A hull deformation measuring device based on a wideband kalman filter and a measuring method thereof

Abstract

The application discloses a hull deformation measuring device based on a wideband Kalman filter and a measuring method thereof. The wideband Kalman filter comprises an initial alignment module, an initial binding module, a filtering cycle calculation unit and a parameter updating feedback module. In order to obtain the angular velocity of two sets of optical gyro combination bodies (LGU), the initial alignment module is introduced to transform the angular velocity so as to meet a preset small angle condition. The angular velocity meeting the preset small angle condition is simultaneously input into the initial binding module to calculate the optimal state order p0 of the Kalman filter and the initial Kalman filter parameter. The Kalman filter cycle calculation unit is substituted to obtain the filtering optimal estimation which is input into the parameter updating feedback module to update the Kalman filter parameter in real time and output the hull deformation angle estimation. The application realizes the adaptive adjustment of the filtering order and the filtering parameter by using the generalized wavelet moment estimator, expands the filtering bandwidth and is suitable for the real-time, autonomous and high-precision measurement of the hull deformation angle under different ship types and sea wave conditions.

Description

Technical Field

[0001] This invention belongs to the field of ship angular deformation measurement technology, specifically relating to a ship hull deformation measurement device and method based on a broadband Kalman filter. Background Technology

[0002] Modern large warships are equipped with numerous high-precision measurement devices and weapon systems, such as radar, electro-optical tracking and aiming systems, navigation systems, naval guns, missiles, and carrier-based aircraft. In integrated joint intelligent warfare, a unified time and space reference is essential. Typically, the space reference coordinate system is provided to the subsystems at each combat position by the ship's highest-precision main inertial navigation system (MINS). However, due to the non-rigid structure of ships, when navigating at sea, they are affected by wave impacts, load changes, and ambient temperature. This causes minute hull deformations between the subsystems and the main inertial navigation system. The spatial reference coordinate system, when transferred from the main inertial navigation system to the subsystems, suffers from alignment errors due to these hull deformations. Therefore, high-precision measurement technology of hull deformation has become a key issue restricting the improvement of transfer alignment accuracy, attracting significant attention from major maritime powers worldwide. Currently, publicly reported measurement methods mainly include optical measurement, camera measurement, stress / strain measurement, GPS measurement, GPS-assisted inertial navigation measurement, and inertial quantity matching measurement. Among these, optical measurement directly measures hull deformation with stable and reliable accuracy; however, when measuring deformation at two points far apart on a ship, special channel designs are required due to optical visibility conditions, affecting the overall spatial integrity of the ship. Camera measurement uses computer vision image technology to calibrate and transfer the spatial reference coordinate system to the subsystem, but its accuracy has limitations and it is not suitable for long-distance use. Stress / strain measurement mainly monitors localized, minute deformations of the ship's solid structure in real time; its cost-effectiveness makes it difficult to implement on a large scale across the entire ship. GPS measurement requires atmospheric visibility conditions and... Ground-based base station-assisted differential measurement; GPS-assisted inertial navigation measurement involves installing an inertial navigation system in each subsystem, with each system calibrated to the current latitude and longitude coordinate system without directly measuring hull deformation. However, GPS assistance still requires atmospheric line-of-sight conditions. The inertial quantity matching measurement method uses only two sets of optical gyroscope units to autonomously measure inertial angular velocity. By analyzing the statistical characteristics of hull deformation, a real-time state filter is constructed to calculate the hull deformation in the current local coordinate system. It has the advantages of strong adaptability to extreme environments, such as not requiring optical line-of-sight conditions, not requiring third-party observation information (such as GPS), and long-distance measurement. It can serve as a backup supplementary solution for hull deformation measurement in extreme environments, effectively improving the safety of military applications.

[0003] The article "Master reference system for rapid at seaalignment of aircraft inertial navigation systems," published in the Proceeding AIAA / JACC Conference Guidance and Control in 1966, introduced the method of transfer alignment and proposed the concept of hull deformation measurement. In his 2002 paper "Use of the ring laser units for measurement of the moving object deformations" published in *Proceedings of SPIE*, issue 4680, Russian expert Mochalov disclosed a method for measuring angular deformation using a laser gyroscope assembly based on inertial angular velocity matching. The advantage of this method is that it uses angular velocity as the observable, approximating the dynamic flexural deformation as a second-order Gaussian-Markov stationary stochastic model, and constructs a Kalman filter, achieving real-time and autonomous measurement of angular deformation. However, its disadvantages include: the laser gyroscope outputs a pulse signal proportional to the angle, making it impossible to obtain the instantaneous angular velocity; the output average angular velocity has significant quantization noise; using the average angular velocity instead of the instantaneous angular velocity introduces theoretical errors; and the measurement signal-to-noise ratio is low. Furthermore, the parameters of the dynamic flexural deformation model are time-invariant, which does not conform to the statistical characteristics of ship deformation parameters changing over time. Therefore, the angular velocity matching measurement method proposed by Mochalov has relatively low accuracy (greater than 1 arcminute). The paper "A Method for Measuring Hull Deformation Based on Attitude Matching" published in the 2010 issue of the Journal of Chinese Inertial Technology, Vol. 2, pp. 175-180, proposed to integrate the angular increment of the laser gyroscope output and re-derive the attitude matching measurement method in the carrier coordinate system, which greatly improved the signal-to-noise ratio and considered modeling the slowly changing static deformation. However, the deformation model parameters are not time-invariant.The 2012 paper "Online estimation of ship dynamic flexure model parameters for transferalignment," published in *IEEE Transactions on Control Systems Technology*, Vol. 96, proposed using the difference in angular increments output by two sets of laser gyroscopes as identification data and employing an exponentially decaying sinusoidal parameter estimation algorithm (also known as the Kumaresan-Tufts, KT algorithm) to solve for the parameters of the dynamic flexure deformation model. This achieved good results. However, the dynamic flexure deformation model was identified through KT spectral decomposition using a double Gaussian Markov decomposition, resulting in only two peak frequency points and thus limited bandwidth, leading to insufficient model bandwidth. The 2013 paper "Coupling influence of ship dynamic flexure on high accuracy," published in *Int. J. Modeling, Identification, and Control*, Vol. 19, No. 3, pp. 224-234, further addressed this issue. The paper "Transfer Alignment" and the paper "A Method for Measuring Hull Deformation Based on Adaptive Compensation of Laser Gyroscope" published in the 2017 issue of the Journal of Chinese Inertial Technology, Vol. 2, pp. 166-170, both conducted in-depth research on the correlation coupling mechanism of the inertial attitude matching method for measuring deformation using laser gyroscopes and its impact on deformation measurement. The former proposed that due to the influence of shear strain / stress of the hull structure, there is a weak cross-correlation coupling effect between dynamic flexural deformation and hull angular motion. This effect presents as a random walk type of bias error angle under stable and slow hull angular motion. The paper studied the method of using the ARMAX model to characterize the cross-correlation coupling between dynamic flexural deformation and hull angular motion and calculated the bias error deformation angle. The latter proved that when the hull angular motion observation is changed significantly, the bias error angle will decrease. The fundamental reason for this is that the identified dynamic flexural deformation model (double Gaussian Markov plus decomposition form) is non-optimal (whether the order is optimal and whether the parameters are robust).

