The Pseudoinverse Gradient Descent Method with Eight Branch Directions (8B-PGDM): An Improved Dead Reckoning Algorithm Based on the Local Invariance of Navigation
This paper establishes a fundamental connection between the local time invariance of motion parameters and dead reckoning (DR) accuracy. This insight enables the reformulation of navigation parameter estimation as a convex optimization problem solvable through our novel Eight-Branch Pseudoinverse Gr...
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
|
| Series: | Applied Sciences |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2076-3417/15/9/5049 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849312835043065856 |
|---|---|
| author | Jialong Gao Quan Liu Hanqiang Deng Lei Sun Jian Huang Ming Lei |
| author_facet | Jialong Gao Quan Liu Hanqiang Deng Lei Sun Jian Huang Ming Lei |
| author_sort | Jialong Gao |
| collection | DOAJ |
| description | This paper establishes a fundamental connection between the local time invariance of motion parameters and dead reckoning (DR) accuracy. This insight enables the reformulation of navigation parameter estimation as a convex optimization problem solvable through our novel Eight-Branch Pseudoinverse Gradient Descent Method (8B-PGDM). This method addresses non-cooperative positioning challenges in sparse-sensor regimes, particularly enabling real-time trajectory prediction when facing intermittent measurements (e.g., <5 Hz sampling rates) or persistent signal blockages. This method achieves an excellent estimation accuracy with only three samplings and an prediction MSE of <inline-formula data-eusoft-scrollable-element="1"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" data-eusoft-scrollable-element="1"><semantics data-eusoft-scrollable-element="1"><mrow data-eusoft-scrollable-element="1"><mn data-eusoft-scrollable-element="1">0.7906</mn></mrow></semantics></math></inline-formula>, significantly better than traditional dead reckoning (DR) methods. This approach effectively mitigates the impact of data scarcity, enabling robust and accurate trajectory predictions in challenging environments. |
| format | Article |
| id | doaj-art-63ab0e4251b94e69b8701cf812e4f3d8 |
| institution | Kabale University |
| issn | 2076-3417 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj-art-63ab0e4251b94e69b8701cf812e4f3d82025-08-20T03:52:57ZengMDPI AGApplied Sciences2076-34172025-05-01159504910.3390/app15095049The Pseudoinverse Gradient Descent Method with Eight Branch Directions (8B-PGDM): An Improved Dead Reckoning Algorithm Based on the Local Invariance of NavigationJialong Gao0Quan Liu1Hanqiang Deng2Lei Sun3Jian Huang4Ming Lei5College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, ChinaCollege of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, ChinaCollege of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, ChinaCollege of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, ChinaCollege of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, ChinaDepartment of Automation, Tsinghua University, Beijing 100084, ChinaThis paper establishes a fundamental connection between the local time invariance of motion parameters and dead reckoning (DR) accuracy. This insight enables the reformulation of navigation parameter estimation as a convex optimization problem solvable through our novel Eight-Branch Pseudoinverse Gradient Descent Method (8B-PGDM). This method addresses non-cooperative positioning challenges in sparse-sensor regimes, particularly enabling real-time trajectory prediction when facing intermittent measurements (e.g., <5 Hz sampling rates) or persistent signal blockages. This method achieves an excellent estimation accuracy with only three samplings and an prediction MSE of <inline-formula data-eusoft-scrollable-element="1"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" data-eusoft-scrollable-element="1"><semantics data-eusoft-scrollable-element="1"><mrow data-eusoft-scrollable-element="1"><mn data-eusoft-scrollable-element="1">0.7906</mn></mrow></semantics></math></inline-formula>, significantly better than traditional dead reckoning (DR) methods. This approach effectively mitigates the impact of data scarcity, enabling robust and accurate trajectory predictions in challenging environments.https://www.mdpi.com/2076-3417/15/9/5049dead reckoning algorithmlocal invariancesparse sensor dataiterative optimization algorithm |
