A method for correcting baseline errors based on an airborne interferometric imaging altimeter platform

Abstract

The application belongs to the field of airborne interferometric imaging altimeter error correction, and particularly relates to a platform and baseline error correction method based on an airborne interferometric imaging altimeter, which comprises the following steps: obtaining a height measurement data sequence X1 continuously collected along a flight track; pre-processing X1 to obtain a pre-processed data matrix X2; performing empirical orthogonal function decomposition on X2 along a track direction to extract spatial modes, time coefficients and eigenvalues; determining main characteristic modes according to the variance contribution rate corresponding to the eigenvalues; combining the distribution characteristics of the spatial modes and the time coefficients to identify and separate platform error components, baseline error components and real height signal components; and reconstructing the real height signal based on the separation result to realize comprehensive correction of the platform error and the baseline error. The application effectively separates the platform error and the baseline error which are different from the real signal in the time and space characteristics through EOF decomposition, and significantly improves the height measurement accuracy of the airborne interferometric imaging altimeter.

Description

Technical Field

[0001] This invention belongs to the field of error correction for airborne interferometric imaging altimeters, specifically a method for baseline error correction based on an airborne interferometric imaging altimeter platform. Background Technology

[0002] Interferometric imaging radar altimeters, as a novel observational device integrating synthetic aperture and interferometry techniques, achieve a harmonious balance between wide swath and high-precision observation thanks to their short baseline, small incident angle, and dual-receiver operation mode. This makes them irreplaceable in fields such as ocean sub-mesoscale process detection and surface elevation mapping. Compared to the limitations of traditional nadir radar altimeters, which can only acquire one-dimensional elevation profiles, their wide swath observation capability can cover a broader spatial range, making it possible to capture ocean sub-mesoscale phenomena at scales of 0.1-10 kilometers. These processes play a crucial role in ocean energy transfer, nutrient transport, and global climate change research, but their weak signals have long exceeded the resolution limits of traditional remote sensing.

[0003] Among various observation platforms, airborne interferometric imaging altimeters, with their unique advantages of close proximity to the observation target and high signal-to-noise ratio, have become the core equipment for overcoming the bottleneck of sub-mesoscale sea surface height anomaly (SSHA) observation. Although the US SWOT satellite has improved SSHA resolution from 100 kilometers to the 10-kilometer level, the high phase sensitivity of interferometry makes the altimeter accuracy of airborne platforms extremely susceptible to error interference. Among these errors, baseline error and platform error together constitute the core source of systematic error and have become the main obstacle restricting the improvement of observation performance.

[0004] Baseline errors primarily stem from mechanical vibrations, thermal deformation of the airborne platform, and limitations in the accuracy of measuring instruments, manifesting in two main types: baseline tilt deviation and phase imbalance. Baseline tilt error causes the altimeter deviation at the observation point to vary linearly with the distance from the nadir point, masking the weak characteristics of sub-mesoscale signals. Practice shows that these errors are spatially coupled with ocean dynamic signals; if they cannot be effectively separated and corrected, even if the theoretical altimeter accuracy of the original observation data can reach the centimeter level after processing, data failure will still occur in practical applications due to error accumulation.

[0005] With the increasing demands for precision in sub-mesoscale observations in marine scientific research, and the advancement of operational applications of airborne interferometric imaging altimeters, there is an urgent need to establish a technical method that adapts to the characteristics of airborne platforms and can efficiently correct platform and baseline errors. This not only addresses the current practical need for insufficient accuracy in observational data, but also provides significant scientific and engineering value for promoting breakthroughs in marine interferometric remote sensing technology. Summary of the Invention

[0006] The purpose of this invention is to address the technical bottleneck of existing airborne interferometric imaging altimeters, which suffer from platform errors caused by mechanical vibration, thermal deformation, and instrument precision limitations of the airborne platform, as well as baseline errors caused by baseline tilt deviation and phase imbalance. These two types of systematic errors are coupled and difficult to separate effectively from real ocean dynamic signals, severely restricting the accuracy of observation data and the ability to detect sub-mesoscale phenomena. This invention provides a platform and baseline error correction method based on an airborne interferometric imaging altimeter. This method utilizes the differences in the spatiotemporal characteristics of errors and ocean dynamic signals along the track direction. Through along-track empirical orthogonal function (EOF) decomposition, it achieves accurate identification and separation of platform error components, baseline error components, and real altitude signal components, thereby reconstructing a corrected high-precision altitude signal, significantly improving the altimetry accuracy and data availability of the airborne interferometric imaging altimeter.

