Ship heave measurement research method based on minimum mean square error integrated navigation

Abstract

The invention discloses a ship heave measurement research method based on minimum mean square error integrated navigation, belongs to the technical field of navigation, and aims at different sea condition environments, the method not only effectively inhibits noise frequency bands by using frequency domain point-by-point weighting, but also retains useful signals; efficient calculation is realized in combination with fast Fourier transform, and the method is suitable for real-time processing; and finally, a high-precision time domain heaving signal is obtained through inverse transformation, so that the output accuracy of the GNSS / INS integrated navigation system is remarkably improved, relatively high adaptability and reliability are achieved, and high-precision measurement of ship heaving motion is realized. The method comprises the following steps: constructing a frequency response function of a ship heave filter based on a minimum mean square error criterion; the method specifically comprises the following steps: carrying out difference on an elevation observation value obtained by a GNSS / INS integrated navigation system and heave true value data to obtain an elevation error sequence; then, power spectral density analysis is performed on the elevation error and the heave truth value signal to describe the energy distribution characteristics of the error and the target signal in the frequency domain so as to deduce the frequency response function of the filter. And after the construction is completed, multiplying the frequency response function by the frequency spectrum of the combined navigation elevation signal frequency point by frequency point to obtain a filtered frequency spectrum result. And finally, performing inverse Fourier transform on the frequency spectrum, and restoring the frequency spectrum to a time domain so as to obtain more accurate ship heaving motion information.

Description

Technical Field

[0001] This invention belongs to the field of navigation technology, specifically relating to a research method for ship heave measurement based on minimum mean square error combined navigation. Background Technology

[0002] In marine engineering, shipboard lifting equipment is an indispensable component, with applications covering numerous aspects such as offshore installation, offshore maintenance, offshore replenishment, deep-sea exploration, and deep-sea drilling. Because operating vessels are subject to six degrees of freedom of motion due to wind, waves, currents, and their own movement, the safety and efficiency of offshore operations are significantly affected. The impact of heave is particularly prominent, potentially leading to collisions between the lifted load and other offshore structures or personnel, or even sling breakage. Therefore, to mitigate the adverse effects of vessel motion, improve the safety of offshore lifting operations, and extend the operational window, incorporating heave compensation into the lifting equipment is crucial.

[0003] In inertial navigation systems, the output signal of vertical acceleration typically contains real motion information (such as heave motion with a period of tens of seconds) and low-frequency systematic errors (such as Schuler oscillations and Earth oscillations). The period of Schuler oscillations is approximately 84.4 minutes, while the period of Earth oscillations is even longer, approaching 24 hours. Since the frequency of these systematic errors is much lower than the frequency of heave motion, if the vertical displacement is calculated by directly integrating the acceleration twice, the low-frequency errors will be significantly amplified due to the cumulative effect of the integration operation. In particular, the slowly changing characteristics of the Schuler oscillation component can cause the integrated displacement to exhibit a rapid divergence trend in a short period of time, even completely masking the real heave motion signal.

[0004] In the area of ​​ship heave motion information calculation, some experts have used high-pass digital filter technology to solve the problem of instability in heave motion estimation based on accelerometer measurement; others have designed a heave measurement method based on inertial navigation and time-delay filtering to solve the phase error problem in the calculated heave information, but there are still problems such as the difficulty in constructing Kalman filters, the acquisition of digital filter parameters, and the high complexity of the method of two integrations and three filterings through inertial navigation. Summary of the Invention

[0005] To address the problems in the existing technologies, this invention provides a method for studying ship heave measurement based on minimum mean square error (MSE) integrated navigation. First, a frequency response function for a ship heave filter is constructed based on the minimum mean square error criterion. Specifically, the elevation observations acquired by the GNSS / INS integrated navigation system are differencing the true heave data to obtain an elevation error sequence. Then, power spectral density analysis is performed on both the elevation error and the true heave signals to characterize the energy distribution characteristics of the error and the target signal in the frequency domain, thereby deriving the filter's frequency response function. After construction, this frequency response function is multiplied frequency-by-frequency by the spectrum of the integrated navigation elevation signal to obtain the filtered spectrum. Finally, an inverse Fourier transform is performed on this spectrum to restore it to the time domain, thus obtaining more accurate ship heave motion information.

