# Estimation of Wave Period from Pitch and Roll of a Lidar Buoy

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## Abstract

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^{TM}buoy. Parametric analysis showed good agreement (correlation coefficient, $\rho $ = 0.86, root-mean-square error (RMSE) = 0.46 s, and mean difference, MD = 0.02 s) between the proposed L-dB method and the oceanographic zero-crossing method when the threshold L was set at 8 dB.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

^{TM}wave buoy measured the main wave and current parameters. The main instruments used in this study were (i) a 3DM-GX3-45 inertial measurement unit (IMU) on the lidar buoy measuring the buoy’s tilt (roll, pitch, and yaw); accelerations in the x, y, and z axes; and global-positioning-system (GPS) position at a sampling rate of approximately 8 Hz and (ii) a Triaxys

^{TM}wave buoy next to the metmast measuring the reference wave parameters at a sampling period of 1 h [29]. Figure 1 shows the instrumentation setup of the campaign and the location of IJmuiden’s test facilities. For this study, 1920 wave-buoy data records from 29 March to 17 June (80 days) were used.

^{TM}300 lidar [27]. It had 3.77 m width, weighed 3 tons, and had a modular four-floater structure designed to satisfy wind-energy measurement requirements and to perform wave measurements from buoy accelerations [16,31]. It was equipped with additional sensors in order to measure a wide variety of wind- and sea-related data. Specifically, it hosted a MicroStrain 3DM-GX3-45 IMU combining a high-precision GPS unit, an accelerometer, and a gyro. The gyro measures Euler’s angles (roll, pitch, and yaw), the accelerometer measures translational accelerations on these axes, and the GPS module measures the position of the buoy. An extended Kalman filter was applied over the IMU measurements in order to track the buoy’s attitude [31]. However, only altitude recorded higher than 0 m were available. From one of the 4 corners of the buoy, a mounted tail acted as a “stern” for the buoy, so that the opposite corner faced the wind direction. The buoy was moored to the seabed by a mooring system consisting of two main parts: (i) upper mooring consisting of four lines connected to each of the buoy’s floaters united in its bottom to a single line and (ii) lower mooring consisting of a clump weight (see Figure 2).

^{TM}wave buoy is a wave sensor designed for accurate measurement of directional waves and currents at a sampling period of 1 h. It is equipped with 3 accelerometers, 3 gyroscopes, and a compass [32] in order to measure the most relevant directional and nondirectional wave parameters. Some of the parameters yielded by the wave sensor were wave-height definitions (${H}_{max}$, ${H}_{10}$, ${H}_{sig}$, and ${H}_{avg}$), wave-period definitions (${T}_{max}$, ${T}_{10}$, ${T}_{sig}$, ${T}_{z}$, ${T}_{avg}$, ${T}_{p}$, and ${T}_{p5}$), $MeanDirection$, and $MeanSpread$. Subindices max, 10, sig, avg, z, p, and p5 refer to the maximal wave height and its corresponding period (${H}_{max}$ and ${T}_{max}$, respectively), the highest tenth of the waves’ average height and period (${H}_{10}$ and ${T}_{10}$, respectively), the highest third of the waves’ average height and period (${H}_{sig}$ and ${T}_{sig}$, respectively), the average wave height and period (${H}_{avg}$ and ${T}_{avg}$, respectively), the average zero upcrossing period (${T}_{z}$), the period corresponding to the highest spectral component of the wave energy spectrum (${T}_{p}$), and the peak wave period computed by the READ method (${T}_{p5}$), respectively [33]. Wave period parameters ${T}_{z}$, ${T}_{avg}$ and ${T}_{p}$ are formulated in Section 2.2.

^{TM}computes these parameters from heave, pitch, and roll measurements estimated from the 6 DoF measurements by 3 accelerometers and 3 gyros by solving the nonlinear differential equations relating the buoy motion to accelerations and angular rates. It follows a similar procedure to that in [34] to obtain heave, surge, and sway translational motions and roll, pitch, and yaw rotational motions. Wave analysis was then carried out on the buoy by performing zero-crossing analysis of wave elevation in the time domain, nondirectional analysis by means of FFT methods, and lastly directional wave analysis [33].

