Radar sensor and method for boat speed measurement

Abstract

A marine speed measurement system for determining speed through water (STW) of a vessel comprises a first radar device mounted on the vessel and configured to emit at least one electromagnetic beam directed toward a water surface at an incidence angle θ relative to a vessel reference plane. The system further comprises an inertial measurement unit (IMU) rigidly attached to the vessel, the IMU provides an output that conveys linear acceleration of the vessel, angular velocities of the vessel, and heading of the vessel. The IMU may comprise three-axis accelerometers configured to measure linear accelerations of the vessel, three-axis gyroscopes configured to measure angular velocities of the vessel, and three-axis magnetometers configured to measure the heading of the vessel relative to Earth's magnetic field. The system further comprises a second radar device mounted on the vessel, symmetrically positioned on an opposite side of the centerline of the vessel.

Description

Docket No. 0278.2055-001Radar Sensor and Method for Boat Speed MeasurementRELATED APPLICATION

[0001] This application claims the benefit of U. S. Provisional Application No.63 / 773,967, filed on March 18, 2025. The entire teachings of the above application are incorporated herein by reference.BACKGROUND

[0002] The maritime industry continues to grapple with challenges in accurately measuring vessel speed and distance in real time, particularly for high-performance vessels such as foiling boats, where precise data is critical for ensuring both safety and optimal performance.

[0003] Foiling technology, i.e., boats that use hydrofoils to lift off the water for reduced drag, has grown popular in recreational sailing, military applications, and electric-powered boats. With foiling also extending to other sporting categories like windsurfing, the need for precise speed measurement in these high-performance crafts has become paramount.

[0004] Although GPS provides Speed Over Ground (SOG) data, measuring Speed Through Water (STW) remains essential for understanding the impact of currents and tides. This facilitates accurate navigation adjustments and ensures optimal engine and propulsion performance. For example, in a scenario where a boat is sailing in a narrow channel with a strong current, its SOG might read 10 knots while its STW could be 15 knots. Focusing only on SOG might obscure the extra effort required to overcome the current, potentially leading to inefficiencies. STW monitoring enables operators to optimize trim, speed, and fuel consumption.SUMMARY

[0005] The embodiments described herein are directed to systems for, and methods of, employing radar sensor technology for measuring parameters associated with water-based vessels. The parameters may include, for example, vessel speed with respect to the water surface, distance from the vessel to the water, and distance from the vessel to other objects.

[0006] In one aspect, the invention may be a marine speed measurement system for determining speed through water (STW) of a vessel, comprising a first radar device mounted- 1 - 5055169. vlDocketNo. 0278.2055-001on the vessel and configured to emit at least one electromagnetic beam directed toward a water surface at an incidence angle 9 relative to a vessel reference plane, and an inertial measurement unit (IMU) rigidly attached to the vessel. The IMU provides an output that conveys (i) linear acceleration of the vessel, (ii) angular velocities of the vessel, and (iii) heading of the vessel. The system may further comprise a processing unit that uses the IMU output to correct an error in a measurement from the first radar device due to induced motion.

[0007] The IMU may further comprise at least one three-axis accelerometer, configured to measure linear acceleration of the vessel, at least one three-axis gyroscope, configured to measure one or more angular velocities of the vessel, and at least one three-axis magnetometer, configured to measure heading of the vessel. The radar device may be further configured to measure a time-of-flight of the electromagnetic beam between emission and reception after reflection from the water surface, thereby determining a slant range to the water, and measure a Doppler frequency shift of the reflected electromagnetic beam, to determine a radial velocity component between the vessel and the water surface along a direction of the electromagnetic beam.

[0008] The processing unit may be operatively connected to the radar device and the IMU, the processing unit may be configured to determine an attitude (pitch, roll, yaw) of the vessel, in real time, from IMU data, determine a motion-induced velocity vector of the vessel in an Earth-fixed reference frame from the IMU data, including contributions from pitch, roll, heave, and yaw motions, resolve a motion-induced velocity vector into a direction of the electromagnetic beam, thereby determining a motion-induced Doppler bias affecting the determined radial velocity component, determine a corrected radial velocity by subtraction of the motion-induced Doppler bias from a determined radial velocity component, and resolve the corrected radial velocity into a forward direction of the vessel, using the incidence angle 9 and the attitude of the vessel, to determine the STW of the vessel.

[0009] The system may further comprise a second radar device mounted on the vessel, symmetrically positioned on an opposite side of a centerline of the vessel relative to the first radar device, wherein both the first radar device and the second radar device face toward a forward direction of the vessel and are directed toward the water surface at equal but opposite incidence angles (+ / - 9) relative to the forward direction of the vessel. Each of the first radar device and the second radar device may be configured to (i) emit an electromagnetic beam at the incidence angle (+ / - 9), (ii) measure the time-of-flight and Doppler frequency shift of its- 2 - 5055169. vlDocket No. 0278.2055-001reflected beam, and (iii) output a port-side radial velocity and a starboard- si de radial velocity, respectively.

[0010] The processing unit may be further configured to (i) for each of the first radar device and the second radar device, determine a port-side Doppler bias and an independent starboard- si de Doppler bias using an attitude (pitch, roll, yaw) of the vessel and motion data from the IMU, (ii) determine a port-side corrected radial velocity and a starboard- si de corrected radial velocity by subtracting respective motion-induced Doppler biases from the measured radial velocities, (iii) resolve each corrected radial velocity into the vessel’s forward direction to obtain a port-side STW value and a starboard- si de STW valuem, and (iv) determine a leeway angle ((])) of the vessel by comparing the two STW values as (|)=tan'1(2-STWavg-sin(9)STWstarboard-STWport), where STWavg is an average of port-side STW and starboard-side STW, and 9 is the incidence angle of the radar beams.

[0011] In another aspect, the invention may be a method of determining speed through water (STW) of a vessel, comprising emitting, from a first radar device mounted on the vessel, at least one electromagnetic beam directed toward a water surface at an incidence angle 9 relative to a vessel reference plane, providing, from an inertial measurement unit (IMU) rigidly attached to the vessel, an output that conveys (i) linear acceleration of the vessel, (ii) angular velocities of the vessel, and (iii) heading of the vessel, and correcting, using the IMU output, an error in a measurement from the first radar device due to induced motion.

[0012] The method may further comprise, by the IMU, measuring linear acceleration of the vessel, measuring one or more angular velocities of the vessel, and (iii) measuring heading of the vessel. The radar device may be further configured to measure a time-of-flight of the electromagnetic beam between emission and reception after reflection from the water surface, thereby determining a slant range to the water, and measure a Doppler frequency shift of the reflected electromagnetic beam, to determine a radial velocity component between the vessel and the water surface along a direction of the electromagnetic beam.

