Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Total areas with a median position error E p (Equation ) below 1 c m , 3 c m , 5 c m , and 9 c m for the training and optimisation sets with a varying minimum distance between source states D s (see and ) and the (x + y) sensor configuration at the σ = 1.0 × 10 − 5 m / s noise level. The median position error was computed for 2 × 2 c m 2 cells. Note, the bar for LSQ* is based the (x + y) condition in Analysis Method 2.

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Total areas with a median movement direction error E φ (Equation ) below 0.01 π rad , 0.03 π rad , 0.05 π rad for the training and optimisation sets with a varying minimum distance between source states D s (see and ) and the (x + y) sensor configuration at the σ = 1.0 × 10 − m / s noise level. The median movement direction error was computed for 2 × 2 c m 2 cells. Note, the bar for LSQ* is based on the (x + y) condition in Analysis Method 2.

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Boxplots of the position error distributions for all dipole localisation algorithms in each condition of first analysis method. This analysis varied the minimum distance D s between source states in the training and optimisation set (see and ) and used the (x + y) sensor configuration at the σ = 1.0 × 10 − 5 m / s noise level. The whiskers of the boxplots indicate the 5th and 95th percentiles of the distributions. Predictions with errors outside these percentiles are shown individually. LSQ* is based on the (x + y) condition in Analysis Method 2.

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Boxplots of the movement direction error distributions for all dipole localisation algorithms in each condition of first analysis method. This analysis varied the minimum distance D s between source states in the training and optimisation set (see and ) and used the (x + y) sensor configuration at the σ = 1.0 × 10 − 5 m / s noise level. The whiskers of the boxplots indicate the 5th and 95th percentiles of the distributions. Predictions with errors outside these percentiles are shown individually. LSQ* is based on the (x + y) condition in Analysis Method 2.

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: All hyperparameter values for the first analysis optimised using the training set. This analysis varied the minimum distance D s between source states in the training and optimisation sets to show how the amount of training and optimisation data influences the dipole localisation algorithms’ performance. The (x + y) sensor configuration at the σ = 1.0 × 10 − 5 m / s noise level was used in this analysis. Table 1 describes the respective data sets in more detail.

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Total area with a median position error E p (Equation ) below 1 c m , 3 c m , 5 c m , and 9 c m for varying sensitivity axes of the sensors: (x + y) measured both velocity components at all sensors, (x|y) alternated measuring v x and v y for subsequent sensors, (x) measured only v x at all sensors, (y) measured only v y at all sensors. This analysis method used the D s = 0.01 training and optimisation set and the σ = 1.0 × 10 − 5 m / s noise level. The median position error was computed in 2 × 2 c m 2 cells. Note, the bar for QM* is based on the D s = 0.01 condition in Analysis Method 1.

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Total area with a median movement direction error E p (Equation ) below 1 c m , 3 c m , 5 c m , and 9 c m for varying sensitivity axes of the sensors: (x + y) measured both velocity components at all sensors, (x|y) alternated measuring v x and v y for subsequent sensors, (x) measured only v x at all sensors, (y) measured only v y at all sensors. This analysis method used the D s = 0.01 training and optimisation set and the σ = 1.0 × 10 − 5 m / s noise level. The median movement direction error was computed in 2 × 2 c m 2 cells. Note, the bar for QM* is based on the D s = 0.01 condition in Analysis Method 1.

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Boxplots of the position error distributions for all algorithms in the second analysis method. This analysis varied the sensitivity axes of the sensors: (x + y) measured both velocity components at all sensors, (x|y) alternated measuring v x and v y for subsequent sensors, (x) measured only v x at all sensors, (y) measured only v y at all sensors. The D s = 0.01 training and optimisation set and σ = 1.0 × 10 − 5 m / s noise level were used. The whiskers of the boxplots indicate the 5th and 95th percentiles of the distributions. Predictions with errors outside these percentiles are shown individually. QM* is based on the D s = 0.01 condition in Analysis Method 1.

