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Figure 4.9: Estimates of attitude parameters obtained through adaptive Kalman filtering with N = 4 and 8 = 0.987.

Figure 4 9: Estimates of attitude parameters obtained through adaptive Kalman filtering with N = 4 and 8 = 0.987.

Related Figures (67)

Figure 1.1: Typical operational] setting of a side-scan sonar. Lateral sound beams scan the seabed as the sonar towfish is towed above the bottom by a deploying vessel.
Figure 1.1: Typical operational] setting of a side-scan sonar. Lateral sound beams scan the seabed as the sonar towfish is towed above the bottom by a deploying vessel.
Figure 1.3: The slant-range distortion is caused by the fact that horizontal distances in the sonograph correspond to ranges to the towfish, rather than distances on the seabed.
Figure 1.3: The slant-range distortion is caused by the fact that horizontal distances in the sonograph correspond to ranges to the towfish, rather than distances on the seabed.
Figure 1.4: Rotational] instabilities of the towfish: pitching (top), yawing (middle), and rolling (bottom).
Figure 1.4: Rotational] instabilities of the towfish: pitching (top), yawing (middle), and rolling (bottom).
Figure 2.1: Coordinate systems defined on the seabed and on the sonograph.
Figure 2.1: Coordinate systems defined on the seabed and on the sonograph.
Figure 2.2: Sampling patterns on the bottom, in the ideal case (a) and in the presence of towfish instabilities (b).
Figure 2.2: Sampling patterns on the bottom, in the ideal case (a) and in the presence of towfish instabilities (b).
Figure 2.3: The position of the towfish is denoted by (rs, yy,zy), its pitch angle by ¢, and its yaw angle by 8.
Figure 2.3: The position of the towfish is denoted by (rs, yy,zy), its pitch angle by ¢, and its yaw angle by 8.
Figure 2.4: Relation between a sampling point on the seabed and the location and orientation of the effective beam. Assume a sonar pulse is transmitted at time t = ty and that the returned signal is
Figure 2.4: Relation between a sampling point on the seabed and the location and orientation of the effective beam. Assume a sonar pulse is transmitted at time t = ty and that the returned signal is
Figure 2.5: The variation in sampling coordinates from one line of the image to the next is described by the sampling displacements A,2/[I,n] and A,y![I,n], shown here in the (z,y) coordinate system.
Figure 2.5: The variation in sampling coordinates from one line of the image to the next is described by the sampling displacements A,2/[I,n] and A,y![I,n], shown here in the (z,y) coordinate system.
Figure 2.6: Sampling displacements in the (z’, y’) coordinate system, defined to have the same orientation as the effective beam for each pulse.
Figure 2.6: Sampling displacements in the (z’, y’) coordinate system, defined to have the same orientation as the effective beam for each pulse.
Figure 3.1: Calculation of the sample cross-correlation sequence between line segments, that is used as an estimate of the local autocorrelation sequence of the image. Only every N.th pixel is taken in the segments indicated by braces, so that the averaging is done over (2L + 1) points, for computational savings (see Footnote 2 on page 47).
Figure 3.1: Calculation of the sample cross-correlation sequence between line segments, that is used as an estimate of the local autocorrelation sequence of the image. Only every N.th pixel is taken in the segments indicated by braces, so that the averaging is done over (2L + 1) points, for computational savings (see Footnote 2 on page 47).
Figure 3.3: Sampling displacements in the cross-track direction, A,,z}[I,n], are estimated from the location of the main peak of the cross-correlation sequence p[Al’, An’; 1N,,nN,]J, at an along-track lag An’ = N,,.
Figure 3.3: Sampling displacements in the cross-track direction, A,,z}[I,n], are estimated from the location of the main peak of the cross-correlation sequence p[Al’, An’; 1N,,nN,]J, at an along-track lag An’ = N,,.
Figure 3.6: Effect of variations in speed and pitch angle (a) and yaw angle (b) on the sampling pattern, according to the linear model derived in Section 2.2.3.
Figure 3.6: Effect of variations in speed and pitch angle (a) and yaw angle (b) on the sampling pattern, according to the linear model derived in Section 2.2.3.
cross-correlation sequence at Al’ = 0 reflects the distortions in the image by becoming
cross-correlation sequence at Al’ = 0 reflects the distortions in the image by becoming
Figure 3.9: Relation between the sampling interval, P,,{I,n], and the sampling displace- ments, A,z/[I,n] and A,y?[l, n). the sonar beam has to travel on the seabed from point (z,[!,n],y,[?,n]) before the au- tocorrelation function of b(z,y) falls below that same threshold. Assuming for now that
Figure 3.9: Relation between the sampling interval, P,,{I,n], and the sampling displace- ments, A,z/[I,n] and A,y?[l, n). the sonar beam has to travel on the seabed from point (z,[!,n],y,[?,n]) before the au- tocorrelation function of b(z,y) falls below that same threshold. Assuming for now that