[0004] In summary, the inertial quantity matching measurement method based on optical gyroscopes still faces key technical challenges, such as the order of the state filtering model for hull angular deformation and the optimal estimation of model parameters, which restrict the engineering application of the inertial quantity matching measurement method. Summary of the Invention

[0005] Purpose of the invention: In order to overcome the shortcomings of the prior art, the present invention provides a hull deformation measurement device and method based on a broadband Kalman filter, which achieves the purpose of robustness of filter model parameter identification and adaptive bandwidth adjustment.

[0006] Technical Solution: Firstly, this invention provides a measurement method based on a broadband Kalman filter, comprising the following steps:

[0007] The angular velocities of the first optical gyroscope assembly (LGU1) and the second optical gyroscope assembly (LGU2) are obtained, and the angular velocities are imported into the initial alignment module for transformation, so that the relative deformation angle between the first optical gyroscope assembly (LGU1) and the second optical gyroscope assembly (LGU2) satisfies the preset angle condition.

[0008] The angular velocities of the first set of optical gyroscope assemblies (LGU1) and the second set of optical gyroscope assemblies (LGU2) that meet the preset angle conditions are simultaneously input into the initial binding module for calculation, so as to obtain the optimal state order p0 of the Kalman filter and the initial Kalman filter parameters.

[0009] Substituting the optimal state order p0 and the initialized Kalman filter parameters into the Kalman filter loop calculation unit, the optimal filter estimate is obtained.

[0010] Filter optimal estimate The parameters are fed into the parameter feedback module to update the Kalman filter parameters in real time, and the hull deformation angle is estimated based on the Kalman filter output with the updated Kalman filter parameters.

[0011] In a further embodiment, the initialization of Kalman filter parameters includes: Kalman filter one-step state transfer matrix F(k, k-1), Kalman filter one-step state noise variance matrix W(k), and Kalman filter observation noise variance matrix R(k).

[0012] In a further embodiment, the method for obtaining the angular velocities of the first optical gyroscope assembly (LGU1) and the second optical gyroscope assembly (LGU2), and importing the angular velocities into the initial alignment module for transformation, so that the relative deformation angle between the obtained first optical gyroscope assembly (LGU1) and the second optical gyroscope assembly (LGU2) satisfies a preset small angle condition includes:

[0013] The angular velocities measured in real time by the first optical gyroscope assembly (LGU1) and the second optical gyroscope assembly (LGU2) are obtained, and two sets of angular velocity vectors with a time length of M are constructed based on the angular velocities.

[0014] Construct a coordinate transformation matrix based on the two sets of angular velocity vectors;

[0015] The initial alignment calculation of the angular velocity of the second optical gyroscope assembly (LGU2) is performed based on the coordinate transformation matrix to obtain the relative deformation angle between the first optical gyroscope assembly (LGU1) and the second optical gyroscope assembly (LGU2) that meet the preset small angle condition.

[0016] The formula for calculating the angular velocity vector is as follows:

[0017]

[0018] In the formula, The measured angular velocity of the first optical gyroscope assembly at time M. The measured angular velocity of the second optical gyroscope assembly at time M;

[0019] The expression for calculating the coordinate transformation matrix is ​​as follows:

[0020]

[0021] In the formula, This is the coordinate transformation matrix;

[0022] The angular velocity of the second set of optical gyroscopes was measured at all points in time based on the coordinate transformation matrix. The expression for performing the initial alignment calculation is:

[0023]

[0024] In the formula, To obtain a new angular velocity by initially aligning the second set of optical gyroscopes. Represented as relative deformation angle, To meet the preset small angle conditions.

[0025] In a further embodiment, the angular velocities of the first set of optical gyroscope assemblies (LGU1) and the second set of optical gyroscope assemblies (LGU2) that meet the preset angle conditions are simultaneously input into the initial binding module for calculation. The method to obtain the optimal state order p0 of the Kalman filter and initialize the Kalman filter parameters is as follows:

[0026] The angular velocities of the first and second optical gyroscope assemblies after initial alignment are measured at time k. The observation vector Z(k) is calculated.

