Ship inclination measuring method and system based on Kalman filtering fusion

Abstract

The invention discloses a ship inclination measurement method and system based on Kalman filtering fusion, and relates to the technical field of ship stability measurement, and the method comprises the steps: multi-sensor synchronous data collection, state space modeling and Kalman filtering fusion, adaptive dynamic adjustment of process noise, drift compensation, and fault tolerance and output. When the method and the system provided by the invention are used for measuring inclination, inclination angle error accumulation caused by gyroscope zero offset integral error, accelerometer dynamic interference, sensor noise and temperature drift, GNSS dependency and the like can be effectively avoided, available precision can still be maintained through multi-sensor depth coupling and an intelligent filtering algorithm, and the accuracy of inclination measurement is improved. The method is simple in operation, independent of satellite data, higher in stability, capable of greatly reducing hardware cost compared with GNSS and IMU schemes, and especially has the advantages of being simple in cost and installation configuration in ship refitting; and the method is also suitable for GNSS rejection or cost sensitive scenes such as inland ships, unmanned ships, offshore buoys and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of ship stability measurement, and in particular to a ship inclination measurement method and system based on Kalman filter fusion. Background Art

[0002] List (roll) is the tilt angle of a ship in the lateral direction, which has an important impact on the safety, stability and navigation performance of the ship. Moderate roll is the normal response of a ship to wind and waves, but excessive roll may lead to loss of stability and even the risk of capsizing. In ship design, the stability curve must ensure that the roll restoring moment is sufficient to resist external forces. Especially when the cargo is unevenly loaded or encounters transverse waves, if the roll angle exceeds the critical value, it will weaken the recovery ability and threaten navigation safety. In addition, roll significantly affects passenger comfort and cargo fixation, and severe roll may cause equipment damage or seasickness. At the maneuvering level, excessive roll will reduce rudder efficiency and affect steering accuracy, especially in emergency collision avoidance, which may delay response. Therefore, roll management is a core issue in ship engineering and navigation operations, and is directly related to the economy, safety and seaworthiness of the ship.

[0003] Application number: CN202210575109.2 proposes a method for tilt monitoring of a shipborne Beidou integrated machine. The sensor signal obtained by the shipborne Beidou integrated machine is the global satellite navigation system GNSS receiver data, which is used to calculate the position, speed and acceleration; the sensor signal obtained by the shipborne Beidou integrated machine is the inertial measurement unit IMU data, which is used to calculate the tilt angle based on motion analysis.

[0004] The gyroscope in the IMU is used to measure angular velocity, and the angle change is obtained by integration. However, the gyroscope has zero bias. Factors such as temperature change and noise can cause the integrated angle to drift over time, which is the so-called "gyroscope drift". Similarly, the accelerometer is used to measure acceleration, but in a dynamic environment (such as the turbulence of the ship), the output of the accelerometer contains not only the gravity component but also the motion acceleration, which will affect the calculation of the tilt angle, especially in continuous motion. This error may accumulate. In long-term operation, parameter changes such as sensor noise and temperature drift will also affect the accuracy. Although the fusion of GNSS data with IMU can correct some errors, GNSS itself has limitations, such as low update frequency and unavailability when the signal is blocked. At this time, the system will rely on IMU for dead reckoning, resulting in error accumulation. When the GNSS signal is lost or the IMU is not corrected in real time, the error may grow linearly or exponentially and accumulate over time. In addition, the cost of installing or modifying the global satellite navigation system GNSS in the above patent is high, and its applicability is also limited. Summary of the invention