#### 2.2. Method (I): Estimation of Sea-Wave Period

- mean zero-crossing period, which is defined as$${T}_{z}=\sqrt{\frac{{m}_{0}}{{m}_{2}}};$$
- average period$${T}_{avg}=\frac{{m}_{0}}{{m}_{1}};$$
- and peak period$${T}_{p}=\frac{1}{{f}_{p}},$$

#### 2.3. Method (II): Buoy-Motion Model

#### 2.4. PSD Estimation

#### 2.5. PSD Significant-Wave-Period Estimation

## 3. Results and Discussion

^{TM}buoy. Because the Triaxys

^{TM}buoy yielded multiple estimations of the wave period according to the different oceanographic definitions (Section 2), we first needed to assess which of these best matched the PSD wave period estimated by using the L-dB method (${T}_{L-dB}$, Equation (24)).

^{TM}, ${T}_{L-dB}$ was resampled to the temporal resolution of Triaxys

^{TM}(1 h). Root-mean-square error is defined as

^{TM}, which were used as references. Figure 8 shows statistical indicators when comparing ${T}_{L-dB}$ as a function of L with each of these Triaxys

^{TM}reference periods. Figure 8 shows the results of these comparisons in terms of $\rho $ (Figure 8a), RMSE (Figure 8b), and MD (Figure 8c). The zero-crossing and the average-period methods (${T}_{z}$ and ${T}_{avg}$, respectively) from the experiment yielded identical statistical indicators, which is evidenced by the overlapping blue and dashed black lines in the three subfigures (Figure 8a–c). When comparing ${T}_{z}$ and ${T}_{avg}$ to ${T}_{L-dB}$, maximal $\rho $, minimal RMSE, and MD closest to 0 were evidenced. The largest differences occurred for the wave energy spectrum peak methods (${T}_{p5}$ and ${T}_{p}$). A possible explanation for that is that wave energy spectrum peak methods measured the period corresponding to the peak spectral component and did not consider wave multimodality. Lastly, ${T}_{10}$ and ${T}_{sig}$, which consider the highest tenth and third of the wave energy spectrum as the relevant wave spectral components, respectively, showed better agreement than the latter set did (${T}_{p5}$ and ${T}_{p}$), with ${T}_{sig}$ showing better indicators. ${T}_{sig}$ showed higher $\rho $, lower RMSE, and MD closer to 0 than ${T}_{10}$ due to the broader frequency span. It emerged that the L-dB method best matched ${T}_{z}$ and ${T}_{avg}$ (with virtually identical indicators). In the following, the L-dB method is compared with reference to ${T}_{z}$.

^{TM}computation of reference period ${T}_{z}$ was affected by the buoy’s translational and rotational movements; in our modelling, (Section 2.3 and Section 2.5) only roll and pitch were considered (2 DoF). Second, our methodology was experimentally tested under the assumption of small angles, the median of maximal tilt excursion was ±13 deg (Figure 6), which incurred 2.5% and 0.8% errors when using first-order cosine and sine approximation, respectively. Lastly, the DWL and Triaxys

^{TM}reference buoys were 200 m apart during the campaign, which may also have accounted for small wind, current, and wave differences.

## 4. Summary and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

DOAJ | Directory of open access journals |

DoF | Degree of freedom |

DWL | Doppler wind lidar |

FEM | Fourier expansion method |

HWS | Horizontal Wind Speed |

LR | Linear regression |

MD | Mean deviation |

MEM | Maximum entropy method |

NED | North–east–down |

FFT | Fast Fourier transform |

IMU | Inertial measurement unit |

MDPI | Multidisciplinary Digital Publishing Institute |

Metmast | Meteorological mast |

PSD | Power spectral density |

RMSE | Root-mean-square error |

WE | Wind Energy |

## Appendix A. Power-Spectral-Density Derivation

- (i)
- the cross-PSD (also called cross spectral density) between two processes $x\left(t\right)$ and $y\left(t\right)$ is the Fourier transform ($\mathit{FT}$) of the cross-correlation function, ${S}_{x,y}={\int}_{-\infty}^{\infty}{R}_{x,y}\left(\tau \right){e}^{-i2\pi f\tau}d\tau $, and
- (ii)
- ${R}_{\theta ,\varphi}^{*}\left(\tau \right)\to {S}_{\theta ,\varphi}^{*}\left(f\right)$ according to the $FT$ conjugation property, ${x}^{*}\left(t\right)\to {X}^{*}(-f)$, with X the $FT$ of signal $x\left(t\right)$ and the arrow symbol denoting $FT$,