[0027] The observation vector Z(k) is arranged in time order to form an angular velocity vector sequence. The angular velocity vector sequence is substituted into the generalized wavelet moment estimator, and a linear autoregressive model paradigm is defined to estimate the optimal state order p0. The state order p is set to range from 2 to 6, and the generalized wavelet moment estimator adopts the Bayesian information criterion (BIC) as the criterion.

[0028] Substituting the optimal state order p0 into the parameter estimator in the generalized wavelet moment estimator, we obtain the noise variance estimation vector of the random walk RW model. The parameter estimation vector [Γ(1), Γ(2), ..., Γ(p0)] and the noise variance estimation vector of the linear autoregressive AR model White noise WN model variance estimation vector The estimation model paradigm of the parameter estimator is RW() + AR(p0) + WN().

[0029] The noise variance estimation vector of the random walk (RW) model The parameter estimation vector [Γ(1), Γ(2), ..., Γ(p0)] and the noise variance estimation vector of the linear autoregressive AR model White noise WN model variance estimation vector Substitute the one-step state transition matrix F(k, k-1), the one-step state noise matrix W(k), and the one-step observation noise matrix R(k) into the matrix in sequence to solve for the initial Kalman filter parameters.

[0030] The expressions for the one-step state transition matrix F(k, k-1), the one-step state noise matrix W(k), and the one-step observation noise matrix R(k) are as follows:

[0031]

[0032]

[0033]

[0034] In the formula, I represents the (3×3) identity matrix; 0 3×3 The zero matrix is ​​represented as (3×3); diag(·) represents converting a vector into a (3×3) diagonal matrix. Let i be the rotation transformation matrix corresponding to the inertial attitude of LGU1 at time k, which transforms the LGU1 from the carrier coordinate system b1 to the inertial coordinate system i1. The matrix is ​​formed by diagonalizing the noise variance vector of the gyroscope's zero-bias random walk error and is determined according to the gyroscope's accuracy level; ΔT is the filtering period (i.e., ΔT = 1 / f).

[0035] In a further embodiment, the Kalman filter cyclic calculation module consists of a one-step state transition equation and a one-step state observation equation;

[0036] The one-step state transition equation consists of a static deformation model, a dynamic flexural deformation model, an attitude error difference model, and a gyroscope zero bias error model, and its specific expression is as follows:

[0037] The expression for the static deformation model is:

[0038]

[0039] The expression for the dynamic flexural deformation model is:

[0040]

[0041] The expression for the attitude error difference model is:

[0042]

[0043] The expression for the gyroscope zero-bias error model is:

[0044]

[0045]

[0046] In the formula, These represent the long-term deformations at time k and time k-1, respectively. The vector is a white noise vector that follows a Gaussian distribution with a mean of zero and a variance of 1. Represents the dynamic flexural deformation component described by the linear autoregressive (AR) model at time k; These represent the attitude error difference at time k and time k-1, respectively. and The zero-bias errors of the first set of optical gyroscopes (LGU1) and the second set of optical gyroscopes (LGU2) at time k and k-1, respectively; Let be the rotation transformation matrix of LGU1 at time k, transforming it from the carrier coordinate system b1 to the inertial coordinate system i1, where Let Γ(p0) be the matrix formed by diagonalizing the noise variance vector of the static deformation model to be identified, and let [Γ(1), Γ(2), ..., Γ(p0)] be the diagonalized matrix of the parameter vector of the dynamic flexural deformation AR model of order p0. The matrix formed by diagonalizing the noise variance vector of the dynamic flexural deformation model needs to be periodically identified and bound in the parameter update feedback module. The Kalman filter one-step state transfer matrix F(k, k-1) and the Kalman filter one-step state noise variance matrix W(k) are both matrices.

[0047] The expression for the one-step state observation equation is:

[0048]

[0049] In the formula, A(k) is the observation vector and observation matrix at time k calculated based on the angular velocities measured by LGU1 and LGU2;

[0050] The matrix expressions for the transition equation and observation equation for the one-step state are as follows:

[0051]

[0052]

[0053] In the formula, The state estimate at time k; and Let F(k, k-1) be the state noise and H(k) be the observation noise at time k, both following a zero-mean Gaussian white noise distribution. F(k, k-1) is the one-step state transition matrix, H(k) is the one-step observation matrix, W(k) is the state noise matrix, and R(k) is the observation noise matrix. The state noise matrix W(k) is derived from the state noise... The diagonalized matrix formed by arranging the amplitude variances, and the observation noise matrix R(k) is formed by the observation noise. A diagonalized matrix formed by arranging the amplitude variances;

[0054] One-step state estimator Defined as:

[0055]

[0056] The definitions of the one-step state transition matrix F(k, k-1), the one-step state noise matrix W(k), and the one-step observation noise matrix R(k) are given in formulas (25) to (27);

[0057] The one-step observation matrix H(k) is defined as:

[0058] H(k)=[IA(k) 0 3×3 0 3×3 I 0 3×3 … 0 3×3 ] T (37)

[0059] In the formula, the superscript (T) denotes matrix transpose;

[0060] From equations (34) and (35), the expression for the Kalman filter loop calculation can be obtained as follows:

[0061] P(k,k-1)=F(k,k-1)P(k-1,k-1)F T (k, k-1)+W(k) (38)

[0062] K(k)=P(k,k-1)H T (k)[H(k)P(k,k-1)H T (k)+R(k)] -1 (39)

[0063]

[0064] P(k,k)=[IK(k)H(k)]P(k,k-1) (41)

[0065] In the formula, P(k, k-1) is the one-step state transition covariance matrix at time k, K(k) is the gain matrix, and P(k, k) is the estimated covariance at time k.