[0013] The method may further comprise, by a processing unit onboard the vessel operatively connected to the radar device and the IMU, determining an attitude (pitch, roll, yaw) of the vessel, in real time, from IMU data, determining a motion-induced velocity vector of the vessel in an Earth-fixed reference frame from the IMU data, including contributions from pitch, roll, heave, and yaw motions, resolving a motion-induced velocity vector into a direction of the electromagnetic beam, thereby determining a motion-induced- 3 - 5055169. vlDocketNo. 0278.2055-001Doppler bias affecting the determined radial velocity component, determining a corrected radial velocity by subtraction of the motion-induced Doppler bias from a determined radial velocity component, and resolving the corrected radial velocity into a forward direction of the vessel, using the incidence angle 9 and the attitude of the vessel, to determine the STW of the vessel.

[0014] The method may further comprise a second radar device on the vessel, symmetrically positioned on an opposite side of a centerline of the vessel relative to the first radar device, wherein both the first radar device and the second radar device face toward a forward direction of the vessel and are directed toward the water surface at equal but opposite incidence angles (+ / - 9) relative to the forward direction of the vessel.

[0015] The method may further comprise emitting an electromagnetic beam at the incidence angle (+ / - 9), measuring the time-of-flight and Doppler frequency shift of its reflected beam, and outputting a port-side radial velocity and a starboard-side radial velocity.

[0016] The method may further comprise (i) for each of the first radar device and the second radar device, determining a port-side Doppler bias and an independent starboard- si de Doppler bias using an attitude (pitch, roll, yaw) of the vessel and motion data from the IMU, (ii) determining a port-side corrected radial velocity and a starboard-side corrected radial velocity by subtracting respective motion-induced Doppler biases from the measured radial velocities, (iii) resolving each corrected radial velocity into the vessel’s forward direction to obtain a port-side speed through water value and a starboard-side speed through water value, and (iv) determining the leeway angle ((])) of the vessel by comparing the two STW values as ( =tan-1(2-STWavg-sin(9)STWstarboard-STWport), where STWavg is an average of port-side STW and starboard-side STW, and 9 is the incidence angle of the radar beams.

[0017] In another aspect, the invention may be a non-transitory computer-readable medium with computer code instruction stored thereon, the computer code instructions, when executed by a processor, causes a marine speed measurement system for determining speed through water (STW) of a vessel to emit at least one electromagnetic beam directed toward a water surface at an incidence angle 9 relative to a vessel reference plane, provide an output that conveys (i) linear acceleration of the vessel, (ii) angular velocities of the vessel, and (iii) heading of the vessel, and correct, using the IMU output, an error in a measurement from the first radar device due to induced motion.

[0018] The computer code instructions may further cause a marine speed measurement system to measure a time-of-flight of the electromagnetic beam between emission and- 4 - 5055169. vlDocket No. 0278.2055-001reception after reflection from the water surface, thereby determining a slant range to the water, and measure a Doppler frequency shift of the reflected electromagnetic beam, to determine a radial velocity component between the vessel and the water surface along a direction of the electromagnetic beam.

[0019] The computer code instructions may further cause a marine speed measurement system to determine an attitude (pitch, roll, yaw) of the vessel, in real time, from IMU data, determine a motion-induced velocity vector of the vessel in an Earth-fixed reference frame from the IMU data, including contributions from pitch, roll, heave, and yaw motions, resolve a motion-induced velocity vector into a direction of the electromagnetic beam, thereby determining a motion-induced Doppler bias affecting the determined radial velocity component, determine a corrected radial velocity by subtraction of the motion-induced Doppler bias from a determined radial velocity component, and resolve the corrected radial velocity into a forward direction of the vessel, using the incidence angle 9 and the attitude of the vessel, to determine the STW of the vessel.

[0020] The computer code instructions may further cause each of a first radar device and a second radar device to (i) emit an electromagnetic beam at the incidence angle (+ / - 9), (ii) measure the time-of-flight and Doppler frequency shift of its reflected beam, and (iii) output a port-side radial velocity and a starboard- si de radial velocity.

[0021] In another aspect, a vessel speed measurement system may comprise a radar device configured to emit an electromagnetic beam toward a water surface at an incidence angle 9, measure a time-of-flight and Doppler frequency shift of the reflected beam, and output a raw radial velocity, an inertial measurement unit (IMU) comprising one or more accelerometers, one or more gyroscopes, and one or more magnetometers, configured to measure the vessel’s attitude (pitch, roll, yaw) and motion (heave, surge, sway), a weather station configured to measure true wind speed and true wind direction, a processing unit configured to determine a motion-induced Doppler bias from IMU data, model a wind-induced surface velocity from the weather station data, wherein said model comprises: a wave orbital velocity determined from the true wind speed and an estimated wave height and period; a wind-driven shear velocity determined from the true wind speed. The processing unit may be further configured to determine a corrected radial velocity by subtracting the motion-induced bias and the wind-induced surface velocity from the raw radial velocity, resolve the corrected radial velocity into the vessel’s forward direction to obtain Speed Through Water and output the Speed Through Water to a navigation system.- 5 - 5055169. vlDocketNo. 0278.2055-001

[0022] The processing unit may be further configured to estimate wave height from said true wind speed using an empirical wave spectrum model, and output said wave height to a flight control system for dynamic stabilization of a foiling vessel.

[0023] The system may further comprise a weather station configured to measure true wind speed and true wind direction, wherein the processing unit is further configured to: apply the wind-induced surface velocity correction independently to both port and starboard radar measurements, recompute the leeway angle using the wind-corrected Speed Through Water values.

[0024] The processing unit may be further configured to apply a low-pass filter to the raw Doppler measurements to suppress high-frequency noise from wind-generated turbulence, and dynamically adjust the filter’s cutoff frequency based on the true wind speed.BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The foregoing will be apparent from the following more particular description of example embodiments, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating embodiments.

[0026] FIG. 1 shows an example embodiment of a radar-based measurement sensor system.

[0027] FIG. 2 shows a sensor system installed on a rail at the front of the boat.

[0028] FIG. 3 shows a sensor system installed on the top of the roof looking forward.

[0029] FIG. 4 shows that the cosine of the angle 0, reduces the sensed velocity as compared to the actual velocity Vr.

[0030] FIG. 5 shows that the angle 0 / varies in time due to complex 3D motion of the boat.

[0031] FIG. 6 shows the use of two sensors, one on each side of the boat.

[0032] FIG. 7 shows the use of multiple sensors to implement a docking-assist.

[0033] FIG. 8 is a diagram of an example internal structure of a processing system 800 that may be used to implement one or more of the embodiments described herein.DETAILED DESCRIPTION

[0034] A description of example embodiments follows.- 6 - 5055169. vlDocketNo. 0278.2055-001

[0035] Level 1: Basic Doppler Radar (Single FMCW or Pulse-Coherent) measures radial velocity (Vr) of the water surface using the Doppler effect. Two radar types may be used.

[0036] First radar type is FMCW (Frequency Modulated Continuous Wave), which transmits a frequency-chirped signal (sawtooth or triangular), measures beat frequency (fb) between transmitted and received signals. Range (R) and Doppler (Vr) are extracted simultaneously.

