Abstract:
A moored buoy floating at the ocean surface and anchored to the seafloor precisely measures acceleration, pitch, roll, and Earth&#39;s magnetic flux field of the buoy over a limited sampling period. The system includes: 1) A buoy, 2) A mooring system, 3) An electronic data logger controlling communications between the system and the on-board remote telecommunications system, 4) an embedded computer for data input/output, temporary or permanent data storage, and algorithms to convert the measured time series data into surface ocean wave spectra and quality assurance statistics and encode the results for transfer to the data logger, 5) Sensors include one or three acceleration sensors, three orthogonal angular rate sensors, and three orthogonal magnetometers to measure the Earth&#39;s magnetic flux field, 6) A telecommunications system that links the buoy data logger and a shoreside processing system, and 7) A shoreside processing system that decodes the transmitted data, performs, quality control, and computes derived wave parameters.

Description:
STATEMENT OF GOVERNMENT INTEREST 
     The research that led to the development of the present invention was sponsored by the National Oceanic and Atmospheric Administration&#39;s (NOAA&#39;s) National Data Buoy Center. NOAA is a part of the U.S. Department of Commerce, a component of the U.S. Federal government. The United States Government has certain rights in the present invention. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to wave measurement using moored buoys. In particular, the present invention is directed toward the National Data Buoy Center&#39;s (NDBC) directional wave measurement system, which uses a system of sensors, processors, algorithms, and communications on a moored buoy to measure the components of a directional wave spectrum and transmit the spectrum to a shoreside processing center for analysis and dissemination. 
     BACKGROUND OF THE INVENTION 
     Off-Shore buoys are used for a number of purposes: for navigation, communication, and also to measure weather and wave conditions. The National Oceanic Atmospheric Administration (NOAA) through the National Data Buoy Center, maintains a number of offshore buoys to measure water temperature and wave height, among other parameters. This data may then be transmitted to shore and processed and presented as part of weather forecasts, either on the NOAA website, or through NOAA weather radio, for use by Mariners and others, in predicting weather and wave conditions. 
     The U.S. National Data Buoy Center (NDBC) of the National Weather Service (NWS), a part of the U.S. National Oceanic and Atmospheric Administration (NOAA), operates a large number of buoys in areas of interest to the United States. Each hour (in a few cases every 30 minutes) meteorological, oceanographic, and wave data are acquired, transmitted to shore via satellite telecommunications, and distributed to users following real-time, automated data quality control. NDBC made its first non-directional wave measurements from buoys in 1973 and its first directional wave measurements in 1975. The program has expanded so that now all NDBC buoys make wave measurements and most make directional wave measurements. 
     While many existing weather data buoys adequately measure wave height, oftentimes other wave data, such as direction, may be useful in marine weather forecasts and for other uses. For example if wave direction is opposite tidal direction, oftentimes conditions can exist near shore where wave heights may increase. In addition, wave direction may differ from wind direction, and thus a report of wind direction may not always be indicative of wave direction. When plotting a course, a mariner may wish to avoid certain wave orientations (e.g., broaching waves) and thus wave direction data may be useful to mariners. Scientists and others may find wave direction data useful in studying shore erosion and other environmental impacts of waves. Furthermore, other wave data, such as wave slope and the like may be useful to oceanographers and engineers, as well as mariners. The term wave spectra is used in the art to describe the distribution of wave parameters as a function of frequency (Hertz (Hz)). 
     Various idealized spectra are used in oceanography and ocean engineering. Perhaps the simplest is that proposed by Pierson and Moskowitz (1964). They assumed that if the wind blew steadily for a long time over a large area, the waves would come into equilibrium with the wind. This is the concept of a fully developed sea. Here, a long time is roughly ten-thousand wave periods, and a “large area” is roughly five-thousand wave-lengths on a side. Hasselmann et al., (1973), after analyzing data collected during the Joint North Sea Wave Observation Project JONSWAP, found that the wave spectrum is never fully developed. It continues to develop through non-linear, wave-wave interactions even for very long times and distances. The JONSWAP spectrum is similar to the Pierson-Moskowitz spectrum except that waves continues to grow with distance (or time), and the peak in the spectrum is more pronounced. The latter turns out to be particularly important because it leads to enhanced non-linear interactions and a spectrum that changes in time according to the theory of Hasselmann (1966). 
     A number of buoys are known in the art which measure wave height and other data using accelerometers or other instruments. Hue, U.S. Pat. No. 4,515,013, issued May 7, 1985, and incorporated herein by reference, discloses a buoy with accelerometers and magnetometers, for measuring the vertical acceleration, but fails to teach or suggest an algorithm for determining wave direction or wave slope from wave spectra. Luscombe, U.S. Pat. No. 4,986,121, issued Jan. 21, 1991, and incorporated herein by reference, discloses an apparatus for measuring the vertical movement of a floating platform. This reference appears to be along the lines of Hue above, in that it only measures vertical motion. Such devices are useful in determining wave heights but do not appear to detect wave direction or other spectral data. 
     Harigae, U.S. Pat. No. 6,847,326, issued Jan. 25, 2005, and incorporated herein by reference, discloses a floating device for measuring wave height and tidal current direction and speed using GPS technology. This apparently free-floating buoy uses GPS data to determine tidal current direction and speed. The reference does not appear to teach measuring wave direction, slope, or other spectra. Von Wald, Jr., U.S. Pat. No. 3,310,047, issued Jan. 31, 1967, and incorporated herein by reference, discloses a wave gauge array for obtaining ocean wave spectra. This device appears to only measure wave height. 
     Mayberry, Published Japanese Patent Application 6014991 published Aug. 7, 1985, and incorporated herein by reference, discloses an apparatus for detecting of wave motion azimuth. From the translated Abstract, it does not appear that this reference measures more than wave height. Yamaguchi, Published Japanese Patent Application 2005083998, published Mar. 31, 2005, and incorporated herein by reference, discloses a GPS Ocean Wave Measuring Device. This device appears to measure only the period of the wave. 
     A number of non-patent literature documents disclose wave-measuring buoys. Pitch-Roll Buoy Wave Directional Spectra Analysis, Accession Number: ADP000383, by LeBlanc, L. R.; Middleton, F. H. (November 1982, Rhode Island University, Kingston) discloses a single small buoy, either free-floating or tethered to an anchor, designed not to follow the slope of the water surface, but instead to pitch and roll according to the orbital particle-velocity gradient. The dynamics of this buoy system are such that the data obtained on heave, pitch, roll, and compass bearing can be transformed into complete directional wave spectra. The buoy used to produce these data was an Endeco Model 956 Wave-Track buoy and the experiment was conducted as part of ARSLOE (Atlantic Remote Sensing Land-Ocean Experiment, fall 1980). 
     While Middleton&#39;s technique may provide directional wave spectra, his system does not account for acceleration data noise created when a buoy pitches and rolls. Thus, it remains a requirement in the art to provide a technique for generating a complete wave data spectra while compensating for accelerometer data noise induced by pitch and roll in a buoy, in a manner that is compact and easy to implement in a cost-effective manner. 
     SUMMARY OF THE INVENTION 
     The present invention comprises a portable moored system for the real-time measurement of the ocean surface directional wave spectrum. Measurement and reporting of the surface ocean wave spectra with the present invention provides data from the ocean that is essential for marine weather analysis, forecasts, and warnings. Additional applications of the present invention include maritime operations and safety (e.g., marine transportation, offshore operations, etc.), planning and design of coastal structures and processes, information for ocean and coastal zone activities (e.g., boating, fishing, surfing, etc.), validation of remotely sensed surface ocean wave systems and method and numerical ocean wave models, and the use for forensic purpose for at-sea mishaps. 
     The invention can be used by research organizations (government—Federal, State, etc.), commercial entities, such as Harbor Pilot&#39;s Associations, Oil and Gas Exploration Companies, Ship Routing Services or Weather Forecast Services, or the general public to obtain detailed sea state information for safe and efficient maritime operations. 
     The invention uses a moored buoy floating at the ocean surface and anchored to the seafloor that precisely measures the acceleration, pitch, roll, and Earth&#39;s magnetic flux field of the buoy over a limited sampling period. A moored buoy system is essential to the progress of maritime weather forecast and safety by providing a more accurate and precise determination of the surface ocean wave spectra than can be determined from traditional observations from ships or from remote sensing applications. The moored buoy system maintains its position in the face of hazardous maritime conditions that ships would normally avoid and thus can make measurements without hazarding vessels or life. NDBC has developed reliable, cost-effective surface ocean wave spectra measurements that can be integrated into a moored system. An operational network of instrumented, moored buoys making real-time ocean surface spectra measurements has been established off-shore of the United States and on the Great Lakes. In real-time the surface buoy communicates with shoreside processing facility to decode, analyze, and re-distribute the ocean wave spectral data and its derived parameters to national and international maritime weather, safety, and operations. 
     Until the development of the present invention, at sea ocean wave spectra measurements were limited to a few costly, bulky, expensive, and specialized observing systems. The use of a moored buoy system together with a compact wave measurement system allows the expansion of a network of surface ocean wave spectral measurements co-located with other important maritime environmental observations, such as wind speed and direction, air temperature, and atmospheric pressure. 
     The Digital Directional Wave Module (DDWM) was developed in support of the National Weather Service and maritime operations interest (e.g., commercial shipping, Coast Guard Search and Rescue, Oil and Gas drilling platforms). The primary goal of the system was to provide accurate, precise, timely, and low-cost surface ocean wave spectra measurements. Additional goals included compatibility with existing NDBC systems and reduced life-cycle costs. 
     The DDWM was developed and tested as a prototype by NDBC in 2007. Currently the DDWM is operational on more than 18 moored buoys of the NDBC network of 105. NDBC is responsible for all aspects of system maintenance, operation, deployment recovery, documentation, and life-cycle management. 
     The components of the surface ocean wave spectra measurement system include: 1) A buoy, 2) A mooring system consisting of an anchor on the seafloor, mooring line connecting the anchor and the buoy, 3) An electronic datalogger that controls the communications between the wave measuring system and the on-board remote telecommunications system, 4) an embedded computer including printed circuit board for data input/output, temporary or permanent data storage, and algorithms to convert the measured time series data into surface ocean wave spectra and quality assurance statistics and encode the results for transfer to the datalogger, 5) Sensors include one or three acceleration sensors, three orthogonal angular rate sensors, and three orthogonal magnetometers to measure the Earth&#39;s magnetic flux field, 6) A telecommunications system that links the buoy datalogger and a shoreside processing system, and 7) A shoreside processing system that decodes the transmitted data, performs, quality control, and computes derived wave parameters. 
     The buoy measures vertical acceleration (the up and down) and the tilt of the buoy to get the slope. It takes a combination of accelerometers, magnetometers, and angular rate sensors to determine wave direction with respect to True North. The wave directions are first calculated using accelerometers and angular rate sensors in the buoy frame of reference (fore and aft, starboard and port). The magnetometers are used to tell how the buoy is oriented with respect to the magnetic direction, and the wave direction is rotated, determined in the buoy frame of reference into the magnetic direction. Lastly the directions are rotated using the magnetic declination or variation to get the wave directions with respect to earth True North directions. 
     The algorithm, which is actually a collection of algorithms, is unique. The noise correction does not use the tilt data. The tilt data causes noise in the acceleration data, but the algorithm of the present invention uses the presence of signals in the very lowest frequencies, which do not contain relevant wave information, to estimate what that noise is. 
     The algorithm is used shoreside and on the buoy. Shoreside it is used to remove the noise from the vertical acceleration spectrum. On the buoy it used to determine the lowest frequency at which to start the integration of the angular rate measurements to get pitch and roll. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The embodiments, features and advantages of the invention described herein will occur to those skilled in the art from the following description of a preferred embodiment and the accompanying drawings, in which: 
         FIG. 1  shows a typical mooring system used in accordance with the present invention. 
         FIG. 2  is a flow chart illustrating the steps in the operation of the algorithm portion of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to  FIG. 1 , each surface ocean wave spectra measurement system uses a discus-shaped surface buoy  10  to measure heave, pitch, and roll of the buoy&#39;s hull  13 , as the waves pass beneath. Within discus-shaped surface buoy  10  is a Digital Directional Wave Module (DDWM)  12 , a datalogger  20 , a power system  15 , and a communications system  40 . Surface buoy  10  follows wave motions (both water surface elevation and wave slopes) as closely as possible so ocean wave information can be determined from the buoy motion (buoy&#39;s heave and tilt motion). Thus, a discus-shaped surface buoy  10 , which can follow wave height and slopes better than other shapes, is usually used for directional wave measurement. Buoy tilt data may be used to determine wave slope, an important component of the overall wave spectra. 
     A mooring system  50  keeps discus-shaped surface buoy  10  within a general vicinity but sufficient slack or scope is provided to allow discus-shaped surface buoy  10  to respond to the waves for better directional wave measurement. A typical mooring system, from the ocean bottom to the surface, may comprise an anchor  131 , a length of chain  130 , shackles  127 , nylon rope  128  and syntactic floats  129 , shackles, another section of chain  126 , swivel and shackles  125  that connect to the buoy bridle  34 . Size and length of the components vary depending on the ocean depth and bottom surface characteristics. 
     The DDWM consists of sensors  60 , an embedded computer  70 , connections to the sensors  71 , and a serial communication link  72  to the datalogger  20 . Sensors  60  comprise at least one and up to three orthogonal acceleration sensors ( 61 , 62 , 63 ), three orthogonal magnetometers ( 64 , 65 , 66 ), and three angular rate sensors ( 67 , 68 , 69 ). 
     All sensors  60  are sampled at the same rate to make a cotemporaneous times series of the measurements. Sampling is controlled by the embedded computer  70  of the wave processing system and its associated processing algorithm. DDWM  12  controls and regulates the power to the sensors used to measure buoy hull motion and the earth&#39;s magnetic field. 
     Sensors  60  on discus-shaped surface buoy  10  measure vertical acceleration (the up and down) and the tilt of discus-shaped surface buoy  10  to get the slope. It takes a combination of accelerometers ( 61 , 62 , 63 ), magnetometers ( 64 , 65 , 66 ), and angular rate sensors ( 67 , 68 , 69 ) to determine wave direction with respect to True North. The wave directions are first calculated in computer  70  using accelerometers ( 61 , 62 , 63 ) and angular rate sensors ( 67 , 68 , 69 ) in the buoy frame of reference (fore and aft, starboard and port). Magnetometers ( 64 , 65 , 66 ) are used to tell how the buoy is oriented with respect to the magnetic direction, and the wave direction is rotated, determined in the buoy frame of reference into the magnetic direction. Lastly the directions are rotated using the magnetic declination or variation to get the wave directions with respect to earth True North directions. 
     The algorithm, which is actually a collection of algorithms shown in the attached appendices, is unique. The noise correction does not use the tilt data. The tilt data causes noise in the acceleration data, but the algorithm of the present invention uses the presence of signals in the very lowest frequencies, which do not contain relevant wave information, to estimate what that noise is. 
     The algorithm is used shoreside and on discus-shaped surface buoy  10 . Shoreside it is used to remove the noise from the vertical acceleration spectrum. On discus-shaped surface buoy  10  it used to determine the lowest frequency at which to start the integration of the angular rate measurements to get pitch and roll. 
     The buoy electronics use a +12V (nominal), solar recharged battery system. Primary batteries (non-rechargeable) are switched on by a power system controller if the secondary (re-chargeable) system fails. Datalogger  20  controls operation of the wave system by applying the battery power to the DDWM  12  and may send control parameters via a serial communications link. Once the DDWM  12  has acquired the raw sensor data and the wave processing algorithm has completed, the data are sent to the datalogger  20  via a serial communications link  72 . The datalogger  20  then includes this data in its environmental data telemetry to shoreside processing system  103  in near real-time via the communication system  40 . 
     The embedded computer  70  contains the processing code to use Fast Fourier Transforms (FFTs) to transform the data from the time domain into the frequency domain (that is, spectrum) that provides Fourier coefficients at discrete frequencies. The Fourier coefficients of adjacent discrete frequencies are averaged (known as band-averaging) to smooth the spectrum and reduce the amount of data that needs to be transmitted to the shoreside processing system  103 . The embedded computer  70  then transforms the band-averaged Fourier coefficients into a set of directional wave parameters in terms of spectral density, directions, and spreading functions of the waves via a unique NDBC-developed algorithm. The embedded computer  70  also computes statistics (mean, maximum, minimum, and standard deviation) of the time series measurements and other quality control parameters, which are very useful for monitoring wave data quality and for assisting in troubleshooting system malfunctions. 
     The embedded computer  70  finally encodes the directional wave spectral data and the statistics into an efficient format for relay to the datalogger  20  when the datalogger  20  requests the message from the wave processing system at scheduled times. 
     The primary measurement is the heave or the acceleration of the buoy perpendicular to the normal surface of the ocean. The accelerometer is fixed to be aligned perpendicular to the buoy&#39;s horizontal deck. The intent is to measure the accelerations with respect to perpendicular of the undisturbed steady state sea surface, but in reality the pitch and roll of the buoy cause the accelerometer to tilt from the true vertical. Several previous studies conducted by NDBC show some level of low-frequency noise could be present due to the tilt effect on fixed accelerometers. In addition, other noise (e.g., electronic noise) could also exist, especially at low frequencies. Accelerations or acceleration spectra measured by an accelerometer need to be converted into displacements (or displacement spectra) via an integration algorithm. To remove noise that can be amplified by the integrations, NDBC developed a unique algorithm to determine a cut-off frequency and to remove/correct low-frequency noise. 
     The angular rate sensors measure the buoys rotation about three orthogonal axes and can be integrated using Fast Fourier Transforms (FFT) and inverse FFT (IFFT) to compute the time-dependent portion, time-series of pitch and roll following the method of Steele et al., 1998. The forward and inverse FFTs are performed until the algorithm converges on a solution. Another algorithm was developed and is used to determine the mean pitch and roll to be added to the time-dependent pitch and roll calculations. 
     Once pitch and roll time series are determined, in conjunction with the acceleration time series the co-spectra and quadrature spectra are computed from FFTs and directional wave spectra with respect to the buoy&#39;s coordinates system are determined following the method of Longuet-Higgins et al., 1963. 
     The orientation of the buoy with respect to True North is determined from the measurements of the horizontal and vertical Earth&#39;s flux made by the three orthogonal magnetometers ( 64 , 65 , 66 ), the buoy&#39;s pitch and roll, the expected Earth&#39;s magnetic flux at the buoy location, and correcting factors for the electro-magnetic effects of the hull and on-board electronics. The expected Earth&#39;s magnetic flux may be determined from the mean flux measurements or from a magnetic flux model. If used, the model information is entered into the DDWM before deployment. 
     The determined orientation of the buoy is applied to the directional components in the buoy hull coordinate system to produce directional data with respect to Magnetic North. Finally the directional data are transformed to True North by applying the known magnetic declination at the buoy location to the magnetic results. The magnetic declination is entered into the DDWM before deployment. 
     The datalogger  20  adds the wave spectral data message to the environmental data message of the other on-board measuring systems (for example, anemometers and barometers) and transmits the message to the shoreside processing system  103  from an on-board transmitter  101  via satellite  102 . The shoreside system  103  generally receives the wave data within 30 minutes of the conclusion of the wave sampling period. 
     The shoreside processing system  103  decodes the messages, processes the wave data, computes derived wave parameters, performs automated quality control, and then encodes the wave data for further dissemination. The shoreside processing applies algorithms to the acceleration spectra to remove noise caused by the tilting of the buoy and adjusts the acceleration spectra by applying transfer functions for the hull-mooring response and the sensor responses. After the acceleration spectra are corrected and adjusted, the acceleration spectra are transformed into displacement spectra by double integration. Double integration is accomplished in the frequency domain by dividing the spectra by the radian frequency to the fourth power. Corrections or adjustments may or may not be made to the directional spectra. From the displacement spectra various wave parameters may be derived, such as Significant Wave Height, Dominant or Peak Period (the inverse of the frequency that has the maximum spectral density within the spectrum), Average Period, and Mean Wave Direction at the Dominant Period. The shoreside processing facility also has the capability to reprocess the received spectral data using different response functions. 
       FIG. 2  is a block diagram illustrating the process of the present invention. Source code for these algorithm portions is shown in Appendices A and B attached herewith. Referring to  FIG. 2 , in step  200 , the real-time clock is initialized to a default time of 01/01/00 00:00:00. In step  205 , the parameter table is loaded from the EPROM. In step  210 , the system baud rate is setup up, along with the clock rate. In step  215 , data is then collected for 20 minutes. 
     In step  220 , the raw data is stored to flash memory (if setup to do so) and in step  225 , collected data is loaded into global arrays used in processing. In step  230 , a mean pitch and roll of the buoy is calculated from acceleration data from accelerometers and rate sensors in the buoy. In step  235 , collected wave data based on mean pitch and roll is then processed. In step  240 , a message is built up for shoreside transmission. In step  245 , the processed data is then stored to flash memory, and in step  250  the message is sent to shore. In step  255 , the parameter table is then written to EPROM and in step  260  it is determined whether 30 minutes has elapsed. If so, processing returns to step  215  to repeat the process and collect another 20 minutes of data. 
     The Wave Processing Algorithms for the Digital Directional Wave Module (DDWM) for computing mean pitch and roll in step  230  and processing collected wave data in step  235  are described as follows. The on-board processing of the Digital Directional Wave Module (DDWM) consists of several modules from the main program illustrated in  FIG. 2 . The wave processing is performed with the Process_Waves (Table 1) module within the process.c Program (Appendix A is the Source Code Listing). Process_Directional (Table 2) performs the remainder of the wave processing before results are saved for encoding. 
     Other routines are used to Save intermediate and final results, perform both the forward and backward FFT depending on the calling argument (R1fft), and Compute mean pitch and roll from the ratio of the horizontal components of acceleration to the vertical component (meanPitchRoll.c, Appendix B for source code) as set forth in step  230  of  FIG. 2 . 
     Once the data are transmitted to the shoreside processing facility, NDBC removes noise that appears in the low-frequencies for fixed or strapped down accelerometers by applying empirically derived algorithms to the measured acceleration spectral densities. The algorithm assumes that the energy in the lowest frequency band (f(n=0)) of the DDWM represents noise from the tilt of the accelerometer. This unwanted noise is amplified when the double integration takes place to compute displacement spectral densities from the acceleration spectral densities. 
     
       
         
               
             
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 Process_Waves Flow 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Load_Arrays 
                 Loads test data from a user specified file 
               
               
                   
                 and loads it into the data arrays. 
               
               
                 ↓ 
               
               
                 Process_Waves 
                 Handles flow control for wave data 
               
               
                   
                 processing. 
               
               
                 ↓ 
               
               
                 Calc_Magnetic_Fields 
                 Calculate the magnetic fields B and Bd. 
               
               
                 ↓ 
               
               
                 GetBey 
                 Gets the Earth&#39;s magnetic field from buoy 
               
               
                   
                 measurements. 
               
               
                 ↓ 
               
               
                 Run_Input_Stats 
                 Calculates and displays the mean, 
               
               
                   
                 minimum, maximum, and standard 
               
               
                   
                 deviation of the input arrays. 
               
               
                 ↓ 
               
               
                 Stat 
                 Calculates and displays the mean, 
               
               
                   
                 minimum, maximum, and standard 
               
               
                   
                 deviation of the specified array. 
               
               
                 ↓ 
               
               
                 Process_Directional 
                 Handles all the processing necessary for 
               
               
                   
                 a directional wave. 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 Processs_Directional Flow 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Setup_Nfreq 
                 Sets up the nfreq data array to be used for 
               
               
                   
                 spectral analysis. 
               
               
                 ↓ 
               
               
                 NonDirectional_Spectra 
                 Performs non-directional spectral analysis 
               
               
                   
                 on wave data. 
               
               
                 ↓ 
               
               
                 Noise_Correction 
                 Finds the low frequency cutoff for the 
               
               
                   
                 integration of the angular rate. 
               
               
                 ↓ 
               
               
                 ARS_pitch and roll 
                 This routine calculates Pitch and Roll from 
               
               
                   
                 angular rate sensors. 
               
               
                 ↓ 
               
               
                 ARS_XYslope_Azimuth 
                 Calculate azimuth using angular rate pitch 
               
               
                   
                 and roll. 
               
               
                 ↓ 
               
               
                 Run_Stats_II 
                 Calculates and outputs statistical data on 
               
               
                   
                 processed data. 
               
               
                 ↓ 
               
               
                 Cross_Spectra 
                 Performs cross spectral analysis on wave 
               
               
                   
                 data. 
               
               
                 ↓ 
               
               
                 Calc_Equations 
                 Calculates values needed for further 
               
               
                   
                 processing of wave data. 
               
               
                 ↓ 
               
               
                 Save_Results 
               
               
                   
               
             
          
         
       
     
     The algorithm is used shoreside and within the on-board processing (see Routine name Noise Correction). In the on-board processing, it is used to determine the lowest frequency at which to start the integration of the angular rate measurements to determine pitch and roll. 
     C11M(f(n)): Acceleration spectral density for a frequency, f(n), where n presents the index of the frequency band. For the DDWM, n={0:46}. 
     The Noise Correction for each frequency band (NC(f(n))) is computed as follows:
 
 NC ( f ( n ))=20 *C 11 M ( f ( n= 0))*(0.18 −f ( n )), for  NC ( f ( n ))&gt;=0;
 
 NC ( f ( n ))=0, for  NC ( f ( n ))&lt;0;
 
NC(f(n)) is then subtracted from each C11M(f(n)). If the result of the subtraction is less than zero, then the result is set to zero.
 
     The advantages of the invention over other wave measuring systems are the adjustments and corrections of the spectra. In many cases, these adjustments and corrections complicate the processing and are not considered cost-effective measures. These adjustments and corrections elevate the invention&#39;s measurements to more exacting precision and accuracy than if they were ignored. 
     As noted in the Background of the Invention, the Prior Art of Middleton, while providing directional wave spectra, does not provide a means for filtering out acceleration data noise. The present invention provides an algorithm that uses the VLF signals to estimate acceleration data noise and to automatically identify the cut-off frequency for starting integration of angular rate measurements. Thus, the present invention, provides a number of improvements over the apparatus and methods of the Prior Art, including more accurate &amp; less noisy measurements due to the unique algorithms disclosed herein, and the entire system which, together, provide a more affordable and deployable capability than others have achieved in terms of less costly/bulky/compact. 
     While the preferred embodiment and various alternative embodiments of the invention have been disclosed and described in detail herein, it may be apparent to those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope thereof.