CN107101631A - A kind of ship heave measuring method based on auto-adaptive filtering technique - Google Patents
A kind of ship heave measuring method based on auto-adaptive filtering technique Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
- G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
- G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/20—Instruments for performing navigational calculations
- G01C21/203—Specially adapted for sailing ships
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Abstract
The invention belongs to Ship Motion field of measuring technique, it is related to a kind of ship heave measuring method based on auto-adaptive filtering technique.To solve phase advanced problem of the prior art when ship heave is measured.Vertical acceleration information is gathered first, the heave information with the advanced error of phase is obtained after processing, then real-time frequency estimation is carried out to vertical acceleration information, obtain estimating frequency, the phase information for needing to compensate is calculated further according to estimation frequency, then calculates and obtains wiener solution, and design auto-adaptive fir filter, phasing finally is carried out to the heave information with the advanced error of phase, the correct signal of output phase information is obtained.This invention removes phase difference, realize real―time precision measurment, further improve stability, the requirement of real-time and accuracy in heave measurement process is met, the landing, the transmitting of shipborne weapon, aircushion vehicle that can widely apply to carrier-borne aircraft are logged in, the Compensation Design of drilling platforms heave compensator and ship replenishment.
Description
Technical field
The invention belongs to Ship Motion field of measuring technique, more particularly to solve the heave advanced problem of wave filter output phase
A kind of ship heave measuring method based on auto-adaptive filtering technique.
Background technology
During naval vessel rides the sea, inevitably disturbed by the complicated Marine Environment Factors such as wave and sea wind
It is dynamic, passively produce the motion of swaying of 6DOF, including 3 angular movement pitchings, rolling and yawing, and 3 lines motion horizontal strokes
Swing, surging and heaving, wherein the influence and harm shaken in length and breadth with heave movement to naval vessel are maximum.Naval vessel average physique is big and ton
Position weight, its acceleration and deceleration and steering are required for the long period, and these actively navigate by water motion and are generally viewed as low frequency movement, and the cycle exists
More than 30s；Comparatively speaking, passive motion of swaying is the reciprocating motion unanimous on the whole with ocean wave motion frequency, can be considered high frequency
Motion, the cycle is generally in 10s or so.In many occasions, the real―time precision measurment of ship heave information has very important answer
With value, such as the landing of carrier-borne aircraft, the transmitting of shipborne weapon, aircushion vehicle are logged in, the compensation of drilling platforms heave compensator
Design and ship replenishment etc..
Strapdown inertial navigation system is using gyroscope and the angular movement of accelerometer measures carrier and line motion, by resolving
Posture, speed and positional information can be exported in real time, independent of any external information, and with higher precision and stably
Property.And strapdown inertial navigation system can export vertical acceleration information in real time.
Current domestic and foreign scholars just attempt to seek measurement of the effective means for ship heave information.Come from
Oceans.IEEE,1998:174-178vol.1 document《Adaptive tuning of heave filter in motion
sensor》, heave wave filter is proposed first and the characteristic for heaving wave filter is analyzed.Heave the parameter root of wave filter
Corrected in real time according to marine environment, but fail to eliminate phase error, it is as a result unsatisfactory.
Later, navigator fix journal, 2016,4 (2) are come from:91-93 document《Based on inertial navigation and without Time-Delay Filter
Ship heave is measured》, it is proposed that the ship heave measuring method based on inertial navigation and without Time-Delay Filter, solve phase error
Problem, but have the shortcomings that low cut is relatively slow and convergence time is longer.
Come from IFAC Proceedings Volumes, 2014,47 (3):10119-10125 document《Real-time
heave motion estimation using adaptive filtering techniques》, in the base of heave wave filter
Phase error problems, but existence and stability problem are solved by correcting the zero point and limit of transmission function in real time on plinth, therefore
There is limitation.
Come from IEEE Engineering in Medicine＆Biology Magazine, 1996,15 (3):29-36's
Document《Modeling and canceling tremor in human-machine interfaces》Describe in weighting Fu
Leaf linear combination algorithms are simultaneously applied in terms of the signal that trembles, and the algorithm is in an iterative process by continuing to optimize the base of fitted signal
Frequently, preferable fitting result can be reached.
