# Intention Estimation Using Set of Reference Trajectories as Behaviour Model

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Contributions

#### 1.2. Structure of the Paper

## 2. Method

#### 2.1. Behaviour Model

#### 2.2. Using Particle Filtering

- Make the observation ${z}_{d}$, i.e., measuring the feature value at current grid location of the query instance.
- Calculate the weight factor for each particle depending on how consistent the current measurement ${z}_{d}$ is with each of map trajectories.$${w}_{d}^{m}=p\left({z}_{d}\right|{x}_{d}^{m})$$This is implemented by calculating the Euclidean distance between ${z}_{d}$ and the corresponding feature value in each of the map trajectories.
- Draw, with replacement, m particles from the updated particle set, with probability equal to particles’ associated importance weights to create updated particle set ${X}_{d}$. Many alternative resampling methods also exist in the literature and an in-depth study on such methods is presented in [27].

#### 2.3. Using Decision Trees

#### 2.4. Validation Method

## 3. Results

#### 3.1. Data

#### 3.2. Basic Experiment Using Particle Filtering

#### 3.3. Aggregate Results Using Particle Filtering

#### 3.4. Aggregate Results Using Decision Trees

#### 3.5. Results Comparing Particle-Filer and Decision-Tree Methods on Roundabout Dataset

## 4. Discussion

#### 4.1. Speed as an Attribute

#### 4.2. Performance of $\theta $, l and ($\theta $, v, l) as Feature

#### 4.3. Cell Size

#### 4.4. Incorporating History vs. Local Snapshots

#### 4.5. Overall Performance of Particle-Filter and Decision-Tree Based Methods

#### 4.6. Utility and Applications of Intention Estimation

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Brooks, R. The Big Problem with Self-Driving Cars Is People. IEEE Spectr. Available online: https://spectrum.ieee.org/transportation/self-driving/the-big-problem-with-selfdriving-cars-is-people (accessed on 14 December 2018).
- Kwak, J.Y.; Ko, B.C.; Nam, J.Y. Pedestrian intention prediction based on dynamic fuzzy automata for vehicle driving at nighttime. Infrared Phys. Technol.
**2017**, 81, 41–51. [Google Scholar] [CrossRef] - Lidström, K.; Larsson, T. Model-based Estimation of Driver Intentions Using Particle Filtering. In Proceedings of the 11th International IEEE Conference on Intelligent Transportation Systems, Beijing, China, 12–15 October 2008. [Google Scholar]
- Lidström, K.; Larsson, T. Act normal: Using uncertainty about driver intentions as a warning criterion. In Proceedings of the 16th World Congress on Intelligent Transportation Systems, Stockholm, Sweden, 21–25 September 2009. [Google Scholar]
- Li, S.; Wang, W.; Mo, Z.; Zhao, D. Cluster Naturalistic Driving Encounters Using Deep Unsupervised Learning. arXiv, 2018; arXiv:1802.10214. [Google Scholar]
- Liebner, M.; Baumann, M.; Klanner, F.; Stiller, C. Driver intent inference at urban intersections using the intelligent driver model. In Proceedings of the IEEE Intelligent Vehicles Symposium, Madrid, Spain, 3–7 June 2012. [Google Scholar]
- Martinez, C.M.; Heucke, M.; Wang, F.Y.; Gao, B.; Cao, D. Driving Style Recognition for Intelligent Vehicle Control and Advanced Driver Assistance: A Survey. IEEE Trans. Intell. Transp. Syst.
**2018**, 19, 666–676. [Google Scholar] [CrossRef] - Jain, A.; Koppula, H.S.; Raghavan, B.; Soh, S.; Saxena, A. Car that Knows Before You Do: Anticipating Maneuvers via Learning Temporal Driving Models. In Proceedings of the IEEE International Conference on Computer Vision, Santiago, Chile, 13–16 December 2015. [Google Scholar]
- Maghsood, R.; Johannesson, P. Detection of steering events based on vehicle logging data using hidden Markov models. Int. J. Veh. Des.
**2016**, 70, 278–295. [Google Scholar] [CrossRef] - Okamoto, K.; Berntorp, K.; Cairano, S.D. Driver Intention-based Vehicle Threat Assessment using Random Forests and Particle Filtering. Int. Fed. Autom. Control
**2017**, 50, 13860–13865. [Google Scholar] [CrossRef] - Bokare, P.S.; Maurya, A.K. Acceleration-Deceleration Behaviour of Various Vehicle Types. In Proceedings of the World Conference on Transport Research, Shanghai, China, 10–15 July 2016. [Google Scholar]
- Maurya, A.K.; Bokare, P.S. Study of deceleration behaviour of different vehicle types. Int. J. Traffic Transp. Eng.