[0006] To achieve the above technical objectives, this invention provides a method for studying ship heave measurement based on minimum mean square error combined navigation, comprising:

[0007] S1. The frequency response function of the ship heave filter is constructed by power spectral density analysis using the minimum mean square error.

[0008] S2, by subtracting the ship's elevation information from the true elevation obtained through GNSS / INS integrated navigation, the power spectral density of the elevation error is obtained, and the power spectral density of the ship's true heave is obtained.

[0009] S3. The spectrum of the filtered elevation signal is obtained by multiplying the frequency response function of the GNSS / INS integrated navigation elevation signal with the frequency response function of the rise and fall filter point by point.

[0010] S4. Based on the frequency of the filtered elevation signal, the result is converted to the time domain through inverse Fourier transform to obtain the ship's heave motion.

[0011] In the steps described above, the basis described in S1 is used to construct the frequency response function H(f) of the ship heave filter through power spectral density analysis and with minimum mean square error:

[0012]

[0013] In the formula: S xx (f) represents the power spectral density of the actual heave motion information;

[0014] S nn (f) represents the power spectral density of the elevation error of the integrated navigation system;

[0015] f represents the sampling frequency.

[0016] S1 obtains the ship's elevation information through GNSS / INS integrated navigation and subtracts it from the true elevation to obtain the elevation error n(t).

[0017] n(t) = Z meas (t)-Z true (t)

[0018] In the formula: Z meas (t) represents the elevation information obtained through GNSS / INS integrated navigation;

[0019] Z true (t) represents the elevation information obtained through high-precision equipment.

[0020] S2 describes the power spectral density analysis based on elevation error to obtain the power spectral density S of the elevation error. nn (f) and the power spectral density S of the true value of ship heave motion information xx (f):

[0021] S nn (f) = PSD(Z) meas (t)-Z true (t))

[0022] S xx (f) = PSD(Z) heave )

[0023] In the formula: PSD represents power spectral density analysis;

[0024] Z heave This represents the truth value of information about the ship's heave motion.

[0025] The frequency response function of the GNSS / INS integrated navigation elevation signal described in S3 is multiplied point-by-point to obtain the spectrum Y(f) of the filtered elevation signal:

[0026] Y(f) = H(f)·X(f)

[0027] In the formula: X(f) represents the elevation information obtained by GNSS / INS integrated navigation.

[0028] As described in S4, based on the frequency Y(f) of the filtered elevation signal, the result is transformed to the time domain using an inverse Fourier transform to obtain the ship's heave motion.

[0029]

[0030]

[0031] In the formula: F represents the Fourier transform.

[0032] Beneficial effects: This invention provides a method for studying ship heave measurement based on minimum mean square error combined navigation, which has the following advantages compared with existing technologies:

[0033] 1. This invention clearly distinguishes the frequency domain characteristics of heave signals and errors through power spectral density analysis. The frequency response function designed based on the minimum mean square error criterion can selectively retain the effective frequency band of heave, while suppressing low-frequency system errors (such as Schuler oscillations) and high-frequency noise, thereby improving the accuracy of signal extraction.

[0034] 2. This invention utilizes frequency domain multiplication and inverse Fourier transform to achieve filtering, avoiding the error accumulation problem caused by time domain recursive integration. While ensuring the stability of the algorithm, it significantly reduces the risk of data distortion caused by integral divergence.

[0035] 4. To verify the effectiveness of the algorithm, GNSS / INS integrated navigation data was processed, and three methods were compared: POS MV, traditional bandpass filter, and ship heave measurement based on minimum mean square error. The POS MV result was used as the reference truth value, and the RMS values ​​of the errors between the three methods and the reference truth value were obtained. Compared with the traditional bandpass filter and the ship heave measurement method based on minimum mean square error, the method proposed in this invention improves the ship heave accuracy by 67.9%. Attached Figure Description

[0036] Figure 1 This is a flowchart of the research method for ship heave measurement based on minimum mean square error combined navigation according to the present invention.

[0037] Figure 2 This is the power spectral density diagram of the true values ​​of ship heave and sag in this invention;

[0038] Figure 3 The conventional bandpass filter of this invention is used to obtain ship heave diagrams;

[0039] Figure 4 The ship heave diagram obtained by the ship heave filter with minimum mean square error of the present invention;

[0040] Figure 5 The error diagram and RMS value of the conventional bandpass filter of this invention compared with the true value of ship heave;

[0041] Figure 6 The minimum mean square error heave filter of the present invention is used to obtain the ship heave error diagram and RMS value; Detailed Implementation

[0042] The present invention will now be described in detail with reference to the accompanying drawings.

