll angle , and heading angle ) to the quaternion representation is achieved. This conversion formula utilizes the half-angle formula of rotation, and by dividing each Euler angle by two to calculate the sine and cosine, the components of the quaternion are obtained. For example, the scalar part of the quaternion is composed of , and its connotation reflects the superposition effect of each rotation component, thus realizing the comprehensive expression of the overall rotation state. Here, the reason for adopting the half-angle formula is that the mathematical structure of the quaternion is naturally suitable for describing three-dimensional rotation. Its operation not only has high computational efficiency but also avoids the common gimbal lock problem in the Euler angle conversion process, ensuring the stability and continuity of the attitude representation in numerical calculations.

[0067] In practical applications, the ceilometer is usually attached to the buoy platform, and the buoy is affected by a complex dynamic environment in the ocean, often having multi-dimensional angular deviations. Using the quaternion representation can effectively convert the actual attitude of the buoy into a singularity-free, continuous, and compact mathematical description, which is convenient for subsequent precise correction of the ceilometer measurement data through rotation transformation. Specifically, the roll angle , pitch angle , and heading angle reflect the attitude changes of the buoy in the left-right, front-back, and horizontal planes. The combination of the quaternion components not only reflects the coupling relationship between these three angles but also accurately captures the rotation direction and amplitude through the periodicity and symmetry of the sine and cosine functions. Especially , and The components respectively represent the rotational contributions of the buoy around different axes and can be used as rotational vectors during the attitude correction process, thus smoothly converting the original Euler angle data into a form suitable for subsequent data fusion and filtering. This quaternion-based attitude representation method has obvious advantages compared with traditional methods. First of all, the quaternion transformation not only reduces the computational amount, but also can maintain a high computational accuracy even in the case of complex actual sea conditions and frequent buoy movements. Secondly, through the accurate description of the actual attitude of the buoy, when using the discrete Fourier transform to extract the main wave frequency and high-frequency residual components subsequently, the systematic deviation introduced by the attitude error can be further eliminated, making the measurement correction of the ceilometer more accurate. Because of this mathematical advantage of quaternions, when performing real-time attitude correction in the present invention, whether it is the rotational transformation of the measurement direction of the ceilometer or the processing of the buoy disturbance variables during the dynamic compensation process, it can be effectively supported. In addition, the construction of the reference attitude quaternion also provides a good mathematical basis for subsequent attitude fusion, filtering and error compensation. By converting the continuous attitude data into a quaternion sequence, filtering processing can be performed in the frequency domain to reduce high-frequency noise interference, and data smoothing can be achieved by using the Kalman filter or other adaptive filtering algorithms, and finally a stable and representative attitude correction amount is output. Thus, when the ceilometer is actually measuring, even affected by complex sea conditions and buoy vibrations, it can ensure that the output cloud height data is consistent with the true value height.

[0068] Embodiment 4: In step 2, define the main wave frequency as ; The number of times of collecting the attitude data of the buoy is times, and a set of reference attitude quaternion sequences changing with time is obtained:

[0069] ;

[0070] is an integer index; Use the discrete Fourier transform to process each component in the reference attitude quaternion sequence to obtain corresponding result 、 corresponding result 、 corresponding result and corresponding result ; is a frequency domain variable; Define the main wave frequency change threshold ; For , extract the main wave frequency components corresponding to each component in the reference attitude quaternion sequence as 、 、 and .

[0071] Specifically, in the buoy-based ceilometer attitude correction method of the present invention, the motion state of the buoy is periodically affected by ocean waves, and is also superimposed with high-frequency disturbances and random noise, resulting in a complex change pattern of the buoy attitude over time. If the buoy attitude is directly analyzed in the time domain, it will be interfered by various high-frequency noises and non-periodic disturbances, making it difficult to accurately extract the main frequency component of the waves. Therefore, in order to more accurately separate different motion components of the buoy attitude, it is necessary to use the discrete Fourier transform (DFT) to perform frequency-domain analysis on the attitude data, and extract the main attitude change pattern based on the main frequency of the waves. In Example 4, through this method, the spectral representation of the reference attitude quaternion is constructed, and the quaternion component corresponding to the main frequency of the waves is extracted, making the attitude correction more accurate. In the data acquisition stage, the system measures the attitude of the buoy at a fixed sampling rate times, obtaining a set of reference attitude quaternion sequences that vary with time:

[0072] ,

[0073] where is the discrete-time index. This means that the system records the attitude changes of the buoy at different time points in the form of a discrete-time series, and these data imply the motion pattern of the buoy under the action of the waves. However, since the waves are periodically changing, the attitude changes acting on the buoy should also have a certain specific main frequency characteristic, and this main frequency is usually determined by the sea state. For example, when the wind speed is low, the wave period is long, and when the wind speed is high, the wave period shortens, thereby affecting the main motion frequency of the buoy. Therefore, in order to analyze the contributions of the buoy attitude at different frequencies, it is necessary to convert these discrete time-domain data into a frequency-domain representation.