[0037] The second radar type is Pulse-Coherent Radar, which transmits short pulses and measures phase shift between pulses. Pulse-Coherent radar provides Higher Doppler sensitivity at low speeds, which is better for turbulent water.

[0038] Key equations are:Doppler Shift: Af = (2 * Vr * fo) / c,FMCW Range: R = (c * fb) / (2 * S),Pulse-Coherent Doppler (Vr): Vr = (X * Acp) / (4 * 7t *

[0039] Motion Compensation (IMU-Based): In nautical terms, boat attitude describes the orientation of a vessel in three dimensions: pitch (tilting forward or backward about the transverse axis), roll (tilting side to side about the longitudinal axis), and yaw (rotation around the vertical axis). A ship can also move linearly along any of its axes — longitudinal, transverse, and vertical. These translational motions (or translatory motions) are known as surge, sway, and heave respectively. Boat motion may introduce false Doppler shifts. To solve this problem, an IMU (Inertial Measurement Unit) may measure boat attitude, and a Kalman filter may compensate for motion-induced bias.

[0040] Doppler Bias Due to Boat Motion - the apparent radial velocity (Vr aPP) is:Vr app = Vboat * COS(9) + VmotionWhere:Vboat = True boat speed9 = Angle between radar beam and water surfaceV motion = Doppler bias from boat motion (pitch, roll, heave)

[0041] IMU-Based Correction - measure boat attitude (pitch, roll, yaw) from IMU, compute the expected Doppler bias due to motion, then subtract bias from radar measurement to get true STW. The following is a description of a system for measuring a vessel’s speed through water (STW) using radar, with compensation for motion-induced errors via an IMU.- 7 - 5055169. vlDocket No. 0278.2055-001The system integrates radar, IMU, and weather station data to correct for wind-induced Doppler biases (wave orbital motion and surface shear) and vessel motion-induced Doppler biases (pitch, roll, heave, and yaw).

[0042] Wind generates waves and surface currents, introducing false Doppler shifts. Vessel motion (pitch, roll, heave, yaw) causes the radar beam to move relative to the water, introducing additional false Doppler shifts. An example system that compensates for such false Doppler shifts combines radar, which measures raw Doppler velocity, an IMU, which measures vessel motion (acceleration, angular velocity, magnetic field), and a weather station, which measures wind speed and direction. Data from these sensors is fused to compute a corrected STW.

[0043] Wind affects STW measurements via Wave Orbital Motion, which is circular motion of water particles in waves. Wind also affects STW measurements via Surface Shear, which is wind-driven surface currents.

[0044] The total wind-induced velocity Vwind is Vwind = Vwave + Vshear, where Vwave is wave orbital velocity (derived from wave spectrum), and Vshear is surface shear velocity (empirically modelled as Vshear k* Vwind, where k~0.03).

[0045] When a vessel moves through water, its radar measures the combined velocity of (i) True Speed Through Water (STW) which is the vessel’s actual motion relative to the water, and (ii) Motion-Induced Doppler Bias (Vbias ), which are False Doppler shifts caused by pitch / roll / heave (vertical and angular motion), yaw / sway / surge (horizontal and rotational motion), and acceleration / deceleration (linear motion changes).

[0046] These motion effects introduce radial velocity components along the radar beam, distorting the raw Doppler measurement by 0.1-2 knots (depending on sea state and vessel dynamics).

[0047] The Inertial Measurement Unit (IMU) comprises three key sensors:Sensor Measured Quantity Output Key Equation Accelerometer Specific force a* [a*, tiy, az]r(m / s2) a* - R*(a" - g*) Gyroscope Angular velocity to6' — [a>x, ojy, - R* • [u? x](rad / s) Magnetometer Earth’s magnetic m? — (p. T) V->field — atan2(~m.y, m.,,) Reference Frames:• Body frame (b): Fixed to the vessel ( ■■■ bow, y - starboard, z - down).• Navigation frame ( ); Earth-fixed (NED: North-East-Down).5055169. vlDocketNo. 0278.2055-001

[0048] The attitude (orientation) of the vessel is computed using the following methods.

[0049] 1. Gyroscope Integration (Short-Term Accuracy)Quaternion kinematics (avoids gimbal lock):1Euler angle extraction (for compatibility with radar beam models):- atan2(2(ty><?34- tyj<ty)> q% - qi - q% 4- q%) (roll)0 asin( ••• 2(qI< / 3. q0q2))$ atan2(2(c / if / 24- < / 0c / 3), q% + ql •••• •••• q& (yaw)

[0050] 2, Magnetometer Correction (Long-Term Heading Stability)Tilt-compensated heading (with magnetic declination compensation):iimag=atan2(— mycos + mzsin< >, mxcos0 + mysin0sin< > + mzsin0cos )

[0051] 3, Accelerometer-Based Roll / Pitch Refinement (Gravity Vector)Low-frequency attitude correction (to mitigate gyro drift):(b d..v,.v,. = atan2( x.n yv, ’ n z7) y, ’ 0adcvcv = atan21 i — ar, i a y? + a z? ) i

[0052] Velocity and position estimation may be accomplished with:

[0053] L Accelerometer Integration (Body Frame)Specific force to acceleration (remove gravity):a - R a* 4- g«Velocity integration (navigation frame);vri~ J afidtPosition integration:p« J dt

[0054] Z Error Mitigation (Sensor Fusion)A Kalman Filter (KF) or Complementary Filter fuses the gyroscope (high-frequency, shortterm accuracy), the accelerometer (low-frequency, long-term stability), and the magnetometer (heading reference). Key KF equations are:State vector: x = [, 0, ip, vx, vy, vz, px, py, pzTPrediction step (gyro integration): xfc|fc-x= F xk-1+ B tkb_1- 9 - 5055169. vlDocket No. 0278.2055-001Update step (accelerometer / magnetometer correction): xk= x^-! + Kfc(zfc—

[0055] The motion-induced Doppler bias (bias) is the radial velocity component of the vessel’s motion along the radar beam direction. The radar beam is typically mounted at an angle a (e.g., 30° downward) and offset from the vessel’s centerline. Its direction in the body frame is:coscrsin / ?'^beam cosacosfi. — sin a.where:a = downward tilt angle (e.g., 30°).P = azimuth angle (e.g., 0° for forward-looking radar).

[0056] Motion-Induced Velocity Vector (Navigation Frame)The vessel’s velocity in the navigation frame is:[Uv]v mo+ti-on vEwhere:vN= north velocity (from IMU integration).vE= east velocity.vD= downward velocity (heave).The motion-induced Doppler bias is the dot product of the vessel’s velocity and the radar beam direction:biasvmotionubeamwhere:ubeam= ubeam (beam direction in navigation frame).= rotation matrix from body to navigation frame (derived from attitude angles). Expanding the equations gives:- 10 - 5055169. vlDocket No. 0278.2055-001^bias= VN ’ (coscrsin / ?cosi / > — coscrcos / ?sim / >)+vE· (cosαsinβsinψ + cosαcosβcosψ)+vD· (−sinα)

[0057] Corrected STW CalculationThe true Speed Through Water (STW) is obtained by subtracting the motion-induced Doppler bias from the raw radar measurement:STWcorrected= STWraw− Vbias− Vwindwhere:Vwind= Wind-induced surface velocity.

