DOPPLER VELOCITY LOG ALGORITHMS: DETECTION, ESTIMATION, AND ACCURACY
Open Access
- Author:
- Taudien, Jerker
- Graduate Program:
- Electrical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 11, 2018
- Committee Members:
- Sven Bilén, Dissertation Advisor/Co-Advisor
Sven Bilén, Committee Chair/Co-Chair
David J. Miller, Committee Member
John F. Doherty, Committee Member
Thomas B. Gabrielson, Outside Member - Keywords:
- DVL
Doppler velocity log
sonar
Bottom detection
Estimation
Velocity
Accuracy
Detection
Doppler
ADCP - Abstract:
- One of the most common navigation methods employed by underwater vehicles consists of estimating position from Doppler-velocity-log and inertial-navigationsystem data. The Doppler-velocity-log sonar measures the relative velocity between an instrument and the bottom of a body of water by estimating the Doppler shift of back-scattered sound in multiple beams that point in different directions. A three-dimensional velocity vector is then obtained by transforming the measured radial beam velocities to an orthogonal coordinate system, typically aligned with the instrument or Earth reference frame. A recent trend in unmanned underwater vehicle design is man-portable autonomous underwater vehicles, enabling low-cost and rapid deployments. Due to limited payload space on man-portable autonomous underwater vehicles, there is a need for high-fidelity and reduced-size Doppler velocity logs, capable of operating at altitudes on the order of 100–200 m. A high-level Doppler-velocity-log tradespace consists of size, power, range, variance, and long-term accuracy. The aperture size of existing Doppler velocity logs can be decreased for the purpose of reducing the required payload space, but the implications are reduced range, increased variance, and degraded long-term accuracy, leading to a lower-fidelity navigation solution. A major contribution of this work is an expanded tradespace, allowing for either improved performance or decreased size to enable small unmanned underwater vehicles with Doppler-velocitylog- based navigation. Specific problems solved are the following: 1) modeling long-term accuracy, 2) boundary detection in low signal-to-noise ratio, and 3) tradeoff between range and variance. To solve these problems, a methodology that consists of theory, simulation, and testing of existing and new prototype instruments, is utilized. Theory is first developed to describe the problem at hand and is validated using simulation such as Monte Carlo and ray-tracing methods. Verification of the theory and simulation results is then accomplished through testing of Doppler velocity logs in a tow tank, on reservoirs, and at sea. A model—including terrain bias, absorption bias, side-lobe coupling, and speediii of-sound errors—for predicting the long-term accuracy was developed. A combination of analytical derivations and simulations, for which the simulation results were fit to closed-form equations, was used to construct the long-term error model. Validity of the error model was demonstrated by tank testing of Doppler velocity logs of different configurations under a range of operating conditions. We envision that the error model will be of great use to system designers for optimizing the long-term accuracy and for error compensation to achieve the highest possible long-term accuracy for a given size constraint. The maximum operating range of a Doppler velocity log can be limited by the minimum required signal-to-noise ratio at which detection algorithms can operate with high enough fidelity. Two bottom-detection methods are proposed that compute the covariance and correlation coefficient at a time lag. A closed-form solution is derived for the joint characteristic function of the real and imaginary parts of the detector signal and it is numerically inverted to obtain the probability density function of the amplitude under the null and alternative hypotheses. The detection probability is then computed over a range of operating conditions, including code length, number of samples, and signal-to-noise ratio. It is shown that the performance of the proposed detectors is substantially similar for a wide range of conditions. However, the correlation-coefficient detector has an important advantage in that it can operate on amplitude-limited signals for which the amplitude information has been suppressed. Additionally, the performance of the detectors varies widely depending on the values of the parameters, and it is shown that certain codes perform much better than other codes. Field test of a 614-kHz Doppler velocity log were performed and the measured and predicted detection-rate curves agreed to within 8 m for altitudes ranging from 110 m to 160 m. A hybrid-mode algorithm was implemented consisting of the correlation-coefficient boundary-detection algorithm and adaptive-narrowband filtering to reduce the velocity-error variance in low signal-to-noise-ratio environments. A repeated lengthtwo code, consisting of two main spectral peaks in the Fourier domain, is transmitted and the adaptive filter is tailored for that spectrum. Theory predicts that the variance of the velocity error decreases with increasing number of iterations, in which the bandwidth successively is reduced by a factor of two. The theoreticallypredicted variance as a function of altitude was compared to the measured variance of the estimated velocity error. The standard deviation of field-test results agreed with the theoretical predictions to within 6 mm/s over altitudes ranging from 110 m to 160 m. Solutions to the three aforementioned problems are provided. The improvements contribute to an expansion of the tradespace, allowing either for improved performance or decreased size, and enable small unmanned underwater vehicles with Doppler-velocity-log-based navigation.