Sensor Fusion for Underwater Vehicle Navigation Compensating Misalignment Using Lie Theory
This paper presents a sensor fusion method for navigation of unmanned underwater vehicles. The method combines Lie theory into Kalman filter to estimate and compensate for the misalignment between the sensors: inertial navigation system and Doppler Velocity Log (DVL). In the process and measurement...
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MDPI AG
2024-03-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/24/5/1653 |
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| author | Da Bin Jeong Nak Yong Ko |
| author_facet | Da Bin Jeong Nak Yong Ko |
| author_sort | Da Bin Jeong |
| collection | DOAJ |
| description | This paper presents a sensor fusion method for navigation of unmanned underwater vehicles. The method combines Lie theory into Kalman filter to estimate and compensate for the misalignment between the sensors: inertial navigation system and Doppler Velocity Log (DVL). In the process and measurement model equations, a 3-dimensional Euclidean group (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="italic">SE</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula>) and 3-sphere space (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="italic">S</mi><mn>3</mn></msup></semantics></math></inline-formula>) are used to express the pose (position and attitude) and misalignment, respectively. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="italic">SE</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula> contains position and attitude transformation matrices, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="italic">S</mi><mn>3</mn></msup></semantics></math></inline-formula> comprises unit quaternions. The increments in pose and misalignment are represented in the Lie algebra, which is a linear space. The use of Lie algebra facilitates the application of an extended Kalman filter (EKF). The previous EKF approach without Lie theory is based on the assumption that a non-differentiable space can be approximated as a differentiable space when the increments are sufficiently small. On the contrary, the proposed Lie theory approach enables exact differentiation in a differentiable space, thus enhances the accuracy of the navigation. Furthermore, the convergence and stability of the internal parameters, such as the Kalman gain and measurement innovation, are improved. |
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| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-04-25T00:18:49Z |
| publishDate | 2024-03-01 |
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| spelling | doaj.art-5e3fe67a4bd44b01ba7e68cbb70d0a1b2024-03-12T16:55:32ZengMDPI AGSensors1424-82202024-03-01245165310.3390/s24051653Sensor Fusion for Underwater Vehicle Navigation Compensating Misalignment Using Lie TheoryDa Bin Jeong0Nak Yong Ko1Department of Electronic Engineering, Interdisciplinary Program in IT-Bio Convergence Systems, Chosun University, Gwangju 61452, Republic of KoreaDepartment of Electronic Engineering, Interdisciplinary Program in IT-Bio Convergence Systems, Chosun University, Gwangju 61452, Republic of KoreaThis paper presents a sensor fusion method for navigation of unmanned underwater vehicles. The method combines Lie theory into Kalman filter to estimate and compensate for the misalignment between the sensors: inertial navigation system and Doppler Velocity Log (DVL). In the process and measurement model equations, a 3-dimensional Euclidean group (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="italic">SE</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula>) and 3-sphere space (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="italic">S</mi><mn>3</mn></msup></semantics></math></inline-formula>) are used to express the pose (position and attitude) and misalignment, respectively. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="italic">SE</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula> contains position and attitude transformation matrices, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="italic">S</mi><mn>3</mn></msup></semantics></math></inline-formula> comprises unit quaternions. The increments in pose and misalignment are represented in the Lie algebra, which is a linear space. The use of Lie algebra facilitates the application of an extended Kalman filter (EKF). The previous EKF approach without Lie theory is based on the assumption that a non-differentiable space can be approximated as a differentiable space when the increments are sufficiently small. On the contrary, the proposed Lie theory approach enables exact differentiation in a differentiable space, thus enhances the accuracy of the navigation. Furthermore, the convergence and stability of the internal parameters, such as the Kalman gain and measurement innovation, are improved.https://www.mdpi.com/1424-8220/24/5/1653Lie theorymisalignmentattitudenavigationKalman filterunderwater vehicle |
| spellingShingle | Da Bin Jeong Nak Yong Ko Sensor Fusion for Underwater Vehicle Navigation Compensating Misalignment Using Lie Theory Sensors Lie theory misalignment attitude navigation Kalman filter underwater vehicle |
| title | Sensor Fusion for Underwater Vehicle Navigation Compensating Misalignment Using Lie Theory |
| title_full | Sensor Fusion for Underwater Vehicle Navigation Compensating Misalignment Using Lie Theory |
| title_fullStr | Sensor Fusion for Underwater Vehicle Navigation Compensating Misalignment Using Lie Theory |
| title_full_unstemmed | Sensor Fusion for Underwater Vehicle Navigation Compensating Misalignment Using Lie Theory |
| title_short | Sensor Fusion for Underwater Vehicle Navigation Compensating Misalignment Using Lie Theory |
| title_sort | sensor fusion for underwater vehicle navigation compensating misalignment using lie theory |
| topic | Lie theory misalignment attitude navigation Kalman filter underwater vehicle |
| url | https://www.mdpi.com/1424-8220/24/5/1653 |
| work_keys_str_mv | AT dabinjeong sensorfusionforunderwatervehiclenavigationcompensatingmisalignmentusinglietheory AT nakyongko sensorfusionforunderwatervehiclenavigationcompensatingmisalignmentusinglietheory |