[0007] The technical solution adopted by the present invention to achieve the above objectives is: a baseline error correction method based on an airborne interferometric imaging altimeter platform, comprising the following steps:

[0008] Step S1: Acquire the sequence of altitude measurement data X1 continuously collected by the airborne interferometric imaging altimeter along the flight trajectory;

[0009] Step S2: Preprocess the height measurement data sequence X1 to obtain the preprocessed data matrix X2;

[0010] Step S3: Perform Empirical Orthogonal Function (EOF) decomposition on the preprocessed data matrix X2 along the track direction to extract spatial modes, time coefficients, and corresponding eigenvalues; determine the main feature modes based on the variance contribution rate corresponding to each eigenvalue;

[0011] Step S4: Combining the distribution characteristics of spatial modes and time coefficients, identify and separate the platform error components, baseline error components, and true height signal components;

[0012] Step S5: Reconstruct the true altitude signal based on the separation results, thereby achieving comprehensive correction of the platform error and baseline error of the airborne interferometric imaging altimeter.

[0013] Step S2 includes the following steps:

[0014] Step S2-1: Obtain the global or regional mean sea level model and determine the mean sea level reference elevation value corresponding to each observation point along the track;

[0015] Step S2-2: Subtract the mean sea level reference elevation value point by point from the height measurement data sequence X1 to obtain the sea level height anomaly SSHA sequence or surface elevation residual sequence along the track direction;

[0016] Step S2-3: Arrange the sea surface height anomaly SSHA sequence or surface elevation residual sequence into a data matrix X2, where the rows of the data matrix X2 correspond to the observation samples along the track, and the columns correspond to the location parameters of the sampling points along the track.

[0017] Step S3 includes the following steps:

[0018] Step S3-1: Perform singular value decomposition on the preprocessed data matrix X2 using EOF decomposition along the track;

[0019] Step S3-2: Extract the singular value diagonal matrix L from the singular value decomposition results;

[0020] Step S3-3: Calculate the spatial mode and time coefficients of each mode based on the singular value decomposition results;

[0021] Step S3-4: Calculate the variance contribution rate of each mode based on the singular values ​​and determine the main characteristic modes.

[0022] Step S3-1 specifically includes:

[0023] The number of along-track modes is set to N;

[0024] Transpose the data matrix X2 and execute... ;

[0025] in, The number of samples measured along the track, For parameter dimensions; This is the transpose of the data matrix X2;

[0026] Trend removal and normalization are performed on X2':

[0027] ;

[0028] in, To remove constant trends from the transpose matrix X2' and eliminate the fixed baseline offset along the entire track; for The square root of; The data matrix obtained after trend removal and normalization; This indicates the removal of constant offsets;

[0029] Calling MATLAB Functions on matrices Perform singular value decomposition, represented as:

[0030] ;

[0031] Where C is the left singular vector matrix, L is the singular value diagonal matrix, and CC is the right singular vector matrix. To convert the matrix F to double precision type, is the singular value decomposition function.

[0032] The step S3-2 is specifically as follows:

[0033] Extract the diagonal elements of the singular value diagonal matrix L and satisfy ;

[0034] The squares of each singular value are equivalent to the eigenvalues and satisfy:

[0035] ;

[0036] where is the i-th singular value, is the i-th eigenvalue;

[0037] Through the correspondence between the singular values and the eigenvalues, the quantitative characterization of the dominant change structure of the along-track data is realized.

[0038] The step S3-3 is specifically as follows:

[0039] Calculate the principal component matrix:

[0040] ;

[0041] where is the data matrix after trend removal and normalization, is the principal component matrix

[0042] Extract the spatial mode and time coefficient of each mode through a loop:

[0043] For each mode i (i = 1, 2,..., N), its spatial mode and time coefficient are respectively expressed as:

[0044] ;

[0045] ;

[0046] where is the i-th column of the right singular vector matrix CC, is the i-th column of the principal component matrix PC, squeeze() is to remove the dimension with dimension 1 in the matrix, and ()' represents the transpose of the matrix; The : of represents taking all rows of the matrix CC; The : of represents taking all columns of the matrix;

[0047] Spatial mode Reflecting the spatial distribution characteristics of the i-th mode along the track direction, the time coefficient It reflects the dynamic characteristics of this mode as it changes with the observed samples.