[0058] The real-time STW correction process is summarized below.Step Action1 Measure raw Doppler velocity vradarfrom radar.2 Measure wind speed / direction from weather station.3 Compute vwind(wave orbital + surface shear).4 Measure vessel motion (acceleration, angular velocity) fromIMU.5 Estimate attitude (φ, θ, ψ) using sensor fusion.6 Compute vn(vessel velocity in navigation frame).7 Project vnonto radar beam to compute Doppler bias.8 Compute corrected STW vSTW.

[0059] Wind-Induced Surface Doppler Correction for Radar-Based STW MeasurementWhen a vessel’s radar measures Speed Through Water (STW) via Doppler shift from the water surface, the measurement is contaminated by wind effects, including:Wave orbital motion (Stokes drift) - Water particles in waves move in circular orbits, creating a false Doppler shift even in zero current.Wind-driven surface shear - Wind stress induces localized velocity gradients at the air-water interface, distorting the radar’s reflection.Turbulent eddies - Wind-generated turbulence introduces random velocity fluctuations, increasing noise in Doppler measurements.These effects do not depend on deep-water currents (e.g., Ekman transport) but instead directly alter the surface velocity field that the radar samples. Existing systems either:(i) ignore wind effects entirely (leading to STW errors of 0.5-2 knots in strong winds), or- 11 - 5055169. vlDocket No. 0278.2055-001(ii) use empirical corrections without real-time wind data (e.g., fixed offsets for "windy conditions").

[0060] A solution to these issues is to use True Wind Measurement + Wave Orbital Velocity Model. An onboard weather station (e.g., Airmar 200WX / 300WX) measures:(i) True wind speed (W) and true wind direction (0_W) (relative to vessel heading). (ii) Air temperature, pressure, and humidity (for density corrections).The system models wind-induced surface motion using:1. Wave orbital velocity (Stokes drift) - The dominant source of false Doppler shift in radar measurements.2. Wind-driven surface shear - Localized velocity gradients near the interface.3. Turbulent noise suppression - Filtering of high-frequency Doppler fluctuations.

[0061] The corrected STW is computed as:STWcorrected = STW raw Vbias Vwindwhere:Vwind = Wind-induced surface velocity (modeled from weather station data).Vbias IMU-based motion compensation.

[0062] Mathematical Model for Wind-Induced Surface MotionWave Orbital Velocity (Stokes Drift)The orbital velocity of water particles in a wave is:Vwave= TπH · e−kzwhere:H = Wave height (estimated from wind speed via Pierson-Moskowitz or JONSWAP spectra). Empirical relationship: H ~ 0.02 • W2 (for fully developed seas).T = Wave period (empirically derived from wind fetch F) T ~ 0.8 • F (for fetch-limited waves)k = λ2π = Wavenumber (λ = wavelength, λ ≈ 2πgT2).z = Depth (radar measures at z ~ 0, i.e., surface).Simplified surface orbital velocity (z = 0): Vwave= TπH

[0063] Wind-Driven Surface ShearWind stress induces a thin shear layer at the surface, with velocity:Vshear= ρw· √τwhere:τ = ρa· Cd· W2= Wind stress (N / m2).- 12 - 5055169. vlDocket No. 0278.2055-001ρa= Air density (~1.225 kg / m3).Cd= Drag coefficient (~0.001–0.002 for water).ν = Kinematic viscosity of water (~1 × 10−6m2 / s).Simplified approximation: Vshear - 0.01 • W (for W in m / s)

[0064] Total Wind-Induced Surface Velocity - the combined effect of waves and shear is:Vwind= Vwave+ VshearThe direction is aligned with true wind direction (0w) (for waves) and wind stress direction (for shear).

[0065] System ImplementationWeather Station Inputs are True wind speed (W) and direction (9w), Air temperature and pressure (for density corrections).

[0066] Wave Model - Estimates H and T from W and fetch (F), and Computes Vwave. The shear model computes Vshear from wind stress. Doppler Correction subtracts Vwind from raw radar Doppler measurement. The output is wind-corrected STW (for navigation) and wave height estimate (for foiling applications).

[0067] The system flow for this level of processing may be given by:[Radar (FMCW or Pulse-Coherent)][Doppler & Range Processing][IMU (Accel + Gyro + Mag)][Kalman Filter (Motion Compensation)][STW Output (NMEA2000 / CAN)]

[0068] Level 2: Dual-Radar System (forward port and forward starboard OR backward port and backward starboard). At this level, two radars (port and starboard) measure Doppler shifts from different angles. Differential Doppler analysis enables Leeway detection (lateral drift), foiling altitude measurement (distance to water), and improved STW accuracy (redundancy).

[0069] Key Equations for Dual-Radar System are:

[0070] For Leeway Detection- 13 - 5055169. vlDocket No. 0278.2055-001Forward port radar (Vfwd _prt) measures forward + lateral velocity.Forward starboard radar (Vfwd stb) measures forward - lateral velocity.Leeway (Vieeway) is computed as:Vleeway=(Vfwd_prt—Vfwd stb) / (2 * sin(d))where:a = Angle between radar beam and boat centerline.The equations above may alternatively be modified for backward port radar and backward starboard radar.

[0071] For Foiling Altitude MeasurementTime-of-Flight (ToF) from both radars gives distance to water (h).Trigonometry corrects for boat pitch / roll:h=(Rfwd_prt + Rfwd stb) / 2 * COS(0pitch) * COS(0roll) where:Rfwd _prt, Rfwd stb = Range from forward port and starboard radars, respectively©pitch, ©roll = Boat attitude from IMU

[0072] The system flow for this level of processing may be given by:[Forward port Radar] — [Doppler & Range Processing][Forward starboard Radar] — [Doppler & Range Processing][IMU (Attitude Data)][Sensor Fusion (Kalman Filter)][STW + Leeway + Altitude Output (NMEA2000 / CAN)]

[0073] Level 3: 2D Radar + Wave Modeling (FFT-Based Compensation). Single or dual 2D FMCW radar may be used to measure Doppler shifts at multiple ranges. Fast Fourier Transform (FFT) may be used to analyze wave frequency spectrum to identify wave orbital velocities, compensate for wave-induced Doppler bias. Weather station data (true wind) is- 14 - 5055169. vlDocket No. 0278.2055-001used to model wind-driven waves, for example an Airmar Weatherstation® 140 as shown in FIG. 1

[0074] Wave-Induced Doppler Compensation. Wind-driven waves create orbital water motion, introducing false Doppler shifts. The orbital velocity (Vwave) at depth z is:Vwave = (7t * H / T) * e('k*z)* cos(k * X - co * t) where:H = Wave heightT = Wave periodk = Wavenumber (2π / λwave)ω = Angular frequency (2π / T)

[0075] FFT-Based Wave Period Detection - Radar measures Doppler shifts at multiple ranges. An FFT is applied to extract dominant wave frequencies, and wave-induced Doppler bias is subtracted from STW.