[0066] The one-step state estimation vector from equation (40) The optimal estimate of the hull deformation angle at time k can be extracted as follows:

[0067]

[0068] In the formula, Let be the hull deformation angle at time k.

[0069] In a further embodiment, a generalized wavelet moment estimator is used to periodically identify the parameters of the static deformation model and the dynamic flexural deformation model, and to update the Kalman filter one-step state transfer matrix F(k, k-1) and the Kalman filter one-step state noise variance matrix W(k).

[0070] Among them, the static deformation model is a first-order random walk RW model represented by formula (7), the dynamic flexural deformation model is a p0-order linear autoregressive AR model represented by formula (8), and the gyroscope zero bias error model is a first-order random walk RW model represented by formulas (31) and (32).

[0071] In a further embodiment, the optimal filter estimate is... The parameters are fed into the parameter feedback module to update the Kalman filter parameters in real time, and the hull deformation angle is estimated based on the Kalman filter output with the updated Kalman filter parameters. The steps are as follows:

[0072] The state estimation vector for each step is obtained by the receiving Kalman filter iterative calculation. This will yield the state estimation vector for each step. Import formula (42) to extract the optimal estimate of the hull deformation angle. and the optimal estimate The sequential queue is saved to the data buffer;

[0073] To determine if the buffer is full, if the buffer is full at time k, first check the state estimation vector sequence. The parameter estimator, loaded into the generalized wavelet moment estimator, is used to identify the noise variance estimation vector of the static deformation model. The parameter estimation vector [Γ(1), Γ(2), ..., Γ(p0)] and noise variance estimation vector of the dynamic flexural deformation model Among them, the parameter estimator in the generalized wavelet moment estimator sets the model paradigm as a random walk RW model + p0-order linear autoregressive AR model RW() + AR(p0);

[0074] Noise variance estimation vector of static deformation model The parameter estimation vector [Γ(1), Γ(2), ..., Γ(p0)] and noise variance estimation vector of the dynamic flexural deformation model Construct the Kalman filter one-step state transfer matrix F(k, k-1) and the Kalman filter one-step state noise variance matrix W(k) according to formulas (25) and (26);

[0075] The Kalman filter one-step state transfer matrix F(k, k-1) and the Kalman filter one-step state noise variance matrix W(k) are fed back into the one-step state transition equation (34) calculated by the Kalman filter loop, and the hull deformation angle estimate is output.

[0076] Secondly, the present invention provides a measurement device based on a broadband Kalman filter, comprising:

[0077] Initial alignment module, initial binding module, filter loop calculation unit, parameter update feedback module;

[0078] The initial alignment module is used to perform initial alignment transformation on the angular velocities of the received first set of optical gyroscope assemblies (LGU1) and second set of optical gyroscope assemblies (LGU2), so that the relative deformation angle between the obtained first set of optical gyroscope assemblies (LGU1) and second set of optical gyroscope assemblies (LGU2) meets the preset angle condition.

[0079] The initial binding module is used to calculate the angular velocities of the first set of optical gyroscope assemblies (LGU1) and the second set of optical gyroscope assemblies (LGU2) that meet the preset angle conditions, so as to obtain the optimal state order p0 of the Kalman filter and initialize the Kalman filter parameters.

[0080] The filter loop calculation unit is used to import the optimal state order p0 and initialize the Kalman filter parameters to obtain the optimal filter estimate.

[0081] The parameter update feedback module is used to update the optimal filter estimate. The Kalman filter parameters are updated in real time, and the hull deformation angle is estimated based on the output of the Kalman filter with updated parameters.

[0082] In a further embodiment, the first optical gyroscope assembly (LGU1) and the second optical gyroscope assembly (LGU2) are placed on two points to be measured at different local locations on the hull, and each optical gyroscope assembly (LGU) consists of three mutually orthogonal optical gyroscopes.

[0083] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0084] (1) This invention introduces an online identification algorithm for Kalman filter parameters based on generalized wavelet moment estimation, which can realize adaptive adjustment of filter order and filter parameters, expand the filter bandwidth, and provide technical support for engineering applications.

[0085] (2) This invention can be applied to the real-time, autonomous, and high-precision measurement of hull deformation angle under different ship types and different sea wave conditions. Attached Figure Description

[0086] Figure 1 This is a schematic diagram of the ship's hull configuration for the optical gyroscope assembly;

[0087] Figure 2 It is a self-feedback broadband Kalman filter structural design;

[0088] Figure 3 This is the algorithm flowchart for the parameter update feedback module based on generalized wavelet moment estimation. Detailed Implementation

[0089] To better understand the technical content of the present invention, the technical solution of the present invention will be further introduced and explained below with reference to specific embodiments, but is not limited thereto.

[0090] like Figure 1 The embodiment shown further illustrates a measurement device for a broadband Kalman filter based on generalized wavelet moment estimation, including:

[0091] Initial alignment module, initial binding module, filter loop calculation unit, parameter update feedback module;

[0092] The initial alignment module is used to perform initial alignment transformation on the angular velocities of the first set of optical gyroscope assemblies (LGU1) and the second set of optical gyroscope assemblies (LGU2) so that the relative deformation angle between the first set of optical gyroscope assemblies (LGU1) and the second set of optical gyroscope assemblies (LGU2) satisfies the preset small angle condition.

[0093] The initial binding module is used to calculate the angular velocities of the first set of optical gyroscope assemblies (LGU1) and the second set of optical gyroscope assemblies (LGU2) that meet the preset small angle conditions, to obtain the optimal state order p0 of the Kalman filter and initialize the Kalman filter parameters.

[0094] The filter loop calculation unit is used to import the optimal state order p0 and initialize the Kalman filter parameters to obtain the optimal filter estimate.