[0048] Steps S3-4 are specifically as follows:

[0049] Calculate the variance contribution rate of each mode:

[0050] ;

[0051] Where N is the number of preset modes. The sum of the squares of all singular values. The variance contribution rate of the i-th mode;

[0052] The eigenvalue vector formed by squaring the diagonal elements extracted from the singular value diagonal matrix L is:

[0053] ;

[0054] Where, diag(L) extracts the diagonal elements of L. This is an element-wise squaring operation;

[0055] pass Calculate the percentage contribution rate of each modality to the variance; where, For the eigenvalue vector, This is the sum of the eigenvalues, i.e., the total variance;

[0056] Calculate the cumulative variance contribution rate:

[0057] ;

[0058] in, The number of primary feature modes selected. The cumulative variance contribution rate of the first k' modes;

[0059] Select the cumulative variance contribution rate The first k' modes are taken as the main feature components, k' ≤ N, corresponding to the spatial mode e(1:k', :) and the time coefficient pc(1:k', :); where e(1:k', :) represents the spatial mode matrix of the first k' main feature modes, with rows corresponding to modes and columns corresponding to positions along the track; pc(1:k', :) represents the time coefficient matrix of the first k' main feature modes, with rows corresponding to modes and columns corresponding to observation samples along the track.

[0060] Step S4 specifically includes:

[0061] Step S4-1: Based on the main characteristic modes obtained by EOF decomposition along the track, analyze the variation law of spatial mode and time coefficient of each mode respectively;

[0062] Step S4-2: Identify the characteristic modes that exhibit random fluctuations or periodic oscillations along the track direction and whose time coefficients show irregular and non-systematic changes as platform error components; the platform error components correspond to random or periodic height measurement interference caused by mechanical vibration, thermal deformation, or accuracy limitations of the measuring instruments on the airborne platform.

[0063] Step S4-3: Identify the characteristic modes that exhibit linear or slow systematic changes with distance from the nadir point and whose time coefficients show a slow trend as baseline error components; the baseline error components correspond to the systematic altimetry deviations caused by baseline tilt deviation and phase imbalance that change with distance.

[0064] Step S4-4: Identify the remaining main feature modes as true height signal components; the true height signal components represent the true elevation information of the sea surface or land surface along the track direction.

[0065] In step S5, the true altitude signal is reconstructed, specifically as follows:

[0066] After removing platform error and baseline error, the true sea surface or land surface elevation signal along the track direction is reconstructed; the true height signal component corresponds to the main characteristic mode remaining after removing platform error component and baseline error component in the EOF decomposition along the track, and its corresponding spatial mode and time coefficient.

[0067] An error correction system based on an airborne interferometric imaging altimeter platform and a baseline error correction method includes:

[0068] An airborne interferometric imaging altimeter is used to continuously acquire an altitude measurement data sequence X1 along the flight trajectory; the altitude measurement data sequence X1 is continuous altimeter observation sample data along the track direction.

[0069] The data preprocessing module, connected to the airborne interferometric imaging altimeter, is used to remove the mean sea level from the altitude measurement data sequence X1 to obtain the preprocessed data matrix X2.

[0070] The orbital EOF decomposition module, connected to the data preprocessing module, is used to perform empirical orthogonal function EOF decomposition on the data matrix X2 along the orbital direction to extract spatial modes, time coefficients and corresponding eigenvalues.

[0071] The main feature mode determination module is connected to the orbital EOF decomposition module and is used to determine the main feature modes based on the variance contribution rate corresponding to each feature value.

[0072] The error identification and separation module, connected to the main feature mode determination module, is used to identify and separate the platform error component, baseline error component, and true height signal component by combining the distribution characteristics of spatial mode and time coefficient.

[0073] The signal reconstruction module, connected to the error identification and separation module, is used to reconstruct the true height signal based on the separation result and output the corrected height signal.

[0074] The present invention has the following beneficial effects and advantages:

[0075] 1. This invention utilizes the empirical orthogonal function (EOF) decomposition method. Based on the differences in the spatial distribution characteristics and temporal variation patterns of platform error, baseline error, and real ocean / surface signals along the track direction, it achieves accurate identification and separation of the three types of components, effectively solving the technical problem that traditional methods struggle to distinguish between systematic errors and weak dynamic signals.

[0076] 2. The accuracy of the true height signal reconstructed by separating and eliminating platform error and baseline error can meet the stringent requirements for sub-mesoscale sea surface height anomaly observation.

[0077] 3. The method of the present invention performs error correction on the wide-swath observation data acquired in the single-transmitter dual-receiver working mode. While improving the data accuracy, it fully retains the technical advantage of the wide-swath coverage of the interferometric imaging altimeter. It can break through the limitation of traditional nadir radar altimeters that can only acquire one-dimensional elevation profiles and realize fine measurement of a large area on both sides of the nadir point.

[0078] 4. The method of this invention is not only applicable to the observation of sea surface height anomalies in ocean sub-mesoscale processes (0.1-10 km scale), but can also be extended to remote sensing applications with high requirements for elevation measurement accuracy, such as surface elevation mapping and glacier dynamic monitoring. It has good versatility and promotion value.