[0005] In view of the above deficiencies in the prior art, the present invention proposes a ship roll measurement method based on Kalman filter fusion, which includes the following steps: S1. Synchronously collect data from multiple sensors: Obtain triaxial angular velocity and triaxial acceleration data through the IMU module, obtain absolute inclination data through a pendulum-type or capacitive inclination sensor, and obtain temperature data through a temperature sensor; S2. State space modeling and Kalman filter fusion: First, define a set of state variables, including: roll angle, angular velocity, gyroscope zero bias, pendulum delay time, pendulum scale factor, where the roll angle is the value to be output, the angular velocity is obtained from the IMU module, the gyroscope zero bias is the corrected value, the pendulum delay time is a preset value, and the pendulum scale factor is dynamically adjusted according to real-time temperature data; Then, construct a state prediction equation based on the ship roll dynamics model; In the state prediction equation, the gyro integrated angle, the compensated pendulum angle, and the accelerometer inclination are used as the three observation values of multi-source observation and input; S3. Adaptive dynamic adjustment of process noise: Dynamically adjust the process noise parameters according to the change rate of the roll angle, and adjust the observation noise weight based on the energy of the high-frequency component of the acceleration; The change rate of the roll angle is obtained by integrating the gyroscope angular velocity; S4. Drift compensation: Online estimate and correct the gyroscope zero bias under quasi-static conditions; S5. Fault tolerance and output: Monitor the health status of the sensors, and switch to the degraded mode when abnormal; Output the fused high-precision roll angle and angular velocity data.

[0006] Preferably, the state prediction equation in step S2 further includes: Predict the roll angle at the next moment through a discrete-time model, and the calculation formula is: predicted roll angle = roll angle at the previous moment + time interval × angular velocity - time interval × gyroscope zero bias; The angular velocity, gyroscope zero bias, pendulum delay time, and pendulum scale factor remain constant without interference, but are affected by process noise.

[0007] Preferably, the triggering condition for online estimation of the gyroscope zero bias in step S4, that is, the quasi-static condition, is: the deviation between the vertical acceleration detected by the accelerometer and the gravitational acceleration is less than 0.01g, and it lasts for more than 2 seconds; The gyroscope zero bias correction formula is: new zero bias = old zero bias + learning rate × (pendulum angle - gyro integrated angle) / stationary duration, where the learning rate is 0.1 to 0.3.

[0008] Preferably, between step S4 and S5, it further includes: S41: Use the Smith predictor structure to perform forward prediction and feedback correction on the pendulum data; the forward prediction is to calculate the delayed pendulum angle using the current angular velocity, and the formula is: predicted pendulum angle = current roll angle estimate + pendulum delay time × angular velocity; the feedback correction is to feedback the deviation between the actual pendulum data and the predicted value to the Kalman filter to dynamically update the pendulum delay time parameter; S42: Temperature drift compensation, dynamically adjust the pendulum scale factor according to the real-time temperature data; the temperature drift compensation includes: calibration stage: record the relationship between the pendulum output and the reference angle in the temperature control environment of -20°C to 60°C, and generate a temperature-scale factor look-up table; real-time stage: interpolate the current scale factor from the look-up table according to the temperature sensor data to correct the original pendulum data.

[0009] Preferably, the fault tolerance in step S5 includes: when the deviation between the pendulum data and the Kalman estimate exceeds 3 times the standard deviation, switch to the IMU and accelerometer fusion mode; when the gyroscope angular velocity exceeds 300° / s, temporarily disable the integral calculation and only use the accelerometer and pendulum data.

[0010] Preferably, in the said step S2, the state variables: ; In the formula, θ: roll angle; θ(·): angular velocity; b g : gyroscope zero bias; τ: pendulum delay time; s p : pendulum scale factor; State prediction equation: ; Δt: sampling time interval; Q k : process noise covariance matrix; Multi-source observation equation: ; In the formula, θ gyro is the gyroscope integrated angle; θ accel is the accelerometer inclination angle; θ pendulum is the compensated pendulum angle.

[0011] Preferably, in the said step S3, the dynamic adjustment of the process noise adopts: ; When the angular acceleration θ(··) increases, that is, during intense motion, the process noise tolerance is increased accordingly, λ = 0.1 to 0.5; Observation noise parameter: ; Through the high-frequency component energy of the acceleration, where the vibration is 5 - 20Hz, dynamically reduce the accelerometer weight K = 0.1 to 0.3, σaccel is the statistical standard deviation of the random noise component in the accelerometer output signal, which is used to characterize the uncertainty of acceleration measurement.

