CN115876194A - Self-adaptive ship heave measurement method based on strapdown inertial navigation - Google Patents
Self-adaptive ship heave measurement method based on strapdown inertial navigation Download PDFInfo
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Abstract
The invention provides a self-adaptive ship heave measurement method based on strapdown inertial navigation, which comprises the following steps of: 1. solving to obtain vertical acceleration a containing low-frequency harmonic waves by strapdown inertial navigation z .2. To a is to z Carrying out N-point fast Fourier transform to obtain the main heave frequency omega of the ship 0 .3. To a is to z Integrating to obtain vertical velocity information v containing low-frequency noise no_filter And using an adaptive vertical velocity high-pass filter pair v no_filter Filtering to obtain the vertical velocity v with amplitude-phase error z .4. Using RLS-BMFLC pairs v z Fitting is carried out, and the amplitude and the phase of each fundamental frequency point are corrected to obtain the accurate vertical velocity v ″ z .5. For v ″) z Integral is carried out to obtain heave information x containing low-frequency noise no_filter Using adaptive vertical displacement high pass filter to x no_filter Filtering to obtain a phase-amplitude errorDisplacement x of sink z .6. Using RLS-BMFLC pairs x z Fitting, and correcting the amplitude and phase of each fundamental frequency point to obtain accurate heave displacement x ″) z。
Description
Technical Field
The invention provides a ship heave measurement method of an adaptive band-limited Fourier linear combiner based on a recursive least square optimization weight.
Background
In the process of sea surface movement of a ship, the ship is inevitably disturbed by complex marine environment factors such as sea waves, sea winds and the like, so that the six-degree-of-freedom swinging movement is passively generated. The six degrees of freedom are even if they are rotated about three axes in a cartesian coordinate system: pitch, roll, and yaw, and move along three axes: swaying, surging, and heaving (i.e., heaving). Wherein the influence and damage to the ship by heave motions with a certain periodicity along the vertical axis are greatest. Therefore, the accurate measurement of the ship heave parameter has a great application value to the actual engineering. Because the altitude channel of the strapdown inertial navigation system comprises low-frequency harmonic interference such as Schuler oscillation, earth oscillation and the like besides zero offset and noise of the accelerometer, the velocity obtained by directly integrating the vertical acceleration is divergent. Therefore, the accurate heave motion information can be obtained by properly processing the specific gravity solved by the strapdown inertial navigation system.
Some scholars at home and abroad have some relevant researches on ship heaving information. John-Morten Godhavn provides a standard fourth-order heave filter in an Adaptive harmonic filter in motion sensor published by IEEE ocean Engineering Society, so that low-frequency harmonics are filtered and second-order integration is carried out on signals of a required frequency band, but the high-pass filter mainly has the problems of phase advance, amplitude attenuation and the like, and the measured heave information has larger error. Strictly speaking, in the navigation positioning bulletin 2016, ship heave measurement based on inertial navigation and non-delay filters, published by the 'navigation positioning bulletin' at stage 002, an IIR digital low-pass filter is designed, and then the IIR digital low-pass filter is converted into a digital high-pass filter without delay by adopting a complementary method, but the parameters of the IIR digital low-pass filter are strict and the design is difficult. Real-time Zero Phase Filtering for Heave Measurement, published by Hu Yongpan in IEEE International Conference on Electronic Measurement and Instruments, combines a digital all-pass filter to compensate for Phase, but the output Heave displacement still has amplitude attenuation and small Phase error. A Drift-Free Position Estimation of Periodic or Quasi-Periodic Motion Using initial Sensors published by Win Tun Latt in Sensors 2011 6 firstly proposes to use a band-limited Fourier linear combination (BMFLC) algorithm to fit Periodic signals, and perform phase compensation and amplitude compensation on the fitted signals, so as to estimate Periodic Motion and obtain better effect. In a patent document with the application patent number of 201710202159.5 and the name of a ship heave measurement method based on band-limited Fourier linear combination, a BMFLC algorithm is applied to measurement of ship heave information for the first time, and the method mainly comprises the steps of fitting the heave information and compensating amplitude and phase, so that amplitude-phase-frequency characteristics of a heave filter in a specific frequency band approach a quadratic integration link. But because the method has no prior heave frequency information, the fitting bandwidth is large, and the phase compensation is difficult. And the weight iteration adopts an LMS algorithm, so the algorithm precision is slightly low.