[0095] The parameter update feedback module is used to update the optimal filter estimate. The Kalman filter parameters are updated in real time, and the hull deformation angle is estimated based on the output of the Kalman filter with updated parameters.

[0096] Preferably, the first optical gyroscope assembly (LGU1) and the second optical gyroscope assembly (LGU2) are placed on two points to be measured at different local locations on the hull, and each optical gyroscope assembly (LGU) consists of three mutually orthogonal optical gyroscopes.

[0097] like Figure 2 The illustration further illustrates that this embodiment provides a measurement method based on a broadband Kalman filter, including:

[0098] The angular velocities of the first optical gyroscope assembly (LGU1) and the second optical gyroscope assembly (LGU2) are obtained, and the angular velocities are imported into the initial alignment module for transformation, so that the relative deformation angle between the first optical gyroscope assembly (LGU1) and the second optical gyroscope assembly (LGU2) satisfies the preset small angle condition.

[0099] The angular velocities of the first set of optical gyroscope assemblies (LGU1) and the second set of optical gyroscope assemblies (LGU2) that meet the preset angle conditions are simultaneously input into the initial binding module for calculation, so as to obtain the optimal state order p0 of the Kalman filter and the initial Kalman filter parameters.

[0100] Substituting the optimal state order p0 and the initialized Kalman filter parameters into the Kalman filter loop calculation module, the optimal filter estimate is obtained.

[0101] Filter optimal estimate The parameters are fed into the parameter feedback module to update the Kalman filter parameters in real time, and the hull deformation angle is estimated based on the Kalman filter output with the updated Kalman filter parameters.

[0102] The initial Kalman filter parameters include: the Kalman filter one-step state transfer matrix F(k, k-1), the Kalman filter one-step state noise variance matrix W(k), and the Kalman filter observation noise variance matrix R(k).

[0103] The method for obtaining the angular velocities of the first optical gyroscope assembly (LGU1) and the second optical gyroscope assembly (LGU2), and importing the angular velocities into the initial alignment module transformation to ensure that the relative deformation angle between the obtained first optical gyroscope assembly (LGU1) and the second optical gyroscope assembly (LGU2) meets the preset small angle condition includes:

[0104] The angular velocities of the first optical gyroscope assembly (LGU1) and the second optical gyroscope assembly (LGU2) are obtained in real time, and two sets of angular velocity vectors with a time length of M are constructed based on the angular velocities.

[0105] Construct a coordinate transformation matrix based on the two sets of angular velocity vectors;

[0106] The initial alignment calculation of the angular velocity of the second optical gyroscope assembly (LGU2) is performed based on the coordinate transformation matrix to obtain the relative deformation angle between the first optical gyroscope assembly (LGU1) and the second optical gyroscope assembly (LGU2) that meet the preset small angle condition.

[0107] The formula for calculating the angular velocity vector is as follows:

[0108]

[0109] In the formula, The measured angular velocity of the first optical gyroscope assembly at time M. The measured angular velocity of the second optical gyroscope assembly at time M;

[0110] The expression for calculating the coordinate transformation matrix is ​​as follows:

[0111]

[0112] In the formula, This is the coordinate transformation matrix;

[0113] The angular velocity of the second set of optical gyroscopes was measured at all points in time based on the coordinate transformation matrix. The expression for performing the initial alignment calculation is:

[0114]

[0115] In the formula, To obtain a new angular velocity by initially aligning the second set of optical gyroscopes. Represented as relative deformation angle, To meet the preset small angle conditions;

[0116] The angular velocities of the first set of optical gyroscope assemblies (LGU1) and the second set of optical gyroscope assemblies (LGU2) that meet the preset angle conditions are simultaneously input into the initial binding module for calculation. The method to obtain the optimal state order p0 of the Kalman filter and initialize the Kalman filter parameters is as follows:

[0117] The angular velocities of the first and second optical gyroscope assemblies after initial alignment are measured at time k. The observation vector Z(k) is calculated.

[0118] The observation vector Z(k) is arranged in time order to form an angular velocity vector sequence. The angular velocity vector sequence is substituted into the generalized wavelet moment estimator, and the linear autoregressive model paradigm is defined to obtain the optimal state order p0. The search range of the state order is set to 2 to 6, and the generalized wavelet moment estimator adopts the Bayesian information criterion (BIC) as the criterion.

[0119] Substituting the optimal state order p0 into the parameter estimator in the generalized wavelet moment estimator, we obtain the noise variance estimation vector of the random walk RW model. The parameter estimation vector [Γ(1), Γ(2), ..., Γ(p0)] and the noise variance estimation vector of the linear autoregressive AR model White noise WN model variance estimation vector The estimation model paradigm of the parameter estimator is RW()+AR(p0)+WN();

[0120] The noise variance estimation vector of the random walk (RW) model The parameter estimation vector [Γ(1), Γ(2), ..., Γ(p0)] and the noise variance estimation vector of the linear autoregressive AR model White noise WN model variance estimation vector Substitute these values ​​sequentially to solve for the one-step state transition matrix F(k, k-1), the one-step state noise matrix W(k), and the one-step observation noise matrix R(k) to obtain the initial Kalman filter parameters;

[0121] In this embodiment, the filtering frequency is set to f = 20Hz and the acquisition time is 600 seconds for the observation vector sequence. Substitute the model selector (i.e., the select_ar and best_model functions) from the generalized wavelet moment estimator (the source code is the time series analysis tool simts0.2.0 run in R language); the parameter estimator in the generalized wavelet moment estimator is the estimate function, with adaptive conditions;

[0122] The expressions for the one-step state transition matrix F(k, k-1), the one-step state noise matrix W(k), and the one-step observation noise matrix R(k) are as follows:

[0123]

[0124]

[0125]

[0126] In the formula, I represents the (3×3) identity matrix; 0 3×3 The zero matrix is ​​represented as (3×3); diag(·) represents converting a vector into a (3×3) diagonal matrix. Let i be the rotation transformation matrix corresponding to the inertial attitude of LGU1 at time k, which transforms the LGU1 from the carrier coordinate system b1 to the inertial coordinate system i1. The matrix is ​​formed by diagonalizing the noise variance vector of the gyroscope's zero-bias random walk error, which can be determined according to the gyroscope's accuracy level; ΔT is the filtering period (i.e., ΔT = 1 / f).