[0012] Preferably, in the step S42, the relationship between the temperature T and the scale factor s p is based on: ; The coefficients k1 and k2 are calibrated through a temperature chamber experiment, and s p0 is obtained during calibration.

[0013] Preferably, in the step S1, the IMU module and the tilt sensor need to be fixed near the vertical line of the ship's center of gravity to avoid errors introduced by hull deformation, and through laser calibration, ensure that the X-axis of the IMU is strictly parallel to the ship's roll axis, with an error < 0.5°. After installation, enter the calibration process, including: A1. Static calibration, the ship is in the calm waters of the dock: Collect 10 minutes of static data to calibrate the initial zero bias b g0 and the pendulum scale factor s p0 Calculate the installation error angle: ; A2. Dynamic calibration, ship navigation test: Through a sine swing experiment with a period of 5 - 10 seconds, calibrate the dynamic parameters I, C, K, and record the noise parameters Q k , R k under different sea conditions, and establish a pattern library.

[0014] Based on the above method, a ship tilt measurement system based on Kalman filter fusion is also proposed, which includes: an IMU unit, a pendulum or capacitive tilt sensor, a temperature sensor, a multi-source data synchronous acquisition module, and a core processor; the IMU unit includes a gyroscope and an accelerometer; the core processor is built-in with a Kalman filter fusion core algorithm and a fault diagnosis and degradation control logic; the IMU unit, the pendulum or capacitive tilt sensor are rigidly installed near the vertical line of the ship's center of gravity, and through laser calibration, ensure that the coordinate system alignment error is less than 0.5°.

[0015] The innovation points of the present invention are: 1. Delay dynamic compensation: Through the combined action of the Smith predictor and the Kalman state estimation, the influence of the pendulum delay is reduced from 200 ms to within 50 ms; 2. Noise adaptability: Based on the dynamic noise adjustment of vibration spectrum analysis, the accelerometer can still effectively participate in the fusion under severe vibration; 3. Full parameter online estimation: Simultaneously estimate the sensor zero bias, scale factor, delay time, and dynamic parameters to achieve calibration-free deployment.

[0016] The present invention has cost and performance advantages. Its hardware cost is less than $200 (IMU $50 + pendulum sensor $120 + processor $30). For the benchmark systems, the cost of the fiber optic gyroscope solution with the same performance is more than $5000, and the cost of the GNSS / INS fusion solution is more than $3000.

[0017] The applicable ship types of the present invention include but are not limited to: inland river ships, small unmanned boats, and ocean buoys.

[0018] The detection accuracy requirements of the present invention are: static ±0.3°, dynamic ±1.0°, meeting the requirements of IMO MSC.267(85) for inclination monitoring.

[0019] By using the method and system provided by the present invention for inclination measurement, it is possible to effectively avoid the cumulative error of the inclination angle caused by the integration error of the gyroscope zero bias, the dynamic interference of the accelerometer, the sensor noise and temperature drift, the GNSS dependence, etc. This solution deeply explores the physical characteristics of low-cost sensors through Kalman filtering, and realizes the performance close to that of high-end systems at the algorithm level, providing a cost-effective engineering solution for ship attitude monitoring and having significant technological progress in this field. Description of the Drawings

[0020] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0021] Figure 1 It is a flowchart of the inclination measurement method described in the present invention. Detailed Embodiments

[0022] All the components selected in this application (components without specific structures described) are common standard components or components known to those skilled in the art, and their structures and principles can be known by those skilled in the art through technical manuals or by conventional experimental methods.

[0023] In the description of the embodiments of the present invention, unless otherwise clearly defined and limited, the terms "installation", "connection", and "coupling" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0024] In the description of the present invention, it should be noted that the orientation or positional relationship indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention. In addition, the terms "first", "second", "third" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance.

[0025] In several embodiments provided by the present application, it should be understood that the disclosed systems, devices, and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of the units is only a logical function division, and there can be other division methods in actual implementation. For another example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed coupling or direct coupling or communication connection to each other can be through some communication interfaces, and the indirect coupling or communication connection of the devices or units can be in electrical, mechanical, or other forms.