[0076] The system flow for this level of processing may be given by:[Radar (2D FMCW)] — [Doppler & Range Processing][Weather Station (True Wind Data)][FFT Wave Analysis][IMU (Attitude Data)][Sensor Fusion (Kalman Filter)][STW + Leeway + Altitude + Wave-Corrected STW (NMEA2000 / CAN)]

[0077] Level 4: 3D Radar with Beamforming & Autonomous Docking - 3D MIMO (Multiple-Input Multiple-Output) radar with antenna matrix enables digital beamforming (steering radar beams electronically), 3D point cloud generation (docking & obstacle- 15 - 5055169. vlDocket No. 0278.2055-001avoidance), real-time wave modeling (full 3D Doppler compensation), and software-based splash filtering (rejects near-hull turbulence).

[0078] Digital Beamforming (DBF): Problem: Boat motion (pitch, roll, yaw) tilts the radar beam, introducing Doppler bias. A solution is to electronically steer the beam to maintain a fixed Earth-referenced direction (e.g., always pointing downward).

[0079] Beamforming Equations: The steered beam direction is controlled by phase shifts applied to each antenna element:Δφn= (2 * π / λ) * dn* sin(θsteer)where:Δφn= Phase shift for the nthantennadn = Position of antenna n©steer = Desired steering angle

[0080] This results in the radar always pointing in the same direction (e.g., downward), eliminating motion-induced Doppler bias. Further, no mechanical gimbals are needed, so the beam steering can be fully solid-state.

[0081] 3D Point Cloud Generation - The antenna matrix scans azimuth & elevation, and each reflection point is assigned a Range (R) (from FMCW), a Doppler (Vr) (for moving objects), and Angle (0, cp) (from beamforming). A 3D point cloud is generated in real time.

[0082] Splash & Turbulence Filtering - These are software-based techniques used to reject near-hull turbulence, including (i) Range gating (ignores reflections <0.5 m from hull), (ii) Doppler filtering (rejects high-Doppler clutter), Spatial filtering (distinguishes splash from true water surface), and Temporal filtering (moving average smooths noise).

[0083] Autonomous Docking & AR Navigation - A 3D point cloud is fused with camera data for augmented reality (AR) navigation. Docking lines & obstacle markers are overlaid on a live camera feed.

[0084] The system flow for this level of processing may be given by:[3D MIMO Radar] — [Digital Beamforming][Doppler & Range Processing] — [FFT Wave Analysis][IMU (Attitude Data)] — [Motion Compensation]- 16 - 5055169. vlDocket No. 0278.2055-001[Weather Station (True Wind)] — [Wave Modeling][3D Point Cloud Generation] — [Splash Filtering][Sensor Fusion (Kalman Filter + Al)][STW + Leeway + Altitude + 3D Map + AR Docking (NMEA2000 / Ethernet)]

[0085] The described embodiments are configured to implement one or more of the following functionalities in one single package.• Fl: Longitudinal Speed through water layer• F2: Transverse Speed through water layer• F3: height above sea surface• F4: Air temperature• F5: Barometric pressure• F6: Choc detection• F7: Pitch and Roll euler angle• F 8: NME AO 183 output• F9: NMEA2000 output• F10: Ethernet output (web server for HTML5)• F 11: Docking-distance to dock-speed toward dock• F12: Sensor registration and calibration• F 13: Firmware update• F 14: Firmware configuration

[0086] FIG. 1 shows an example embodiment of such a radar-based measurement sensor system 100, which includes a microcontroller 102, a monolithic microwave integrated circuit (MMIC) 104, a transmit antenna 106, a receive antenna 108, a wireless communication module 110, an alternative wireless connectivity module 112, a three-axis accelerometer 114, a three-axis gyroscope 116, a three axis magnetometer 118, a barometric pressure and temperature module 120, a controller area network (CAN) bus driver 122, a serial data driver 124, an Ethernet driver 126, a power supply 128, a battery 130, and a recharge unit 132.- 17 - 5055169. vlDocket No. 0278.2055-001

[0087] In an example embodiment, the microcontroller 102 is a dual core, 32-bit system with at least 1MB of available memory. The MMIC 104 is electrically coupled to the transmit (TX) antenna 106 and the receive (RX) antenna 108 and provides in-phase and quadrature (I / Q) baseband data to the microcontroller 102.

[0088] For this example embodiment, the TX antenna 106 and the RX antenna 108 may be either a 24 GHz configuration or a 61 GHz configuration. The 61 GHz configuration exhibits a smaller physical footprint than the 24 GHz configuration. The design of either the 24GHz antenna or the 61 GHz antenna requires careful consideration on the printed circuit board (PCB) material with respect to its dielectric constant loss tangent, its substrate thickness, and its thermal stability. Standard FR4 material has an inconsistent dielectric constant (e.g., from 4.3 to 4.7), and a tangent loss of 0.02, which exhibits a high loss at 24GHz. In one example embodiment, the PCB material is Rogers RT / Duroid 5880 type laminate material with an er= 2.2, and a loss tangent of 0.0009. In an example embodiment, 50ohm transmission lines are fabricated using an electroless nickel immersion gold (ENIG) process for a low loss surface finish.

[0089] The use of radar systems on a boat is regulated by various international and national authorities, including the International Telecommunication Union (ITU), the Federal Communications Commission (FCC), and the European Telecommunications Standards Institute (ETSI).24 GHz Radar System

[0090] The 24 GHz frequency band is allocated for various purposes, including radar systems. The ITU has designated the 24.05-24.25 GHz frequency band for " Radar and Radiolocation" services. For a small radar system with a limited range of 30m, the described embodiments may be configured to conform to the following regulations and guidelines:• FCC (USA): The FCC permits the use of 24 GHz radar systems for "vehicular radar systems" with a maximum transmission power of 0.5W (27 dBm) and a maximum antenna gain of 10 dBi. The FCC requires systems to operate within the 24.05-24.25 GHz frequency band and comply with the FCC's Part 15 regulations.• ETSI (Europe): The ETSI has published a standard for " Radar equipment operating in the 24,05 GHz to 24,25 GHz frequency range" (EN 301 489-14). The standard limits the maximum transmission power to 0.25W (24 dBm) and- 18 - 5055169. vlDocket No. 0278.2055-001requires compliance with the EU's RED (Radio Equipment Directive) regulations.• ITU: The ITU recommends that 24 GHz radar systems operate within the 24.05-24.25 GHz frequency band and with a maximum transmission power of 1W (30 dBm).60 GHz Radar System

[0091] The 60 GHz frequency band is also allocated for various purposes, including radar systems. The ITU has designated the 59-64 GHz frequency band for " Radar and Radiolocation" services. For a small radar system with a limited range of 30m, the following regulations and guidelines apply:• FCC (USA): The FCC permits the use of 60 GHz radar systems for "vehicular radar systems" with a maximum transmission power of 0.5W (27 dBm) and a maximum antenna gain of 10 dBi. The FCC requires systems to operate within the 59-64 GHz frequency band and comply with the FCC's Part 15 regulations.• ETSI (Europe): The ETSI has published a standard for " Radar equipment operating in the 59 GHz to 64 GHz frequency range" (EN 301 489-14). The standard limits the maximum transmission power to 0.25W (24 dBm) and requires compliance with the EU's RED (Radio Equipment Directive) regulations.• ITU: The ITU recommends that 60 GHz radar systems operate within the 59- 64 GHz frequency band and with a maximum transmission power of 1W (30 dBm).