Disclosure of Invention
The invention aims to provide a ship heave measurement method based on self-adaptive recursive least square band-limited Fourier linear combiner (RLS-BMFLC) of strapdown inertial navigation, which aims to solve the problems of amplitude attenuation and phase advance of the traditional heave measurement and realize accurate measurement of ship heave information.
The purpose of the invention is realized as follows: the method comprises the following steps:
Step 2, the a obtained in the step 1 is treated z The frequency domain characteristics are obtained by an N-point Fast Fourier Transform (FFT). Because the wave period is generally 1-25 s, the corresponding frequency is 0.04-1 Hh z, the obtained amplitude values are compared in the frequency range, and the corresponding maximum value is the main wave frequency marker omega 0 。
Step 3, the vertical acceleration a obtained in the step 1 is subjected to z Performing primary integration to obtain a vertical velocity v containing low-frequency noise z_nofilter 。
Step 4, determining the transfer function of the vertical velocity high-pass filter
Wherein xi is a damping coefficient; omega c For the cut-off frequency of the system, typically take ω c ＝0.37ω 0 . Let v obtained in step 3 z_nofilter Through a vertical high pass filter. Since the signal passing through the high pass filter will produce amplitude attenuation and phase advance, the vertical velocity v obtained after filtering z Including amplitude phase errors.
Step 5. Applying RLS-BMFLC to v in step 4 z Fitting is carried out to obtain the vertical velocity v 'after fitting' z In an iterative fashion as follows
W k+1 ＝W k +G k e k
In the formula, k is iteration times; x rk ＝[X 1k X 2k … X 2Mk ] Τ Is X k One element in the RLS-BMFLC is the basic fitting quantity of each frequency point in the self-adaptive frequency band; t is a system sampling period; f. of r Fitting fundamental frequency in Hz; m is the number of frequency points in the self-adaptive frequency band; v. of k Is a vertical velocity v z The kth element of (1); v' k To the vertical velocity v k Fitting results obtained by adopting RLS-BMFLC; g k Is a recursive least squares gain; λ is a recursive least squares factor, usually in the range of [0.9,1]；P k Recursion of the least square error covariance for the previous time instant; e.g. of a cylinder k Is a recursive least squares error; w k ＝[W 1k W 2k … W 2Mk ] Τ Is W k One element in the RLS algorithm is a coefficient for correcting the weight of each frequency point in real time in the last RLS algorithm.
Step 6, calculating the amplitude attenuation m of each basic frequency point in the RLS-BMFLC according to the amplitude-phase-frequency characteristic of the vertical velocity high-pass filter in the step 4 r And phase lead p r And compensating the fitted curve to obtain the accurate vertical velocity v ″ z . The specific calculation method is as follows
m r ＝|H 1 (jω i )|
p r ＝∠H 1 (jω i )
Step 7, the accurate vertical velocity v' obtained in the step 6 is processed z Performing primary integration to obtain a vertical displacement x containing low-frequency noise z_nofilter 。
Step 8, determining the transfer function of the vertical displacement high-pass filter
Let x obtained in step 7 z_nofilter Through a digital high pass filter. Because the signal passes through the high-pass filter to generate amplitude attenuation and phase lead, the vertical displacement x obtained after filtering z Including amplitude phase errors.
Step 9. Using the same calculation method as in steps 5 and 6, first, RLS-BMFLC is used to measure the vertical displacement x z Fitting to obtain a curve x z ', subsequently to x z ' accurate heave displacement x can be obtained by compensating amplitude and phase z ″。
Compared with the prior art, the invention has the beneficial effects that: the invention can fully utilize the wave frequency as prior information, thereby adaptively changing the parameters of the vertical speed and the heave filter and the base frequency band of the Fourier linear combination, further realizing the fitting and compensation of the vertical speed and the heave parameter which generate amplitude phase errors after passing through the high-pass filter by utilizing the RLS-BMLFC, and realizing the high-precision measurement of the heave information.
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FIG. 1 is an overall flow chart of the present invention;
fig. 2 and 3 show the inventionMing H 1 (s)、H 2 (s) Bode diagram;
FIGS. 4 and 5 are schematic diagrams of the RLS-BMFLC and a schematic diagram of amplitude and phase compensation according to the present invention;
FIG. 6 is a graph comparing the error of conventional digital high pass filter measured heave (method A), conventional digital high pass filter and digital all pass filter combined measured heave (method B) and RLS-BMFLC measured heave of the present invention (method C).
