Algorithm for Trajectory Simplification Based on Multi-Point Construction in Preselected Area and Noise Smoothing Processing
Abstract
1. Introduction
- (1)
- Unlike other simplification algorithms that utilize only the feature information of recorded trajectory points, this algorithm also considers the influence of inflection points and approximately restores unrecorded implicit trajectory points, using their feature information to aid in simplification.
- (2)
- By defining a preselected area and predicting the landing point of the trajectory, a one-way error-bounded simplified trajectory is achieved.
- (3)
- A novel error measurement method is defined to quantify the deviation between the original and simplified trajectories.
- (4)
- The Kalman filter is used to smooth the trajectory, which effectively reduces the influence of noise on the performance of the simplified algorithm and obtains the most realistic performance index of the algorithm.
- (5)
- This algorithm offers high compression rates and efficient real-time simplification while effectively preserving the original trajectory’s contour.
2. Related Work
3. Trajectory Simplification Algorithm SSFI
3.1. Preliminaries
3.2. Error Measurement Method Based on Implicit Trajectory Points
3.3. Algorithm Implementation and Its Pseudo-Code
Algorithm 1 SSFI pseudo-code |
Output: Simplified trajectory S with IED bounded error |
1: i = 1;S = P[1]; |
N do{ |
3: AnchorPoint = P[i]; |
4: i = i + 1; |
5: PreselectonArea.initialive(StartPoint,i); |
) |
7: S.append(P[i]); |
8: else{ |
9: while(P[i] in PreselectonArea and (i < N) do{ |
); |
11: i = i + 1;} |
12: i = i − 1;} |
13: S.append(P[i]);} |
14: return S: |
4. Trajectory Data Noise Reduction
4.1. GPS Error Analysis
4.2. Trajectory Data Noise Reduction Model
4.3. Kalman Filter Prediction Phase
4.4. Update Phase of Kalman Filter
5. Experiments and Analysis
5.1. Noise Reduction Model Analysis
5.2. Performance Analysis of Simplified Algorithm
5.2.1. Simplification Rate Analysis
5.2.2. Error Comparison
5.2.3. Time Cost
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
References
- He, P.; Klarevas-Irby, J.A.; Papageorgiou, D.; Christensen, C.; Strauss, E.D.; Farine, D.R. A guide to sampling design for GPS-based studies of animal societies. Methods Ecol. Evol. 2023, 14, 1887–1905. [Google Scholar] [CrossRef]
- Qian, K.; Li, X. A user LBS dual privacy protection scheme based on trajectory similarity. Comput. Simul. 2023, 40, 459–465. [Google Scholar]
- Wang, S.; Bao, Z.; Culpepper, J.S.; Cong, G. A survey on trajectory data management, analytics, and learning. ACM Comput. Surv. 2021, 54, 1–36. [Google Scholar] [CrossRef]
- Wang, P.; Wang, J.; Zhang, L.; Jing, D. An improved Douglas-Peucker NC machining trajectory compression method. Microcomput. Syst. 2024, 1, 1–9. [Google Scholar]
- Zhang, Y.; Pan, J.; Zhao, M. Threshold guided sampling method for ship trajectory simplification algorithm. J. Jimei Univ. 2021, 26, 425–432. [Google Scholar]
- Liu, J.; Zhao, K.; Sommer, P.; Shang, S.; Kusy, B.; Lee, J.-G.; Jurdak, R. A Novel Framework for Online Amnesic Trajectory Compression in Resource-Constrained Environments. IEEE Trans. Knowl. Data Eng. 2016, 28, 2827–2841. [Google Scholar] [CrossRef]
- Liu, J.; Zhao, K.; Sommer, P.; Shang, S.; Kusy, B.; Jurdak, R. Bounded Quadrant System: Error-bounded trajectory compression on the go. In Proceedings of the 2015 IEEE 31st International Conference on Data Engineering, Seoul, Republic of Korea, 13–17 April 2015; pp. 987–998. [Google Scholar]
- Lin, X.; Ma, S.; Zhang, H.; Wo, T.; Huai, J. One-pass error bounded trajectory simplification. Proc. VLDB Endow. 2017, 10, 841–852. [Google Scholar] [CrossRef]
- Jiang, H.; Han, D.; Liu, H.; Nie, W. Time Synchronized Velocity Error for Trajectory Compression. Comput. Model. Eng. Sci. 2022, 130, 1193–1219. [Google Scholar] [CrossRef]
- Zhong, Y.; Kong, J.; Zhang, J.; Jiang, Y.; Fan, X.; Wang, Z. A trajectory data compression algorithm based on spatio-temporal characteristics. PeerJ Comput. Sci. 2022, 8, e1112. [Google Scholar] [CrossRef] [PubMed]
- Gu, J.; Song, X.; Shi, X.; Chang, D. Online compression algorithm of fishing vessel trajectory based on improved sliding window. J. Shanghai Marit. Univ. 2023, 44, 17–24. [Google Scholar]
- Kim, M.W.; Park, S.K.; Ju, J.G.; Noh, H.C.; Choi, D.G. Clean Collector Algorithm for Satellite Image Pre-Processing of SAR-to-EO Translation. Electronics 2024, 13, 4529. [Google Scholar] [CrossRef]
- Sui, L.; Ma, F.; Chen, N. Mining Subsidence Prediction by Combining Support Vector Machine Regression and Interferometric Synthetic Aperture Radar Data. ISPRS Int. J. Geo-Inf. 2020, 9, 390. [Google Scholar] [CrossRef]
- Wang, H.; Jin, X.; Hou, C.; Zhou, L.; Xu, Z.; Jin, Z. A micro-nano satellite relative positioning algorithm based on robust adaptive estimation. J. Zhejiang Univ. 2023, 57, 2325–2336. [Google Scholar]
- Xu, W.; Yan, C.; Du, W.; Zhang, G.; Wang, T.; Xu, M. Comparative analysis of navigation and positioning performance between GPS system and BDS system. Glob. Position. Syst. 2017, 42, 77–82. [Google Scholar]
- Xu, C.; Chen, G.; Hu, N. Beidou/GPS dual-mode data fusion trajectory positioning based on Kalman filter. Metering Test. Technol. 2024, 51, 10–13. [Google Scholar]
- Zhao, Y.X.; Hsieh, Y.Z.; Lin, S.S.; Pan, C.J.; Nan, C.W. Design of an IoT-Based Mountaineering Team Management Device Using Kalman Filter Algorithm. J. Internet Technol. 2020, 21, 2085–2093. [Google Scholar]
- Xu, D.; Wang, B.; Zhang, L. A New Adaptive High-Degree Unscented Kalman Filter with Unknown Process Noise. Electronics 2022, 11, 1863. [Google Scholar] [CrossRef]
- Zhou, L.; Zhang, L.; Jin, Y.; Hu, Z.; Li, J. Distributed Cubature Kalman Filter Cooperative Localization Based on Parameterized-belief Propagation. J. Internet Technol. 2022, 23, 497–507. [Google Scholar] [CrossRef]
- Yuan, J.; Zheng, Y.; Xie, X.; Sun, G. Driving with knowledge from the physical world. In Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’11, San Diego, CA, USA, 21–24 August 2011. [Google Scholar]
- Yao, R.; Wang, F.; Chen, S.; Zhao, S. GroupSeeker: An Applicable Framework for Travel Companion Discovery from Vast Trajectory Data. ISPRS Int. J. Geo-Inf. 2020, 9, 404. [Google Scholar] [CrossRef]
- Ding, M. Research on Trajectory Big Data Compression Technology. Master’s Thesis, University of Electronic Science and Technology of China, Chengdu, China, 2019. [Google Scholar]
- Ru, J.; Wang, S.; Jia, Z.; Wang, Y.; He, T.; Wu, C. Sunshine-Based Trajectory Simplification. IEEE Access 2019, 7, 47781–47793. [Google Scholar] [CrossRef]
Algorithm | Time Complexity | Space Complexity |
---|---|---|
SSFI | ||
DP | ||
FBQS | ||
OPERB | ||
OPERB-A |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Huang, S.; Yang, Z. Algorithm for Trajectory Simplification Based on Multi-Point Construction in Preselected Area and Noise Smoothing Processing. Data 2024, 9, 140. https://doi.org/10.3390/data9120140
Huang S, Yang Z. Algorithm for Trajectory Simplification Based on Multi-Point Construction in Preselected Area and Noise Smoothing Processing. Data. 2024; 9(12):140. https://doi.org/10.3390/data9120140
Chicago/Turabian StyleHuang, Simin, and Zhiying Yang. 2024. "Algorithm for Trajectory Simplification Based on Multi-Point Construction in Preselected Area and Noise Smoothing Processing" Data 9, no. 12: 140. https://doi.org/10.3390/data9120140
APA StyleHuang, S., & Yang, Z. (2024). Algorithm for Trajectory Simplification Based on Multi-Point Construction in Preselected Area and Noise Smoothing Processing. Data, 9(12), 140. https://doi.org/10.3390/data9120140