CN115950423A - Ship heave motion measurement method based on adaptive filtering - Google Patents
Ship heave motion measurement method based on adaptive filtering Download PDFInfo
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Abstract
The invention discloses a ship heave motion measurement method based on adaptive filtering, which collects the output data of each axis gyroscope and accelerometer of an inertia measurement unit in real time; obtaining the heave motion acceleration of the ship and the heave acceleration of the ship at the Nth point in the geographic coordinate system; carrying out FFT (fast Fourier transform) on the ship heave acceleration information so as to determine the fundamental wave frequency and wave height of the heave displacement; analyzing the error of the filter and the error of the sensor, and obtaining the self-adaptive cut-off frequency when the error function is the minimum value; designing a transfer function of the analog high-pass filter according to the self-adaptive cut-off frequency; obtaining an analog low-pass filter through a complementary idea; and (3) utilizing a non-delay digital high-pass filter to carry out three-time filtering on acceleration, speed and displacement and outputting the information of the heave movement and the displacement of the ship in real time. The invention can adaptively adjust the cut-off frequency according to various sea conditions and combine a self-adaptive time-delay-free high-pass digital filter with complementary ideas, so that the heave displacement error is minimum.
Description
Technical Field
The invention belongs to the field of ship motion measurement, and particularly relates to a ship heave motion measurement method based on adaptive filtering.
Background
Many offshore operations, such as sailing supply, take-off and landing of carrier-based aircraft, seabed surveying and mapping, and operation of offshore cranes, etc., require compensation for vessel heave motions caused by complex marine environmental factors such as sea waves, sea winds, ocean currents, etc., which requires real-time and accurate vessel heave motion information. The strapdown inertial navigation technology is an autonomous navigation technology which is mature in development, high in precision and excellent in stability. Therefore, the method adopts the strapdown inertial navigation system to measure the heave speed and displacement information of the ship, and the measured data of the inertial navigation system needs to be processed because the high-precision speed and displacement information can not be continuously obtained for a long time due to the error accumulation and high channel divergence characteristics of the inertial navigation system.
At present, scholars at home and abroad try to find an effective means for measuring ship heave information, and a standard heave filter realizes the quick attenuation of low-frequency components of input signals and the quadratic integration of a specific frequency band. This method has certain limitations due to the phase problem of the standard heave filter and the dependence of the result on the characteristics of the marine environment and noise. The time delay is reduced as much as possible by a complementary filtering method to ensure the correctness of the signal phase, but the pre-designed filter parameters cannot meet the real-time requirement of sea state change. By designing the Butterworth filter capable of adaptively adjusting the cut-off frequency according to various sea conditions and different ship bodies, the heave displacement error is minimized.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a ship heave measurement method based on adaptive filtering, so that the method can realize real-time accurate measurement of heave information under different sea conditions.
The technical scheme is as follows: the invention relates to a ship heave measurement method based on adaptive filtering, which comprises the following steps of:
(1) Acquiring output data of gyroscopes and accelerometers of various axes of an inertial measurement unit installed in a ship in real time;
(2) Calculating to obtain an attitude matrix of the carrier coordinate system b and the geographic coordinate system N, and obtaining the heave motion acceleration of the ship under the geographic coordinate system and the heave acceleration of the ship at the Nth point;
(3) FFT is carried out on the ship heave acceleration information to obtain the heave accelerationAmplitude spectrum and phase spectrum of the degree, and further determining fundamental frequency omega of heave displacement i Sum wave height A i ；
(4) Noise σ of the sensor 2 Constant in operation, analyzing the error of filter and the error of sensor to obtain the total estimated error function, deriving it, and obtaining the self-adaptive cut-off frequency omega when the error function is minimum c ；
(5) Analog high-pass filter H designed according to adaptive cut-off frequency h (s) a transfer function; by means of complementary idea, an analog low-pass filter H is obtained l (s); converting the analog low-pass transfer function to a digital low-pass transfer function using bilinear z-transform; finally, a complementary method is utilized again to obtain the needed digital high-pass filter without time delay;
(6) And (3) utilizing a non-delay digital high-pass filter to carry out three-time filtering on the acceleration, the speed and the displacement and outputting the heave movement and the displacement information of the ship in real time.