[0043] like Figure 1As shown, the research method for ship heave measurement based on minimum mean square error combined navigation includes the following steps:

[0044] Step 1: Construct the frequency response function of the ship heave filter using the minimum mean square error through power spectral density analysis;

[0045] Step 2: Obtain the ship's elevation information through GNSS / INS integrated navigation and subtract it from the true elevation to obtain the power spectral density of the elevation error, and obtain the power spectral density of the ship's true heave.

[0046] Step 3: The spectrum of the filtered elevation signal is obtained by multiplying the frequency response function of the GNSS / INS integrated navigation elevation signal with the frequency response function of the rise and fall filter point by point.

[0047] Step 4: Based on the frequency of the filtered elevation signal, the result is converted to the time domain by inverse Fourier transform to obtain the ship's heave motion;

[0048] like Figure 2 The power spectral density of the ship's heave motion information is obtained by analyzing the power spectral density of the ship's heave motion information based on the power spectral density diagram of the ship's heave motion information. The horizontal axis represents frequency and the vertical axis represents power spectral density.

[0049] like Figure 3 As shown, the ship's heave acceleration is filtered and double-integrated using a traditional bandpass filter to obtain the ship's heave. The horizontal axis represents time, and the vertical axis represents the ship's heave motion.

[0050] like Figure 4 As shown, the ship heave is obtained using a ship heave filter with minimum mean square error. The horizontal axis represents time, and the vertical axis represents the ship heave motion.

[0051] like Figure 5 As shown, the ship heave obtained by POS MV is subtracted from the ship heave obtained by the traditional bandpass filter to obtain the ship heave error diagram of the traditional bandpass filter, and its RMS value is calculated to be 0.056m.

[0052] like Figure 6 As shown, the ship heave obtained by POS MV is subtracted from the ship heave obtained by the ship heave filter based on minimum mean square error to obtain the ship heave error diagram of the minimum mean square error heave filter, and its RMS value is calculated to be 0.018m.

[0053] In this embodiment, the above method can be implemented using the following scheme:

[0054] Through power spectral density analysis, the frequency response function H(f) of the ship heave filter is constructed using the minimum mean square error:

[0055]

[0056] In the formula: S xx (f) represents the power spectral density of the actual heave motion information;

[0057] S nn (f) represents the power spectral density of the elevation error of the integrated navigation system;

[0058] f represents the sampling frequency.

[0059] The elevation information of the ship obtained by GNSS / INS integrated navigation is subtracted from the true elevation to obtain the elevation error n(t).

[0060] n(t) = Z meas (t)-Z true (t)

[0061] In the formula: Z meas (t) represents the elevation information obtained through GNSS / INS integrated navigation;

[0062] Z true (t) represents the elevation information obtained through high-precision equipment.

[0063] Power spectral density analysis was performed based on the elevation error to obtain the power spectral density S of the elevation error. nn (f) and the power spectral density S of the true value of ship heave motion information xx (f):

[0064] S nn (f) = PSD(Z) meas (t)-Z true (t))

[0065] S xx (f) = PSD(Z) heave )

[0066] In the formula: PSD represents power spectral density analysis;

[0067] Z heave This represents the truth value of information about the ship's heave motion.

[0068] By multiplying the frequency response function of the GNSS / INS integrated navigation elevation signal by the rise-sag filter point by point, the spectrum Y(f) of the filtered elevation signal is obtained as follows:

[0069] Y(f) = H(f)·X(f)

[0070] In the formula: X(f) represents the elevation information obtained by GNSS / INS integrated navigation.

[0071] Based on the frequency Y(f) of the filtered elevation signal, the result is transformed to the time domain using an inverse Fourier transform to obtain the ship's heave motion.

[0072]

[0073]

[0074] In the formula: F represents the Fourier transform.

[0075] Based on the obtained error images and the RMS values ​​corresponding to different methods, it can be seen that the research on ship heave measurement based on sliding adaptive time-delay bandpass filter described in this invention can effectively improve the accuracy and reliability of heave measurement.