[0079] 5. This invention solves the core error problem that restricts the operational application of airborne interferometric imaging altimeters, and provides effective technical verification and experience accumulation for subsequent data processing of spaceborne or airborne interferometric altimeters, which strongly promotes the engineering and practical application of marine interferometric remote sensing technology. Attached Figure Description

[0080] Figure 1 This is a flowchart of the altimeter platform and baseline error correction method of the present invention;

[0081] Figure 2 This is a spatial mode distribution diagram of the platform error obtained by the EOF decomposition along the track in this invention;

[0082] Figure 3This is a spatial mode distribution diagram of the baseline error obtained by the EOF decomposition along the track in this invention;

[0083] Figure 4 This is the corrected true sea surface elevation anomaly (SSHA) obtained by the method of this invention.

[0084] Figure 5 This is a noise-free sine wave data graph obtained after simulation verification of the present invention;

[0085] Figure 6 This is a noisy sine wave data graph obtained after simulation verification of the present invention;

[0086] Figure 7 This is a graph of the airborne (platform) error parameter signal after the first mode of EOF decomposition in this invention;

[0087] Figure 8 This is a graph showing the original airborne (platform) error parameter signal after EOF decomposition in this invention.

[0088] Figure 9 This is a graph of the baseline error parameter signal of the second mode after EOF decomposition in this invention;

[0089] Figure 10 This is a graph of the original baseline error parameter signal after EOF decomposition in this invention. Detailed Implementation

[0090] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0091] like Figure 1 The diagram shown is a flowchart of the altimeter platform and baseline error correction method of the present invention. The present invention provides a method for correcting baseline errors based on an airborne interferometric imaging altimeter platform, comprising the following steps:

[0092] Step S1: Acquire the sequence of altitude measurement data X1 continuously collected by the airborne interferometric imaging altimeter along the flight trajectory;

[0093] Step S2: Preprocess the height measurement data sequence X1 to obtain the preprocessed data matrix X2;

[0094] Step S2-1: Obtain the global or regional mean sea level model and determine the mean sea level reference elevation value corresponding to each observation point along the track;

[0095] Step S2-2: Subtract the mean sea level reference elevation value point by point from the height measurement data sequence X1 to obtain the sea level height anomaly SSHA sequence or surface elevation residual sequence along the track direction;

[0096] Step S2-3: Arrange the sea surface height anomaly SSHA sequence or surface elevation residual sequence into a data matrix X2, where the rows of the data matrix X2 correspond to the observation samples along the track, and the columns correspond to the location parameters of the sampling points along the track.

[0097] Step S3: Perform Empirical Orthogonal Function (EOF) decomposition on the preprocessed data matrix X2 along the track direction to extract spatial modes, time coefficients, and corresponding eigenvalues;

[0098] This embodiment employs EOF decomposition along the track direction (i.e., along-track EOF) to focus on the fluctuation characteristics of the altimeter's measurement data along the track direction, accurately capturing the distribution patterns of baseline error and platform error along the track dimension. The decomposition is implemented using MATLAB programs and pre-defined code, as detailed below:

[0099] Step S3-1: Perform singular value decomposition on the preprocessed data matrix X2 using EOF decomposition along the track;

[0100] Step S3-1-1: First, set the number of modes for EOF decomposition along the track, i.e. N=80. The 80 modes along the track are used to fully extract 80 feature modes along the track direction, covering the main data fluctuation information in the track dimension (including baseline deviation and airborne (platform) error fluctuations along the track direction).

[0101] Step S3-1-2: Subsequently, clarify the data dimension along the track direction, and perform the following steps on the preprocessed data matrix X2: Operations, among which, The number of samples measured along the track, For parameter dimensions; This is the transpose of the data matrix X2;

[0102] Step S3-1-3: Next, perform trend removal and standardization processing on the X2' data along the track direction. ;in, To remove constant trends from the transpose matrix X2' and eliminate the fixed baseline offset along the entire track; for The square root of; The data matrix obtained after trend removal and normalization; Used to remove constant trends in the data along the track direction (adapting to the initial suppression of baseline errors along the track direction, eliminating fixed baseline offset interference throughout the track), divided by Normalization of the data along the track is performed to eliminate the influence of the number of samples along the track on the decomposition results, resulting in a data matrix processed along the track direction. ;

[0103] Step S3-1-4: Subsequently, the svds function is called to perform singular value decomposition along the orbital EOF. The calling format is as follows: ;in, This is used to convert along-track data into a double-precision type to ensure decomposition accuracy. N=80 is the preset number of along-track feature modes. C, L, and CC correspond to the left singular vector matrix, singular value diagonal matrix, and right singular vector matrix after along-track EOF decomposition, respectively. (This is different from the conventional...) The decomposed [U,S,V] correspond one-to-one (C corresponds to U, L corresponds to S, CC corresponds to V), and the svds function sorts the singular values ​​in descending order by default, without the need for additional sorting operations;

