A method for measuring ship heave motion based on adaptive filtering

Abstract

The present invention discloses a ship heave motion measurement method based on adaptive filtering. The method collects the output data of the gyroscopes and accelerometers of each axis of the inertial measurement unit in real time; obtains the ship heave motion acceleration and the acceleration of the ship's heave direction at the Nth point in the geographic coordinate system; performs a FFT on the ship's heave acceleration information to determine the fundamental frequency and wave height of the heave displacement; analyzes the filter error and sensor error, and obtains an adaptive cutoff frequency when the error function is at a minimum; designs an analog high-pass filter transfer function based on the adaptive cutoff frequency; obtains an analog low-pass filter through the concept of complementarity; and uses a time-delay-free digital high-pass filter to perform triple filtering on the acceleration, velocity, and displacement, and outputs the ship's heave motion and displacement information in real time. The method can adaptively adjust the cutoff frequency according to various sea conditions and combines the adaptive time-delay-free high-pass digital filter based on the concept of complementarity to minimize the heave displacement error.

Description

Technical Field

[0001] The present invention belongs to the field of ship motion measurement, and in particular relates to a ship heave motion measurement method based on adaptive filtering. Background Art

[0002] Many maritime operations, such as replenishment underway, aircraft takeoff and landing, seabed mapping, and offshore crane operations, require compensation for the ship's heave motion caused by complex marine environmental factors such as waves, winds, and currents. This requires real-time, accurate information on the ship's heave motion. Strapdown inertial navigation technology is a relatively mature, highly accurate, and stable autonomous navigation technology. Therefore, this method uses a strapdown inertial navigation system to measure the ship's heave velocity and displacement information. However, due to the error accumulation and altitude channel divergence characteristics of the inertial navigation system, it is impossible to continuously obtain high-precision velocity and displacement information over a long period of time. Therefore, the inertial navigation system measurement data needs to be processed.

[0003] Currently, scholars at home and abroad are seeking effective methods for measuring ship heave information. Standard heave filters achieve rapid attenuation of the low-frequency components of the input signal and quadratic integration in specific frequency bands. However, this method has certain limitations due to phase issues and its dependence on the characteristics of the ocean environment and noise. Complementary filtering is used to minimize time delay to ensure signal phase accuracy, but pre-designed filter parameters cannot meet the real-time requirements of changing sea conditions. By designing a Butterworth filter that can adaptively adjust the cutoff frequency according to various sea conditions and different ship hulls, heave displacement errors are minimized. Summary of the Invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a ship heave measurement method based on adaptive filtering, so that it can achieve real-time and accurate measurement of heave information under different sea conditions.

[0005] Technical solution: The method for measuring ship heave based on adaptive filtering described in the present invention comprises the following steps:

[0006] (1) Real-time acquisition of output data from the gyroscopes and accelerometers on each axis of the inertial measurement unit installed in the ship;

[0007] (2) Calculate the attitude matrix of the carrier coordinate system b and the geographic coordinate system n, and obtain the acceleration of the ship's heave motion in the geographic coordinate system and the acceleration of the ship's heave direction at the Nth point;

[0008] (3) Perform FFT on the ship's heave acceleration information to obtain the amplitude spectrum and phase spectrum of the heave acceleration, and then determine the fundamental frequency ω of the heave displacement i and wave height A i ;

[0009] (4) Sensor noise σ 2 It is constant during operation. The filter error and sensor error are analyzed to obtain the total estimated error function, and its derivative is taken. When the error function is the minimum, the adaptive cutoff frequency ω is obtained. c ;

[0010] (5) Design analog high-pass filter H based on adaptive cutoff frequency h (s) transfer function; through the complementary idea, the analog low-pass filter H is obtained l (s); using bilinear z-transformation, the analog low-pass transfer function is converted into a digital low-pass transfer function; finally, the complementary method is used again to obtain the required delay-free digital high-pass filter;

[0011] (6) Use a time-delay-free digital high-pass filter to filter the acceleration, velocity, and displacement three times and output the ship's heave motion and displacement information in real time.

[0012] Furthermore, the implementation process of step (2) is as follows:

[0013]

[0014] Among them, v n is the speed in the geographic coordinate system; is the acceleration in the carrier coordinate system; g n is the projection of gravitational acceleration in the navigation coordinate system; is the Earth's rotation and the Coriolis compensation term;

[0015] The acceleration of the ship in the heave direction at point N is:

[0016] a h (N) = a z (N)-g n (N)-b-ζ

[0017] Among them, a z (N) is is the anteroposterior component of the Nth point, b is the constant deviation, and ζ is the random noise error of the sensor itself.

[0018] Furthermore, the wave height A in step (3) i for:

[0019]

[0020]

[0021] A i Further use the i-th value a collected from the acceleration signali To express, i=1,2...N:

[0022]

[0023] Among them, ω i is the fundamental frequency of the heave displacement, a i is the i-th value collected by the acceleration signal.

[0024] Furthermore, the adaptive cutoff frequency ω described in step (4) c This is achieved through the following formula:

[0025] The variance of the total estimation error as an error function:

[0026]

[0027] Among them, σ 2 is the sensor noise variance, and then take its derivative to obtain ω when the error function is at its minimum value c :

[0028]

[0029] Among them, ω i is the fundamental frequency of the heave displacement, a i is the i-th value collected by the acceleration signal.

[0030] Furthermore, the high-pass filter H in step (5) h The transfer function of (s) is:

[0031]

[0032] Among them, ω c is the adaptive cutoff frequency.

[0033] Beneficial effects: Compared with the prior art, the present invention has the following beneficial effects: When the same ship performs heave motion under different sea conditions, there will be signal errors when solving its heave motion, so filtering is required first, but the optimal cutoff frequency of the designed filter is different under different sea conditions. Therefore, the present invention minimizes the heave displacement error by designing an adaptive delay-free high-pass digital filter that can adaptively adjust the cutoff frequency according to various sea conditions and combines the complementary idea. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 A flowchart of the present invention;

[0035] Figure 2 This is the algorithm flow chart of the adaptive high-pass filter;

[0036] Figure 3 The heave motion curve diagram under the following conditions:

[0037] Figure 4 This is the heave motion curve for condition 2. DETAILED DESCRIPTION

[0038] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0039] The present invention provides a ship heave measurement method based on adaptive filtering, such as Figure 1 As shown, the specific steps include:

[0040] Step 1: Collect the output data of the gyroscopes and accelerometers of each axis of the inertial measurement unit installed in the ship in real time, mainly the angular velocity of the three-axis gyroscope and the acceleration of the three-axis accelerometer.

[0041] Step 2: Calculate the attitude matrix of the carrier coordinate system b and the geographic coordinate system n. The acceleration of the ship's heave motion in the geographic coordinate system can be obtained by the following formula:

[0042]

[0043] Where: v n is the speed in the navigation coordinate system; is the acceleration in the carrier coordinate system; g n is the projection of gravitational acceleration in the navigation coordinate system; is the Earth's rotation and the Coriolis compensation term, which can be ignored when the ship's speed is not large. The above formula can be simplified to:

[0044]

[0045] In summary, the acceleration of the ship in the heave direction at point N can be expressed as:

[0046] a h (N) = a z (N)-g n (N)-b-ζ

[0047] Where: a z (N) is is the anteroposterior component of the Nth point, b is the constant deviation, and ζ is the random noise error of the sensor itself.

[0048] Step 3: Perform FFT on the ship's heave acceleration information to obtain the amplitude spectrum and phase spectrum of the heave acceleration, and then determine the fundamental frequency ω of the heave displacement. i and wave height A i :

[0049]

[0050]

[0051] Where: h2(t) represents the displacement of the heave motion. Therefore, A i We can further use the i-th value a collected from the acceleration signal i To express, i=1,2...N:

[0052]

[0053] Among them, ω i is the fundamental frequency of the heave displacement, and ai is the i-th value collected by the acceleration signal.

[0054] Step 4: We can assume that the sensor noise σ 2 It is constant during operation. The filter error and sensor error are analyzed to obtain the total estimated error function, and its derivative is taken. When the error function is at its minimum value, the adaptive cutoff frequency ω is c .

[0055] The ship heave displacement error after filter processing can be expressed as:

[0056] h1(n)=h2(n)-h(n)=(1-s 2 H(s))h2-H(s)(g+b+ζ)

[0057] Where: h2(n) is the estimated value of the ship's heave displacement after filtering, and h(n) is the true value of the ship's heave displacement. The variance of the total estimation error is used as the error function:

[0058]

[0059] Among them, σ 2 is the sensor noise variance, and then take its derivative to obtain ω when the error function is at its minimum value c :

[0060]

[0061] Among them, ω i is the fundamental frequency of the heave displacement, a i is the i-th value collected by the acceleration signal.

[0062] Step 5: Figure 2 As shown, the adaptive frequency is substituted into the system function of the second-order normalized Butterworth high-pass filter to design the analog high-pass filter H h (s) transfer function; through the complementary idea, the analog low-pass filter H is obtained l(s); using bilinear z-transform, the analog low-pass transfer function is converted into a digital low-pass transfer function; finally, the complementary method is used again to obtain the required delay-free digital high-pass filter.

[0063]

[0064]

[0065] There is only one variable in the formula: adaptive cutoff frequency ω c , find ω c The Butterworth high-pass filter system function can be obtained.

[0066] Step 6: Use a time-delay-free digital high-pass filter to filter the acceleration, velocity, and displacement three times and output the ship's heave motion and displacement information in real time.

[0067] A certain type of MEMS inertial navigation system was used to conduct experiments on a wave simulation motion platform. A laser rangefinder was placed on the wave simulation motion platform to measure the relative motion between the platform and the laboratory roof. After conversion, the real-time heave displacement was obtained. The gyro constant drift in the MEMS inertial navigation system was about 0.75° / s, and the successive start constant of the accelerometer was about 15mg (g = 9.8m / s 2 The heave acceleration data measured by the inertial navigation system and the heave displacement data measured by the laser rangefinder were recorded for post-processing and analysis. In order to compare the accuracy of the heave motion processing algorithm, the heave displacement measured by the laser rangefinder was used as a reference.