[0074] The discrete Fourier transform (DFT) is an important mathematical tool that can decompose a discrete time-domain signal into a superposition form of different frequency components, thereby revealing the energy distribution of the data in the frequency domain. In this embodiment, the DFT transform is performed on each component in the reference attitude quaternion sequence to obtain the frequency-domain representation , , and , where is the frequency-domain variable, representing different frequency components. Through this transformation, the contribution degree of the buoy attitude in different frequency ranges can be analyzed, and the key information related to the main frequency of the waves can be further extracted. After obtaining the frequency-domain representation, the next step is to extract the attitude component related to the main frequency of the waves related. The main frequency of the waves is the main motion frequency of the buoy under the action of ocean waves, which can usually be determined by sea condition monitoring or historical data analysis. However, due to the complexity of the ocean environment, the dominant wave frequency is not a single fixed value but fluctuates within a certain range. Therefore, in order to more accurately extract the attitude components related to the dominant wave frequency, Embodiment 4 sets a threshold for the change in the dominant frequency , and filters the dominant frequency components of the reference attitude quaternion within the frequency range. Specifically, within this frequency range, the corresponding quaternion frequency domain components are respectively , , and , which represent the main motion parts of the buoy attitude caused by the dominant wave frequency. This frequency domain decomposition method has obvious advantages compared with the traditional time domain filtering method. Traditional time domain filtering, such as low-pass filtering or moving average filtering, although it can reduce the influence of high-frequency noise to a certain extent, its filtering effect depends on the choice of window size and is prone to over-smoothing of attitude data, resulting in the loss of key dynamic characteristics. In contrast, the DFT-based method can directly select different frequency components in the frequency domain and accurately extract the motion components within a specific frequency range without affecting other valid data.

[0075] For example, in this method, by selecting the frequency range, it can ensure that only the attitude changes related to the dominant wave frequency are extracted without being affected by other random motions or high-frequency disturbances of the buoy. In addition, another advantage of Embodiment 4 using frequency domain analysis is the improvement of computational efficiency. By applying the Fast Fourier Transform (FFT) algorithm, the computational complexity can be significantly reduced, enabling the system to complete attitude decomposition and correction in a shorter time and meet the real-time requirements. During the buoy attitude measurement process, real-time performance is crucial because the data acquisition of the ceilometer requires synchronous attitude correction to avoid errors in the measurement data due to the movement of the buoy. By extracting the dominant wave frequency components using FFT, it can ensure that the correction calculation can be completed in a short time and applied to the adjustment of the ceilometer measurement data in real time. In practical applications, after extracting the dominant wave frequency attitude components, filtering methods can be further used to optimize the data. For example, Kalman filtering or Wiener filtering methods can be used to smooth the data after frequency domain decomposition to reduce the influence of measurement noise. In addition, if the motion characteristics of the buoy change (such as a sudden change in sea conditions), the system can also dynamically adjust the threshold for the change in the dominant frequency to adapt to different wave conditions. This adaptive attitude correction strategy enables the ceilometer to maintain a high measurement accuracy under different sea conditions.

[0076] Example 5: In step 2, the high-frequency residual components corresponding to each component in the reference attitude quaternion sequence are extracted through the following formula:

[0077] ;

[0078] ;

[0079] ;

[0080] ;

[0081] where , and and are respectively , , and corresponding high-frequency residual components.

[0082] Specifically, in the previous steps, the discrete Fourier transform (DFT) has been performed on the reference attitude quaternion sequence to obtain the representations of each quaternion component in the frequency domain. In other words, each quaternion component can be regarded as a comprehensive superposition of a series of frequency components in the frequency domain. By screening the corresponding frequency components within the main frequency range , the , , and representing the main wave frequency components are obtained. On this basis, Example 5 introduces the concept of high-frequency residual components, that is, subtracting the entire frequency domain representation from the main frequency components to obtain the quaternion components representing the remaining frequency components. These remaining frequency components are called "high-frequency residuals" because outside the main wave frequency, the buoy attitude will change more rapidly and randomly due to various factors such as wind, ocean current, vortex, swell, and the structural vibration of the buoy itself.