**2012**, 2, 253–270. [Google Scholar] [CrossRef] - Alonso, J.D.; Vidal, E.R.; Rotter, A.; Muhlenberg, M. Lane-Change Decision Aid System Based on Motion-Driven Vehicle Tracking. IEEE Trans. Veh. Technol.
**2008**, 57, 2736–2746. [Google Scholar] [CrossRef][Green Version] - Sivaraman, S.; Morris, B.; Trivedi, M. Learning multi-lane trajectories using vehicle-based vision. In Proceedings of the IEEE International Conference on Computer Vision Workshop, Barcelona, Spain, 6–13 November 2011. [Google Scholar]
- Dong, C.; Dolan, J.M.; Litkouhi, B. Intention estimation for ramp merging control in autonomous driving. In Proceedings of the IEEE Intelligent Vehicles Symposium, Los Angeles, CA, USA, 11–14 June 2017; pp. 1584–1589. [Google Scholar]
- Kucner, T.; Saarinen, J.; Magnusson, M.; Lilienthal, A.J. Conditional transition maps: Learning motion patterns in dynamic environments. In Proceedings of the IEEE International Conference on Intelligent Robots and Systems, Tokyo, Japan, 3–7 November 2013. [Google Scholar]
- Tango, F.; Botta, M. ML Techniques for the Classification of Car-Following Maneuver. In AI*IA 2009: Emergent Perspectives in Artificial Intelligence; Serra, R., Cucchiara, R., Eds.; Springer: Berlin/Heidelberg, Germany, 2009; pp. 395–404. [Google Scholar]
- Salomonson, I.; Rathai, K.M.M. Mixed Driver Intention Estimation and Path Prediction Using Vehicle Motion and Road Structure Information. Master’s Thesis, Chalmers University of Technology, Gothenburg, Sweden, 2015. [Google Scholar]
- Zhao, M.; Kathner, D.; Jipp, M.; Soffker, D.; Lemmer, K. Modeling Driver Behavior at Roundabouts: Results from a Field Study. In Proceedings of the IEEE Intelligent Vehicles Symposium, Los Angeles, CA, USA, 11–14 June 2017. [Google Scholar]
- Zhao, M.; Kathner, D.; Soffker, D.; Jipp, M.; Lemmer, K. Modeling Driving Behavior at Roundabouts: Impact of Roundabout Layout and Surrounding Traffic on Driving Behavior. Workshop Paper. Available online: https://core.ac.uk/download/pdf/84275712.pdf (accessed on 8 December 2018).
- Sivaraman, S.; Trivedi, M.M. Looking at Vehicles on the Road: A Survey of Vision-Based Vehicle Detection, Tracking, and Behavior Analysis. IEEE Trans. Intell. Transp. Syst.
**2013**, 14, 1773–1795. [Google Scholar] [CrossRef][Green Version] - Cappé, O.; Godsill, S.J.; Moulines, E. An overview of existing methods and recent advances in sequential Monte Carlo. Proc. IEEE
**2007**, 95, 899–924. [Google Scholar] [CrossRef] - Thrun, S.; Fox, D.; Burgard, W.; Dellaert, F. Robust Monte Carlo lozalization for mobile robots. Artif. Intell.
**2001**, 128, 99–141. [Google Scholar] [CrossRef] - Wolf, J.; Burgard, W.; Burkhardt, H. Robust Vision-Based Localization by Combining an Image Retreival System with Monte Carlo Localization. IEEE Trans. Robot.
**2005**, 21, 208–216. [Google Scholar] [CrossRef] - Arulampalam, M.S.; Maskell, S.; Gordon, N.; Clapp, T. A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans. Signal Process.
**2002**, 50, 174–188. [Google Scholar] [CrossRef][Green Version] - Doucet, A.; Johansen, A.M. A Tutorial on Particle Filtering and sMoothing: Fifteen Years Later; Oxford University Press: Oxford, UK, 2011. [Google Scholar]
- Li, T.; Bolic, M.; Djuric, P.M. Resampling Methods for Particle Filtering: Classification, implementation, and strategies. IEEE Signal Process. Mag.
**2015**, 32, 70–86. [Google Scholar] [CrossRef] - Mitchell, T. Machine Learning; McGraw Hill: New York, NY, USA, 1997. [Google Scholar]
- Ho, T.K. Random Decision Forests. In Proceedings of the International Conference on Document Analysis and Recognition, Montreal, QC, Canada, 14–16 August 1995; pp. 278–282. [Google Scholar]
- Wang, Y.; Xiu, C.; Zhang, X.; Yang, D. WiFi Indoor Localization with CSI Fingerprinting-Based Random Forest. Sensors
**2018**, 18, 2869. [Google Scholar] [CrossRef] [PubMed] - Verikas, A.; Gelzinis, A.; Bacauskiene, M. Mining data with random forests: A survey and results of new tests. Pattern Recognit.
**2011**, 44, 330–349. [Google Scholar] [CrossRef] - Viscando Traffic Systems AB, Sweden. Available online: https://viscando.com/ (accessed on 14 December 2018).
- Fan, H.; Kucner, T.P.; Magnusson, M.; Li, T.; Lilienthal, A.J. A Dual PHD Filter for Effective Occupancy Filtering in a Highly Dynamic Environment. IEEE Trans. Intell. Transp. Syst.
**2018**, 19, 2977–2993. [Google Scholar] [CrossRef]

