A fiber shape sensing eccentric error correction method based on a differential Kalman filter and a common mode observation model, a program, a device and a storage medium

Abstract

This invention belongs to the field of fiber optic sensing and shape reconstruction technology, specifically relating to a method, program, device, and storage medium for correcting eccentricity errors in fiber optic shape sensing based on differential Kalman filtering and a common-mode observation model. This invention utilizes the estimated eccentricity trajectory to compensate for eccentricity in multi-core strain and curvature estimations, and provides residuals and error indices for quality assessment and trigger strategy adjustment. Compared with existing technologies, this invention achieves stable separation estimation of curvature and eccentricity through differential-common-mode decoupling; it automatically reduces weights during low-observable periods using uncertainty-driven adaptive weighting, improving robustness; it avoids blind updates of unobservable windows and reduces end-point cumulative errors through observability gating and multi-type anchor point constraints; it balances slow and abrupt changes in eccentricity, improving usability in real-world operating scenarios; and it requires no additional hardware, making it easy to integrate and deploy in existing multi-core fiber optic shape sensing systems.

Description

Technical Field

[0001] This invention belongs to the field of fiber optic sensing and shape reconstruction technology, specifically relating to a method, program, device, and storage medium for correcting eccentricity errors in fiber optic shape sensing based on differential Kalman filtering and a common-mode observation model. Background Technology

[0002] Fiber optic shape sensing typically employs multi-core optical fibers or multi-fiber combinations. It utilizes the differential strain response of each fiber core / fiber to invert deformation parameters such as the bending curvature and bending direction of a flexible carrier, thereby achieving three-dimensional shape reconstruction. Compared to electromagnetic positioning, visual tracking, or inertial measurement systems, multi-core fiber optic shape sensing offers advantages such as small size, resistance to electromagnetic interference, long-distance distributed measurement capabilities, and the ability to operate in confined or obstructed environments. It has been applied in fields such as flexible equipment navigation, robot structural sensing, and industrial pipeline inspection.

[0003] In engineering applications, shape reconstruction accuracy is highly sensitive to the assembly consistency between the shape sensing fiber / cable and the measured carrier. It typically requires calibration or standardization processes to characterize and compensate for systematic errors caused by structural and assembly deviations. Existing research indicates that the main sources of error include: firstly, assembly and packaging errors, such as geometric offsets of the shape sensing fiber / cable relative to its design position, uneven adhesive layer thickness, and asymmetric stress caused by curing shrinkage; secondly, operational disturbances, such as free slip / stick-slip, changes in local frictional constraints, and transient changes caused by operational actions. These factors can cause offsets or time-varying drifts in the geometric center of the shape sensing fiber / cable cross-section, introducing common-mode systematic biases coupled with curvature in strain measurements. This leads to increased instability in curvature estimation scale deviation and bending direction error, ultimately manifesting as cumulative drift at the end of the three-dimensional shape reconstruction.

[0004] Eccentricity error has a more pronounced impact in the following situations: when the curvature amplitude is low or the bending direction is not adequately covered, the decreased observability leads to strong coupling between eccentricity and curvature, making the estimation prone to drift; a single static calibration is difficult to cover all directions, resulting in "blind directions" and unstable compensation effects; when eccentricity changes slowly or experiences small steps / abrupt changes, fixed compensation parameters or offline calibration methods are difficult to balance real-time performance and stability, and are prone to compensation lag or error jumps.

[0005] In existing technologies, handling eccentricity errors typically relies on offline geometric calibration, fixed compensation parameters, or assuming constant eccentricity under ideal operating conditions. The sources of these errors, calibration dependencies, and typical failure modes have been systematically discussed in previous research on fiber optic shape sensing. While these methods can achieve some success under experimental conditions of consistent packaging, no slippage, and controllable motion modes, they often lack adaptive mechanisms to adapt to changes in observability in real-world applications, particularly in situations involving free sliding, stick-slip abrupt changes, insufficient orientation coverage, and noise variations. This makes it difficult to maintain real-time performance while stably suppressing systematic errors caused by eccentricity over the long term. Therefore, there is an urgent need for a method that can stably compensate for eccentricity errors in multi-core fiber optic shape sensing scenarios by utilizing multi-channel strain observation combined with observability discrimination, online estimation, and global constraint optimization. This would improve the accuracy and robustness of curvature estimation and 3D shape reconstruction. Summary of the Invention