## References

- Global Wind Energy Council. Global Wind Report 2018; Technical Report; Global Wind Energy Council: Brussels, Belgium, 2019. [Google Scholar]
- Offshore Wind in Europe Key Trends and Statistics 2019; Technical Report; WindEurope: Brussels, Belgium, 2020.
- Timmons, D. 25—Optimal Renewable Energy Systems: Minimizing the Cost of Intermittent Sources and Energy Storage. In A Comprehensive Guide to Solar Energy Systems; Letcher, T.M., Fthenakis, V.M., Eds.; Academic Press: Cambridge, MA, USA, 2018; pp. 485–504. [Google Scholar] [CrossRef]
- Carbon Trust. Carbon Trust Offshore Wind Accelerator Roadmap for the Commercial Acceptance of Floating LIDAR Technology; Technical Report; Carbon Trust: London, UK, 2013. [Google Scholar]
- Courtney, M.S.; Hasager, C.B. Remote Sensing Technologies for Measuring Offshore Wind. In Offshore Wind Farms; Elsevier: Amsterdam, The Netherlands, 2016; Chapter 4; pp. 59–82. [Google Scholar]
- Antoniou, I.; Jorgensen, H.E.; Mikkelsen, T.; Frandsen, S.; Barthelmie, R.; Perstrup, C.; Hurtig, M. Offshore wind profile measurements from remote sensing instruments. In Proceedings of the European Wind Energy Association Conference & Exhibition 2006, Athens, Greece, 27 February–2 March 2006; European Wind Energy Association Conference & Exhibition: Athens, Greece, 2006; Volume 1, pp. 471–480. [Google Scholar]
- Pichugina, Y.; Banta, R.; Brewer, W.; Sandberg, S.; Hardesty, R. Doppler Lidar–Based Wind-Profile Measurement System for Offshore Wind-Energy and Other Marine Boundary Layer Applications. J. Appl. Meteorol. Climatol.
**2012**, 51, 327–349. [Google Scholar] [CrossRef] - Gottschall, J.; Wolken-Möhlmann, G.; Lange, B. About offshore resource assessment with floating lidars with special respect to turbulence and extreme events. J. Phys. Conf. Ser.
**2014**, 555, 12–43. [Google Scholar] [CrossRef] - Tiana-Alsina, J.; Rocadenbosch, F.; Gutierrez-Antunano, M.A. Vertical Azimuth Display simulator for wind-Doppler lidar error assessment. In Proceedings of the 2017 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Fort Worth, TX, USA, 23–28 July 2017; pp. 1614–1617. [Google Scholar] [CrossRef][Green Version]
- Kelberlau, F.; Neshaug, V.; Lønseth, L.; Bracchi, T.; Mann, J. Taking the Motion out of Floating Lidar: Turbulence Intensity Estimates with a Continuous-Wave Wind Lidar. Remote Sens.
**2020**, 12, 898. [Google Scholar] [CrossRef][Green Version] - Gutiérrez-Antuñano, M.; Tiana-Alsina, J.; Salcedo, A.; Rocadenbosch, F. Estimation of the Motion-Induced Horizontal-Wind-Speed Standard Deviation in an Offshore Doppler Lidar. Remote Sens.
**2018**, 10, 2037. [Google Scholar] [CrossRef][Green Version] - Mangat, M.; des Roziers, E.B.; Medley, J.; Pitter, M.; Barker, W.; Harris, M. The impact of tilt and inflow angle on ground based lidar wind measurements. In Proceedings of the EWEA 2014 Proceedings, The European Wind Energy Associationm, Barcelona, Spain, 10–13 March 2014. [Google Scholar]
- Pitter, E.B.d.R.M.; Medley, J.; Mangat, M.; Slinger, C.; Harris, M. Performance Stability of Zephir in High Motion Enviroments: Floating and Turbine Mounted; Technical Report; ZephIR: Ledbury, UK, 2014. [Google Scholar]