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
The invention provides a ship heave measurement method of an adaptive band-limited Fourier linear combiner (RLS-BMFLC) based on a recursive least square optimization weight. The method mainly comprises the following steps: 1. solving to obtain vertical acceleration a containing low-frequency harmonic waves by strapdown inertial navigation z .2. To a z Carrying out N-point fast Fourier transform to obtain ship dominant heave frequency omega 0 .3. To a z Integrating to obtain vertical velocity information v containing low-frequency noise no_filter And using an adaptive vertical velocity high-pass filter pair v no_filter Filtering to obtain the vertical velocity v with amplitude-phase error z .4. Using RLS-BMFLC pairs v z Fitting, and correcting the amplitude and phase of each fundamental frequency point to obtain accurate vertical velocity v z ". 5. For v z "integrate to get heave information x containing low frequency noise no_filter Using adaptive vertical displacement high pass filter to x no_filter Filtering to obtain a heave displacement x containing an amplitude-phase error z .6. Using RLS-BMFLC pairs x z Fitting, and correcting the amplitude and phase of each fundamental frequency point to obtain accurate heave displacement x z ″。
(1) The period of the sea wave is mainly concentrated on 1-25 s, and the frequency of the heave motion of the ship is mainly concentrated in a narrow frequency band centered on a certain frequency. Thus, by pairing calculated a z Fast Fourier transform is carried out, the distribution condition of the dominant frequency of the heave motion in the whole heave frequency band is fully known, and a subsequent high-pass filter is subjected toThe design and RLS-BMFLC have very important significance.
(2) High-pass filter H 1 (s)、H 2 The Bode diagram of(s) is shown in fig. 2, and the cut-off frequency of the filter can be adaptively adjusted according to the ship dominant heave frequency measured by the FFT, so that the adaptive high-pass filter can effectively remove low-frequency harmonics and noise in the signal. Since the high-pass filter is a second-order Butterworth analog filter, the damping coefficient xi is generally taken as
Because the sampling signals output by the IMU are all discrete signals, the analog filter needs to be converted into a digital filter by adopting a bilinear transformation method, and the specific form of the self-adaptive high-pass digital filter is as follows
Wherein T is an IMU sampling period; omega c Is the system cutoff frequency; ξ is the damping coefficient.
(3) The ship dominant heave frequency measured by the FFT can more accurately divide the window frequency band of the RLS-BMFLC, further reduce the base frequency band width and the frequency interval in the frequency band fitted by the RLS-BMFLC, enable the estimation result to cover the base frequency point in the frequency band as much as possible, thereby realizing the high-precision fitting of the signal in the frequency band and further improving the compensation precision of the amplitude and the phase.
(4) FIG. 4 is a schematic block diagram of RLS-BMFLC. After the dominant frequency and the RLS-BMFLC fitting frequency band are determined, M parts of equal division are carried out in the frequency band to obtain each frequency point f r A linear fit is made with a sine-cosine function as the fundamental frequency. In the iteration process, a recursive least square algorithm is adopted to optimize the weight of the fundamental frequency, so that the fitting can achieve higher precision. Combining analog signals y with sine and cosine trigonometric functions k The frequency interval Δ f of the fundamental frequency point in the sum frequency band is as follows
Wherein,
is a direct current component; a is a r And b r Are respectively sine and cosine coefficients; f. of M Is the upper limit of the fitted band; f. of 1 Is the fitting lower band limit; m is the number of fundamental frequency points, and is usually 25-200. Since the high-pass filter attenuates the direct current more strongly, the direct current component can be ignored->
(5) The specific phase advance and amplitude attenuation in step 6 are as follows
Wherein the fundamental angular frequency omega i ＝2πf r ，f r Is a base frequency point.
(6) FIG. 5 is a schematic block diagram of the RLS-BMFLC compensating for amplitude and phase. The specific iterative formula for fitting and amplitude-phase compensation of heave displacement in step 9 is as follows
W k+1 ＝W k +G k e k
m r ＝|H 2 (jω i )|
p r ＝∠H 2 (jω i )
In the formula, x k Is a heave displacement x z The element at time k; x' k To a heave displacement x k Fitting results obtained by adopting RLS-BMFLC; x ″) k Is of to x' k And (4) carrying out amplitude and phase compensation to obtain accurate heave displacement.