**Figure 1.**Trajectories and the discretisation grid for: (

**a**) bicycle dataset; (

**b**) car-turning dataset; and (

**c**) roundabout dataset.

**Figure 2.**Attribute definitions: For a given position on a trajectory (trajectory represented by the dashed red line and a given position by the red dot), $\theta $ is absolute angle in degrees, l is the shortest distance from the border of the path (which can be arbitrarily drawn), and v is speed along the trajectory.

**Figure 3.**Attribute values for the bicycle dataset: (

**a**–

**c**) observations across time; and (

**d**–

**f**) grid-cell-wise zero-mean and unit-variance normalised attribute values.

**Figure 4.**Attribute values for the car-turning dataset: (

**a**–

**c**) observations across time; and (

**d**–

**f**) grid-cell-wise zero-mean and unit-variance normalized attribute values.

**Figure 5.**Trajectories and normalized attribute values for four categories corresponding to the East entrance in the roundabout dataset. Note that, only one u-turn trajectory exists (fourth column) in the whole dataset, which makes intuitive sense as vehicles rarely use roundabouts for performing u-turns compared to traffic exiting at first, second or third exits (with respect to any entry point). Similarly, second column of the figure includes one trajectory where a vehicle enters from East, and takes one complete circle around the roundabout, before finally exiting at the West.

**Figure 6.**Evolution of beliefs, over the iterations of particle filter, on how belief for first or second category evolved.

**Figure 7.**Aggregate results for bicycle dataset using particle filtering: (

**a**) the five grid cells show locations where 60%, 70%, 80%, 90%, and 99% of the total bicycle path length (for the path discretised using the grid shown in Figure 1a) has been traversed; and (

**b**–

**f**) box plots at each of the five grid-cell locations in (

**a**). Each subfigure (

**b**–

**f**) shows a box plot for percentage of correct category recognition for different feature types used including $(\theta ,v,l)$, $(\theta ,l)$, v, l and $\theta $.

**Figure 8.**Aggregate results for car-turning dataset using particle filtering: (

**a**) the five grid cells show locations where 60%, 70%, 80%, 90%, and 99% of the total car path length (for the path discretised using the grid shown in Figure 1b) has been traversed; and (

**b**)–(

**f**) box plots at each of the five grid-cell locations in (

**a**). Each subfigure (

**b**)–(

**f**) shows a box plot for percentage of correct category recognition for different feature types used including $(\theta ,v,l)$, $(\theta ,l)$, v, l and $\theta $.