[0083] Mathematically, the extraction method of high-frequency residual components can be concisely expressed as: in the frequency domain, subtracting the main frequency components from the reference attitude quaternion components , , , . For example, the high-frequency residual component is defined as This operation can be understood as follows: after the "band - pass" part of the main wave frequency is separated, all the remaining frequency components are regarded as high - frequency perturbations. It should be noted that these high - frequency components may also contain some intermediate - frequency or ultra - low - frequency components in some cases. However, since they do not belong to the main wave periodic motion, they are collectively referred to as "high - frequency residues" in the attitude correction process of the present invention, mainly for the purpose of distinguishing them from the part affected by the main wave in the measurement direction of the ceilometer. In this way, whether in subsequent attitude compensation or in more refined spectral analysis, these two types of components can be processed separately. For the main wave components, accurate modeling can be carried out by using sea - state analysis, wave spectrum modeling or low - frequency filtering methods; for the high - frequency residue components, due to their stronger randomness and instantaneousness, adaptive filtering or other noise suppression means can be adopted to improve the stability and robustness of attitude correction. The reason for such separation is mainly that in the marine environment, buoys usually face multiple disturbance sources. In addition to typical periodic waves, there are also swells, short - period wind waves, elastic vibrations of the buoy structure, and even the noise of the sensor itself, which will all be reflected in the attitude data. Once all frequency components are mixed together for attitude calculation, it is often very difficult to accurately locate the main error sources and key influencing factors, resulting in error accumulation in the measurement results of the ceilometer under certain sea - state conditions. By separately extracting the main wave frequency components and high - frequency residue components, the relative magnitudes of the structural changes and random perturbations of the buoy attitude can be more clearly grasped, and a differential strategy can be adopted in the attitude correction link. For example, for the main wave frequency components, they can be regarded as the main motion mode of the buoy, and by combining with the comprehensive attitude quaternion or interpolation processing, a reliable attitude estimate on the main - period scale can be obtained; while for the high - frequency residue components, methods such as filtering and amplitude limiting can be used to suppress them to a certain extent, so that the final correction result will not produce too much jitter in the high - frequency range.

[0084] In implementation, this step of calculating the high-frequency residual component in the frequency domain is very similar to the common filtering concept. Suppose in the time domain, we perform a band-pass or band-stop filtering operation on the reference attitude quaternion sequence. Then, the part retained by the filter is equivalent to the main frequency component, and the part filtered out is the high-frequency component. However, directly performing such a large-scale filtering in the time domain may lead to unnecessary phase delays and edge effects, causing distortion in the instantaneous attitude recovery of the buoy. In contrast, in Example 5, the high-frequency component is obtained by taking the difference in the frequency domain, which can more precisely control the frequency range to be extracted and can more flexibly combine the fast Fourier transform (FFT) to process large-scale data sequences. Especially when the system sampling rate is high and the amount of buoy attitude data is huge, using FFT and inverse FFT for frequency-domain filtering and data reconstruction can significantly improve efficiency, thus making real-time correction of the ceilometer possible. In addition, frequency-domain analysis can also help us determine which high-frequency components need further attention. For example, in some severe sea conditions, wind and waves may have a significant impact on the buoy at higher frequencies. If this part of the component is ignored, there will be a certain residual error in the subsequent attitude correction. By observing the spectral characteristics of the high-frequency residual component, we can understand the amplitude response of the buoy at these frequencies. Combining sea condition analysis or structural dynamics models, we can confirm whether certain abnormal peaks are sensor noise or real attitude changes, and then take targeted measures. In this way, whether it is adopting corresponding filtering methods or adjusting the sampling and measurement strategies of the ceilometer itself, there will be sufficient data support to avoid potential systematic biases in the measurement results.

[0085] Example 6: In step 2, the main wave attitude is:

[0086] ;

[0087] where , , and are respectively the results of the inverse discrete Fourier transform of , , and ; the high-frequency attitude sequence is:

[0088] ;

[0089] where , , and are respectively , and and The result of the inverse discrete Fourier transform.

[0090] Specifically, the system has performed a discrete Fourier transform (DFT) on the reference attitude quaternion of the buoy, extracting the components related to the main wave frequency and the high-frequency residual components corresponding to the faster-changing components outside the main frequency. The purpose of this is to first separate the significant motion patterns of the buoy under the main wave period from the more random and shorter-period perturbations. When we obtain the , , and representing the main wave components in the frequency domain, we can then reconstruct these frequency-domain components back into the time domain through the inverse discrete Fourier transform (IDFT or IFFT). The reconstructed result is the main wave attitude sequence, which is the part of the components that is most representative of the buoy attitude change in the low-frequency range. Such an attitude sequence usually has the characteristics of being smooth and having a long period, and can directly reflect the angular changes such as pitch, roll, and heading of the buoy within the main wave period, without being overwhelmed by short-term violent perturbations. In specific implementation, each quaternion component is inversely transformed separately. The advantage of doing this is that it can accurately retain the energy distribution of different components near the main wave frequency, so as to ensure that the recovery of the main wave attitude is as consistent as possible with the attitude of the real buoy driven by the main wave. Since the quaternion contains a scalar part and three imaginary parts, each component has a corresponding spectral value in the frequency domain. The inverse transformation process is actually to recombine and synthesize these spectral values in the low-frequency range and then generate a smooth sequence in the time domain. For example, if the scalar component has a relatively large amplitude at some frequencies close to the main wave frequency, it indicates that the attitude of the buoy is more significant at these frequency components; after the inverse transformation, this part of the energy will be concentrated in the periodic fluctuations of the time-domain sequence. In this way, the obtained can be regarded as the time-series expression of the scalar component of the buoy under the action of the low-frequency main wave, and the corresponding , and also respectively represent the main wave characteristics of the rotation components of the buoy around different axes over time.