- Bischoff, O.; Würth, I.; Cheng, P.; Tiana-Alsina, J.; Gutiérrez, M. Motion effects on lidar wind measurement data of the EOLOS buoy. In Proceedings of the Renewable Energies Offshore—1st International Conference on Renewable Energies Offshore, RENEW 2014, Lisbon, Portugal, 24–26 November 2014; pp. 197–203. [Google Scholar]
- Gottschall, J.; Lilov, H.; Wolken-Möhlmann, G.; Lange, B. Lidars on floating offshore platforms; About the correction of motion-induced lidar measurement errors. In Proceedings of the EWEA 2012 Proceedings, The European Wind Energy Association, Lisbon, Portugal, 16–19 April 2012. [Google Scholar]
- Schuon, F.; González, D.; Rocadenbosch, F.; Bischoff, O.; Jané, R. KIC InnoEnergy Project Neptune: Development of a Floating LiDAR Buoy for Wind, Wave and Current Measurements. In Proceedings of the DEWEK 2012 German Wind Energy Conference, Bremen, Germany, 19–20 May 2012. [Google Scholar]
- N.D.B. Center. Nondirectional and Directional Wave Data Analysis Procedures; Technical Report; National Oceanic and Atmospheric Administration: Washington, DC, USA, 1996. [Google Scholar]
- Faltinsen, O. Sea Loads on Ships and Offshore Structures; Cambridge University Press: Cambridge, UK, 1993; Volume 1. [Google Scholar]
- Suh, K.D.; Kwon, H.D.; Lee, D.Y. Some statistical characteristics of large deepwater waves around the Korean Peninsula. Coast. Eng.
**2010**, 57, 375–384. [Google Scholar] [CrossRef][Green Version] - Ardhuin, F.; Stopa, J.E.; Chapron, B.; Collard, F.; Husson, R.; Jensen, R.E.; Johannessen, J.; Mouche, A.; Passaro, M.; Quartly, G.D.; et al. Observing Sea States. Front. Mar. Sci.
**2019**, 6, 124. [Google Scholar] [CrossRef][Green Version] - Chun, H.; Suh, K.-D. Estimation of significant wave period from wave spectrum. J. Ocean. Eng. Technol.
**2018**, 163, 609–616. [Google Scholar] [CrossRef] - Gottschall, J.; Catalano, E.; Dörenkämper, M.; Witha, B. The NEWA Ferry Lidar Experiment: Measuring Mesoscale Winds in the Southern Baltic Sea. Remote Sens.
**2018**, 10, 1620. [Google Scholar] [CrossRef][Green Version] - He, Y.; Fu, J.; Shu, Z.; Chan, P.; Wu, J.; Li, Q. A comparison of micrometeorological methods for marine roughness estimation at a coastal area. J. Wind. Eng. Ind. Aerodyn.
**2019**, 195, 104010. [Google Scholar] [CrossRef] - Kuik, A.J.; van Vledder, G.P.; Holthuijsen, L.H. A Method for the Routine Analysis of Pitch-and-Roll Buoy Wave Data. J. Phys. Oceanogr.
**1988**, 18, 1020–1034. [Google Scholar] [CrossRef] - Gutiérrez-Antuñano, M.A.; Tiana-Alsina, J.; Rocadenbosch, F. Performance evaluation of a floating lidar buoy in nearshore conditions. Wind Energy
**2017**, 20, 1711–1726. [Google Scholar] [CrossRef][Green Version] - Salcedo-Bosch, A.; Gutierrez-Antunano, M.A.; Tiana-Alsina, J.; Rocadenbosch, F. Motional Behavior Estimation Using Simple Spectral Estimation: Application to the Off-Shore Wind Lidar. In Proceedings of the 2020 IEEE International Geoscience and Remote Sensing Symposium, (IGARSS-2020), Virtual Event, 26 September–2 October 2020; Available online: https://igarss2020.org/ (accessed on 27 September 2020).
- Gutierrez-Antunano, M.A.; Tiana-Alsina, J.; Rocadenbosch, F.; Sospedra, J.; Aghabi, R.; Gonzalez-Marco, D. A wind-lidar buoy for offshore wind measurements: First commissioning test-phase results. In Proceedings of the 2017 IEEE International Geoscience and Remote Sensing Symposium (IGARSS-2017), Fort Worth, TX, USA, 23–28 July 2017; pp. 1607–1610. [Google Scholar] [CrossRef]