[0076] Those skilled in the art will clearly understand that the technical solutions in the embodiments of the present invention can be implemented using computer programs and their corresponding general-purpose hardware platforms. Based on this understanding, the technical solutions in the embodiments of the present invention, or the parts that contribute to the prior art, can be embodied in the form of computer programs, i.e., software products. These computer program software products can be stored in a storage medium and include several instructions to cause a device containing a data processing unit (which may be a personal computer, server, microcontroller, or network device, etc.) to execute the methods described in various embodiments or certain parts of the embodiments of the present invention.

[0077] The above description is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention. All components not explicitly stated in this embodiment can be implemented using existing technology.

Claims

1. A research method for ship heave measurement based on minimum mean square error combined navigation, characterized in that, Includes the following steps: S1. The frequency response function of the ship heave filter is constructed by power spectral density analysis using the minimum mean square error. S2, by subtracting the ship's elevation information from the true elevation obtained through GNSS / INS integrated navigation, the power spectral density of the elevation error is obtained, and the power spectral density of the ship's true heave is obtained. S3. The spectrum of the filtered elevation signal is obtained by multiplying the frequency response function of the GNSS / INS integrated navigation elevation signal with the frequency response function of the rise and fall filter point by point. S4. Based on the frequency of the filtered elevation signal, the result is converted to the time domain through inverse Fourier transform to obtain the ship's heave motion.

2. The method for studying ship heave measurement based on minimum mean square error combined navigation as described in claim 1, characterized in that, The frequency response function H(f) of the ship heave filter, as described in S1, is constructed using power spectral density analysis and minimum mean square error: In the formula: S xx (f) represents the power spectral density of the actual heave motion information; S nn (f) represents the power spectral density of the elevation error of the integrated navigation system; f represents the sampling frequency.

3. The method for studying ship heave measurement based on minimum mean square error combined navigation as described in claim 1, characterized in that, The elevation error n(t) is obtained by subtracting the true elevation from the elevation information of the ship obtained through GNSS / INS integrated navigation as described in S2. n(t)=Z meas (t)-Z true (t) In the formula: Z meas (t) represents the elevation information obtained through GNSS / INS integrated navigation; Z true (t) represents the elevation information obtained through high-precision equipment.

4. The method for studying ship heave measurement based on minimum mean square error combined navigation as described in claim 1, characterized in that, S2 describes the power spectral density analysis based on elevation error to obtain the power spectral density S of the elevation error. nn (f) and the power spectral density S of the true value of ship heave motion information xx (f): S nn (f)=PSD(Z meas (t)-Z true (t)) S xx (f)=PSD(Z heave ) In the formula: PSD represents power spectral density analysis; Z heave This represents the truth value of information about the ship's heave motion.

5. The method for studying ship heave measurement based on minimum mean square error combined navigation as described in claim 1, characterized in that, The frequency response function of the GNSS / INS integrated navigation elevation signal described in S3 is multiplied point-by-point to obtain the spectrum Y(f) of the filtered elevation signal: Y(f) = H(f)·X(f) In the formula: X(f) represents the elevation information obtained by GNSS / INS integrated navigation.

6. The method for studying ship heave measurement based on minimum mean square error combined navigation as described in claim 1, characterized in that: As described in S4, based on the frequency Y(f) of the filtered elevation signal, the result is transformed to the time domain through an inverse Fourier transform to obtain the ship's heave motion. In the formula: F represents the Fourier transform.

7. A method for studying ship heave measurement based on minimum mean square error combined navigation as described in claims 1-6, characterized in that, The invented methods include: First, a frequency response function for the ship's heave filter is constructed based on the minimum mean square error criterion. Specifically, the elevation observations acquired by the GNSS / INS integrated navigation system are differencing the true heave data to obtain an elevation error sequence. Subsequently, power spectral density analysis is performed on both the elevation error and the true heave signals to characterize the energy distribution characteristics of the error and target signal in the frequency domain, thereby deriving the filter's frequency response function. After construction, this frequency response function is multiplied frequency-by-frequency by the spectrum of the integrated navigation elevation signal to obtain the filtered spectrum. Finally, an inverse Fourier transform is performed on this spectrum to restore it to the time domain, thus obtaining more accurate information on the ship's heave motion.

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