[0091] However, relying solely on the main wave attitude is not sufficient to describe all the motion characteristics of the buoy. The wind waves and swells on the sea surface often bring faster perturbations, and the buoy's own structure may also generate additional attitude changes due to vortex-induced vibration or other high-frequency mechanical effects. If these high-frequency components are completely ignored, then in sea conditions where high-frequency perturbations are significant, there will be residual errors in attitude correction, resulting in inaccurate measurement results of the ceilometer in short-term fluctuations. Therefore, in Example 6, the high-frequency residual components , , and Perform the inverse discrete Fourier transform to obtain the corresponding high-frequency attitude sequence in the time domain This high-frequency attitude sequence accurately depicts the disturbance condition of the buoy in the non-primary waveband, including short-period or instantaneous changes intertwined with various factors. In terms of its time-domain performance, high-frequency attitudes often do not have significant periodicity and tend to be random fluctuations or small-amplitude rapid vibrations. However, it is precisely these small-amplitude high-frequency changes that will accumulate into non-negligible short-time deviations in the buoy attitude. If not accurately identified and compensated, the measurement direction of the ceilometer may deviate significantly in the short term, resulting in significant errors in measuring the cloud height. After the inverse transformation of the primary wave attitude and the high-frequency attitude to the time domain respectively, the system simultaneously has information on the buoy in both the low-frequency primary waveband and high-frequency disturbances. The next step is usually to combine these two parts to generate a comprehensive attitude description. For example, if the system adopts a fusion strategy, then the high-frequency attitude can be filtered or limited first to reduce sharp changes introduced by sensor noise, etc., while retaining the true high-frequency disturbance components; for the primary wave attitude, it will be considered to combine it with the wave disturbance variables obtained in the sea state analysis step to more accurately compensate for the overall rotation of the buoy within the primary wave period of the waves. Finally, these fusion or compensation results will be reflected when correcting the measurement vector of the ceilometer, ensuring that the relative error between the ceilometer and the ideal attitude is always within a controllable range. When the amplitude of the primary wave is huge, the weight of the primary wave attitude in the correction process relatively increases, which can greatly adjust the measurement direction of the ceilometer; when the high-frequency interference increases significantly, the high-frequency attitude component can promptly reveal the characteristics of short-term fluctuations, thereby quickly fine-tuning the measurement result and avoiding instantaneous large measurement errors in rapidly changing sea conditions. Essentially, this approach of decomposing in the frequency domain and reconstructing the time-domain sequence through inverse transformation is precisely to clearly distinguish the multi-scale structure of the attitude. The energy distribution of the ocean wave motion is usually most concentrated near the main frequency, but the sea state does not only contain a single periodic fluctuation, and there must be various high-frequency disturbances in the actual motion of the buoy. By separating these two types of components in the frequency domain and performing inverse transformation on each, on the one hand, it ensures that the low-frequency primary wave component will not be distorted by high-frequency noise interference, and on the other hand, it also provides an independent channel for high-frequency disturbances to be retained. This processing method inherits the advantages of traditional frequency-domain filtering but retains the most original multi-dimensional description of the attitude data (because each component of the quaternion has undergone inverse transformation). For the precise measurement of the ceilometer, this multi-dimensional and multi-scale attitude reconstruction method has obvious advantages: it can accurately capture the overall undulation and rotation of the buoy in a relatively long period and can also respond to rapid and small-amplitude high-frequency changes.