[0026] The units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they can be located in one place or distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0027] In addition, in each embodiment of the present invention, the functional units can be integrated into one processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit. Embodiment 1

[0028] As Figure 1 shown, the ship roll measurement method based on Kalman filter fusion of the present invention includes the following steps: S1. Synchronously collect data from multiple sensors: Obtain triaxial angular velocity and triaxial acceleration data through the IMU module, obtain absolute roll angle data through a pendulum-type or capacitive tilt sensor, and obtain temperature data through a temperature sensor; S2. State space modeling and Kalman filter fusion, with the goal of: establishing a multi-variable model that describes the dynamic change of the ship's roll angle, covering sensor errors and environmental disturbances; first define the state variables: θ: The roll angle to be estimated (core output) θ(·): Angular velocity (obtained by integrating the gyroscope angular velocity) b g : Gyroscope zero bias (error accumulated over time, which needs to be dynamically corrected) τ: Mechanical delay time of the pendulum sensor (compensate for signal lag) s p : Pendulum scale factor (correct sensitivity changes caused by temperature / aging); Then construct a state prediction equation based on the ship's rolling dynamics model; in the state prediction equation, input the gyro-integrated angle, the compensated pendulum angle, and the accelerometer inclination angle as the three observation values of multi-source observation; Observation value definition: Observation 1 (gyro integration): Subtract b from the gyroscope angular velocity g and then integrate to get θ gyro ; Observation 2 (pendulum sensor): Original pendulum angle × s p + τ × θ(·) (compensate for delay and scale error); Observation 3 (accelerometer): Calculate the instantaneous inclination angle θ through the acceleration component accel ; Data weight assignment: Static condition: High weight for the accelerometer (θ accel is reliable), low weight for the gyroscope; Dynamic condition: When vibration is detected, reduce the weight of the accelerometer and increase the proportion of gyroscope and pendulum data;; Delay compensation: Use the predicted θ(·) to correct the lag of the pendulum data in advance. The goal of this step: Establish a multivariate model describing the dynamic change of the ship's roll angle, covering sensor errors and environmental disturbances; S3. Adaptive dynamic adjustment of process noise: Dynamically adjust the process noise parameter according to the change rate of the roll angle, and adjust the observation noise weight based on the energy of the high-frequency component of the acceleration; The change rate of the roll angle is obtained by integrating the gyroscope angular velocity; Decomposition of this step: a. Process noise adjustment Vigorous motion detection: Judge by the fluctuation amplitude of the roll angle change rate θ(·).

[0029] Adjustment strategy: The more vigorous the motion, the larger the process noise parameter Q k increases (allowing a larger model prediction deviation); Observation noise adjustment Accelerometer weight reduction: When high-frequency vibration (such as engine vibration) is detected, increase its noise parameter R accel .

[0030] Pendulum reliability assessment: Statistically analyze the deviation between the pendulum and the Kalman estimated value in the long term. When the deviation is too large, increase R pendulum .

[0031] S4. Drift Compensation: Online estimate and correct the gyroscope zero bias under quasi-static conditions; S5. Fault Tolerance and Output: Monitor the health status of the sensors, and switch to the degraded mode in case of anomalies; Output the high-precision roll angle and angular velocity data after fusion.

[0032] More specifically, the state prediction equation in step S2 further includes: Predict the roll angle at the next moment through a discrete-time model, and the calculation formula is: Predicted roll angle = Roll angle at the previous moment + Time interval × Angular velocity - Time interval × Gyroscope zero bias; In this example, the time interval is fixedly set to 10 ms; The angular velocity, gyroscope zero bias, pendulum delay time, and pendulum scale factor remain constant without interference, but are affected by process noise. Noise management: Dynamically adjust the prediction credibility according to the severity of ship motion, and relax the constraints during severe motion.

[0033] More specifically, the trigger condition for online estimation of the gyroscope zero bias in step S4, i.e., the quasi-static condition, is: The deviation between the vertical acceleration detected by the accelerometer and the gravitational acceleration is less than 0.01g and lasts for more than 2 seconds; The gyroscope zero bias correction formula is: New zero bias = Old zero bias + Learning rate × (Pendulum angle - Gyro integral angle) / Static duration, where the learning rate is 0.1 - 0.3.