[0092] Both 24 GHz and 60 GHz radar systems can be used on a boat. For a small radar system with a limited range of about 30m, the following considerations apply. The system's power output should be limited to the minimum necessary for the application to avoid interference with other systems or devices. The antenna gain should be designed to minimize the radiation pattern and reduce the risk of interference with other systems or devices. The system should operate within the designated frequency band to avoid interference with other systems or devices. The system should comply with the relevant regulations and guidelines, including those related to radiated power, antenna gain, and frequency band.- 19 - 5055169. vlDocket No. 0278.2055-001

[0093] The maximum range and speed accuracy of a radar system depend on factors such as the carrier frequency, bandwidth, transmit power, antenna gain, noise floor, and signal processing techniques. The described embodiments focus on the 24 GHz and 60 GHz bands, assuming frequency modulated continuous wave (FMCW) modulation.

[0094] The FCC allows for the use of 24 GHz or 60Ghz radar systems on boats, provided they comply with specific requirements, such as a maximum TX power of lOOmW effective isotropic radiated power (EIRP), a maximum antenna gain of 30 dBi, and a limited range of operation, typically up to 20m.

[0095] In FMCW modulation, the radar transmitter emits a continuous wave with a frequency that is modulated over time. The frequency modulation is typically a sawtooth or triangular waveform, with a frequency sweep bandwidth (B) and a sweep time (T).

[0096] The range resolution (AR) of an FMCW radar system is given by:AR = c / (2 * B)

[0097] where c is the speed of light (300000 km / s). The velocity resolution (Av) of an FMCW radar system is given by:Av = 1 / (2 * T)where 1 is the wavelength of the transmitted signal.24 GHz band with FMCW modulation:

[0098] In an example embodiment, the available bandwidth is about 250 MHz (typical for 24 GHz radar systems). The wavelength (1) at 24 GHz is approximately 12.5 mm. The sweep bandwidth (B) is about 250 MHz, and the sweep time (T) is typically in the range of 1-10 ms (longer sweep times are not compatible without having heavy filtering, over many seconds).

[0099] Using the FMCW modulation equations, range and velocity resolutions can be estimated as Range resolution (AR): approximately 0.6-1.2 meters (depending on the sweep bandwidth), and Velocity resolution (Av): approximately 0.075-0.75 m / s (depending on the sweep time).

[0100] The maximum range of an FMCW radar system is typically determined by the available signal-to-noise ratio (SNR) and the system's sensitivity. Assuming a typical FMCW radar system with a moderate SNR, the maximum range can be estimated as approximately 100-150 meters (depending on the system design and environment).60 GHz band with FMCW modulation:- 20 - 5055169. vlDocket No. 0278.2055-001

[0101] In an example embodiment, the available bandwidth is about 5 GHz (typical for 60 GHz radar systems). The wavelength (1) at 60 GHz is approximately 5 mm. The sweep bandwidth (B) is about 5 GHz, and the sweep time (T) is typically in the range of 1ms to 10ms.

[0102] Using the FMCW modulation equations, we can estimate the range and velocity resolutions as: Range resolution (AR): approximately 0.03-0.06 meters (depending on the sweep bandwidth), and Velocity resolution (Av): approximately 0.025-0.25 m / s (depending on the sweep time)

[0103] The maximum range of an FMCW radar system at 60 GHz is typically limited by the high atmospheric attenuation at this frequency. Assuming a typical FMCW radar system with a moderate SNR, the maximum range can be estimated as approximately 10-50 meters (depending on the system design and environment). The power used in short range radar is usually in the range of 10mW to 100mW, which facilitates low power consumption while implementing all required functionalities.

[0104] In an example embodiment, the wireless communication module 110 is a Bluetooth Low Energy (BLE) module, and the alternative wireless module may be, for example, an NB-IOT module or an LTE-M module.

[0105] An example embodiment may include three hardware-link communication interfaces: the CAN bus interface 122, the serial data interface 124, and the Ethernet interface 126. Each of these interfaces may be configured as a software defined interface. In an example embodiment, the system may provide software-based support of multiple CAN bus protocols, such as NMEA2000, CANopen marine, CANopen, DeviceNet, SAE J1939, SAE J1587, and ISOBUS (i.e., ISO11783). The example system may support, by software, multiple serial protocols, for example RS232 / 422 / 485 / current loop 4-20mA, Modbus RTU / ASCII, PROFIBUS (RS485 layer), HART over 4-20mA, SDI12, NMEA 0183, and NMEA 0183 HS. The example embodiments may facilitate an Ethernet connection to support multiple ethernet based protocol, such as EtherCAT, EtherNet / IP, Profinet, Modbus TCP / IP, CC-Link IE, ISOBUS over Ethernet (ISO11783). The Ethernet interface may also support discovery and webserver to allow MFD integration for advanced features such as docking.Sensor installation:- 21 - 5055169. vlDocket No. 0278.2055-001

[0106] The sensor system 100 may be installed in a place where it can point at the sea in front of the boat, to limit the splash that would create RF absorption. The sensor system may be installed on a rail at the front of the boat (see, for example, FIG. 2), or the sensor system may be installed on the top of the roof looking forward (see, for example, FIG. 3). Mounting as shown in FIG. 3 may extend the range capability of the sensor system, and most likely create a high grazing angle, reducing sensitivity.

[0107] The cosine of the angle 0, reduces the sensed velocity as compared to the actual velocity Vr and will be corrected from real pitch and roll measurement made by the internal motion sensing device (see, e.g., FIG. 4). The example embodiment exhibits a low latency to allow for proper correction. The example embodiments compensate for the fact that the angle 0, varies in time due to complex 3D motion of the boat (see, e.g., FIG. 5) as well as wave motion (surface wave being the RF reflectors).

[0108] Use of two sensors, one on each side of the boat (see, e.g., FIG. 6), allows to determine the leeway of the boat, by combining both speed measurements, with the difference allowing determination of the angle of drift (0L in FIG. 6). Looking backward in the jetflow and wake, where the water is accelerated, provides an excellent reflector for radio frequency waves, but the speed increase due to the engine, and boat, would bias the speed measurement. Further, the use of multiple sensors around the boat hull, enables the sensing system to implement a docking-assist and / or an automatic docking functionality (see FIG. 7). In some embodiments, the sensor system may comprise a forward-looking sensor along with one or more side-looking sensors.