Figure 3.10: The widening of the sonar beam pattern with increasing range is responsible for a corresponding increase in the correlation lengths of the image. where in the last step we used Eq. (2.12). If we symmetrically add the g[l,n] for
Figure 3.10: The widening of the sonar beam pattern with increasing range is responsible for a corresponding increase in the correlation lengths of the image. where in the last step we used Eq. (2.12). If we symmetrically add the g[l,n] for
Figure 4.1: Example of a line affected by undersampling. The straight line is obtained by fitting the linear model to the estimates of sampling displacements on the starboard side (/ > 0). Because of undersampling, the estimates of sampling displacements on the port side (1 < 0) are smaller than what the linear model indicates they should be.
Figure 4.1: Example of a line affected by undersampling. The straight line is obtained by fitting the linear model to the estimates of sampling displacements on the starboard side (/ > 0). Because of undersampling, the estimates of sampling displacements on the port side (1 < 0) are smaller than what the linear model indicates they should be.
Figure 4.3: Estimates of distortion parameters obtained through deterministic least- squares approximation.
Figure 4.3: Estimates of distortion parameters obtained through deterministic least- squares approximation.
Ay.|n] for different lines of the sonograph are independent, we have variances of the estimates of distortion parameters are given by
Ay.|n] for different lines of the sonograph are independent, we have variances of the estimates of distortion parameters are given by
described more compactly in matrix form if we write Eqs. (4.1a) and (4.1b) as
described more compactly in matrix form if we write Eqs. (4.1a) and (4.1b) as
Figure 4.5: The Kalman filter and recursive least-squares algorithms (a) are combined in the extended least-squares method (b).
Figure 4.5: The Kalman filter and recursive least-squares algorithms (a) are combined in the extended least-squares method (b).
Figure 4.7: Estimates of attitude parameters obtained through the extended least-squares algorithm with N = 4 and # = 1.
Figure 4.7: Estimates of attitude parameters obtained through the extended least-squares algorithm with N = 4 and # = 1.
at each line. The interpolation is carried out by multiplying the discrete Fourier trans
at each line. The interpolation is carried out by multiplying the discrete Fourier trans
Figure 5.4: Determining the points for interpolation in the along-track direction. along the l’-th column of s,[I',n] are denoted by n,[I’,n'] and are in general non-integer. Paralleling the procedure of the previous section, these are calculated by finding the two through Eq. (5.5) are located immediately before and immediately after y,[n’], i. e
Figure 5.4: Determining the points for interpolation in the along-track direction. along the l’-th column of s,[I',n] are denoted by n,[I’,n'] and are in general non-integer. Paralleling the procedure of the previous section, these are calculated by finding the two through Eq. (5.5) are located immediately before and immediately after y,[n’], i. e
Figure 5.7: An image unaffected by aliasing-related blurring can be obtained by estimat- ing the distortion parameters separately from each side of the sonograph, as illustrated in this example.
Figure 5.7: An image unaffected by aliasing-related blurring can be obtained by estimat- ing the distortion parameters separately from each side of the sonograph, as illustrated in this example.
Figure 5.11: Simulated attitude parameters (SIM) and estimates obtained through deter- ministic least-squares estimation (DLS) , adaptive Kalman filtering (AKF), and standard Kalman filtering (KF).
Figure 5.11: Simulated attitude parameters (SIM) and estimates obtained through deter- ministic least-squares estimation (DLS) , adaptive Kalman filtering (AKF), and standard Kalman filtering (KF).
Figure 5.16: Estimates of attitude parameters for the sonograph of Fig. 5.13.
Figure 5.16: Estimates of attitude parameters for the sonograph of Fig. 5.13.
Figure 5.20: Estimates of attitude parameters for the sonograph of Fig. 5.17.
Figure 5.20: Estimates of attitude parameters for the sonograph of Fig. 5.17.
Table A.1: Definitions from Chapter 2 equations or figures listed in the reference columns.
Table A.1: Definitions from Chapter 2 equations or figures listed in the reference columns.
Table A.4: Definitions from Chapter 4
Table A.4: Definitions from Chapter 4
Table A.5: Definitions from Chapter 5
Table A.5: Definitions from Chapter 5
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EngineeringEarth SciencesComputer ScienceArtificial IntelligenceComputer VisionUnderwater AcousticsGeometryAdaptive Filters
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