[0006] The purpose of this invention is to address the problems of eccentricity error in multi-core fiber shape sensing caused by factors such as assembly deviations, uneven bonding, free slip / stick-slip abrupt changes, and temperature drift creep, which lead to unstable curvature estimation, increased bending direction error, and cumulative drift of the end shape. This invention provides a method, program, device, and storage medium for correcting eccentricity error in fiber shape sensing based on differential Kalman filtering and a common-mode observation model. Without adding additional hardware, this invention utilizes the structural characteristics of multi-core strain observation to achieve decoupled estimation of curvature and eccentricity, and maintains compensation stability and robustness under conditions of observability changes and noise uncertainty, thereby improving the accuracy and long-term stability of 3D shape reconstruction.

[0007] A method for correcting eccentricity error in fiber shape sensing based on differential Kalman filtering and a common-mode observation model includes the following steps:

[0008] For the target multi-core fiber structure, strain observation values ​​of each fiber core are collected over a period of time.

[0009] The original curvature of the target multi-core fiber structure is used as the state vector, and the strain observation value of each fiber core is used as the measurement vector. Kalman filtering is used to obtain the state vector estimate and state covariance matrix at each sampling time, and then the curvature uncertainty index at each sampling time is calculated.

[0010] For each sampling time, the transpose of the state vector estimate is used as the eccentric observation row vector, the mean of all fiber core strain observations is used as the common mode observation, and the equivalent noise variance of the common mode observation is constructed based on the curvature uncertainty index.

[0011] The total sampling duration is divided into time windows. Within each time window, a common-mode observation vector is constructed based on the common-mode observations at each sampling time, a stacked observation matrix is ​​constructed based on the eccentric observation row vectors at each sampling time, and a common-mode observation weight matrix is ​​constructed based on the equivalent noise variance of the common-mode observations at each sampling time. Based on the common-mode observation vector, the stacked observation matrix, and the common-mode observation weight matrix, the eccentric anchor point estimate is calculated, and the middle sampling time of the time window is taken as the anchor point time.

[0012] By taking the eccentric trajectory at each sampling time as the variable to be estimated, and combining the common mode observation consistency, time smoothing constraint and anchor point constraint, a maximum a posteriori global smoothing objective function is constructed.

[0013] Solve the objective function to obtain the optimal estimate of the eccentric trajectory at each sampling time; then correct the original curvature estimate based on the optimal estimate of the eccentric trajectory at each sampling time.

[0014] Furthermore, the Kalman filtering specifically refers to:

[0015] The original curvature of the target multi-core fiber structure as a state vector , ;

[0016] Strain observation values ​​of each fiber core As a measurement vector ;in, , This represents the total number of fiber cores in a multi-core fiber structure. , This represents the total number of sampling times.

[0017] Obtain the nominal position of each fiber core in the cross-sectional coordinate system of the target multi-core fiber structure. Construct the nominal position matrix of the fiber core Based on the common-mode orientation of all cores in the target multi-core fiber structure, determine the difference molecule space orthogonal to the common-mode orientation, and construct a difference projection matrix that projects the original observations onto the difference molecule space. The Hadamard product of the difference projection matrix and the nominal position matrix of the fiber core is used as the measurement matrix. , ;

[0018] Use the identity matrix as the state transition matrix. ;

[0019] Kalman filtering is used, based on the sampling time. Measurement vector and sampling time State vector estimation With the state covariance matrix Perform time updates and measurement updates to obtain the sampling time. State vector estimation and the state covariance matrix That is, to obtain the sampling time Original curvature estimation .

[0020] Furthermore, the time update and measurement update process is as follows:

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] in, The process noise covariance matrix; This is the measurement noise covariance matrix.

[0027] Furthermore, for each sampling time Estimating the state vector The transpose of is used as the eccentric observation row vector ,Right now ;

[0028] The average of all strain observations of the fiber core is taken as the common-mode observation. , ;

[0029] Calculate the curvature uncertainty index ;

[0030]

[0031] in, To calculate the trace of the matrix; parameters To prevent the denominator from being zero;

[0032] Based on curvature uncertainty index Constructing the equivalent noise variance of common-mode observations ;

[0033]

[0034] in, This is the noise expansion coefficient; This represents the common-mode fundamental noise variance.

[0035] Furthermore, the total sampling time Divided into Group time window;

[0036] No. The time interval corresponding to the group time window is , , For the first Group time window Sampling time, , , For the first The number of sampling moments in a group time window;

[0037] Construct a common-mode observation vector based on the common-mode observations at each sampling time. A stacked observation matrix is ​​constructed based on the eccentric observation row vectors at each sampling time. A common-mode observation weight matrix is ​​constructed based on the common-mode observation equivalent noise variance at each sampling time. ;

[0038] Calculate the eccentric anchor point estimation Take the first Intermediate sampling time of the group time window As anchor point moment.

[0039] Furthermore, at each sampling time eccentric trajectory As the variable to be estimated, a maximum a posteriori global smoothing objective function is constructed by combining common-mode observation consistency, temporal smoothing constraints, and anchor point constraints:

[0040]

[0041] in, Sampling time The prior parameters of the eccentricity variation; Anchor point time The anchor point constraint scalar variance parameter;

[0042] Solve the objective function to obtain the results at each sampling time. Optimal estimation of eccentric trajectory .

[0043] Furthermore, the original curvature estimate is corrected based on the optimal estimation results of the eccentric trajectory at each sampling time, specifically as follows:

[0044] Calculate sampling time eccentricity amplitude ;

[0045] Curvature Scale Correction Factor Due to Construction Eccentricity ; The coupling coefficient between eccentricity and curvature;

[0046] Curvature Scale Correction Factor Caused by Eccentricity sampling time Original curvature estimation After making corrections, the corrected curvature estimate is obtained. , .

[0047] A computer device includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-described fiber optic shape sensing eccentricity error correction method based on differential Kalman filtering and common-mode observation model.

[0048] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described fiber optic shape sensing eccentricity error correction method based on differential Kalman filtering and common-mode observation model.

[0049] A computer program product includes computer instructions that, when executed by a processor, implement the steps of the above-described fiber optic shape sensing eccentricity error correction method based on differential Kalman filtering and a common-mode observation model.

[0050] The beneficial effects of this invention are as follows:

[0051] This invention utilizes the estimated eccentric trajectory to compensate for eccentricity in multi-core strain and curvature estimations, and provides residual and error indices for quality assessment and trigger strategy adjustment. Compared with existing technologies, this invention can achieve stable separation estimation of curvature and eccentricity through differential-common-mode decoupling; it can automatically reduce weights during low-observable periods using uncertainty-driven adaptive weighting to improve robustness; it can avoid blind updates of unobservable windows and reduce end-point cumulative errors through observability gating and multi-type anchor point constraints; it can accommodate both slow and abrupt changes in eccentricity, improving usability in real-world operating scenarios; and it requires no additional hardware, making it easy to integrate and deploy in existing multi-core fiber shape sensing systems. Attached Figure Description

[0052] Figure 1 This is the overall flowchart of the present invention.

[0053] Figure 2 This is a schematic diagram of the eccentricity error compensation principle.

[0054] Figure 3 This is a diagram of a multi-core optical fiber eccentricity error measurement model.

[0055] Figure 4 The tracking curves of eccentricity and eccentricity angle of the three-core structure (in terms of...) Alignment).

[0056] Figure 5 Comparison chart of overall performance of three-core structure (comparison of RMSE before and after curvature decoupling, eccentricity and phi). Detailed Implementation

[0057] The present invention will now be further described with reference to the accompanying drawings.

[0058] A method for correcting eccentricity error in fiber shape sensing based on differential Kalman filtering and a common-mode observation model includes the following steps:

[0059] Step 1: For the target multi-core fiber structure, collect strain observations of each fiber core over a period of time. ;

[0060] For the first Sampling time, i.e. The first time the data was collected Strain observations of the fiber core; , This represents the total number of sampling times. , This represents the total number of fiber cores in a multi-core fiber structure.

[0061] Step 2: Determine the original curvature state of the target multi-core fiber structure. as a state vector ,Right now ;

[0062] Strain observation values ​​of each fiber core As a measurement vector ;

[0063] Obtain the nominal position of each fiber core in the cross-sectional coordinate system of the target multi-core fiber structure. Construct the nominal position matrix of the fiber core Based on the common-mode orientation of all cores in the target multi-core fiber structure, determine the difference molecule space orthogonal to the common-mode orientation, and construct a difference projection matrix that projects the original observations onto the difference molecule space. ; Project the difference matrix With the nominal position matrix of the fiber core The Hadamard product as a measurement matrix ,Right now ;

[0064] identity matrix As a state transition matrix ,Right now ;

[0065] Kalman filtering is used, based on the sampling time. Measurement vector and sampling time State vector estimation With the state covariance matrix Estimate sampling time state vector Thus, the sampling time of the target multi-core optical fiber structure is obtained. Original curvature estimation ;

[0066] Updated in time:

[0067]

[0068]

[0069] Filter gain:

[0070]

[0071] Measurement Update:

[0072]

[0073]

[0074] in, The process noise covariance matrix; The measurement noise covariance matrix;

[0075] Step 3: Put The transpose of is used as the eccentric observation row vector ;

[0076]

[0077] sampling time The average strain observations of all fiber cores were used as the common-mode observations. , ;

[0078] According to the sampling time State covariance matrix and original curvature estimation Calculate the sampling time curvature uncertainty index ;

[0079]

[0080] in, To calculate the trace of the matrix; parameters This is used to prevent small positive numbers with a denominator of zero;

[0081] Set common-mode fundamental noise variance and noise expansion coefficient Based on sampling time curvature uncertainty index Calculate the sampling time Common-mode observation equivalent noise variance ;

[0082]

[0083] As can be seen from the above formula, the more unstable the curvature estimation, The larger, the corresponding The larger the value, the lower the weight of the common-mode observation at that moment in subsequent eccentricity estimation. In this way, the influence of unreliable observations can be automatically reduced during periods of low curvature, insufficient orientation coverage, or high noise, thereby improving the stability and robustness of eccentricity estimation.

[0084] Common-mode observations at a single moment Providing only a single scalar constraint on the two-dimensional eccentricity vector is insufficient to directly and stably solve for the complete eccentricity state. Therefore, it is necessary to accumulate common-mode observations at multiple time points within a local time window and combine this with observability gating to filter out reliable local eccentricity estimation results.

[0085] Step 4: Divided into Group time windows, each group of time windows corresponds to a time interval of 10 ... , , , , For the first The number of sampling moments in a group time window. For the first Group time window Sampling time;

[0086] For each time window, construct the common mode observation vector. Stacked observation matrix Common-mode observation weight matrix ;

[0087] Then calculate the first Eccentric anchor point estimation for group time windows ;

[0088]

[0089] Take the first Intermediate sampling time of the group time window As the first The anchor point of the group time window;

[0090] Step 5: For each sampling time Set prior parameters for eccentricity changes For each anchor point, set the scalar variance parameter of the anchor point constraint. ;

[0091] It can be preset according to the working conditions, or set in segments according to the static stage, the moving stage and the state switching stage; It can be determined based on the covariance of the locally weighted least squares anchor point estimate, or it can be preset according to different confidence levels of the main anchor point and the soft anchor point.