[0127] The Kalman filter cyclic computation unit consists of a one-step state transition equation and a one-step state observation equation;

[0128] The one-step state transition equation consists of a static deformation model, a dynamic flexural deformation model, an attitude error difference model, and a gyroscope zero bias error model, and its specific expression is as follows:

[0129] The expression for the static deformation model is:

[0130]

[0131] The expression for the dynamic flexural deformation model is:

[0132]

[0133] The expression for the attitude error difference model is:

[0134]

[0135] The expression for the gyroscope zero-bias error model is:

[0136]

[0137]

[0138] In the formula, These represent the long-term deformations at time k and time k-1, respectively. The vector is a white noise vector that follows a Gaussian distribution with a mean of zero and a variance of 1. Represents the dynamic flexural deformation component described by the linear autoregressive (AR) model at time k; These represent the attitude error difference at time k and time k-1, respectively. and The zero-bias errors of the first set of optical gyroscopes (LGU1) and the second set of optical gyroscopes (LGU2) at time k and k-1, respectively; Let be the rotation transformation matrix of LGU1 at time k, transforming it from the carrier coordinate system b1 to the inertial coordinate system i1, where Let Γ(p0) be the matrix formed by diagonalizing the noise variance vector of the static deformation model to be identified, and let [Γ(1), Γ(2), ..., Γ(p0)] be the diagonalized matrix of the parameter vector of the dynamic flexural deformation AR model of order p0. The matrix formed by diagonalizing the noise variance vector of the dynamic flexural deformation model needs to be periodically identified and bound in the parameter update feedback module. The Kalman filter one-step state transfer matrix F(k, k-1) and the Kalman filter one-step state noise variance matrix W(k) are both matrices.

[0139] The expression for the one-step state observation equation is:

[0140]

[0141] In the formula, A(k) is the observation vector and observation matrix at time k calculated based on the angular velocities measured by LGU1 and LGU2;

[0142] The matrix expressions for the transition equation and observation equation for the one-step state are as follows:

[0143]

[0144]

[0145] In the formula, The state estimate at time k; and Let F(k, k-1) be the state noise and H(k) be the observation noise at time k, both following a zero-mean Gaussian white noise distribution. F(k, k-1) is the one-step state transition matrix, H(k) is the one-step observation matrix, W(k) is the state noise matrix, and R(k) is the observation noise matrix. The state noise matrix W(k) is derived from the state noise... The diagonalized matrix formed by arranging the amplitude variances, and the observation noise matrix R(k) is formed by the observation noise. A diagonalized matrix formed by arranging the amplitude variances;

[0146] One-step state estimator Defined as:

[0147]

[0148] The definitions of the one-step state transition matrix F(k, k-1), the one-step state noise matrix W(k), and the one-step observation noise matrix R(k) are given in formulas (25) to (27);

[0149] The one-step observation matrix H(k) is defined as:

[0150] H(k)=[IA(k) 0 3×3 0 3×3 I 0 3×3 … 0 3×3 ] T (58)

[0151] In the formula, the superscript (T) denotes matrix transpose;

[0152] From equations (34) and (35), the expression for the Kalman filter loop calculation can be obtained as follows:

[0153] P(k,k-1)=F(k,k-1)P(k-1,k-1)F T (k, k-1)+W(k) (59)

[0154] K(k)=P(k,k-1)H T (k)[H(k)P(k,k-1)H T (k)+R(k)] -1 (60)

[0155]

[0156] P(k,k)=[IK(k)H(k)]P(k,k-1) (62)

[0157] In the formula, P(k, k-1) is the one-step state transition covariance matrix at time k, K(k) is the gain matrix, and P(k, k) is the estimated covariance at time k.

[0158] The one-step state estimation vector from equation (40) The optimal estimate of the hull deformation angle at time k can be extracted as follows:

[0159]

[0160] In the formula, Let be the hull deformation angle at time k.

[0161] The parameters of the static deformation model and the dynamic flexural deformation model are periodically identified by a generalized wavelet moment estimator, and the parameters of the Kalman filter, namely the Kalman filter one-step state transfer matrix F(k, k-1) and the Kalman filter one-step state noise variance matrix W(k), are updated.

[0162] Among them, the static deformation model is a first-order random walk RW model represented by formula (7), the dynamic flexural deformation model is a p0-order linear autoregressive AR model represented by formula (8), and the gyroscope zero bias error model is a first-order random walk RW model represented by formulas (31) and (32).

[0163] The parameter feedback module updates the Kalman filter parameters in real time, in a loop manner as follows: Figure 3 As shown, the hull deformation angle is estimated based on the Kalman filter output after updating the Kalman filter parameters. The steps are as follows:

[0164] Construct a queue-type data buffer of length L = 300 * f, where f is the filtering frequency;

[0165] The state estimation vector is obtained at each step by the Kalman filter iterative calculation. At that time, the optimal estimate of the hull deformation angle is extracted by formula (42). and the optimal estimate The sequential queue is saved to the data buffer, and it is determined whether the buffer is full.