[0104] Step S3-2: Extract the singular value diagonal matrix L from the singular value decomposition results;

[0105] (Elements on the diagonal), the square of the singular value is equivalent to the eigenvalue in the orbital EOF decomposition (i.e., The magnitude of the singular values ​​corresponds to the variance contribution of each characteristic mode along the track; the column vectors of the right singular vector matrix CC correspond to the characteristic vectors in the EOF decomposition along the track, and their spatial distribution characteristics are consistent with the error and signal distribution along the track direction. This is combined with the subsequently extracted spatial modes. and time coefficient It can be directly used for the identification of error components along the track direction.

[0106] Since the svds function has already sorted the singular values ​​in the singular value diagonal matrix L in descending order by default ( The column vectors of the corresponding right singular vector matrix CC, and the extracted spatial modes. and time coefficient The data is then sorted in descending order without any additional sorting operations. The sorted singular values, spatial modes, and time coefficients are obtained directly. The sorted data can be directly used for variance contribution rate calculation and error component identification.

[0107] Step S3-3: Calculate the spatial mode and time coefficients of each mode based on the singular value decomposition results;

[0108] Step S3-3-1: Calculate the principal component matrix:

[0109] ;

[0110] in, The data matrix after trend removal and normalization. Principal component matrix

[0111] Step S3-3-2: Extract the spatial mode and time coefficients of each mode through iteration:

[0112] Step S3-3-3: For each mode i (i = 1, 2, ..., N), its spatial modes and the time coefficient are respectively expressed as:

[0113] ;

[0114] ;

[0115] wherein, is the i-th column of the right singular vector matrix CC, is the i-th column of the principal component matrix PC, squeeze() is to remove the dimension of 1 in the matrix, and ()' represents the transpose of the matrix; The ":" of means taking all rows of the matrix CC; The ":" of means taking the matrix All columns;

[0116] Spatial mode reflects the spatial distribution characteristics of the i-th mode in the along-track direction, and the time coefficient reflects the dynamic characteristics of this mode changing with the observation samples.

[0117] Step S3-4: Calculate the variance contribution rate of each mode according to the singular value and determine the main characteristic modes.

[0118] Step S3-4-1: Calculate the variance contribution rate corresponding to each singular value ; (i = 1, 2,..., 80), wherein, is the square of the i-th singular value in the singular value diagonal matrix L, which is equivalent to the eigenvalue in the along-track EOF decomposition. To further simplify the calculation of the variance contribution rate and realize the quantification of eigenvalues, the following MATLAB can be executed:

[0119] Step S3-4-2: The eigenvalue vector formed by squaring the diagonal elements extracted from the singular value diagonal matrix L, that is: ; wherein, diag(L) is to extract the diagonal elements of L, is the element-by-element square operation; convert the singular value diagonal matrix L into an eigenvalue vector (extract the singular values on the diagonal and square them to obtain the eigenvalues corresponding to 80 along-track modes);

[0120] Step S3-4-3: Subsequently execute , calculate the variance contribution rate of each along-track mode, wherein, is the eigenvalue vector, is the sum of eigenvalues, that is, the total variance; each element of the expvar vector corresponds to the variance contribution rate of the i-th along-track mode, and the quantization result can be quickly obtained without manual calculation;

[0121] Step S3-4-4: Cumulative variance contribution rate (i from 1 to k'); Select the first k' along-track characteristic modes with a cumulative variance contribution rate ≥ 95% as the main characteristic components (k' ≤ 80), with the corresponding spatial mode being e(1:k', :) and the time coefficient being pc(1:k', :). Combined with the first k' columns of the right singular vector matrix CC, it is used to separate the error components from the real signal in the subsequent along-track direction.

[0122] Step S4: Combining the distribution characteristics of spatial modes and time coefficients, identify and separate the platform error components, baseline error components, and true height signal components;

[0123] Based on the EOF decomposition results and the characteristics of altimeter errors, the main characteristic components were identified, and the baseline error component, platform error component, and true altitude signal component were separated.

[0124] Step S4-1: Platform Error Component Identification: Airborne (platform) errors manifest as random fluctuations or periodic disturbances along the track direction, comprehensively covering various airborne (platform) error fluctuations along the track direction. For example... Figure 2 The figure shows the spatial mode distribution of platform error obtained through EOF decomposition along the track. The spatial modes in this figure are random fluctuations or periodic oscillations along the track direction. Combined with the time coefficient, they show irregular and non-systematic changes, which can be identified as platform error components, corresponding to altitude measurement interference caused by mechanical vibration and thermal deformation of the airborne platform.

[0125] Step S4-2: Baseline error component identification: Baseline error manifests as a slowly changing systematic deviation along the track direction. By combining the spatial distribution and temporal changes of the track-side modes, the baseline deviation along the track direction can be accurately characterized.

[0126] Step S4-3: Extraction of True Height Signal Components: The remaining track-side feature components correspond to the true height signal along the track direction. For example... Figure 3 The figure shows the spatial mode distribution of baseline error obtained through EOF decomposition along the orbit. The spatial modes in this figure exhibit a linear or slow, systematic change with distance from the nadir point, combined with a slow trend change in the time coefficient. These can be identified as baseline error components, corresponding to the systematic altimetry deviation caused by baseline tilt deviation and phase imbalance.

[0127] Step S5: Reconstruct the true altitude signal based on the separation results, thereby achieving comprehensive correction of the platform error and baseline error of the airborne interferometric imaging altimeter.

[0128] The actual altitude signal is reconstructed, specifically as follows:

[0129] The remaining track-side feature components identified as true height signal components are linearly combined to reconstruct the true sea surface or land surface elevation signal along the track direction; the true height signal components correspond to the main characteristic modes remaining after removing platform error components and baseline error components in the track-side EOF decomposition, and their corresponding spatial modes and time coefficients. Figure 4 The figure shows the residual statistics of the true height signal after correction by the method of this invention. The residual distribution in the figure is concentrated and the fluctuation range is small, indicating that the accuracy of the corrected height signal is significantly improved, meeting the requirements for sub-mesoscale sea surface height anomaly observation.

[0130] Simulation verification:

[0131] Simulations were performed using the parameters shown in Table 1.

[0132] Table 1: Simulation Analysis Parameters

[0133] Signal amplitude sinusoidal signal sind(x) 1 Random noise \ 1 Airborne (platform) error \ 0\3\4\2\1 Baseline error y=sin(2*pi*(x) / 10) 1

[0134] The parameters for EOF decomposition are shown in Table 1, and the simulation results are as follows: Figure 5-10 As shown.

[0135] Figure 5-6 For noise-free sine data and noisy sine data. Figure 7 This is the time series of the first mode after EOF decomposition. Figure 8 For airborne (platform) error parameter signals, Figure 9 This is the spatial sequence of the second mode after EOF decomposition. Figure 10 This refers to the data variation coefficient, which is also the baseline error parameter signal.

[0136] from Figure 7 and Figure 8 It can be seen that the curves of the first mode after EOF decomposition and the original airborne (platform) error parameter signals are basically consistent, with very little difference. (Comparison) Figure 9 and Figure 10 It can be observed that the second mode and the baseline error parameter signal after EOF decomposition have a high degree of agreement.

[0137] Based on the simulation test results above, it can be seen that after EOF decomposition, the first mode and the second mode are the airborne (platform) error and the baseline error, respectively.

[0138] like Figure 1 As shown, the method of the present invention is implemented based on a correction system. In this embodiment, the system includes:

[0139] An airborne interferometric imaging altimeter is used to continuously acquire an altitude measurement data sequence X1 along the flight trajectory; the altitude measurement data sequence X1 is continuous altimeter observation sample data along the track direction.

[0140] The data preprocessing module, connected to the airborne interferometric imaging altimeter, is used to remove the mean sea level from the altitude measurement data sequence X1 to obtain the preprocessed data matrix X2.

[0141] The orbital EOF decomposition module, connected to the data preprocessing module, is used to perform empirical orthogonal function EOF decomposition on the data matrix X2 along the orbital direction to extract spatial modes, time coefficients and corresponding eigenvalues.

[0142] The main feature mode determination module is connected to the orbital EOF decomposition module and is used to determine the main feature modes based on the variance contribution rate corresponding to each feature value.

[0143] The error identification and separation module, connected to the main feature mode determination module, is used to identify and separate the platform error component, baseline error component, and true height signal component by combining the distribution characteristics of spatial mode and time coefficient.

[0144] The signal reconstruction module, connected to the error identification and separation module, is used to reconstruct the true height signal based on the separation result and output the corrected height signal.

[0145] In summary, based on the embodiments of this invention, the core of this invention lies in leveraging the differences in the spatial distribution characteristics and temporal variation patterns of platform errors, baseline errors, and real ocean dynamic signals along the track direction through along-track empirical orthogonal function (EOF) decomposition, thereby achieving accurate identification and separation of the three types of components. This method starts from the original height measurement data and, through steps such as mean sea level removal preprocessing, along-track EOF decomposition, extraction of major feature modes, identification and separation of error components, and reconstruction of the real signal, forms a complete error correction technology process. Compared with existing technologies, this invention does not rely on external reference data or complex physical models; it achieves high-precision error separation solely based on the statistical characteristics of the observation data itself, exhibiting strong universality and engineering applicability. This method effectively solves the problem of insufficient data accuracy caused by the coupling of platform errors and baseline errors in sub-mesoscale sea surface height anomaly observations using airborne interferometric imaging altimeters, providing reliable data support for applications such as ocean sub-mesoscale process research and surface elevation mapping. The invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0146] Those skilled in the art will understand that the above description is merely a preferred embodiment of the present invention, and the features described in the various embodiments and / or claims of this disclosure can be combined or combined in various ways, even if such combinations or combinations are not explicitly described in this disclosure. This is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0147] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if these modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include these modifications and modifications.

Claims

1. A baseline error correction method based on an airborne interferometric imaging altimeter platform, characterized in that, Includes the following steps: Step S1: Acquire the sequence of altitude measurement data X1 continuously collected by the airborne interferometric imaging altimeter along the flight trajectory; Step S2: Preprocess the height measurement data sequence X1 to obtain the preprocessed data matrix X2; Step S3: Perform Empirical Orthogonal Function (EOF) decomposition on the preprocessed data matrix X2 along the track direction to extract spatial modes, time coefficients, and corresponding eigenvalues; determine the main feature modes based on the variance contribution rate corresponding to each eigenvalue; Step S4: Combining the distribution characteristics of spatial modes and time coefficients, identify and separate the platform error components, baseline error components, and true height signal components; Step S5: Reconstruct the true altitude signal based on the separation results, thereby achieving comprehensive correction of the platform error and baseline error of the airborne interferometric imaging altimeter.

2. The baseline error correction method based on an airborne interferometric imaging altimeter platform according to claim 1, characterized in that, Step S2 includes the following steps: Step S2-1: Obtain the global or regional mean sea level model and determine the mean sea level reference elevation value corresponding to each observation point along the track; Step S2-2: Subtract the mean sea level reference elevation value point by point from the height measurement data sequence X1 to obtain the sea level height anomaly SSHA sequence or surface elevation residual sequence along the track direction; Step S2-3: Arrange the sea surface height anomaly SSHA sequence or surface elevation residual sequence into a data matrix X2, where the rows of the data matrix X2 correspond to the observation samples along the track, and the columns correspond to the location parameters of the sampling points along the track.

3. The baseline error correction method based on an airborne interferometric imaging altimeter platform according to claim 1, characterized in that, Step S3 includes the following steps: Step S3-1: Perform singular value decomposition on the preprocessed data matrix X2 using EOF decomposition along the track; Step S3-2: Extract the singular value diagonal matrix L from the singular value decomposition results; Step S3-3: Calculate the spatial mode and time coefficients of each mode based on the singular value decomposition results; Step S3-4: Calculate the variance contribution rate of each mode based on the singular values ​​and determine the main characteristic modes.

4. The baseline error correction method based on an airborne interferometric imaging altimeter platform according to claim 3, characterized in that, Step S3-1 specifically includes: The number of along-track modes is set to N; Transpose the data matrix X2 and execute... ; in, The number of samples measured along the track, For parameter dimensions; This is the transpose of the data matrix X2; Trend removal and normalization are performed on X2': ； in, To remove constant trends from the transpose matrix X2' and eliminate the fixed baseline offset along the entire track; for The square root of; The data matrix obtained after trend removal and normalization; This indicates the removal of constant offsets; Calling MATLAB Functions on matrices Perform singular value decomposition, represented as: ； Where C is the left singular vector matrix, L is the singular value diagonal matrix, and CC is the right singular vector matrix. To convert matrix F to double precision type, It is a singular value decomposition function.

5. The baseline error correction method based on an airborne interferometric imaging altimeter platform according to claim 3, characterized in that, Step S3-2 specifically includes: Extracting the diagonal elements of the singular valued diagonal matrix L And satisfy ; The squares of each singular value are equivalent to the eigenvalues, satisfying: ； in, For the i-th singular value, Let N be the i-th eigenvalue, and N be the set number of along-track modes; By establishing the correspondence between singular values ​​and eigenvalues, a quantitative characterization of the dominant changing structure of data along the track can be achieved.

6. The baseline error correction method based on an airborne interferometric imaging altimeter platform according to claim 3, characterized in that, Step S3-3 specifically includes: Calculate the principal component matrix: ； in, The data matrix after trend removal and normalization. Principal component matrix; Spatial mode and temporal coefficients of each mode are extracted cyclically: For each mode i, i = 1, 2, ..., N, where N is the set number of modes along the track, its spatial modes and time coefficient They are represented as follows: ； ； Among them, is the i-th column of the right singular vector matrix CC, is the i-th column of the principal component matrix PC, squeeze() is to remove the dimension of 1 in the matrix, and ()' represents the transpose of the matrix; The ":" of means taking all rows of the matrix CC; The ":" of means taking the All columns; Spatial modes Reflecting the spatial distribution characteristics of the i-th mode along the track direction, the time coefficient This reflects the dynamic characteristics of the mode as it changes with the observed samples. This represents the number of samples measured along the track.

7. The baseline error correction method based on an airborne interferometric imaging altimeter platform according to claim 3, characterized in that, Steps S3-4 are specifically as follows: Calculate the variance contribution rate of each mode: ； Where N is the set number of modes along the track. The sum of the squares of all singular values. The variance contribution rate of the i-th mode; The eigenvalue vector formed by squaring the diagonal elements extracted from the singular value diagonal matrix L is: ； Where, diag(L) extracts the diagonal elements of L. This is an element-wise squaring operation; pass Calculate the percentage contribution rate of each modality to the variance; where, For the eigenvalue vector, This is the sum of the eigenvalues, i.e., the total variance; Calculate the cumulative variance contribution rate: ； in, The number of primary feature modes selected. The cumulative variance contribution rate of the first k' modes; Select the cumulative variance contribution rate The first k' modes are taken as the main feature components, k' ≤ N, corresponding to the spatial mode e(1:k', :) and the time coefficient pc(1:k', :); where e(1:k', :) represents the spatial mode matrix of the first k' main feature modes, with rows corresponding to modes and columns corresponding to positions along the track; pc(1:k', :) represents the time coefficient matrix of the first k' main feature modes, with rows corresponding to modes and columns corresponding to observation samples along the track.

8. The baseline error correction method based on an airborne interferometric imaging altimeter platform according to claim 1, characterized in that, Step S4 specifically includes: Step S4-1: Based on the main characteristic modes obtained by EOF decomposition along the track, analyze the variation law of spatial mode and time coefficient of each mode respectively; Step S4-2: Identify the characteristic modes that exhibit random fluctuations or periodic oscillations along the track direction and whose time coefficients show irregular and non-systematic changes as platform error components; the platform error components correspond to random or periodic height measurement interference caused by mechanical vibration, thermal deformation, or accuracy limitations of the measuring instruments on the airborne platform. Step S4-3: Identify the characteristic modes that exhibit linear or slow systematic changes with distance from the nadir point and whose time coefficients show a slow trend as baseline error components; the baseline error components correspond to the systematic altimetry deviations caused by baseline tilt deviation and phase imbalance that change with distance. Step S4-4: Identify the remaining main feature modes as true height signal components; the true height signal components represent the true elevation information of the sea surface or land surface along the track direction.

9. The baseline error correction method based on an airborne interferometric imaging altimeter platform according to claim 1, characterized in that, In step S5, the true altitude signal is reconstructed, specifically as follows: After removing platform error and baseline error, the true sea surface or land surface elevation signal along the track direction is reconstructed; the true height signal component corresponds to the main characteristic mode remaining after removing platform error component and baseline error component in the EOF decomposition along the track, and its corresponding spatial mode and time coefficient.

10. An error correction system based on an airborne interferometric imaging altimeter platform and a baseline error correction method according to any one of claims 1 to 9, characterized in that, include: An airborne interferometric imaging altimeter is used to continuously acquire an altitude measurement data sequence X1 along the flight trajectory; the altitude measurement data sequence X1 is continuous altimeter observation sample data along the track direction. The data preprocessing module, connected to the airborne interferometric imaging altimeter, is used to remove the mean sea level from the altitude measurement data sequence X1 to obtain the preprocessed data matrix X2. The orbital EOF decomposition module, connected to the data preprocessing module, is used to perform empirical orthogonal function EOF decomposition on the data matrix X2 along the orbital direction to extract spatial modes, time coefficients and corresponding eigenvalues. The main feature mode determination module is connected to the orbital EOF decomposition module and is used to determine the main feature modes based on the variance contribution rate corresponding to each feature value. The error identification and separation module, connected to the main feature mode determination module, is used to identify and separate the platform error component, baseline error component, and true height signal component by combining the distribution characteristics of spatial mode and time coefficient. The signal reconstruction module, connected to the error identification and separation module, is used to reconstruct the true height signal based on the separation result and output the corrected height signal.

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