The content of the invention
It is an object of the invention to a kind of open solution heave advanced problem of wave filter output phase, stability is good and accurate
The high ship heave measuring method based on auto-adaptive filtering technique of degree.
The object of the present invention is achieved like this, comprises the following steps:
(1) collection is arranged on the vertical acceleration information of the strap-down inertial equipment in naval vessel in real time, is filtered by heaving
The heave information with the advanced error of phase is obtained after ripple device processing vertical acceleration information；
(2) using weight Fourier's linear combination frequency estimation algorithm to vertical acceleration information carry out real-time frequency estimate
Meter, obtains estimating frequency；
(3) phase information for needing to compensate is calculated according to estimation frequency；
(4) phase information compensated according to estimation frequency and needs, which is calculated, obtains wiener solution, and designs automatic adaptation FIR filter
Ripple device；
(5) phasing is carried out to the heave information with the advanced error of phase by auto-adaptive fir filter, obtains defeated
Go out the correct signal of phase information.
Compared with prior art, beneficial effects of the present invention are：
On the basis of heave wave filter, application weighting Fourier's linear combination frequency estimation algorithm, to heave wave filter
Input signal carry out Frequency Estimation, design auto-adaptive fir filter to heave wave filter output carry out phase compensation, eliminate
Phase difference, realizes the real―time precision measurment of ship heave information, further increases stability, meet heave and measured
The requirement of real-time and accuracy in journey, the landing, the transmitting of shipborne weapon, aircushion vehicle that can widely apply to carrier-borne aircraft is stepped on
Land, the Compensation Design of drilling platforms heave compensator and ship replenishment.
Brief description of the drawings
Fig. 1 is the phase compensation flow chart based on auto-adaptive filtering technique；
Fig. 2 is weighting Fourier's linear combination frequency estimation algorithm flow chart；
Fig. 3 is auto-adaptive fir filter structure chart；
Fig. 4 is H1(s)、H2And H (s)int(s) Bode figures；
Fig. 5 is weighting Fourier's linear combination frequency estimation algorithm comparative result figure；
Fig. 6 is to heave the comparing result that wave filter did not compensated and compensated output；
Fig. 7 is the heave uncompensated output error curve of wave filter；
Fig. 8 is to heave the output error curve after filter compensation.
Embodiment
The invention will be further described below in conjunction with the accompanying drawings.Step as shown in Figure 1：
(1) collection is arranged on the vertical acceleration information a of the strap-down inertial equipment in naval vessel in real timez, pass through heave
Wave filter is to vertical acceleration information azHandled, the transmission function for heaving wave filter is as follows
In formula, ζ is damped coefficient, generally takes 0.7071；ωcFor system cut-off frequency, value is 0.08.
The transmission function for heaving the quadratic integral link of wave filter is as follows
The result of output is the heave information y (k) with the advanced error of phase.
H in Fig. 41(s) cut-off frequency ω is representedcIn 0.05Hz heave wave filter, H2(s) 0.08Hz heave filter is represented
Ripple device.Under normal circumstances, the frequency range of ship heave movement is H (s) and H in 0.05Hz~0.2Hz, the frequency rangeint(s) amplitude-frequency
Characteristic is essentially identical, but in phase-frequency characteristic, H (s) is ahead of Hint(s), in the case where system cut-off frequency is constant, in advance
Amount reduces with the increase of frequency input signal；In the case where frequency input signal is constant, advanced argument is with system cutoff frequency
The reduction of rate and reduce.In terms of low frequency characteristic, Fig. 4 shows that H (s) has low cut characteristic, and system cut-off frequency is got over
Greatly, low cut is faster.In terms of influence of the noise to system, ωcSmaller, the error variance that noise is produced is bigger, noise pair
The influence of system is bigger.So for the influence that rejection of acceleration zero is inclined and noise is to system, ωcValue is 0.08.