[0092] Compared with some simple low-pass filtering or moving average methods, the practice of first transforming the data into the frequency domain and then performing inverse transformation has better interpretability and flexibility. Because we can clearly know that the formation process of the main wave attitude is reconstructed by obtaining energy from a certain band-pass interval (usually the frequency band centered on the main wave frequency), while the high-frequency attitude exactly corresponds to the remaining frequency components excluded from the main frequency interval. This clear frequency segmentation enables us to make more refined adjustments at the system design level. For example, we can adjust the main wave frequency band and threshold range according to different sea conditions, different wind and wave sizes, different ship or buoy structural characteristics, or perform special processing on the high-frequency components according to actual needs (such as adaptive filtering, directional suppression, or feature extraction, etc.). Thus, while ensuring the measurement accuracy, it also takes into account the requirements for environmental adaptability. In actual deployment, the main wave attitude and the high-frequency attitude are not only theoretically classified but also can be independently scheduled at the engineering level. For example, if what we are concerned about is the overall attitude trend of the buoy on a large time scale, we can use as the main reference for attitude prediction and ceilometer calibration, while can be used as a dynamic compensation factor for attitude changes in a short period of time. In comparison, generally, the main wave attitude has a larger amplitude and a lower frequency, reflecting the most important motion form of the buoy; the high-frequency attitude has a relatively smaller amplitude but changes rapidly, reflecting the superposition of various random interferences and rapid vibrations. If the two are mixed together, or only distinguished by simple filtering methods, it is often impossible to ensure the accurate restoration of the main wave components, nor can it timely correct the angle of the ceilometer when the proportion of high-frequency disturbances increases. Through the inverse transformation in the frequency domain, this invention separately obtains these two sets of time-domain data, which is equivalent to providing a "dual-track" analysis channel at the attitude level: Track 1 is the low-frequency attitude change centered on the main frequency, and Track 2 is the independent tracking of the high-frequency residue. The two complement each other and jointly support the subsequent attitude fusion algorithm, making the attitude information presented to the ceilometer calibration module have higher accuracy and stability, and being more adaptable to the variability and complexity of sea conditions.

[0093] Example 7: In step 2, calculate the comprehensive attitude quaternion through the following formula :

[0094] ;

[0095] wherein, represents the F-norm; is the quaternion multiplication.

[0096] Specifically, the core idea of the formula proposed in Embodiment 7 is to superimpose the reference attitude, the main wave attitude, and the high-frequency attitude in the form of quaternion multiplication, and perform appropriate normalization on the multiplication result to ensure that the combined attitude can retain the rotation characteristics of multiple frequency bands and remain stable numerically. Specifically, the reference attitude reflects the overall tilt and direction information of the buoy in its most primitive state without filtering or frequency-domain decomposition; the main wave attitude is the low-frequency component extracted by the frequency-domain method and inverse-transformed, representing the main rotation law of the buoy under the drive of large-period waves; while the short-period or random vibration included in the high-frequency attitude comes from the inverse-transform of the high-frequency residual component, which can reflect the rapid tilt change of the buoy during strong wind and waves or sudden fluctuations. If only any one component is considered, it is difficult to completely describe the three-dimensional motion of the buoy in complex sea conditions. Therefore, it is necessary to use the multiplication of quaternions to organically integrate the rotations from these three sources.

[0097] In the quaternion theory, the multiplication operation corresponds to the successive superposition of rotations. This means that when multiplying the reference attitude by the low-frequency main wave attitude, an intermediate result combining the original attitude of the buoy and the rotation of the main waveband can be obtained. On this basis, multiplying by the high-frequency attitude incorporates the small and rapid perturbations that were previously ignored into the overall rotation, enabling the combined attitude to take into account both large-period fluctuations and instantaneous jitters. In this way, whether the buoy is deeply affected by the crests and troughs of long-period waves or undergoes rapid swaying excited by wind and waves in a short period of time, it can be uniformly represented in the same quaternion. The reason for using quaternion multiplication instead of simple addition or interpolation is that quaternions have a more complete representation ability for three-dimensional rotations, which can avoid the common gimbal lock problem of Euler angles and maintain sufficient geometric rigor in the combination of multiple rotations. At the same time, to prevent the modulus of the quaternion from deviating from 1 due to multiple consecutive multiplications in numerical calculations, a normalization factor is introduced into the multiplication result. By taking the F-norm of the multiplication result (i.e., taking the square root of the sum of the squares of the four components of the quaternion) and then taking the ratio with a constant coefficient, the final result can be converged back to near the unit quaternion. This can not only reduce the cumulative rounding error but also ensure that the rotation representation of the combined attitude is more in line with the actual physical meaning. Without this step, with the repeated operation of attitude data, even if there is only a small error accumulation each time, it may cause serious numerical distortion and bring systematic deviations in the subsequent correction of ceilometer data. Through this multiplication and normalization step, the combined attitude quaternion combines the superposition of multi-band attitude information and the stability of mathematical calculations, and can be directly used to correct the measurement direction of the ceilometer in real time, so that it always aligns with an "ideal reference direction" corrected according to the actual movement of the buoy. From the perspective of engineering applications, this strategy of realizing multi-attitude fusion at the quaternion level not only continues the advantages of the aforementioned frequency-domain decomposition but also overcomes the limitations of single-band analysis. It can not only reflect the large-amplitude swing of the buoy driven by the main wave but also pay sufficient attention to those fast and not necessarily large-amplitude perturbations. Finally, when the ceilometer corrects its measurement axis with this combined attitude, the risk of cumulative measurement error over time is greatly reduced.