Further, the step (2) is realized as follows:
wherein v is n Is the speed under the geographic coordinate system;
the acceleration under a carrier coordinate system is adopted; g n The projection of the gravity acceleration under the navigation coordinate system; />
The earth rotation and the Ge-type compensation terms;
the acceleration of the ship heaving direction at the Nth point is as follows:
a h (N)＝a z (N)-g n (N)-b-ζ
wherein, a z (N) is
B is a constant deviation,ζ is the random noise error of the sensor itself.
Further, the wave height A in the step (3) i Comprises the following steps:
A i further using the ith value a acquired from the acceleration signal i To indicate that i =1,2.. N:
wherein, ω is i Is the fundamental frequency of the heave displacement, a i Is the ith value acquired by the acceleration signal.
Further, the adaptive cut-off frequency ω in step (4) c The method is realized by the following formula:
the variance of the total estimation error as an error function:
wherein σ 2 Is the variance of the sensor noise, which is then differentiated to find ω when the error function is at a minimum c ：
Wherein, ω is i Is the fundamental frequency of the heave displacement, a i Is the ith value acquired by the acceleration signal.
Further, the high pass filter H in the step (5) h The transfer function of(s) is:
wherein, ω is c Is an adaptive cut-off frequency.
Has the advantages that: compared with the prior art, the invention has the beneficial effects that: the same ship does heave motion under different sea conditions, when the heave motion is calculated, signal errors exist, filtering is needed to be carried out firstly, but the optimal cut-off frequency of the designed filter is different under different sea conditions, so the invention designs the self-adaptive time-delay-free high-pass digital filter which can carry out self-adaptive adjustment on the cut-off frequency according to various sea conditions and combines complementary ideas, and the heave displacement errors are minimized.
Drawings
FIG. 1 is a diagram of the present invention;
FIG. 2 is a flow chart of an algorithm for an adaptive high pass filter;
FIG. 3 is a heave motion profile for condition one;
fig. 4 is a heave motion profile for condition two.
Detailed Description
The technical scheme of the invention is explained in detail in the following with the accompanying drawings.
The invention provides a ship heave measurement method based on adaptive filtering, which specifically comprises the following steps as shown in figure 1:
Step 2, calculating to obtain an attitude matrix of a carrier coordinate system b and a geographic coordinate system n, wherein the ship heaving motion acceleration under the geographic coordinate system can be obtained by the following formula;
in the formula: v. of n The speed under the navigation coordinate system;
the acceleration under a carrier coordinate system is used; g n The projection of the gravity acceleration under the navigation coordinate system; />
For earth rotation and brother formula compensation term, when the naval vessel speed is not big, can neglect, the above formula can simplify to:
in summary, the acceleration of the vessel heaving direction at the nth point can be expressed as:
a h (N)＝a z (N)-g n (N)-b-ζ
in the formula: a is z (N) is
B is a constant deviation, and ζ is a random noise error of the sensor itself.
Step 3, carrying out FFT (fast Fourier transform) on the ship heave acceleration information to obtain an amplitude spectrum and a phase spectrum of the heave acceleration, and further determining the fundamental frequency omega of the heave displacement i Sum wave height A i ：
In the formula: h is 2 (t) represents the displacement of the heave movement. Thus, A i Further, the ith value a collected from the acceleration signal may be used i To indicate that i =1,2.. N:
wherein, ω is i Is the fundamental frequency of heave displacement and ai is the ith value acquired for the acceleration signal.