[0068] The heave motion curve for the period of 80 to 120 seconds of the simulated wave heave motion with a maximum amplitude of 0.20 m and a period of 10 seconds is as follows: Figure 3 As shown in the figure, the solid line is the baseline heave motion data, and the dotted line, dashed line, and dashed line represent the results of adaptive filter, Butterworth filter, and fixed parameter filter estimation, respectively. At the same time, the accuracy comparison of various methods is shown in Table 1:

[0069] Table 1 is the accuracy statistics under different experimental conditions

[0070]

[0071] Similarly, the heave motion curve for the 80-120s period of the wave heave motion under condition 2, which simulates the maximum amplitude of 0.25m and the period of 11s, can be obtained as follows: Figure 4 The statistics of heave measurement accuracy are shown in Table 1:

[0072] Comparing the various errors in the table shows that, compared with the complementary filter, the adaptive filter reduced the maximum error in Conditions 1 and 2 by 64% and 63%, respectively, the mean error by approximately 50% and 64%, and the mean square error by 58% and 75%, respectively. Compared with Condition 1, the mean and mean square error values ​​for the complementary filter in Condition 2 increased exponentially, while the changes for the adaptive filter were minimal. This suggests that the complementary filter lacks adaptability when sea conditions change, while the adaptive filter can adapt to the amplitude and frequency of heave motion, resulting in higher estimation accuracy and greater adaptability to changes in wave amplitude and period.

[0073] In summary, the present invention relates to an adaptive filtering method for ship heave measurement. This method analyzes heave acceleration in the frequency domain to obtain the frequency characteristics of heave motion, thereby determining the optimal cutoff frequency of the filter. Based on this optimal cutoff frequency and leveraging the principle of complementarity, an adaptive digital high-pass filter is designed, enabling real-time and accurate measurement of heave information.

[0074] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for measuring ship heave motion based on adaptive filtering, characterized in that: The following steps are involved: (1) Real-time acquisition of output data from the gyroscopes and accelerometers on each axis of the inertial measurement unit installed in the ship; (2) Calculate the attitude matrix of the carrier coordinate system b and the geographic coordinate system n, and obtain the acceleration of the ship's heave motion in the geographic coordinate system and the acceleration of the ship's heave direction at the Nth point; (3) Perform FFT on the ship's heave acceleration information to obtain the amplitude spectrum and phase spectrum of the heave acceleration, and then determine the fundamental frequency ω of the heave displacement i and wave height A i ; (4) Sensor noise σ 2 It is constant during operation. The filter error and sensor error are analyzed to obtain the total estimated error function, and its derivative is taken. When the error function is the minimum, the adaptive cutoff frequency ω is obtained. c ; (5) Design analog high-pass filter H based on adaptive cutoff frequency h (s) transfer function; through the complementary idea, the analog low-pass filter H is obtained l (s); using bilinear z-transformation, the analog low-pass transfer function is converted into a digital low-pass transfer function; finally, the complementary method is used again to obtain the required delay-free digital high-pass filter; (6) Using a time-delay-free digital high-pass filter to perform three-way filtering on acceleration, velocity, and displacement and output the ship's heave motion and displacement information in real time; The implementation process of step (2) is as follows: Among them, v n is the speed in the geographic coordinate system; is the acceleration in the carrier coordinate system; g n is the projection of gravitational acceleration in the navigation coordinate system; is the Earth's rotation and the Coriolis compensation term; The acceleration of the ship in the heave direction at point N is: a h (N)=a z (N)-g n (N)-b-z Among them, a z (N) is is the anteroposterior component of the Nth point, b is the constant deviation, and ζ is the random noise error of the sensor itself.

2. The method for measuring ship heave motion based on adaptive filtering according to claim 1, characterized in that: The wave height A described in step (3) i for: Where h2(t) represents the displacement of heave motion; A i Further use the i-th value a collected from the acceleration signal i To express, i=1,2...N: Among them, ω i is the fundamental frequency of the heave displacement, a i is the i-th value collected by the acceleration signal.

3. The method for measuring ship heave motion based on adaptive filtering according to claim 1, characterized in that: The adaptive cutoff frequency ω described in step (4) c This is achieved through the following formula: The variance of the total estimation error as an error function: Where h2(n) is the estimated value of the ship heave displacement after filtering, h1(n) is the error of the ship heave displacement after filtering; σ 2 is the sensor noise variance, and then take its derivative to obtain ω when the error function is at its minimum value c : Among them, ω i is the fundamental frequency of the heave displacement, a i is the i-th value collected by the acceleration signal.

4. The method for measuring ship heave motion based on adaptive filtering according to claim 1, characterized in that: The high-pass filter H in step (5) h The transfer function of (s) is: Among them, ω c is the adaptive cutoff frequency.

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