(2) by weighting Fourier's linear combination frequency estimation algorithm to vertical acceleration information azCarry out Frequency Estimation：
As shown in Fig. 2 the model set up in weighting Fourier's linear combination frequency estimation algorithm is：
In formula, r is the different coefficients related from the number of times of harmonic wave in model, w0kTo need the frequency information estimated, M
For the number of times of harmonic wave.Weighting the error of Fourier's linear combination frequency estimation algorithm in an iterative process is：
wk=[w1k,w2k...w2MK]T,
xk=[X1k,X2k...X2MK]T。
Y (k) is the input signal in adaptive filter algorithm, wkFor the coefficient vector in algorithm, xkFor the model in algorithm
Vector, the frequency information w0 of estimation is found using LMS algorithmkIterative process be
In formula, μ is the convergence factor of fundamental frequency in an iterative process,For with needing the frequency information w of estimation0kRelevant
Error gradient vector.The iterative process that coefficient vector passes through LMS algorithm is
In formula, μwFor the convergence factor of coefficient vector in an iterative process.So, weighting Fourier's linear combination frequency is estimated
Calculating method Global Iterative Schemes process is
It can be seen from above-mentioned weighting Fourier linear combination frequency estimation algorithm Global Iterative Schemes process, coefficient vector wkAnd need
The frequency information w to be estimated0kConstantly it is corrected.In order to ensure algorithmic statement, it is necessary to Rational choice fundamental frequency in an iterative process
Convergence factor μ, the convergence factor μ of coefficient vector in an iterative processw, generally choose less value.
(3) the phase information q for needing to compensate is calculated according to estimation frequency w：In order to solve to heave wave filter output phase
Advanced the problem of, the output of wave filter will be heaved, the heave information y (k) with the advanced error of phase is calculated as adaptive-filtering
Input signal in method, the signal after phase compensation is used as the desired signal in adaptive filter algorithm.Missed in advance with phase
The heave information y (k) of difference, can be described as in a short time：ApFor amplitude information, w is estimation
Frequency,For random phase, ApWithFor random quantity, it is difficult real-time and accurately asks for.Due to the advanced error of phase
The frequency for heaving information is identical with the frequency of vertical acceleration information, therefore estimation frequency w can be by entering to vertical acceleration information
Line frequency estimation is obtained.Desired signal in adaptive filter algorithm can be described as
By heaving the phase information q that phase characteristic of the wave filter with quadratic integral link at estimation frequency w can obtain needing to compensate,
Phase of the quasi- heave wave filter of bidding at estimation frequency w is a (w), then q=- π-a (w).
(4) the phase information q compensated according to estimation frequency w and needs, obtains wiener solution wo：In auto-adaptive filtering technique
In, object function generally uses mean square error, is defined as
ξ (k)=E [e2(k)]
=E [(d (k)-y (k))2]
=E [d2(k)+y2(k) -2d (k) y (k)],
W (k)=[w0(k) w1(k) … wN(k)]T,
Y (k)=wT(k) x (k),
In formula, d (k) is desired signal, and y (k) is the heave information with the advanced error of phase, and w (k) is coefficient vector.
In many applications, input signal vector is made up of the delayed copies of identical signal, then the realization side of sef-adapting filter
Method is to use FIR structures, as shown in Figure 3.Mean square error function is under Stationary Random Environments
X (k)=[x0(k) x1(k) … xN(k)]T。
In formula, R is the autocorrelation matrix of the input signal vector in adaptive filter algorithm, and p is desired signal and adaptive
The cross correlation vector of the input signal vector in filtering algorithm is answered, x (k) is input signal vector.Order is related to coefficient vector
The gradient vector of MSE functions is zero, i.e.,
wo=R-1p。
Obtain the optimal coefficient vector w of auto-adaptive fir filtero, i.e. wiener solution.
If choosing single order auto-adaptive fir filter, ifFor N, thenFor N-w, adaptive-filtering is calculated
The autocorrelation matrix R of input signal vector in method is
Desired signal and the cross correlation vector p of input signal are：
Then its wiener solution is
Because the phase information q for needing to compensate is obtained by estimation frequency w, then above formula shows wiener solution woOnly with estimation frequency
W is relevant.This example is only used as reference, and effect is not limited the invention.
(5) such as Fig. 3, line phase is entered to the heave information y (k) with the advanced error of phase by auto-adaptive fir filter
Correction, obtains the correct signal y ' of output phase informationk。
The extension of estimation frequency over time as seen from Figure 5 becomes accurate, and wave filter is heaved as seen from Figure 6 and is mended
Output becomes accurate after repaying, and can be seen that error largely reduces after heave filter compensation by Fig. 7 and Fig. 8 contrast
.
Here it must be noted that other unaccounted parts that the present invention is provided all are known to those skilled in the art,
According to title of the present invention or function, those skilled in the art can just find the document of related record, therefore not enter one
Walk explanation.
Claims (8)
1. a kind of ship heave measuring method based on auto-adaptive filtering technique, it is characterised in that：Comprise the following steps：
(1) collection is arranged on the vertical acceleration information of the strap-down inertial equipment in naval vessel in real time, by heaving wave filter
The heave information with the advanced error of phase is obtained after processing vertical acceleration information；
(2) using Fourier's linear combination frequency estimation algorithm is weighted to the progress real-time frequency estimation of vertical acceleration information, obtain
To estimation frequency；
(3) phase information for needing to compensate is calculated according to estimation frequency；
(4) phase information compensated according to estimation frequency and needs, which is calculated, obtains wiener solution, and designs automatic adaptation FIR filtering
Device；
(5) phasing is carried out to the heave information with the advanced error of phase by auto-adaptive fir filter, obtains exporting phase
The position correct signal of information.
2. a kind of ship heave measuring method based on auto-adaptive filtering technique according to claim 1, it is characterised in that：
The transmission function of described heave wave filter：
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In formula, ζ is damped coefficient, generally takes 0.7071；ωcFor the cut-off frequency of system, value is 0.08.
3. a kind of ship heave measuring method based on auto-adaptive filtering technique according to claim 1, it is characterised in that：
Weighting the model set up in Fourier's linear combination frequency estimation algorithm is：
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In formula, r is the different coefficients related from the number of times of harmonic wave in model, and M is the number of times of harmonic wave, and μ is fundamental frequency in iteration
During convergence factor, εkFor the error in iterative process.
4. a kind of ship heave measuring method based on auto-adaptive filtering technique according to claim 3, it is characterised in that：
Error in iterative process：
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5. a kind of ship heave measuring method based on auto-adaptive filtering technique according to claim 4, it is characterised in that：
Coefficient vector in algorithm：
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In formula,For with needing the frequency information w of estimation0kRelevant error gradient vector, μwIt is coefficient vector in iteration mistake
Convergence factor in journey, xkFor the model vector in algorithm.
6. a kind of ship heave measuring method based on auto-adaptive filtering technique according to claim 1, it is characterised in that：
Need the phase information of compensation：
Q=- π-a (w),
In formula, a (w) is that standard heaves phase of the wave filter at estimation frequency w.
7. a kind of ship heave measuring method based on auto-adaptive filtering technique according to claim 1, it is characterised in that：
Wiener solution w0：
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<mi>E</mi>
<mo>&lsqb;</mo>
<msup>
<mi>d</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msup>
<mi>w</mi>
<mi>T</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<msup>
<mi>x</mi>
<mi>T</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mi>w</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mn>2</mn>
<mi>d</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<msup>
<mi>w</mi>
<mi>T</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<mi>E</mi>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<msup>
<mi>d</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mo>+</mo>
<msup>
<mi>w</mi>
<mi>T</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mi>E</mi>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<msup>
<mi>x</mi>
<mi>T</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mi>w</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mn>2</mn>
<msup>
<mi>w</mi>
<mi>T</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mi>E</mi>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<mi>d</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<mi>E</mi>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<msup>
<mi>d</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mo>+</mo>
<msup>
<mi>w</mi>
<mi>T</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mi>R</mi>
<mi>w</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mn>2</mn>
<msup>
<mi>w</mi>
<mi>T</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mi>p</mi>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>,</mo>
</mrow>
X (k)=[x0(k) x1(k) … xN(k)]T,
W (k)=[w0(k) w1(k) … wN(k)]T,
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>&xi;</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>k</mi>
</mrow>
</mfrac>
<mo>=</mo>
<msup>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>&xi;</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>w</mi>
<mn>0</mn>
</msub>
</mrow>
</mfrac>
</mtd>
<mtd>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>&xi;</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>w</mi>
<mn>1</mn>
</msub>
</mrow>
</mfrac>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
<mtd>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>&xi;</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>w</mi>
<mi>N</mi>
</msub>
</mrow>
</mfrac>
</mtd>
</mtr>
</mtable>
</mfenced>
<mi>T</mi>
</msup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<mn>2</mn>
<mi>R</mi>
<mi>w</mi>
<mo>-</mo>
<mn>2</mn>
<mi>p</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>,</mo>
</mrow>
wo=R-1P,
In formula, d (k) is desired signal, and x (k) is input signal vector, and w (k) is coefficient vector, and R is in adaptive filter algorithm
Input signal vector autocorrelation matrix, p be desired signal and adaptive filter algorithm in input signal vector it is mutual
Close vector.
8. a kind of ship heave measuring method based on auto-adaptive filtering technique according to claim 1, it is characterised in that：
In short time, the heave information with the advanced error of phase：
Desired signal：
In formula, ApFor amplitude information, w is estimation frequency,For random phase.
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| CN107679016A (en) * | 2017-09-15 | 2018-02-09 | 哈尔滨工程大学 | A kind of marine strapdown inertial navigation system horizontal damping method based on LMS algorithm |
| CN110196050A (en) * | 2019-05-29 | 2019-09-03 | 哈尔滨工程大学 | A kind of vertical height of Strapdown Inertial Navigation System and speed measurement method |
| CN111174974A (en) * | 2020-02-17 | 2020-05-19 | 燕山大学 | Vehicle suspension heave measurement method and system |
| CN112611382A (en) * | 2020-11-27 | 2021-04-06 | 哈尔滨工程大学 | Strapdown inertial navigation system heave measurement method with phase compensation |
| CN112629525A (en) * | 2020-11-13 | 2021-04-09 | 河北汉光重工有限责任公司 | Method for ship heave phase compensation based on historical data cross-correlation |
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Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107679016A (en) * | 2017-09-15 | 2018-02-09 | 哈尔滨工程大学 | A kind of marine strapdown inertial navigation system horizontal damping method based on LMS algorithm |
| CN107679016B (en) * | 2017-09-15 | 2021-01-05 | 哈尔滨工程大学 | Marine strapdown inertial navigation system horizontal damping method based on LMS algorithm |
| CN110196050A (en) * | 2019-05-29 | 2019-09-03 | 哈尔滨工程大学 | A kind of vertical height of Strapdown Inertial Navigation System and speed measurement method |
| CN110196050B (en) * | 2019-05-29 | 2022-11-18 | 哈尔滨工程大学 | Vertical height and speed measuring method of strapdown inertial navigation system |
| CN111174974A (en) * | 2020-02-17 | 2020-05-19 | 燕山大学 | Vehicle suspension heave measurement method and system |
| CN111174974B (en) * | 2020-02-17 | 2021-07-30 | 燕山大学 | Vehicle suspension heave measurement method and system |
| CN112629525A (en) * | 2020-11-13 | 2021-04-09 | 河北汉光重工有限责任公司 | Method for ship heave phase compensation based on historical data cross-correlation |
| CN112611382A (en) * | 2020-11-27 | 2021-04-06 | 哈尔滨工程大学 | Strapdown inertial navigation system heave measurement method with phase compensation |
| CN112611382B (en) * | 2020-11-27 | 2022-06-21 | 哈尔滨工程大学 | Strapdown inertial navigation system heave measurement method with phase compensation |
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