[0109] Processing: The sweep time T may be variable from 1ms to 10ms, to allow for maximum SNR detection, and a longer pulse for maximum accuracy on speed measurement, while the 1ms sweep time T would allow more data to be captured, and to allow for heavy filtering and fusion from the motion sensor. Use of multiple sensors requires spatial separation to avoid interference, and may utilize a different type of sweep frequency, and ideally not sharing the same frequency band. The 60GHz configuration allows for a large bandwidth that can be split into, e.g., four sub-bands for four sensors to work in the same space and time by filtering according to frequency (i.e., frequency division multiplexing).

[0110] FIG. 8 is a diagram of an example internal structure of a processing system 800 that may be used to implement one or more of the embodiments described herein. Each processing system 800 contains a system bus 802, where a bus is a set of hardware lines used for data transfer among the components of a computer or processing system. The system bus- 22 - 5055169. vlDocket No. 0278.2055-001802 is essentially a shared conduit that connects different components of a processing system (e.g., processor, disk storage, memory, input / output ports, network ports, etc.) that enables the transfer of information between the components.

[0111] Attached to the system bus 802 is a user I / O device interface 804 for connecting various input and output devices (e.g., keyboard, mouse, displays, printers, speakers, etc.) to the processing system 800. A network interface 806 allows the computer to connect to various other devices attached to a network 808. Memory 810 provides volatile and nonvolatile storage for information such as computer software instructions used to implement one or more of the embodiments of the present invention described herein, for data generated internally and for data received from sources external to the processing system 800.

[0112] A central processor unit 812 is also attached to the system bus 802 and provides for the execution of computer instructions stored in memory 810. The system may also include support electronics / logic 814, and a communications interface 816.

[0113] In one embodiment, the information stored in memory 810 may comprise a computer program product, such that the memory 810 may comprise a non-transitory computer-readable medium (e.g., a removable storage medium such as one or more DVD-ROM’s, CD-ROM’s, diskettes, tapes, etc.) that provides at least a portion of the software instructions for the invention system. The computer program product can be installed by any suitable software installation procedure, as is well known in the art. In another embodiment, at least a portion of the software instructions may also be downloaded over a cable communication and / or wireless connection.

[0114] It will be apparent that one or more embodiments described herein may be implemented in many different forms of software and hardware. Software code and / or specialized hardware used to implement embodiments described herein is not limiting of the embodiments of the invention described herein. Thus, the operation and behavior of embodiments are described without reference to specific software code and / or specialized hardware - it being understood that one would be able to design software and / or hardware to implement the embodiments based on the description herein.

[0115] Further, certain embodiments of the example embodiments described herein may be implemented as logic that performs one or more functions. This logic may be hardwarebased, software-based, or a combination of hardware-based and software-based. Some or all of the logic may be stored on one or more tangible, non-transitory, computer-readable storage media and may include computer-executable instructions that may be executed by a- 23 - 5055169. vlDocket No. 0278.2055-001controller or processor. The computer-executable instructions may include instructions that implement one or more embodiments of the invention. The tangible, non-transitory, computer-readable storage media may be volatile or non-volatile and may include, for example, flash memories, dynamic memories, removable disks, and non-removable disks.

[0116] While example embodiments have been particularly shown and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the embodiments encompassed by the appended claims.- 24 - 5055169. vl

Claims

1. Docket No. 0278.2055-001CLAIMSWhat is claimed is:

1. A marine speed measurement system for determining speed through water (STW) of a vessel, comprising:a first radar device mounted on the vessel and configured to emit at least one electromagnetic beam directed toward a water surface at an incidence angle 9 relative to a vessel reference plane; andan inertial measurement unit (IMU) rigidly attached to the vessel, the IMU provides an output that conveys (i) linear acceleration of the vessel, (ii) angular velocities of the vessel, and (iii) heading of the vessel; anda processing unit that uses the IMU output to correct an error in a measurement from the first radar device due to induced motion.

2. The marine speed measurement system of claim 1, wherein the IMU comprises:at least one three-axis accelerometer, configured to measure linear acceleration of the vessel;at least one three-axis gyroscope, configured to measure one or more angular velocities of the vessel; andat least one three-axis magnetometer, configured to measure heading of the vessel.

3. The marine speed measurement system of claim 1, wherein the radar device is further configured to:measure a time-of-flight of the electromagnetic beam between emission and reception after reflection from the water surface, thereby determining a slant range to the water; andmeasure a Doppler frequency shift of the reflected electromagnetic beam, to determine a radial velocity component between the vessel and the water surface along a direction of the electromagnetic beam.

4. The marine speed measurement system of claim 3, wherein the processing unit is operatively connected to the radar device and the IMU, the processing unit configured to:- 25 - 5055169. vlDocket No. 0278.2055-001determine an attitude (pitch, roll, yaw) of the vessel, in real time, from IMU data;determine a motion-induced velocity vector of the vessel in an Earth-fixed reference frame from the IMU data, including contributions from pitch, roll, heave, and yaw motions;resolve a motion-induced velocity vector into a direction of the electromagnetic beam, thereby determining a motion-induced Doppler bias affecting the determined radial velocity component;determine a corrected radial velocity by subtraction of the motion-induced Doppler bias from a determined radial velocity component; andresolve the corrected radial velocity into a forward direction of the vessel, using the incidence angle 9 and the attitude of the vessel, to determine the STW of the vessel.

5. The marine speed measurement system of claim 1, further comprising a second radar device mounted on the vessel, symmetrically positioned on an opposite side of a centerline of the vessel relative to the first radar device, wherein both the first radar device and the second radar device face toward a forward direction of the vessel and are directed toward the water surface at equal but opposite incidence angles (+ / - 9) relative to the forward direction of the vessel.

6. The marine speed measurement system of claim 5, wherein each of the first radar device and the second radar device is configured to (i) emit an electromagnetic beam at the incidence angle (+ / - 9), (ii) measure the time-of-flight and Doppler frequency shift of its reflected beam, and (iii) output a port-side radial velocity and a starboardside radial velocity, respectively.

7. The marine speed measurement system of claim 6, wherein the processing unit is further configured to:(i) for each of the first radar device and the second radar device, determine a port-side Doppler bias and an independent starboard- si de Doppler bias using an attitude (pitch, roll, yaw) of the vessel and motion data from the IMU;- 26 - 5055169. vlDocket No. 0278.2055-001(ii) determine a port-side corrected radial velocity and a starboard-side corrected radial velocity by subtracting respective motion-induced Doppler biases from the measured radial velocities;(iii) resolve each corrected radial velocity into the vessel’s forward direction to obtain a port-side STW value and a starboard-side STW value; and(iv) determine a leeway angle ((|>) of the vessel by comparing the two STW values as(|) =tan’1(2 • STW avg- sin(9) S TW starboard- S T Wport), where STWavg is an average of port-side STW and starboard-side STW, and 9 is the incidence angle of the radar beams.