| spellingShingle | Jialong Gao Quan Liu Hanqiang Deng Lei Sun Jian Huang Ming Lei The Pseudoinverse Gradient Descent Method with Eight Branch Directions (8B-PGDM): An Improved Dead Reckoning Algorithm Based on the Local Invariance of Navigation Applied Sciences dead reckoning algorithm local invariance sparse sensor data iterative optimization algorithm |
| title | The Pseudoinverse Gradient Descent Method with Eight Branch Directions (8B-PGDM): An Improved Dead Reckoning Algorithm Based on the Local Invariance of Navigation |
| title_full | The Pseudoinverse Gradient Descent Method with Eight Branch Directions (8B-PGDM): An Improved Dead Reckoning Algorithm Based on the Local Invariance of Navigation |
| title_fullStr | The Pseudoinverse Gradient Descent Method with Eight Branch Directions (8B-PGDM): An Improved Dead Reckoning Algorithm Based on the Local Invariance of Navigation |
| title_full_unstemmed | The Pseudoinverse Gradient Descent Method with Eight Branch Directions (8B-PGDM): An Improved Dead Reckoning Algorithm Based on the Local Invariance of Navigation |
| title_short | The Pseudoinverse Gradient Descent Method with Eight Branch Directions (8B-PGDM): An Improved Dead Reckoning Algorithm Based on the Local Invariance of Navigation |
| title_sort | pseudoinverse gradient descent method with eight branch directions 8b pgdm an improved dead reckoning algorithm based on the local invariance of navigation |
| topic | dead reckoning algorithm local invariance sparse sensor data iterative optimization algorithm |
| url | https://www.mdpi.com/2076-3417/15/9/5049 |
| work_keys_str_mv | AT jialonggao thepseudoinversegradientdescentmethodwitheightbranchdirections8bpgdmanimproveddeadreckoningalgorithmbasedonthelocalinvarianceofnavigation AT quanliu thepseudoinversegradientdescentmethodwitheightbranchdirections8bpgdmanimproveddeadreckoningalgorithmbasedonthelocalinvarianceofnavigation AT hanqiangdeng thepseudoinversegradientdescentmethodwitheightbranchdirections8bpgdmanimproveddeadreckoningalgorithmbasedonthelocalinvarianceofnavigation AT leisun thepseudoinversegradientdescentmethodwitheightbranchdirections8bpgdmanimproveddeadreckoningalgorithmbasedonthelocalinvarianceofnavigation AT jianhuang thepseudoinversegradientdescentmethodwitheightbranchdirections8bpgdmanimproveddeadreckoningalgorithmbasedonthelocalinvarianceofnavigation AT minglei thepseudoinversegradientdescentmethodwitheightbranchdirections8bpgdmanimproveddeadreckoningalgorithmbasedonthelocalinvarianceofnavigation AT jialonggao pseudoinversegradientdescentmethodwitheightbranchdirections8bpgdmanimproveddeadreckoningalgorithmbasedonthelocalinvarianceofnavigation AT quanliu pseudoinversegradientdescentmethodwitheightbranchdirections8bpgdmanimproveddeadreckoningalgorithmbasedonthelocalinvarianceofnavigation AT hanqiangdeng pseudoinversegradientdescentmethodwitheightbranchdirections8bpgdmanimproveddeadreckoningalgorithmbasedonthelocalinvarianceofnavigation AT leisun pseudoinversegradientdescentmethodwitheightbranchdirections8bpgdmanimproveddeadreckoningalgorithmbasedonthelocalinvarianceofnavigation AT jianhuang pseudoinversegradientdescentmethodwitheightbranchdirections8bpgdmanimproveddeadreckoningalgorithmbasedonthelocalinvarianceofnavigation AT minglei pseudoinversegradientdescentmethodwitheightbranchdirections8bpgdmanimproveddeadreckoningalgorithmbasedonthelocalinvarianceofnavigation |