**Figure 9.**Aggregate results for roundabout dataset using particle filtering. The figure shows (colour-coded for each of the 12 test categories) the locations of the points beyond which 100% correct intention estimation was achieved for each test trajectory (plotted as coloured dots). The figure also shows (for each of the 12 test categories) the location of grid cell closest to the mean location of the points belonging to that category beyond which 100% correct intention estimation was achieved.

**Figure 12.**Aggregate results for roundabout dataset using decision trees. The figure shows (colour-coded for each of the 12 test categories) the locations of the points beyond which 100% correct intention estimation was achieved for each test trajectory (plotted as coloured dots). The figure also shows (for each of the 12 test categories) the location of grid cell closest to the mean location of the points belonging to that category beyond which 100% correct intention estimation was achieved.

**Figure 16.**Aggregate results on bicycle dataset using decision trees with history voting over a sliding window—three rows of the subplots (from top to bottom) correspond to window sizes of 1, 3 and 5, and each of the four columns (from left to right) correspond to 60%, 80%, 90% and 99% of the total path length traversed (cf. Figure 10).

**Table 1.**Confusion matrix for predicted vs. ground-truth exits, using particle-filtering method for intention estimation.

Ground-Truth Exit | East | North | West | South | |
---|---|---|---|---|---|

Predicted Exit | |||||

East (entering from N, W, S) | 76.25 | 5.76 | 1.78 | 26.94 | |

North (entering from E, W, S) | 9.59 | 80.30 | 15.05 | 3.81 | |

West (entering from E, N, S) | 4.52 | 13.71 | 82.80 | 4.81 | |

South (entering from E, N, W) | 9.64 | 0.23 | 0.35 | 64.42 |

**Table 2.**Confusion matrix for predicted vs. ground-truth exits, using decision-tree method for intention estimation.

Ground-Truth Exit | East | North | West | South | |
---|---|---|---|---|---|

Predicted Exit | |||||

East (entering from N, W, S) | 78.34 | 4.23 | 1.88 | 21.46 | |

North (entering from E, W, S) | 10.99 | 88.53 | 12.42 | 1.01 | |

West (entering from E, N, S) | 0.79 | 6.71 | 77.78 | 3.24 | |

South (entering from E, N, W) | 9.87 | 0.53 | 7.92 | 74.29 |

**Table 3.**Method and distance, leading (i.e., succeeding earlier in) intention estimation in terms of the grid-cell location closest to the mean decision point for each test category. PF represents particle-filter based method, and S–E represent South–East.

Category | S-E | S-N | S-W | E-N | E-W | E-S | N-W | N-S | N-E | W-S | W-E | W-N |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Leading method | PF | PF | PF | PF | PF | PF | PF | PF | PF | PF | PF | PF |

Leading by (m) | 1.8 | 28.2 | 5.4 | 4.2 | 13.2 | 1.8 | 6 | 17.4 | 33 | 6.6 | 27 | 19.8 |

**Table 4.**Expansion of Table 2 (Column 4) based on entry direction of test trajectories—values in percent.

Entry Direction (for an Eventual Exit at South) | East | North | West | |
---|---|---|---|---|

Predicted Exit | ||||

(Number of test trajectories) | (5) | (30) | (5) | |

East | 10.94 | 23.33 | 20.74 | |

North | 5.26 | 0 | 2.86 | |

West | 25.95 | 0 | 0 | |

South | 57.84 | 76.67 | 76.41 |

© 2018 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Muhammad, N.; Åstrand, B. Intention Estimation Using Set of Reference Trajectories as Behaviour Model. *Sensors* **2018**, *18*, 4423.
https://doi.org/10.3390/s18124423

**AMA Style**

Muhammad N, Åstrand B. Intention Estimation Using Set of Reference Trajectories as Behaviour Model. *Sensors*. 2018; 18(12):4423.
https://doi.org/10.3390/s18124423

**Chicago/Turabian Style**

Muhammad, Naveed, and Björn Åstrand. 2018. "Intention Estimation Using Set of Reference Trajectories as Behaviour Model" *Sensors* 18, no. 12: 4423.
https://doi.org/10.3390/s18124423