From the above iteration form, the fundamental frequency point f is obtained in the fitting iteration process r The weight coefficient W of the frequency point is corrected in real time through the RLS algorithm all the time k To achieve a fit to the signal. In the compensation of signal amplitude and phase, only the basic fitting quantity X is compensated rk Adjusting the amplitude and the phase, not correcting the iteration weight, and still using the optimal weight W estimated by the RLS algorithm at the previous moment k . The accurate heave displacement x' can be obtained by the iteration method k 。
Claims (3)
1. A self-adaptive ship heave measurement method based on strapdown inertial navigation is characterized by comprising the following steps:
step 1: starting a strapdown inertial navigation system installed in a ship, initializing, and acquiring an inertial navigation system after initialization is finished to calculate to obtain the vertical acceleration a of the ship containing low-frequency noise z ；
Step 2: for a obtained in step 1 z Obtaining the frequency omega including the main frequency by N-point Fast Fourier Transform (FFT) 0 The relevant frequency domain characteristics of the inner sea wave;
and step 3: for the vertical acceleration a obtained in the step 1 z Performing primary integration to obtain a vertical velocity v containing low-frequency noise z_nofilter ；
And 4, step 4: determining transfer function of vertical velocity high pass filter
Wherein xi is a damping coefficient; omega c Is the cut-off frequency of the system; and order v z_nofilter Obtaining a vertical velocity v including amplitude attenuation and phase advance by a digital high-pass filter z ；
And 5: v in step 4 Using RLS-BMFLC z Fitting to obtain the fitted vertical velocity v z ′；
And 6: calculating the amplitude attenuation quantity and the phase lead quantity of each fundamental frequency point in the RLS-BMFLC according to the amplitude-phase-frequency characteristic of the vertical velocity high-pass filter in the step 4, and compensating the fitted vertical velocity to obtain the accurate vertical velocity v ″ z ；
And 7: for the precise vertical velocity v ″' obtained in step 6 z Performing primary integration to obtain the vertical displacement x before filtering z_nofilter ；
And 8: determining the transfer function of the vertical displacement high-pass filter as:
wherein xi is a damping coefficient; omega c Is the cut-off frequency of the system; let x obtained in step 7 z_nofilter Obtaining a vertical displacement x containing an amplitude-phase error through a digital high-pass filter z ；
And step 9: using the same calculation method as steps 5 and 6, firstly using RLS-BMFLC to make vertical displacement x z Fitting to obtain a curve x z ', subsequently to x z ' Compensation of amplitude and phase is carried out to obtain accurate heave displacement x z 。
2. The adaptive ship heave measurement method based on strapdown inertial navigation according to claim 1, wherein the specific iterative form of the RLS-BMFLC fitting and compensation of step 5 and step 9 is as follows:
y′ k ＝W k Τ X k
in the formula, k is iteration times; x rk Is the basic amount of fitting X k One element of (1); f. of r Fitting the fundamental frequency; t is a system sampling period; m is the number of frequency points in the self-adaptive frequency band; y is k Is the kth element of the original signal y; y' k To the original signal y k Fitting results obtained by adopting RLS-BMFLC; w is a group of k The corrected weight value of the RLS algorithm at the last moment; g k Is a recursive least squares gain; λ is a recursive least square factor; p k Recursion of the least square error covariance for the previous time instant; e.g. of the type k Is a recursive least squares error.
3. The adaptive ship heave measurement method based on strapdown inertial navigation according to claim 1 or 2, wherein the calculation formula for amplitude-phase compensation in step 6 is as follows:
y′ k ′＝W k Τ X k ′
in the formula, m r And p r Respectively corresponding to the amplitude attenuation and the phase lead in the high-pass filter for each base frequency point; y' k 'is to post-fitting signal y' k And (5) performing amplitude and phase compensation.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116678404A (en) * | 2023-06-08 | 2023-09-01 | 哈尔滨工程大学 | Ship heave measurement method based on multiple Fourier linear combiner |
| 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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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116678404A (en) * | 2023-06-08 | 2023-09-01 | 哈尔滨工程大学 | Ship heave measurement method based on multiple Fourier linear combiner |
| CN116678404B (en) * | 2023-06-08 | 2024-10-15 | 哈尔滨工程大学 | Ship heave measurement method based on multiple Fourier linear combiner |
| 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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