[0166] If the buffer is full at time k, first store the state estimation vector sequence. The parameter estimator, loaded into the generalized wavelet moment estimator, is used to identify the noise variance estimation vector of the static deformation model. The parameter estimation vector [Γ(1), Γ(2), ..., Γ(p0)] and noise variance estimation vector of the dynamic flexural deformation model

[0167] Among them, the parameter estimator in the generalized wavelet moment estimator sets the model paradigm as a random walk RW model + p0-order linear autoregressive AR model (i.e., RW() + AR(p0)), and the parameter estimator (i.e., the estimate function) in the generalized wavelet moment estimator sets the model paradigm as a random walk RW model + p0-order linear autoregressive AR model (i.e., RW() + AR(p0)), with the condition being adaptive (i.e., rgmwm).

[0168] Noise variance estimation vector of static deformation model The parameter estimation vector [Γ(1), Γ(2), ..., Γ(p0)] and noise variance estimation vector of the dynamic flexural deformation model Construct the Kalman filter one-step state transfer matrix F(k, k-1) and the Kalman filter one-step state noise variance matrix W(k) according to formulas (25) and (26);

[0169] The Kalman filter one-step state transfer matrix F(k, k-1) and the Kalman filter one-step state noise variance matrix W(k) are fed back into the one-step state transition equation (34) calculated by the Kalman filter loop, and the hull deformation angle estimate is output.

[0170] Output hull deformation angle estimation Then, clear the data buffer; repeat the process on the newly saved sequential queue.

[0171] In summary, this invention introduces an online identification algorithm for Kalman filter parameters based on generalized wavelet moment estimation, which can achieve adaptive adjustment of the filter order and filter parameters, expand the filter bandwidth, and provide technical support for engineering applications. Secondly, this invention can be applied to the real-time, autonomous, and high-precision measurement of hull deformation angles under different ship types and different sea wave conditions.

[0172] Embodiments of this application may be provided as methods, systems, or computer program products. Therefore, this application may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0173] Embodiments of this application may be provided as methods, systems, or computer program products. Therefore, this application may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0174] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0175] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0176] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0177] The above description is only a preferred embodiment of the present invention. Without departing from the technical principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A measurement method based on a wideband Kalman filter, characterized by, The method comprises the following steps: Obtaining the angular velocities of the first optical gyro combination (LGU1) and the second optical gyro combination (LGU2), and introducing the angular velocities into an initial alignment module transformation, so that the relative deformation angle between the obtained first optical gyro combination (LGU1) and the second optical gyro combination (LGU2) satisfies a preset small angle condition; The angular velocities of the first optical gyro assembly (LGU1) and the second optical gyro assembly (LGU2) meeting the preset small angle condition are simultaneously input to an initial binding module to obtain the optimal state order of the Kalman filter , and the Kalman filter parameters are initialized; wherein the angular velocities of the first optical gyro assembly and the second optical gyro assembly after the initial alignment are measured at the first time point , , The observation vector is calculated . The observation vector The angular velocity vector sequence is composed in time sequence, the angular velocity vector sequence is substituted into the generalized wavelet moment estimator, and a linear autoregressive model paradigm is defined, and an optimal order estimation value is estimated ; The optimal order estimation value The parameter estimator is substituted into the generalized wavelet moment estimator to obtain a noise variance estimation vector of the random walk RW model , a linear autoregressive AR model parameter estimation vector , and a noise variance estimation vector , a white noise WN model variance estimation vector ; wherein the estimation model paradigm of the parameter estimator is ; a noise variance estimation vector of a random walk (RW) model a linear auto-regressive (AR) model parameter estimation vector a noise variance estimation vector a white noise (WN) model variance estimation vector a one-step state transition matrix a one-step state noise matrix a one-step observation noise matrix solving, to obtain the initialized Kalman filter parameters The optimal state order is determined and the initialized Kalman filter parameters are substituted into the Kalman filter loop calculation unit to obtain a filter optimal estimate ; filtering optimal estimation The input to the parameter feedback module updates Kalman filter parameters in real time, and outputs the hull deformation angle estimation according to the Kalman filter with the updated Kalman filter parameters .

2. The measurement method based on a wideband Kalman filter system according to claim 1, characterized in that, The initialized Kalman filtering parameters comprise: a Kalman filtering one-step state transition matrix , a Kalman filtering one-step state noise variance matrix , and a Kalman filtering observation noise variance matrix .

3. The measurement method based on a wideband Kalman filter according to claim 1, characterized in that, The method for obtaining the angular velocities of the first optical gyro combination (LGU1) and the second optical gyro combination (LGU2), and introducing the angular velocities into an initial alignment module transformation, so that the relative deformation angle between the obtained first optical gyro combination (LGU1) and the second optical gyro combination (LGU2) satisfies a preset small angle condition, comprises the following steps: Obtaining the angular velocities measured by the first set of optical gyro combination (LGU1) and the second set of optical gyro combination (LGU2) in real time, and constructing two groups of angular velocity vectors with the time length of respectively according to the angular velocities, According to the two groups of angular velocity vectors, a coordinate transformation matrix is constructed; Based on the coordinate transformation matrix, initial alignment calculation is performed on the angular velocity of the second optical gyro combination (LGU2) to obtain the relative deformation angle between the first optical gyro combination (LGU1) and the second optical gyro combination (LGU2) that satisfies the preset small angle condition; The calculation formula of the angular velocity vector is: ； In the formula, is the first set of optical gyro combination body is the measured angular velocity at the time point, is the second set of optical gyro combination body is the measured angular velocity at the time point; The calculation expression of the coordinate transformation matrix is: ； In the formula, is a coordinate transformation matrix; based on a coordinate transformation matrix to all the momentary angular velocity measurements of the second optical gyro combination The expression for performing the initial alignment calculation is: ； In the formula, To obtain a new angular velocity by initial alignment of the second optical gyro combination, is expressed as a relative deformation angle, To meet the preset small angle condition.