[0098] Example 8: In step 3, based on the sea condition data obtained from real-time monitoring, the wave disturbance variable of the buoy is calculated using wave spectrum analysis through the following formula :

[0099] ;

[0100] where represents the significant wave height; represents the wave angular frequency; is the wave peak frequency; represents the wave direction angle; represents the main wave direction of the wave; is the preset kurtosis parameter; is the direction extension parameter, is the set value; is the frequency weight parameter, and is the set value.

[0101] Specifically, since the buoy is affected by waves of multiple frequencies and directions on the sea surface, its attitude changes often depend on both the main wave peak frequency and a certain degree of discrete wind waves or swell interference. In order to comprehensively evaluate the degree of disturbance caused by wave characteristics to the buoy attitude, a calculation formula for the wave disturbance variable is proposed in Example 8. By incorporating multiple oceanographic parameters and their mutual coupling relationships into the same wave spectrum function, the comprehensive wave driving force on the buoy under real-time sea conditions is quantitatively described. The disturbance variable The core idea is to integrate multiple factors such as wave height, wave frequency distribution, direction distribution and the degree of deviation from the main frequency, so that it can adaptively characterize the intensity and directionality of the waves, thereby providing accurate and adjustable input basis for subsequent attitude correction.

[0102] First, there is a significant wave height in the first half of the formula. In ocean observation and forecasting, significant wave height is usually used to measure the overall wave height level on the sea surface. It is often obtained through statistical methods and represents the significant characteristics of wave height over a period of time. Including the numerator and dividing by the constant term not only allows the wave disturbance variable to be directly linked to the wave height, but also highlights the importance of wave height in energy distribution through the square operation. Because the wave energy is theoretically related to the wave height in a certain square relationship, when the sea surface has a larger effective wave height, the swing amplitude of the buoy and the angular disturbance of the ceilometer will inevitably increase significantly. Next, the formula appears With exponential terms The combination of them together describes the distribution of waves in the frequency domain. (observed angular frequency) and When the peak frequencies are close, the It will not decay excessively, and the negative exponent of the exponential term will also obtain a smaller value in this range, so that the whole term can maintain a higher amplitude, indicating that the energy of the waves is most concentrated near the main frequency at this time, and the driving force on the buoy is also the greatest. Deviation More, then It will cause significant attenuation, and the exponential term will also accelerate this process, so that the influence of wave disturbance on the buoy attitude is relatively reduced in the part far away from the main frequency.

[0103] The design concept is similar to the common wave spectrum models such as JONSWAP spectrum or modified PM spectrum, but in actual application, in order to adapt to more flexible sea conditions, it also incorporates This kurtosis correction coefficient, if takes a relatively large value, the spectral energy around the peak frequency will be more concentrated, indicating that a sharper peak wave pattern appears on the sea surface. In terms of the directional distribution, a term in the form of is added to the formula to describe the spread of ocean waves in the direction domain. Here, is the direction of the incoming waves monitored in real time, while is the direction of the main wave. By the difference between the two, it can be judged whether the buoy is facing the incoming waves directly or in a side-on wave situation, etc. When and are close enough, will approach a value close to 1, meaning that the buoy is near the main wave direction, so the wave action it bears is relatively significant. If the angle difference between the two is large, this term will be significantly attenuated, indicating that the buoy is not facing the main wave direction at this time, and the influence of the waves on its attitude will be weakened. And is an exponent that controls the width of the directional spread. The larger the value, the more sensitive it is to the direction deviation, and the more it can reflect the change in the concentration of incoming waves on the sea surface. Finally, to better control the transition around the peak frequency, the formula introduces a frequency weight correction term. It can slow down the attenuation in the interval where the difference between and is small, and when the gap between the two gradually increases, it will decay exponentially. Physically, it can be explained as: when the wave frequency is approximately the same as the peak frequency, the buoy mainly feels the energy of the main wave, and the perturbation variable should not be weakened too early; once the frequency deviation exceeds a certain threshold, this part of the wave will no longer play a dominant role in the buoy movement, and its contribution to the overall perturbation should be reduced accordingly. By adjusting the parameter , this exponential correction can be made closer to the actual observation in different sea conditions. For example, when there are both wind waves and swells on the sea surface, if takes a slightly larger value, the primary-secondary relationship between the wind waves (high frequency) and swells (low frequency) can be more clearly distinguished, so that the response ratio of the buoy to the former or the latter can be more refined.