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Boxplots of the movement direction error distributions for all algorithms in the second analysis method. This analysis varied the sensitivity axes of the sensors: (x + y) measured both velocity components at all sensors, (x|y) alternated measuring v x and v y for subsequent sensors, (x) measured only v x at all sensors, (y) measured only v y at all sensors. The D s = 0.01 training and optimisation set and σ = 1.0 × 10 − 5 m / s noise level were used. The whiskers of the boxplots indicate the 5th and 95th percentiles of the distributions. Predictions with errors outside these percentiles are shown individually. QM* is based on the D s = 0.01 condition in Analysis Method 1.

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Training and prediction time measurements of all dipole localisation algorithms. The (x + y) sensor configuration was used combined with the largest training and optimisation set D s = 0.01 .

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Spatial contours of the median position error E p (blue) (Equation ) and median movement direction error E φ (orange) (Equation ) of the predictors using the largest training and optimisation set ( D s = 0.01 ) and 2D sensitive sensors (x + y) at the σ = 1.0 × 10 − m / s noise level. The algorithms are ordered with an increasing overall median position error. The median errors were computed in 2 × 2 c m 2 cells.

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: All hyperparameters for the second analysis optimised using the training set. This analysis varied the sensor sensitivity axes to show how the velocity components contribute to the predictions while keeping D s constant. The configurations were: (x + y) both components on all sensors, (x|y) alternating v x and v y for subsequent sensors, (x) only v x on all sensors, (y) only v y on all sensors. The σ = 1.0 × 10 − 5 m / s noise level was used and with the D s = 0.01 training and optimisation set.

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Spatial contours of the median position error (Equation ) for each localisation algorithm in all conditions of Analysis Method 1. This analysis varied the minimum distance D s between sources in the training and optimisation sets while using the (x + y) sensor configuration at the σ = 1 × 10 − 5 m / s noise level. The median position error was computed in 2 × 2 cm 2 cells. The sensors were equidistantly placed between x = ± 0.2 m .

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Spatial contours of the median movement direction error (Equation ) for each localisation algorithm in all conditions of Analysis Method 1. This analysis varied the minimum distance D s between sources in the training and optimisation sets while using the (x + y) sensor configuration at the σ = 1 × 10 − m / s noise level. The median movement direction error was computed in 2 × 2 cm 2 cells. The sensors were equidistantly placed between x = ± 0.2 m .

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Polar contours of the median position error (Equation ) for each localisation algorithm in all conditions of Analysis Method 1. These figures indicate how the movement direction φ and distance d of a source influence the error. This analysis varied the minimum distance D s between sources in the training and optimisation sets while using the (x + y) sensor configuration at the σ = 1 × 10 − 5 m / s noise level. The median position error was computed in 2 × 2 cm 2 cells. The sensors were equidistantly placed between x = ± 0.2 m .

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Polar contours of the median movement direction error (Equation ) for each localisation algorithm in all conditions of Analysis Method 1. These figures indicate how the movement direction φ and distance d of a source influence the error. This analysis varied the minimum distance D s between sources in the training and optimisation sets while using the (x + y) sensor configuration at the σ = 1 × 10 − 5 m / s noise level. The median movement direction error was computed in 2 × 2 cm 2 cells. The sensors were equidistantly placed between x = ± 0.2 m .

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Spatial contours of the median position error (Equation ) for each localisation algorithm in all conditions of Analysis Method 2. This analysis varied the sensitivity axes of the sensors: (x + y) measured both velocity components at all sensors, (x|y) alternated measuring v x and v y for subsequent sensors, (x) measured only v x at all sensors, (y) measured only v y at all sensors. The D s = 0.01 training and optimisation set and σ = 1.0 × 10 − 5 m / s noise level were used. The median position error was computed in 2 × 2 cm 2 cells. The sensors were equidistantly placed between x = ± 0.2 m .

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Spatial contours of the median movement direction error (Equation ) for each localisation algorithm in all conditions of Analysis Method 2. This analysis varied the sensitivity axes of the sensors: (x + y) measured both velocity components at all sensors, (x|y) alternated measuring v x and v y for subsequent sensors, (x) measured only v x at all sensors, (y) measured only v y at all sensors. The D s = 0.01 training and optimisation set and σ = 1.0 × 10 − m / s noise level were used. The median movement direction error was computed in 2 × 2 cm 2 cells. The sensors were equidistantly placed between x = ± 0.2 m .