4. The measurement method based on a wideband Kalman filter according to claim 1, characterized in that, The angular velocities of the first optical gyro combination (LGU1) and the second optical gyro combination (LGU2) meeting the preset small-angle condition are simultaneously input to an initial binding module to obtain the optimal state order of the Kalman filter The method for initializing the Kalman filter parameters comprises: setting the search range of the state order as 2-6, and adopting the Bayesian information criterion (BIC) as the criterion criterion for the generalized wavelet moment estimator. one-step state transition matrix one-step state noise matrix one-step observation noise matrix is given by ； ； ； In the formula, denotes a unit matrix of ; denotes a zero matrix of ; denotes a diagonal matrix of converting a vector into ; is a rotation transformation matrix corresponding to the inertial attitude of the LGU1 at the time corresponding to the carrier coordinate system of the LGU1 transformed to the inertial coordinate system ; ; , is a matrix of the noise variance vector of the gyro zero offset random walk error arranged in a diagonal form, and is determined according to the gyro accuracy level; is a filter period.

5. The measurement method based on a wideband Kalman filter according to claim 1, characterized in that, The Kalman filter cycle calculation unit is composed of a one-step state transition equation and a one-step state observation equation; The one-step state transition equation is composed of a static deformation model, a dynamic flexure deformation model, an attitude error difference model and a gyro zero offset error model, and the specific expression is: The expression of the static deformation model is: ； The expression of the dynamic flexure deformation model is: ； The expression of the attitude error difference model is: ； The expression of the gyro zero offset error model is: ； ； wherein, , are the long-term deformations at time and time ; is a vector of white Gaussian noise with zero mean and unit variance; denotes the dynamic flexure deformation component described by a linear auto-regressive (AR) model at time ; , are the attitude error differences at time and time ; , and , are the gyro bias errors of the first set of optical gyro assemblies (LGU1) and the second set of optical gyro assemblies (LGU2) at time and time ; is the rotation transformation matrix of LGU1 at time from the carrier coordinate system to the inertial coordinate system , wherein, is a matrix of the diagonalized static deformation model noise variance vector to be identified, is a diagonalization matrix of the dynamic flexure deformation AR model parameter vector with order , is a matrix of the diagonalized dynamic flexure deformation model noise variance vector, all of which need to be periodically identified and bound in the parameter update feedback module Kalman filter step state transfer matrix , Kalman filter step state noise variance matrix ; The expression of the one-step state observation equation is: ； In the formula, , The first angular velocity calculated based on the measurements of LGU1 and LGU2 is... The observation vector and observation matrix at each time step; The matrix expression of the one-step state transition equation and the observation equation is: ； ； In the formula, for State estimate at time t; and They are respectively The state noise and observation noise at each time step both follow a zero-mean Gaussian white noise distribution. This is a one-step state transition matrix. For one-step observation matrix, The state noise matrix is... Let be the observation noise matrix; where is the state noise matrix. Due to state noise The diagonalized matrix formed by arranging the amplitude variances, and the observation noise matrix. Due to observation noise A diagonalized matrix formed by arranging the amplitude variances; One-step state estimator is defined as: ； one-step state transition matrix one-step state noise matrix one-step observation noise matrix defined in equations (4)-(6) One-step observation matrix is defined as: ； wherein the superscript denotes matrix transposition; The expression of the Kalman filter cycle calculation is obtained from the equations (13) and (14): ； ； ； ； wherein is a step state transition covariance matrix at time instant is a gain matrix, is is an estimation covariance at time instant The one-step state estimation vector from equation (19) The first one can be extracted The optimal estimate of the hull deformation angle at time t is: ； In the formula, is the first ship deformation angle at the time.

6. The measurement method based on a wideband Kalman filter according to claim 5, characterized in that, The generalized wavelet moment estimator is used to periodically identify parameters of a static deformation model and a dynamic flexure deformation model, and to update a Kalman filter step state transfer matrix of Kalman filter parameters , a Kalman filter step state noise variance matrix ​ Wherein, the static deformation is modeled as a first-order random walk (RW) model represented by equation (7), and the dynamic deflection deformation is modeled as a linear auto-regressive (AR) model of order represented by equation (8), and the gyro bias error is modeled as a first-order random walk (RW) model represented by equations (10) and (11).

7. The measurement method based on a wideband Kalman filter according to claim 1, characterized in that, filtering optimal estimation The input to the parameter feedback module updates Kalman filter parameters in real time, and outputs the hull deformation angle estimation according to the Kalman filter with the updated Kalman filter parameters The steps are as follows: The Kalman filter cycle is received to calculate the state estimation vector of each step The state estimation vector of each step is obtained The optimal estimation value of the ship deformation angle is extracted by importing formula (21) The optimal estimation value of the order queue is saved to the data buffer Check if the cache is full. If the first... When the time buffer is full, the state estimation vector sequence is first stored. The parameter estimator, loaded into the generalized wavelet moment estimator, is used to identify the noise variance estimation vector of the static deformation model. Parameter estimation vector of dynamic flexural deformation model Noise variance estimation vector Among them, the parameter estimator in the generalized wavelet moment estimator sets the model paradigm as a random walk RW model + Linear autoregressive AR model ; Noise variance estimation vector of static deformation model Parameter estimation vector of dynamic flexural deformation model And noise variance estimation vector State transfer matrix of Kalman filter one-step according to formula (4), (5) Noise variance matrix of Kalman filter one-step state ; kalman filter one-step state transition matrix kalman filter one-step state noise variance matrix feedback loading to the kalman filter cycle calculation one-step state transition equation (13), output ship deformation angle estimation .

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