8. A method of determining speed through water (STW) of a vessel, comprising:emitting, from a first radar device mounted on the vessel, at least one electromagnetic beam directed toward a water surface at an incidence angle 9 relative to a vessel reference plane;providing, from an inertial measurement unit (IMU) rigidly attached to the vessel, an output that conveys (i) linear acceleration of the vessel, (ii) angular velocities of the vessel, and (iii) heading of the vessel, andcorrecting, using the IMU output, an error in a measurement from the first radar device due to induced motion.

9. The method of claim 8, further comprising, by the IMU, measuring linear acceleration of the vessel, measuring one or more angular velocities of the vessel, and (iii) measuring heading of the vessel.

1. The method of claim 8, wherein the radar device is further configured to:measure a time-of-flight of the electromagnetic beam between emission and reception after reflection from the water surface, thereby determining a slant range to the water; andmeasure a Doppler frequency shift of the reflected electromagnetic beam, to determine a radial velocity component between the vessel and the water surface along a direction of the electromagnetic beam.- 27 - 5055169. vlDocket No. 0278.2055-00111. The method of claim 10, further comprising, by a processing unit onboard the vessel operatively connected to the radar device and the IMU:determining an attitude (pitch, roll, yaw) of the vessel, in real time, from IMU data;determining a motion-induced velocity vector of the vessel in an Earth-fixed reference frame from the IMU data, including contributions from pitch, roll, heave, and yaw motions;resolving a motion-induced velocity vector into a direction of the electromagnetic beam, thereby determining a motion-induced Doppler bias affecting the determined radial velocity component;determining a corrected radial velocity by subtraction of the motion-induced Doppler bias from a determined radial velocity component; andresolving the corrected radial velocity into a forward direction of the vessel, using the incidence angle 9 and the attitude of the vessel, to determine the STW of the vessel.

12. The method of claim 8, further comprising a second radar device on the vessel, symmetrically positioned on an opposite side of a centerline of the vessel relative to the first radar device, wherein both the first radar device and the second radar device face toward a forward direction of the vessel and are directed toward the water surface at equal but opposite incidence angles (+ / - 9) relative to the forward direction of the vessel.

13. The method of claim 12, further comprising emitting an electromagnetic beam at the incidence angle (+ / - 9), measuring the time-of-flight and Doppler frequency shift of its reflected beam, and outputting a port-side radial velocity and a starboard- si de radial velocity.

14. The method of claim 12, further comprising:(i) for each of the first radar device and the second radar device, determining a port-side Doppler bias and an independent starboard- si de Doppler bias using an attitude (pitch, roll, yaw) of the vessel and motion data from the IMU;- 28 - 5055169. vlDocket No. 0278.2055-001(ii) determining a port-side corrected radial velocity and a starboard-side corrected radial velocity by subtracting respective motion-induced Doppler biases from the measured radial velocities;(iii) resolving each corrected radial velocity into the vessel’s forward direction to obtain a port-side speed through water value and a starboard- si de speed through water value; and(iv) determining the leeway angle ((|>) of the vessel by comparing the two STW values as(|) =tan’1(2 • S TW avg • sin(9) S T W starb oard- S TWport), where STW avg is an average of port-side STW and starboard-side STW, and 9 is the incidence angle of the radar beams.

15. A non-transitory computer-readable medium with computer code instruction stored thereon, the computer code instructions, when executed by a processor, cause a marine speed measurement system for determining speed through water (STW) of a vessel to:emit at least one electromagnetic beam directed toward a water surface at an incidence angle 9 relative to a vessel reference plane;provide an output that conveys (i) linear acceleration of the vessel, (ii) angular velocities of the vessel, and (iii) heading of the vessel; andcorrect, using the IMU output, an error in a measurement from the first radar device due to induced motion.

16. The non-transitory computer-readable medium of claim 17, wherein the computer code instructions further cause a marine speed measurement system to:measure a time-of-flight of the electromagnetic beam between emission and reception after reflection from the water surface, thereby determining a slant range to the water;measure a Doppler frequency shift of the reflected electromagnetic beam, to determine a radial velocity component between the vessel and the water surface along a direction of the electromagnetic beam.

17. The non-transitory computer-readable medium of claim 17, wherein the computer code instructions further cause a marine speed measurement system to:- 29 - 5055169. vlDocketNo. 0278.2055-001determine an attitude (pitch, roll, yaw) of the vessel, in real time, from IMU data;determine a motion-induced velocity vector of the vessel in an Earth-fixed reference frame from the IMU data, including contributions from pitch, roll, heave, and yaw motions;resolve a motion-induced velocity vector into a direction of the electromagnetic beam, thereby determining a motion-induced Doppler bias affecting the determined radial velocity component;determine a corrected radial velocity by subtraction of the motion-induced Doppler bias from a determined radial velocity component;resolve the corrected radial velocity into a forward direction of the vessel, using the incidence angle 9 and the attitude of the vessel, to determine the STW of the vessel.

18. The non-transitory computer-readable medium of claim 17, wherein the computer code instructions further cause each of a first radar device and a second radar device to:(i) emit an electromagnetic beam at the incidence angle (+ / - 9), (ii) measure the time-of-flight and Doppler frequency shift of its reflected beam, and (iii) output a port-side radial velocity and a starboard-side radial velocity.

19. A vessel speed measurement system, comprising:a radar device configured to emit an electromagnetic beam toward a water surface at an incidence angle 9, measure a time-of-flight and Doppler frequency shift of the reflected beam, and output a raw radial velocity;an inertial measurement unit (IMU) comprising one or more accelerometers, one or more gyroscopes, and one or more magnetometers, configured to measure the vessel’s attitude (pitch, roll, yaw) and motion (heave, surge, sway);a weather station configured to measure true wind speed and true wind direction;a processing unit configured to:compute a motion-induced Doppler bias from IMU data;model a wind-induced surface velocity from the weather station data, wherein the model comprises:- 30 - 5055169. vlDocket No. 0278.2055-001a wave orbital velocity computed from the true wind speed and an estimated wave height and period;a wind-driven shear velocity computed from the true wind speed (W);compute a corrected radial velocity by subtracting the motion-induced bias and the wind-induced surface velocity from the raw radial velocity;resolve the corrected radial velocity into the vessel’s forward direction to obtain Speed Through Water (STW); andoutput the STW to a navigation system.

20. The system of claim 19, wherein the processing unit is further configured to:estimate wave height from the true wind speed using an empirical wave spectrum model; andoutput the wave height to a flight control system for dynamic stabilization of a foiling vessel.

21. The system of claim 2, further comprising:a weather station configured to measure true wind speed and true wind direction;wherein the processing unit is further configured to:apply the wind-induced surface velocity correction (V wind) independently to both port and starboard radar measurements; and recompute the leeway angle ((|>) using the wind-corrected STW values.

22. The system of claim 19, wherein the processing unit is further configured to:apply a low-pass filter to the raw Doppler measurements to suppress high- frequency noise from wind-generated turbulence; anddynamically adjust the filter’s cutoff frequency based on the true wind speed.- 31 - 5055169. vl

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