Step 4, the noise σ of the sensor can be assumed 2 Constant in operation, analyzing the filter error and the sensor error to obtain a total estimation error function, deriving the total estimation error function, and adapting the cut-off frequency omega when the error function is minimum c 。
The heave displacement error of the ship processed by the filter can be expressed as:
h 1 (n)＝h 2 (n)-h(n)＝(1-s 2 H(s))h 2 -H(s)(g+b+ζ)
in the formula: h is a total of 2 And (n) is the estimated value of the heave displacement of the ship after filtering treatment, and h (n) is the true value of the heave displacement of the ship. The variance of the total estimation error as an error function:
wherein σ 2 Is the variance of the sensor noise, then it is derived, when the error function is minimum, it is calculated as omega c ：
Wherein, ω is i Is the fundamental frequency of heave displacement, a i Is the ith value acquired by the acceleration signal.
Step 5, as shown in fig. 2, substituting the adaptive frequency into the system function of the second-order normalization butterworth high-pass filter to design the simulation high-pass filter H h (s) a transfer function; by means of complementary idea, an analog low-pass filter H is obtained l (s); converting the analog low-pass transfer function to a digital low-pass transfer function using bilinear z-transform; finally, the complementary method is used again to obtain the needed digital high-pass filter without time delay.
In the formula, only one variable is used for self-adapting cut-off frequency omega c To find ω c A butterworth high pass filter system function is obtained.
And 6, filtering the acceleration, the speed and the displacement for three times by using a non-delay digital high-pass filter and outputting the information of the heave movement and the displacement of the ship in real time.
The method comprises the steps of utilizing a certain type of MEMS inertial navigation system to perform experiments on a sea wave simulation motion platform, placing a laser range finder on the sea wave simulation motion platform, measuring the relative motion from a table top to a laboratory roof, and obtaining real-time heave displacement through conversion, wherein the gyro constant value in the MEMS inertial navigation system drifts by about 0.75 degree/s, and the successive starting constant value of an accelerometer is about 15mg (g =9.8 m/s) 2 ). And recording the heave acceleration data measured by the inertial navigation system and the heave displacement data measured by the laser range finder for post-processing and analysis, and taking the heave displacement measured by the laser range finder as a reference standard for comparing the precision of a heave motion processing algorithm.
A heave motion curve in a period of 80-120 s for simulating a wave heave motion with a maximum amplitude of 0.20m and a cycle of 10s is shown in fig. 3, a solid line is reference heave motion data, and a dotted line, a dash-dot line and a dotted line respectively represent results obtained by estimating an adaptive filter, a Butterworth filter and a fixed-parameter filter. Meanwhile, the accuracy of the various methods is shown in table 1 for the ratios:
table 1 shows the accuracy statistics under different experimental conditions
Similarly, it can be obtained that the heave motion curve graph of 80-120 s period of the wave heave motion with the condition two simulated maximum amplitude of 0.25m and the cycle of 11s is shown in fig. 4, and the heave measurement accuracy statistics are shown in table 1:
comparing the errors in the table shows that: compared with the complementary filter, the maximum error of the adaptive filter estimated under the condition one and the condition two is respectively reduced by 64 percent and 63 percent, the average error value is respectively reduced by about 50 percent and 64 percent, and the mean square error is respectively reduced by 58 percent and 75 percent. Compared with the first condition, the numerical values of the mean value and the mean square error of the error processed by the complementary filter in the second condition are multiplied, and the variation amplitude of the adaptive filter is not large; therefore, when the sea condition changes, the self-adaption of the complementary filter is insufficient, the self-adaption filter can perform self-adaption setting along with the amplitude and the frequency of heave motion, the estimation precision is higher, and the capability of adapting to the amplitude and the periodic variation of sea waves is stronger.