[0092] Each sampling time eccentric trajectory As the variable to be estimated, a maximum a posteriori global smoothing objective function is constructed by combining common-mode observation consistency, temporal smoothing constraints, and anchor point constraints:

[0093]

[0094] The objective function is a standard sparse linear least squares problem, which can be solved using sparse Cholesky decomposition, conjugate gradient, or other sparse solution methods to obtain the full-time domain eccentricity estimation trajectory in one step, thus obtaining the results at each sampling time. Optimal estimation of eccentric trajectory ;

[0095] The global smoothing solution described above yields a continuous, smooth, and consistent eccentricity estimation result across the entire time span, consistent with the overall common-mode observations. This result retains the effective eccentricity information provided by anchor points within the local observable window while suppressing noise disturbances at single moments and drift accumulation caused by low observable periods. Therefore, it can be used as the eccentricity input for subsequent curvature correction.

[0096] Step 6: Based on each sampling time The optimal estimation result of the eccentric trajectory is corrected for the curvature;

[0097] Calculate sampling time eccentricity amplitude ;

[0098] Curvature Scale Correction Factor Due to Construction Eccentricity ; The eccentricity-curvature coupling coefficient is used to characterize the degree of influence of eccentricity amplitude variation on the curvature estimation scale.

[0099] Curvature Scale Correction Factor Caused by Eccentricity sampling time Original curvature estimation After making corrections, the corrected curvature estimate is obtained. ;

[0100]

[0101] The physical significance of the above correction lies in: the difference obtained from the differential channel While the common-mode eccentricity term has been largely suppressed, under actual encapsulation and stress conditions, eccentricity can still affect the curvature estimation amplitude through scale coupling. The global eccentricity trajectory provides a time-varying estimation basis for this coupling effect, and can therefore be used to further decouple and correct the original curvature, thereby improving the accuracy of curvature estimation.

[0102] After obtaining the corrected curvature vector Then, it is input into the shape reconstruction module, which uses a predetermined geometric integration method, rod model method, or other 3D shape reconstruction method to obtain the compensated 3D shape curve. If necessary, it can also simultaneously output the curvature comparison results before and after correction, the eccentricity trajectory, and the residual index to evaluate the eccentricity compensation effect and the stability of the shape reconstruction.

[0103] Thus, eccentricity estimation, curvature correction, and shape output form a complete closed loop: first, the original curvature estimate is obtained from the differential channel; then, the full-time-domain eccentricity trajectory is obtained from the common-mode channel by combining local anchor points and global smoothing; finally, the curvature is decoupled and corrected using the eccentricity result, and the shape reconstruction result is output. For fixed bonding conditions, the stability of eccentricity estimation can be improved by enhancing the smoothing constraint; for free sliding or stick-slip conditions, the prior constraint on eccentricity change can be appropriately relaxed, so that the eccentricity trajectory can track slow changes or small abrupt changes.

[0104] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for correcting eccentricity error in fiber shape sensing based on differential Kalman filtering and a common-mode observation model, characterized in that: For the target multi-core fiber structure, strain observation values ​​of each fiber core are collected over a period of time. The original curvature of the target multi-core fiber structure is used as the state vector, and the strain observation value of each fiber core is used as the measurement vector. Kalman filtering is used to obtain the state vector estimate and state covariance matrix at each sampling time, and then the curvature uncertainty index at each sampling time is calculated. For each sampling time, the transpose of the state vector estimate is used as the eccentric observation row vector, the mean of all fiber core strain observations is used as the common mode observation, and the equivalent noise variance of the common mode observation is constructed based on the curvature uncertainty index. The total sampling duration is divided into time windows. Within each time window, a common-mode observation vector is constructed based on the common-mode observations at each sampling time, a stacked observation matrix is ​​constructed based on the eccentric observation row vectors at each sampling time, and a common-mode observation weight matrix is ​​constructed based on the equivalent noise variance of the common-mode observations at each sampling time. Based on the common-mode observation vector, the stacked observation matrix, and the common-mode observation weight matrix, the eccentric anchor point estimate is calculated, and the middle sampling time of the time window is taken as the anchor point time. By taking the eccentric trajectory at each sampling time as the variable to be estimated, and combining the common mode observation consistency, time smoothing constraint and anchor point constraint, a maximum a posteriori global smoothing objective function is constructed. Solve the objective function to obtain the optimal estimate of the eccentric trajectory at each sampling time; then correct the original curvature estimate based on the optimal estimate of the eccentric trajectory at each sampling time.