[0034] More specifically, between steps S4 and S5, it also includes: S41: Use the Smith predictor structure to perform forward prediction and feedback correction on the pendulum data; Forward prediction is to calculate the delayed pendulum angle using the current angular velocity, and the formula is: Predicted pendulum angle = Current roll angle estimate + Pendulum delay time × Angular velocity; Feedback correction is to feedback the deviation between the actual pendulum data and the predicted value to the Kalman filter to dynamically update the pendulum delay time parameter; S42: Temperature drift compensation, dynamically adjust the pendulum scale factor according to the real-time temperature data; Temperature drift compensation includes: Calibration stage: In the temperature control environment of -20°C to 60°C, record the relationship between the pendulum output and the reference angle to generate a temperature-scale factor look-up table; Real-time stage: Interpolate the current scale factor from the look-up table according to the temperature sensor data to correct the original pendulum data.

[0035] More specifically, the fault tolerance in step S5 includes: When the deviation between the pendulum data and the Kalman estimated value exceeds 3 times the standard deviation, switch to the IMU and accelerometer fusion mode; When the gyroscope angular velocity exceeds 300° / s, temporarily disable the integral calculation and only use the accelerometer and pendulum data.

[0036] More specifically, in step S2, the state variables: ; where θ: Roll angle; θ(·): Angular velocity; bg : Gyroscope zero bias; τ: Pendulum delay time; s p : Pendulum scale factor; State prediction equation: ; Δt: Sampling time interval; Q k : Process noise covariance matrix; Multi-source observation equation: ; Where θ gyro is the gyro integrated angle; θ accel is the accelerometer tilt angle; θ pendulum is the compensated pendulum angle.

[0037] More specifically, in the step S3, the process noise dynamic adjustment adopts: ; When the angular acceleration θ(··) increases, i.e., during intense motion, the process noise tolerance is increased accordingly, λ = 0.1 - 0.5; Observation noise parameters: ; Through the energy of the high-frequency component of the acceleration, where the vibration is 5 - 20 Hz, the weight of the accelerometer is dynamically reduced, K = 0.1 - 0.3, σ accel is the statistical standard deviation of the random noise component in the accelerometer output signal, used to characterize the uncertainty of the acceleration measurement.

[0038] More specifically, in the step S42, the relationship model between the temperature T and the scale factor s p is based on: ; The coefficients k1, k2 are calibrated through a temperature chamber experiment, and s p0 is obtained during calibration.

[0039] More specifically, in the step S1, the IMU module and the tilt sensor need to be fixed near the vertical line of the ship's center of gravity to avoid errors introduced by hull deformation, and through laser calibration, ensure that the X-axis of the IMU is strictly parallel to the ship's roll axis, with an error < 0.5°. After installation, enter the calibration process, including: A1. Static calibration, the ship is in the calm waters of the dock: Collect 10 minutes of static data to calibrate the initial zero bias b g0 and the pendulum scale factor s p0 Calculate the installation error angle: ; A2. Dynamic calibration, ship navigation test: Through a sine sway experiment with a period of 5 - 10 seconds, calibrate the dynamic parameters I, C, K, and record the noise parameters Q, k , R k under different sea conditions, and establish a pattern library. Example 2

[0040] In step S4 of Example 1, the zero-bias online estimation is expressed by the following formula: ; Set the inclination reset mechanism: ; Example 3

[0041] Fault-tolerant design, sensor health monitoring: Gyroscope: Detect the saturation state (angular velocity > 300° / s); Pendulum: Detect jamming (variance < 0.01° for 10 seconds); Degraded mode: When a single sensor fails, switch to the IMU + accelerometer fusion mode; When two sensors fail, enable pure gyro integration (manual intervention required). Example 4

[0042] The ship tilt measurement system based on Kalman filter fusion described in the present invention includes: an IMU unit, a pendulum or capacitive tilt sensor, a temperature sensor, a multi-source data synchronous acquisition module, and a core processor; the IMU unit includes a gyroscope and an accelerometer; the core processor is built-in with a Kalman filter fusion core algorithm and a fault diagnosis and degradation control logic; the IMU unit, the pendulum or capacitive tilt sensor are rigidly installed near the vertical line of the ship's center of gravity, and the coordinate system alignment error is ensured to be less than 0.5° through laser calibration. Example 5

[0043] 1. Simulation test (Monte Carlo method)

[0044] 2. Real ship test (a certain type of inland river cargo ship) Test conditions: Wave height 0.5 - 1.5 m, rolling period 8 - 12 seconds Comparison benchmark: High-precision fiber optic gyro (RMS error 0.1°) Results: RMS error: 0.25° (steady operating condition), 0.45° (severe rolling) Maximum instantaneous error: 1.2° (appearing at the moment of surge impact).

[0045] By using the method and system provided by the present invention for tilt measurement, it is possible to effectively avoid the cumulative error of tilt angle caused jointly by gyro zero-bias integration error, accelerometer dynamic interference, sensor noise and temperature drift, GNSS dependence, etc. Through multi-sensor deep coupling and intelligent filtering algorithms, the available accuracy can still be maintained, without relying on satellite data, with stronger stability. Compared with GNSS and IMU solutions, the hardware cost can be significantly reduced, especially in the ship modification, there are advantages in terms of cost and simple installation and configuration; it is also applicable to GNSS-denied or cost-sensitive scenarios such as inland river ships, unmanned boats, and offshore buoys.

[0046] Although the embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A ship inclination measurement method based on Kalman filter fusion, characterized in that: The steps include: S1. Multi-sensor synchronous data acquisition: obtain three-axis angular velocity and three-axis acceleration data through the IMU module, obtain absolute inclination data through the pendulum or capacitive inclination sensor, and obtain temperature data through the temperature sensor; S2. State space modeling and Kalman filter fusion: First, define a set of state variables, including roll angle, angular velocity, gyro bias, pendulum delay time, and pendulum scale factor. The roll angle is the value to be output, the angular velocity is obtained by the IMU module, the gyro bias is the corrected value, the pendulum delay time is the preset value, and the pendulum scale factor is dynamically adjusted according to the real-time temperature data. Then, a state prediction equation is constructed based on the ship roll dynamics model. In the state prediction equation, the gyro integral angle, the compensated pendulum angle, and the accelerometer inclination angle are input as three observation values ​​of multi-source observation. S3, adaptive dynamic adjustment of process noise: according to the rate of change of the roll angle, dynamically adjust the process noise parameters, and adjust the observation noise weight based on the energy of the high-frequency component of acceleration; the rate of change of the roll angle is obtained by integrating the angular velocity of the gyroscope; S4, drift compensation: online estimation and correction of gyro bias under quasi-static conditions; S5, Fault tolerance and output: monitor the health status of the sensor and switch to degraded mode when an abnormality occurs; output the fused high-precision roll angle and angular velocity data.

2. The ship inclination measurement method based on Kalman filter fusion according to claim 1 is characterized in that: The state prediction equation in step S2 further includes: predicting the roll angle at the next moment through a discrete time model, and the calculation formula is: roll angle prediction value = roll angle at the previous moment + time interval × angular velocity - time interval × gyroscope zero bias; angular velocity, gyroscope zero bias, pendulum delay time and pendulum scale factor remain constant when there is no interference, but are affected by process noise.

3. The ship inclination measurement method based on Kalman filter fusion according to claim 2 is characterized in that: The trigger condition for the online estimation of the gyroscope zero bias in step S4, i.e., the quasi-static condition, is: the accelerometer detects that the deviation between the vertical acceleration and the gravity acceleration is less than 0.01g and lasts for more than 2 seconds; the gyroscope zero bias correction formula is: new zero bias = old zero bias + learning rate × (pendulum angle - gyro integral angle) / static duration, where the learning rate is 0.1~0.

3.