In summary, the invention relates to a self-adaptive filtering method for ship heave measurement. According to the method, the frequency domain analysis is carried out on the heave acceleration to obtain the frequency characteristic of the heave movement, the optimal cut-off frequency of the filter is further obtained, and then the self-adaptive digital high-pass filter is designed on the basis of the optimal cut-off frequency and the complementary idea. And the real-time accurate measurement of the heave information is realized.
The foregoing shows and describes the general principles and broad features of the present invention and advantages thereof. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (5)
1. A ship heave motion measurement method based on adaptive filtering is characterized by comprising the following steps:
(1) Acquiring output data of gyroscopes and accelerometers of various axes of an inertial measurement unit installed in a ship in real time;
(2) Calculating to obtain an attitude matrix of the carrier coordinate system b and the geographic coordinate system N, and obtaining the heave motion acceleration of the ship under the geographic coordinate system and the heave acceleration of the ship at the Nth point;
(3) FFT is carried out on the ship heave acceleration information to obtain the amplitude spectrum and the phase spectrum of the heave acceleration, and then the fundamental wave frequency omega of the heave displacement is determined i Sum wave height A i ；
(4) Noise σ of the sensor 2 Constant in operation, analyzing the error of filter and the error of sensor to obtain the total estimated error function, deriving it, and obtaining the self-adaptive cut-off frequency omega when the error function is minimum c ；
(5) Analog high-pass filter H designed according to adaptive cut-off frequency h (s) a transfer function; by means of complementary idea, an analog low-pass filter H is obtained l (s); converting the analog low-pass transfer function to a digital low-pass transfer function using bilinear z-transform; finally, a complementary method is utilized again to obtain the needed digital high-pass filter without time delay;
(6) And (3) utilizing a non-delay digital high-pass filter to carry out three-time filtering on the acceleration, the speed and the displacement and outputting the heave movement and the displacement information of the ship in real time.
2. The method for measuring the heave motion of the ship based on the adaptive filtering is characterized in that the step (2) is realized by the following steps:
wherein v is n Is the speed under the geographic coordinate system;
the acceleration under a carrier coordinate system is used; g n The projection of the gravity acceleration under the navigation coordinate system; />
Is the earth selfA cross-and-brother compensation term;
the acceleration of the ship heaving direction at the Nth point is as follows:
a h (N)＝a z (N)-g n (N)-b-ζ
wherein, a z (N) is
B is a constant deviation, and ζ is a random noise error of the sensor itself.
3. The method for measuring heave motion of ship based on adaptive filtering as claimed in claim 1, wherein the wave height A in step (3) i Comprises the following steps:
A i further using the ith value a acquired from the acceleration signal i To indicate that i =1,2.. N:
wherein, ω is i Is the fundamental frequency of the heave displacement, a i Is the ith value acquired by the acceleration signal.
4. The method for measuring heave motion of ship based on adaptive filtering as claimed in claim 1, wherein the adaptive cut-off frequency ω in step (4) is c The method is realized by the following formula:
the variance of the total estimation error as an error function:
wherein σ 2 Is the variance of the sensor noise, which is then differentiated to find ω when the error function is at a minimum c ：
Wherein, ω is i Is the fundamental frequency of the heave displacement, a i Is the ith value acquired by the acceleration signal.
5. The ship heave motion measurement method based on adaptive filtering according to claim 1, wherein the high-pass filter H in the step (5) is h The transfer function of(s) is:
wherein, ω is c Is an adaptive cut-off frequency.
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| CN117928528A (en) * | 2024-03-22 | 2024-04-26 | 山东科技大学 | Ship heave measurement method based on self-adaptive time-delay-free complementary band-pass filter |
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| CN117928528A (en) * | 2024-03-22 | 2024-04-26 | 山东科技大学 | Ship heave measurement method based on self-adaptive time-delay-free complementary band-pass filter |
| CN117928528B (en) * | 2024-03-22 | 2024-05-31 | 山东科技大学 | Ship heave measurement method based on self-adaptive time-delay-free complementary band-pass filter |
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