- Sospedra, J.; Cateura, J.; Puigdefàbregas, J. Novel multipurpose buoy for offshore wind profile measurements EOLOS platform faces validation at ijmuiden offshore metmast. Sea Technol.
**2015**, 56, 25–28. [Google Scholar] - Werkhoven, E.J.; Verhoef, J.P. Offshore Meteorological Mast Ijmuiden Abstract of Instrumentation Report; Technical Report; Energy Research Centre of the Netherlands (ECN): Petten, The Netherlands, 2012. [Google Scholar]
- NordNordWest. Netherlands Relief Location Map. 2008. Available online: https://creativecommons.org/licenses/by-sa/3.0/de/legalcode (accessed on 3 November 2020).
- Gutiérrez Antuñano, M.Á. Doppler Wind LIDAR Systems Data Processing and Applications: An Overview Towards Developing the New Generation of Wind Remote-Sensing Sensors for Off-Shore Wind Farms. Ph.D. Thesis, UPC, Departament de Teoria del Senyal i Comunicacions, Barcelona, Spain, 2019. [Google Scholar]
- AXYS Technologies. TRIAXIS Sensor; AXYS Technologies: Sidney, BC, Canada, 2015. [Google Scholar]
- MacIsaac, C.; Naeth, S. TRIAXYS Next Wave II Directional Wave Sensor The evolution of wave measurements. In Proceedings of the 2013 OCEANS, San Diego, CA, USA, 23–27 September 2013; pp. 1–8. [Google Scholar]
- Auestad, Ø.F.; Gravdahl, J.T.; Fossen, T.I. Heave Motion Estimation on a Craft Using a Strapdown Inertial Measurement Unit. In Proceedings of the 9th IFAC Conference on Control Applications in Marine Systems, IFAC, Osaka, Japan, 17–20 September 2013; Volume 46, pp. 298–303. [Google Scholar] [CrossRef][Green Version]
- Barstow, S.F.; Bidlot, J.R.; Caires, S.; Donelan, M.; Drennan, W.E.A. Measuring and Analysing the Directional Spectra of Ocean Waves; Number EUR 21367; COST Office: Brussels, Belgium, 2005. [Google Scholar]
- Tannuri, E.; Sparano, J.; Simos, A.; Cruz, J.D. Estimating directional wave spectrum based on stationary ship motion measurements. Appl. Ocean Res.
**2003**, 25, 243–261. [Google Scholar] [CrossRef] - Massel, S.R. Ocean Surface Waves: Their Physics and Prediction; World Scientific Publishing Company: Singapore, 2017; Volume 45. [Google Scholar]
- Sweitzer, K.A.; Bishop, N.W.; Genberg, V.L. Efficient computation of spectral moments for determination of random response statistics. In Proceedings of the ISMA, Leuven, Belgium, 20–22 September 2004; pp. 2677–2692. [Google Scholar]
- Roithmayr, C.M.; Hodges, D.H. Dynamics: Theory and Application of Kane’s Method. J. Comput. Nonlinear Dyn.
**2016**, 11, 6. [Google Scholar] [CrossRef][Green Version] - Proakis, J.; Manolakis, D. Digital Signal Processing, 4th ed.; Prentice Hall: Upper Saddle River, NJ, USA, 2006. [Google Scholar]
- Brillouin, L.; Massey, H. Wave Propagation and Group Velocity, Pure and Applied Physics; Elsevier Science: Amsterdam, The Netherlands, 2013; Volume 8. [Google Scholar]
- Ricci, A.; Blocken, B. On the reliability of the 3D steady RANS approach in predicting microscale wind conditions in seaport areas: The case of the IJmuiden sea lock. J. Wind. Eng. Ind. Aerodyn.
**2020**, 207, 104437. [Google Scholar] [CrossRef] - Bracewell, R. The Fourier Transform and Its Applications; Circuits and Systems; McGraw Hill: New York, NY, USA, 2000. [Google Scholar]