[0104] In summary, this perturbation variable This formula is more than just a simple multiplication structure; it couples the modeling of random ocean wave characteristics with the dynamics of buoy attitude. Its purpose is to enable the system, after acquiring real-time sea state data (including wave principal direction, peak frequency, wave observation frequency distribution, and significant wave height), to quickly calculate a numerical value representing the magnitude and corresponding directional component of the combined wave disturbance experienced by the buoy at that moment. Combined with the principal wave attitude and high-frequency attitude extracted via discrete Fourier transform (DFT), this value can be used to obtain more accurate compensation for attitude correction and filter fusion. Because buoy attitude often exhibits large and multi-directional disturbances in high wave heights or strong winds and waves, while at low and medium wave heights, the dominant frequency in a particular direction may dominate, the adaptability and adjustability afforded by this formula are highly beneficial for high-precision ceilometer measurements. In this way, the system not only dynamically tracks the distribution of wave energy with frequency and direction, but also infers the buoy's short-term sway tendency, providing a quantitative basis for ceilometer angle correction. This avoids the drawbacks of traditional methods that rely solely on single wave height or frequency indicators and ignore directional scattering or kurtosis variations. In this way, no matter whether the sea condition is caused by high-frequency short waves caused by local strong winds, long-period fluctuations caused by ocean swells, or a mixture of the two, the buoy attitude can be corrected in a targeted manner based on this disturbance variable.

[0105] Example 9: In step 4, the attitude correction is performed based on the buoy wave disturbance variable and the comprehensive attitude quaternion using the following formula:

[0106] ;

[0107] in, is the empirical correction coefficient, is the set value; is the ceilometer measurement value; is the ceilometer correction value; This is the ideal boresight for the ceilometer.

[0108] Specifically, we first need to determine the ideal boresight of the ceilometer, that is, the direction vector that the ceilometer faces when there is no tilt or swing. Under ideal conditions, if the buoy remains stable, the ceilometer will not deviate from the direction and amplitude of the cloud layer, and the measurement results will be It can be directly regarded as the real cloud height. However, when the buoy undergoes multi-scale attitude rotation under the action of waves, the ceilometer's visual axis will inevitably deviate, resulting in an angle between the measurement direction and the ideal visual axis, which in turn causes a certain error in the measured distance. If it is not corrected, the final cloud height data will fluctuate with the swaying of the buoy's attitude. In order to overcome this problem, the formula is passed The rotation of the reference attitude, the main wave attitude, and the high-frequency disturbance is combined, and the most realistic attitude of the buoy at the current moment is represented in the form of quaternions. Then, use to rotate the ideal line of sight to the actual orientation of the buoy. Since the multiplication of quaternions exactly corresponds to the composition relationship of three-dimensional rotations, this operation can map the ideal direction that the ceilometer should face to the current attitude coordinate system without introducing gimbal locks or singularities. Immediately afterwards, through the dot product operation , the cosine value between these two direction vectors can be obtained, thereby obtaining the angular information of the deviation of the buoy attitude. If the two vectors are almost coincident, the dot product result is close to 1; if the buoy is severely tilted, the dot product result will decrease significantly. After sending this cosine value into the inverse cosine function , the angle between the ideal line of sight and the actual line of sight can be directly obtained. Since the sea waves will drive the buoy with different intensities and directions under different sea conditions, the previous steps have defined a perturbation variable to quantify the sea surface energy concentration, the main wave direction, and the response of the buoy to this energy. Here, multiply by an empirical correction coefficient , and then accumulate it with the aforementioned angle, which means that on the basis of calculating the deflection angle of the ceilometer, the real-time wave disturbance characteristics received by the buoy are further superimposed, so as to make a more sensitive compensation for the measurement direction in harsh environments. Then, convert this overall sum again using the cosine function, and the angle adjustment can be remapped back to the correction coefficient for height measurement.

[0109] If the attitude deviation of the buoy and the sea condition disturbance are regarded as small twists to the measurement optical path direction, the closer this cosine function is to 1, the more consistent the ceilometer line of sight is with the ideal direction, and the smaller the measurement error; once the cosine result significantly deviates from 1, it means that the buoy is undergoing obvious attitude changes and a larger correction to the measurement result is required. Finally, multiply the original ceilometer measurement value by this cosine output to obtain the ceilometer correction value . In this way, compared with simply relying on geometric tilt or fixed compensation, this formula not only considers the constantly changing rotation of the buoy during attitude correction, but also actively introduces the wave disturbance variable in the angle calculation stage, helping the system to make real-time and flexible adjustments in large waves or multi-directional sea conditions. Through this attitude correction, the cloud height measured by the ceilometer no longer drifts randomly with the buoy attitude, but can make corresponding compensations for complex wave motions and control the error within a relatively stable range. In other words, when the main wave tilt of the buoy is obvious, the quaternion rotation part in the correction formula will play a major role; once the high-frequency disturbance suddenly increases or the wave direction changes, the inside the This item can promptly reflect the rapid changes in sea conditions, assisting the ceilometer in making dynamic corrections within an extremely short period and avoiding a sharp increase in errors due to being caught off guard. In engineering deployment, It is generally determined by experimental calibration or empirical data. For buoys of different sizes or sensor systems with different structures, this coefficient can be flexibly fine-tuned to balance measurement sensitivity and stability. If it is found in certain scenarios that the buoy is overly sensitive to high-frequency small waves, can be appropriately reduced to make the compensation of the system for wave disturbances smoother; conversely, during high-wind and high-wave operations or in extreme sea conditions, can be increased to enhance the response to instantaneous disturbances. Generally speaking, the logic behind this formula is as follows: First, determine the angle between the actual measurement axis and the ideal direction, then explicitly introduce the wave disturbance factor into the angle calculation process, and finally multiply the measurement value by the cosine function to obtain the corrected cloud height. Its significance lies in simultaneously integrating the geometric rigor of quaternion rotation, the comprehensive characterization of sea conditions by wave disturbance variables, and the adaptability of empirical adjustment coefficients to diverse application scenarios, thereby ensuring that the ceilometer can still maintain a relatively accurate observation of cloud height even when the buoy attitude fluctuates violently, and significantly improving the reliability of measurement results in fields such as marine meteorology, maritime navigation, and scientific observations.