4. The ship inclination measurement method based on Kalman filter fusion according to claim 3 is characterized in that: Also included between steps S4 and S5: S41: The Smith predictor structure is used to perform forward prediction and feedback correction on the pendulum data; the forward prediction is to use the current angular velocity to calculate the delayed pendulum angle, and the formula is: predicted pendulum angle = current roll angle estimate + pendulum delay time × angular velocity; the feedback correction is to feed back the deviation between the actual pendulum data and the predicted value to the Kalman filter, and dynamically update the pendulum delay time parameter; S42: Temperature drift compensation, dynamically adjusting the pendulum scale factor according to real-time temperature data; temperature drift compensation includes: calibration phase: in a temperature-controlled environment of -20°C to 60°C, recording the relationship between the pendulum output and the reference angle, generating a temperature-scale factor lookup table; real-time phase: interpolating the current scale factor from the lookup table according to the temperature sensor data, and correcting the original pendulum data.

5. The ship inclination measurement method based on Kalman filter fusion according to claim 4 is characterized in that: The fault tolerance in step S5 includes: when the deviation between the pendulum data and the Kalman estimation value exceeds 3 times the standard deviation, switching to the IMU and accelerometer fusion mode; when the gyroscope angular velocity exceeds 300° / s, temporarily disabling the integral calculation and using only the accelerometer and pendulum data.

6. The ship inclination measurement method based on Kalman filter fusion according to claim 5 is characterized in that: In step S2, the state variables are: ； Where θ: roll angle; θ(·): angular velocity; b g : gyroscope zero bias; τ: pendulum delay time; s p : pendulum scale factor; State prediction equation: ； Δt: sampling time interval; Q k : process noise covariance matrix; Multi-source observation equation: ； Where θ gyro is the gyro integrated angle; θ accel is the accelerometer inclination angle; θ pendulum To compensate for the rear pendulum angle.

7. The ship inclination measurement method based on Kalman filter fusion according to claim 6 is characterized in that: In step S3, the process noise is dynamically adjusted by: ； When the angular acceleration θ(··) increases, i.e., when the motion is intense, the process noise tolerance increases accordingly, λ=0.1~0.5; Observation noise parameters: ； Through the high-frequency component energy of acceleration, where it is 5-20Hz vibration, dynamically reduce the accelerometer weight K=0.1~0.3, σ accel It is the statistical standard deviation of the random noise component in the accelerometer output signal and is used to characterize the uncertainty of acceleration measurement.

8. The ship inclination measurement method based on Kalman filter fusion according to claim 7 is characterized in that: In step S42, the temperature T and the scaling factor s p The relational model is based on: ； The coefficients k1 and k2 are calibrated by temperature chamber experiments. p0 Obtained during calibration.

9. The ship inclination measurement method based on Kalman filter fusion according to claim 8, characterized in that: In step S1, the IMU module and the inclination sensor need to be fixed near the vertical line of the ship's center of gravity to avoid errors introduced by hull deformation, and laser calibration is used to ensure that the X-axis of the IMU is strictly parallel to the ship's roll axis with an error of less than 0.5°. After installation, the calibration process is entered, including: A1. Static calibration, ship to dock in calm waters: Collect 10 minutes of static data and calibrate the initial zero bias b g0 and the pendulum scaling factor s p0 Calculate the installation error angle: ； A2. Dynamic calibration, ship navigation test: Through the sinusoidal swaying experiment with a period of 5-10 seconds, the dynamic parameters I, C, K are calibrated, and the noise parameter Q under different sea conditions is recorded. k ,R k , build a pattern library.

10. A ship inclination measurement system based on Kalman filter fusion, characterized in that: include: IMU unit, pendulum or capacitive tilt sensor, temperature sensor, multi-source data synchronous acquisition module, core processor; The IMU unit includes a gyroscope and an accelerometer; the core processor has a built-in Kalman filter fusion core algorithm and fault diagnosis and degradation control logic; the IMU unit and pendulum or capacitive inclination sensor are rigidly installed near the vertical line of the ship's center of gravity, and laser calibration is used to ensure that the coordinate system alignment error is less than 0.5°.

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