**Figure 3.**Fixed and moving-body (buoy’s) coordinate systems used: the fixed coordinate system is the right-handed north–east–down (NED) system (dashed arrows with unitary vectors $\widehat{n}$, $\widehat{e}$, and $\widehat{d}$ plotted in blue, green, and red, respectively). The buoy’s coordinate system is denoted as XYZ (solid arrows with unitary vectors $\widehat{x}$, $\widehat{y}$, $\widehat{z}$). $\alpha $ is the buoy’s eigenangle defined as the angle between unitary vectors $\widehat{d}$ and $\widehat{z}$.

**Figure 4.**Motional temporal series (Ijmuiden campaign): (

**a**) heave signal above sea level (a.s.l.) on 11 April 2015 and (

**b**) roll, pitch, and yaw signals on 10 April 2015).

**Figure 5.**Geometrical representation of a buoy’s rotation in the roll and pitch dimensions of movement and vector approximation for small angles: (

**a**) three-dimensional geometry sketch showing eigenangle $\alpha $, roll ($\varphi $), and pitch ($\theta $) angles and vectors $\widehat{d}$ and $\widehat{z}$ in an NED coordinate system. $\widehat{d}$ transforms into $\widehat{z}$ after the roll ($\varphi $) and pitch ($\theta $) rotations about the N and E axes, respectively (Equation (12)). (

**b**) Representation of roll and pitch rotations $\overrightarrow{{r}_{\varphi}}$ and $\overrightarrow{{r}_{\theta}}$, respectively, on the NE plane (Equation (10)) along with the resultant vector $\overrightarrow{{r}_{zd}}$ (Equation (14)).

**Figure 6.**Histograms of the daily minimal and maximal roll and pitch inertial-measurement-unit (IMU) records (57,520,000 records between 29 Match and 17 June): (

**a**) daily minimal tilt-record histogram and (

**b**) daily maximal tilt-record histogram. The dashed lines represent roll (blue) and pitch (red) medians in both panels.

**Figure 7.**Two examples of power-spectral-density (PSD) estimation by periodogram and Blackman–Tukey method of measured tilt data: (

**a**) bimodal case and (

**b**) multimodal case. The L-dB threshold and cutoff frequencies, ${f}_{L-dB}^{min}$ and ${f}_{L-dB}^{max}$, are also indicated by magenta dashed lines and arrows. L = 3 dB.

**Figure 8.**Comparison with 3 statistical indicators of agreement between estimated ${T}_{L-dB}$ and reference wave periods from IJmuiden campaign’s experimental data at different L values: (

**a**) correlation coefficient, $\rho $, as a function of threshold level, L; (

**b**) that for root-mean-square error (RMSE) (Equation (25)); and (

**c**) that for mean deviation (MD) (Equation (26)).

**Figure 9.**Statistical indicators comparing the L-dB method ${T}_{L-dB}$ and zero-crossing method ${T}_{z}$ as a function of threshold value L (dB) parameterized by averaging time (IJmuiden campaign, 29 March–17 June 1920 records). The dashed dots indicate weekly averaged indicators. The dashed line indicates monthly average. The solid trace indicates the indicators computed for the whole 80 day campaign.

**Figure 10.**Scatter plot comparing wave period estimated by 8 dB method ${T}_{8-dB}$ in reference to zero-crossing method ${T}_{z}$. The red trace shows the linear regression modelling relationship between both methods; the dashed black line is the 1:1 ideal line.

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**MDPI and ACS Style**

Salcedo-Bosch, A.; Rocadenbosch, F.; Gutiérrez-Antuñano, M.A.; Tiana-Alsina, J. Estimation of Wave Period from Pitch and Roll of a Lidar Buoy. *Sensors* **2021**, *21*, 1310.
https://doi.org/10.3390/s21041310

**AMA Style**

Salcedo-Bosch A, Rocadenbosch F, Gutiérrez-Antuñano MA, Tiana-Alsina J. Estimation of Wave Period from Pitch and Roll of a Lidar Buoy. *Sensors*. 2021; 21(4):1310.
https://doi.org/10.3390/s21041310

**Chicago/Turabian Style**

Salcedo-Bosch, Andreu, Francesc Rocadenbosch, Miguel A. Gutiérrez-Antuñano, and Jordi Tiana-Alsina. 2021. "Estimation of Wave Period from Pitch and Roll of a Lidar Buoy" *Sensors* 21, no. 4: 1310.
https://doi.org/10.3390/s21041310