[0110] As described above, this is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A method for attitude correction of a ceilometer based on a buoy, characterized in that The method includes: Step 1: Collect the attitude data of the buoy multiple times. For the attitude data of the buoy collected each time, construct a reference attitude quaternion. Step 2: Use the discrete Fourier transform to extract the main wave frequency component and the high-frequency residual component from the reference attitude quaternion sequence composed of all the reference attitude quaternions, and then perform the inverse discrete Fourier transform to reconstruct the main wave attitude and the high-frequency attitude. Based on the main wave attitude, the high-frequency attitude and the reference attitude quaternion sequence, calculate the comprehensive attitude quaternion. Step 3: Based on the sea condition data obtained by real-time monitoring, use wave spectrum analysis to calculate the buoy wave perturbation variable. Step 4: Based on the buoy wave perturbation variable and the comprehensive attitude quaternion, perform attitude correction on the ceilometer measurement value.

2. The method for correcting the attitude of a ceilometer based on a buoy as claimed in claim 1, wherein In Step 1, a triaxial accelerometer and a triaxial magnetometer are used to obtain the measured acceleration of the buoy and the measured geomagnetic field ; based on the components of the measured acceleration on the X-axis, Y-axis, and Z-axis respectively , and , the pitch angle and the roll angle are calculated; based on the components of the measured geomagnetic field on the X-axis, Y-axis, and Z-axis respectively , and the heading angle is calculated.

3. The method for correcting the attitude of a ceilometer based on a buoy as described in claim 2, wherein Define the reference attitude quaternion as , and each of its elements is defined by the following formula: ； ； ； 。 4. The method for correcting the attitude of a ceilometer based on a buoy as claimed in claim 3, wherein, In step 2, define the main wave frequency as ; the number of times of collecting the attitude data of the buoy is times, obtaining a set of reference attitude quaternion sequences varying with time: ； is an integer index; each component in the reference attitude quaternion sequence is processed using the discrete Fourier transform to obtain the corresponding result and the corresponding result and the corresponding result and the corresponding result ; is a frequency domain variable; define the main frequency change threshold ; for , the main wave frequency components corresponding to each component in the reference attitude quaternion sequence are respectively and and and .

5. The method for correcting the attitude of a ceilometer based on a buoy as described in claim 4, characterized in that, In Step 2, the high-frequency residual component corresponding to each component in the reference attitude quaternion sequence is extracted through the following formula: ； ； ； ； Among them, , and and are respectively , , and corresponding high-frequency residual components.

6. The method for attitude correction of a ceilometer based on a buoy as claimed in claim 5, wherein In step 2, the main wave attitude is as follows: ； Among them, , , and are respectively , , and the results of the inverse discrete Fourier transform; the high-frequency attitude sequence is: ； Among them, , , and are respectively , and and the results of the inverse discrete Fourier transform of 7. The method for correcting the attitude of a ceilometer based on a buoy as claimed in claim 6, wherein, In step 2, the combined attitude quaternion is calculated using the following formula :[[]]END]] ； Among them, represents the F norm; is the quaternion multiplication.

8. The method for correcting the attitude of a ceilometer based on a buoy as claimed in claim 7, wherein In step 3, based on the sea condition data obtained through real-time monitoring, the wave disturbance variable of the buoy is calculated using wave spectrum analysis through the following formula : ； Among them, represents the significant wave height; represents the wave angular frequency; is the wave peak frequency; represents the wave direction angle; represents the main wave direction of the wave; is a preset kurtosis parameter; is a direction spread parameter, which is a set value; is a frequency weight parameter, which is a set value.

9. The method for correcting the attitude of a ceilometer based on a buoy as claimed in claim 8, wherein In Step 4, attitude correction is performed based on the buoy wave perturbation variable and the comprehensive attitude quaternion through the following formula: ； Among them, is the empirical correction coefficient, which is a set value; is the measured value of the ceilometer; is the corrected value of the ceilometer; is the ideal line of sight of the ceilometer.

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