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Polar contours of the median position error (Equation ) for each localisation algorithm in all conditions of Analysis Method 2. These figures indicate how the movement direction φ and distance d of a source influence the error. This analysis varied the sensitivity axes of the sensors: (x + y) measured both velocity components at all sensors, (x|y) alternated measuring v x and v y for subsequent sensors, (x) measured only v x at all sensors, (y) measured only v y at all sensors. The D s = 0.01 training and optimisation set and σ = 1.0 × 10 − 5 m / s noise level were used. The median position error was computed in 2 × 2 cm 2 cells. The sensors were equidistantly placed between x = ± 0.2 m .

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Polar contours of the median movement direction error (Equation ) for each localisation algorithm in all conditions of Analysis Method 2. These figures indicate how the movement direction φ and distance d of a source influence the error. This analysis varied the sensitivity axes of the sensors: (x + y) measured both velocity components at all sensors, (x|y) alternated measuring v x and v y for subsequent sensors, (x) measured only v x at all sensors, (y) measured only v y at all sensors. The D s = 0.01 training and optimisation set and σ = 1.0 × 10 − m / s noise level were used. The median movement direction error was computed in 2 × 2 cm 2 cells. The sensors were equidistantly placed between x = ± 0.2 m .

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Spatial contours of the median position error (Equation ) for QM, GN, and MLP using simulated sensors with higher velocity equivalent noise levels. The D s = 0.01 training and optimisation set and (x + y) sensor configuration were used. The values for σ = 1.0 × 10 − 5 m / s are based on the D s = 0.01 condition in Analysis Method 1. The MLP was re-trained for each noise level. Both the MLP and GN used the optimal hyperparameter values from the D s = 0.01 condition of Analysis Method 1. The median position error was computed in 2 × 2 cm 2 cells. The sensors were equidistantly placed between x = ± 0.2 m .

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Spatial contours of the median movement direction error (Equation ) for QM, GN, and MLP using simulated sensors with higher velocity equivalent noise levels. The D s = 0.01 training and optimisation set and (x + y) sensor configuration were used. The values for σ = 1.0 × 10 − m / s are based on the D s = 0.01 condition in Analysis Method 1. The MLP was re-trained for each noise level. Both the MLP and GN used the optimal hyperparameter values from the D s = 0.01 condition of Analysis Method 1. The median movement direction error was computed in 2 × 2 cm 2 cells. The sensors were equidistantly placed between x = ± 0.2 m .

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Polar contours of the median position error (Equation ) for QM, GN, and MLP using simulated sensors with higher velocity equivalent noise levels. These figures indicate how the movement direction φ and distance d of a source influence the error. The D s = 0.01 training and optimisation set and (x + y) sensor configuration were used. The values for σ = 1.0 × 10 − 5 m / s are based on the D s = 0.01 condition in Analysis Method 1. The MLP was re-trained for each noise level. Both the MLP and GN used the optimal hyperparameter values from the D s = 0.01 condition of Analysis Method 1. The median position error was computed in 2 × 2 cm 2 cells. The sensors were equidistantly placed between x = ± 0.2 m .

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques:

Journal: Sensors (Basel, Switzerland)

Article Title: The Quadrature Method: A Novel Dipole Localisation Algorithm for Artificial Lateral Lines Compared to State of the Art

doi: 10.3390/s21134558

Figure Lengend Snippet: Polar contours of the median movement direction error (Equation ) for each localisation algorithm in all conditions of Analysis Method 2. These figures indicate how the movement direction φ and distance d of a source influence the error. The D s = 0.01 training and optimisation set and (x + y) sensor configuration were used. The values for σ = 1.0 × 10 − m / s are based on the D s = 0.01 condition in Analysis Method 1. The MLP was re-trained for each noise level. Both the MLP and GN used the optimal hyperparameter values from the D s = 0.01 condition of Analysis Method 1. The median movement direction error was computed in 2 × 2 cm 2 cells. The sensors were equidistantly placed between x = ± 0.2 m .

Article Snippet: The best combination of d 0 and l was determined in 30 iterations of the Bayesian optimisation algorithm provided by MATLAB [ ].

Techniques: