Abstract
As one of the leading technologies of real-time dynamic deformation monitoring, global navigation satellite system (GNSS) has been widely used in deformation monitoring. Multipath error is the primary error source that limits the application of GNSS high-precision deformation monitoring, which cannot be eliminated by the double-differenced technique. It is a problem to separate and mitigate multipath in the GNSS deformation monitoring series in real-time. Therefore, we propose an approach to solve this problem, named time–frequency mask and convolutional neural network (TFM–CNN). The specific processes are as follows: (1) TFM–CNN network construction. We add a full-band deformation to the multipath and obtain the spectrogram of the signal by the short-time Fourier transform (STFT); meanwhile, the ideal ratio mask (IRM) is used to obtain the corresponding time–frequency mask matrix based on the spectrogram; furthermore, one-dimensional CNN mines the mapping relationship between the spectrogram and the time–frequency mask matrix. (2) Multipath separation. We obtain the spectrogram of the GNSS real-time deformation monitoring series by STFT. Then, we estimate its time–frequency mask matrix by the network. The matrix is multiplied by the spectrogram of the monitoring series to obtain the spectrogram of the multipath. Finally, we perform the inverse STFT to obtain the multipath in the GNSS monitoring series. The experimental results show that by training GNSS data in only a specific direction (such as the north direction), the mapping relationship between the spectrogram of multipath and the time–frequency mask matrix can be obtained, which can effectively separate multipath of the GNSS monitoring series in different observation environment in real-time. TFM-CNN significantly improves the monitoring accuracy and achieves millimeter level dynamic deformation monitoring.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data Availability
Upon a reasonable request, the data that support the findings of this study are available from the first author, Yuan Tao (yuantao0505@gmail.com).
References
Agnew DC, Larson KM (2007) Finding the repeat times of the GPS constellation. GPS Solut 11(1):71–76
Alber C, Ware R, Rocken C, Braun J (2000) Obtaining single path phase delays from GPS double differences. Geophys Res Lett 27(17):2661–2664. https://doi.org/10.1029/2000gl011525
Brunner F, Hartinger H, Troyer L (1999) GPS signal diffraction modelling: the stochastic SIGMA-Δ model. J Geod 73(5):259–267
Cai M, Chen W, Dong D, Song L, Wang M, Wang Z, Zhou F, Zheng Z, Yu C (2016) Reduction of Kinematic Short Baseline Multipath Effects Based on Multipath Hemispherical Map. Sensors 16(10):1677
Choi K, Bilich A, Larson KM, Axelrad P (2004) Modified sidereal filtering: Implications for high-rate GPS positioning. Geophys Res Lett 31(22):178–198
Dai W, Huang D, Cai C (2014) Multipath mitigation via component analysis methods for GPS dynamic deformation monitoring. GPS Solut 18(3):417–428
Danskin S, Bettinger P, Jordan T (2009) Multipath mitigation under forest canopies: A choke ring antenna solution. Forest Sci 55(2):109–116
Dong D, Wang M, Chen W, Zeng Z, Song L, Zhang Q, Cai M, Cheng Y, Lv J (2016) Mitigation of multipath effect in GNSS short baseline positioning by the multipath hemispherical map. J Geod 90(3):255–262. https://doi.org/10.1007/s00190-015-0870-9
Durak L, Arikan O (2003) Short-time Fourier transform: two fundamental properties and an optimal implementation. IEEE Trans Signal Process 51(5):1231–1242
Genrich JF, Bock Y (1992) Rapid resolution of crustal motion at short ranges with the Global Positioning System. J Geophys Res Solid Earth 97(B3):3261–3269
Girshick R, Donahue J, Darrell T, Malik J (2014) Rich feature hierarchies for accurate object detection and semantic segmentation. In: Proceedings of the IEEE conference on computer vision and pattern recognition 2014, Columbus, Ohio, USA, pp 580-587
Groves PD, Jiang Z, Skelton B, Cross PA, Lau L, Adane Y, Kale I (2010) Novel multipath mitigation methods using a dual-polarization antenna. In: Proceedings of ION GNSS 2010, Portland, OR, pp 140–151
Hinton GE, Srivastava N, Krizhevsky A, Sutskever I, Salakhutdinov RR (2012) Improving neural networks by preventing co-adaptation of feature detectors. Preprint at https://arxiv.org/abs/1207.0580
Huang P-S, Kim M, Hasegawa-Johnson M, Smaragdis P (2015) Joint optimization of masks and deep recurrent neural networks for monaural source separation. IEEE/ACM Trans Audio Speech Lang Process 23(12):2136–2147
LeCun Y, Bottou L, Bengio Y, Haffner P (1998) Gradient-based learning applied to document recognition. Proc IEEE 86(11):2278–2324
Luo Y, Mesgarani N (2019) Conv-tasnet: Surpassing ideal time–frequency magnitude masking for speech separation. IEEE/ACM Trans Audio Speech Lang Process 27(8):1256–1266
Maqsood M, Gao S, Brown TW, Unwin M, Steenwijk DVV, R, Xu J, (2013) A compact multipath mitigating ground plane for multiband GNSS antennas. IEEE Trans Antennas Propag 61(5):2775–2782
Nair V, Hinton GE (2010) Rectified linear units improve restricted Boltzmann machines. In: Proceedings of the 27th International Conference on Machine Learning (ICML), Haifa, Israel, pp 807-814
Phan H, Andreotti F, Cooray N, Chén OY, De Vos M (2018) Joint classification and prediction CNN framework for automatic sleep stage classification. IEEE Trans Biomed Eng 66(5):1285–1296
Pourtaghi A, Lotfollahi-Yaghin M (2012) Wavenet ability assessment in comparison to ANN for predicting the maximum surface settlement caused by tunneling. Tunn Undergr Space Technol 28:257–271
Ray J, Cannon M, Fenton P (2001) GPS code and carrier multipath mitigation using a multiantenna system. IEEE Trans Aerosp Electron Syst 37(1):183–195
Srinivasan S, Roman N, Wang D (2006) Binary and ratio time-frequency masks for robust speech recognition. Speech Commun 48(11):1486–1501
Srivastava N, Hinton G, Krizhevsky A, Sutskever I, Salakhutdinov R (2014) Dropout: a simple way to prevent neural networks from overfitting. J Mach Learn Res 15(1):1929–1958
Wang D (2005) On ideal binary mask as the computational goal of auditory scene analysis. Speech separation by humans and machines. Springer, New York, pp 181–197
Wang D, Chen J (2018) Supervised speech separation based on deep learning: An overview. IEEE/ACM Trans Audio Speech Lang Process 26(10):1702–1726
Wang Y, Narayanan A, Wang D (2014) On training targets for supervised speech separation. IEEE/ACM Trans Audio Speech Lang Process 22(12):1849–1858
Wang Z, Chen W, Dong D, Wang M, Cai M, Yu C, Zheng Z, Liu M (2019) Multipath mitigation based on trend surface analysis applied to dual-antenna receiver with common clock. GPS Solut 23(4):104
Weninger F, Eyben F, Schuller B (2014) Single-channel speech separation with memory-enhanced recurrent neural networks. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Florence, Italy, pp 3709–3713
Xi R, Meng X, Jiang W, An X, He Q, Chen Q (2020) A Refined SNR Based Stochastic Model to Reduce Site-Dependent Effects. Remote Sens 12(3):493
Xu B, Wang N, Chen T, Li M (2015) Empirical evaluation of rectified activations in convolutional network. Preprint at https://arxiv.org/abs/1505.00853
Ye S, Chen D, Liu Y, Jiang P, Tang W, Xia P (2015) Carrier phase multipath mitigation for BeiDou navigation satellite system. GPS Solut 19(4):545–557. https://doi.org/10.1007/s10291-014-0409-1
Yuan G, Xie Y, Song Y, Liang H (2010) Multipath parameters estimation of weak GPS signal based on new colored noise unscented Kalman filter. The 2010 IEEE International Conference on Information and Automation. Harbin, China, pp 1852–1856
Zhang K, Li B, Zhu X, Chen H, Sun G (2017) Multipath detection based on single orthogonal dual linear polarized GNSS antenna. GPS Solut 21(3):1203–1211
Zhang Q, Yang W, Zhang S, Liu X (2018) Characteristics of BeiDou Navigation Satellite System Multipath and Its Mitigation Method Based on Kalman Filter and Rauch-Tung-Striebel Smoother. Sensors 18(1):198. https://doi.org/10.3390/s18010198
Zheng H, Fu J, Mei T, Luo J (2017) Learning multi-attention convolutional neural network for fine-grained image recognition. In: Proceedings of the IEEE international conference on computer vision 2017, Venice, Italy, pp 5209-5217
Zheng K, Zhang X, Li P, Li X, Ge M, Guo F, Sang J, Schuh H (2019) Multipath extraction and mitigation for high-rate multi-GNSS precise point positioning. J Geod 93(10):2037–2051
Zhong P, Ding X, Yuan L, Xu Y, Kwok K, Chen Y (2010) Sidereal filtering based on single differences for mitigating GPS multipath effects on short baselines. J Geod 84(2):145–158
Zimmermann F, Eling C, Kuhlmann H (2017) Empirical assessment of obstruction adaptive elevation masks to mitigate site-dependent effects. GPS Solut 21(4):1695–1706
Acknowledgements
We would like to thank the two anonymous reviewers for their constructive comments and suggestions. This research is supported by the National Key Research and Development Program of China (No. 2016YFC0803109), the Hebei Ecological Intelligent Mine Joint Foundation (No. E2020402086), the National Natural Science Foundation of China (No. 41772130) and the Anhui University of Science and Technology Graduate Innovation Foundation (2019CX2077).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Tao, Y., Liu, C., Liu, C. et al. Joint time–frequency mask and convolutional neural network for real-time separation of multipath in GNSS deformation monitoring. GPS Solut 25, 25 (2021). https://doi.org/10.1007/s10291-020-01074-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10291-020-01074-y