2. The fiber optic shape sensing eccentricity error correction method based on differential Kalman filtering and common-mode observation model according to claim 1, characterized in that: The Kalman filter specifically refers to: The original curvature of the target multi-core fiber structure as a state vector , ; Strain observation values ​​of each fiber core As a measurement vector ;in, , This represents the total number of fiber cores in a multi-core fiber structure. , This represents the total number of sampling times. Obtain the nominal position of each fiber core in the cross-sectional coordinate system of the target multi-core fiber structure. Construct the nominal position matrix of the fiber core Based on the common-mode orientation of all cores in the target multi-core fiber structure, determine the difference molecule space orthogonal to the common-mode orientation, and construct a difference projection matrix that projects the original observations onto the difference molecule space. The Hadamard product of the difference projection matrix and the nominal position matrix of the fiber core is used as the measurement matrix. , ; Use the identity matrix as the state transition matrix. ; Kalman filtering is used, based on the sampling time. Measurement vector and sampling time State vector estimation With the state covariance matrix Perform time updates and measurement updates to obtain the sampling time. State vector estimation and the state covariance matrix That is, to obtain the sampling time Original curvature estimation .

3. The fiber optic shape sensing eccentricity error correction method based on differential Kalman filtering and common-mode observation model according to claim 2, characterized in that: The time update and measurement update process is as follows: in, The process noise covariance matrix; This is the measurement noise covariance matrix.

4. The fiber optic shape sensing eccentricity error correction method based on differential Kalman filtering and common-mode observation model according to claim 2, characterized in that: For each sampling time Estimating the state vector The transpose of is used as the eccentric observation row vector ,Right now ; The average of all strain observations of the fiber core is taken as the common-mode observation. , ; Calculate the curvature uncertainty index ; in, To calculate the trace of the matrix; parameters To prevent the denominator from being zero; Based on curvature uncertainty index Constructing the equivalent noise variance of common-mode observations ; in, This is the noise expansion coefficient; This represents the common-mode fundamental noise variance.

5. The fiber optic shape sensing eccentricity error correction method based on differential Kalman filtering and common-mode observation model according to claim 4, characterized in that: Total sampling time Divided into Group time window; No. The time interval corresponding to the group time window is , , For the first Group time window Sampling time, , , For the first The number of sampling moments in a group time window; Construct a common-mode observation vector based on the common-mode observations at each sampling time. A stacked observation matrix is ​​constructed based on the eccentric observation row vectors at each sampling time. A common-mode observation weight matrix is ​​constructed based on the common-mode observation equivalent noise variance at each sampling time. ; Calculate the eccentric anchor point estimation Take the first Intermediate sampling time of the group time window As anchor point moment.

6. The fiber optic shape sensing eccentricity error correction method based on differential Kalman filtering and common-mode observation model according to claim 5, characterized in that: Each sampling time eccentric trajectory As the variable to be estimated, a maximum a posteriori global smoothing objective function is constructed by combining common-mode observation consistency, temporal smoothing constraints, and anchor point constraints: in, Sampling time The prior parameters of the eccentricity variation; Anchor point time The anchor point constraint scalar variance parameter; Solve the objective function to obtain the results at each sampling time. Optimal estimation of eccentric trajectory .

7. The fiber optic shape sensing eccentricity error correction method based on differential Kalman filtering and common-mode observation model according to claim 6, characterized in that: The original curvature estimate is corrected based on the optimal estimation results of the eccentric trajectory at each sampling time, specifically as follows: Calculate sampling time eccentricity amplitude ; Curvature Scale Correction Factor Due to Construction Eccentricity ; The coupling coefficient between eccentricity and curvature; Curvature Scale Correction Factor Caused by Eccentricity sampling time Original curvature estimation After making corrections, the corrected curvature estimate is obtained. , .

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When executed by a processor, the computer program implements the steps of the method according to any one of claims 1 to 7.

10. A computer program product comprising computer instructions, characterized in that: When executed by a processor, the computer instructions implement the steps of the method according to any one of claims 1 to 7.

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