A Geometric Modelling Approach to Determining the Best Sensing Coverage for 3-Dimensional Acoustic Target Tracking in Wireless Sensor Networks
Abstract
:1. Introduction
2. Related Work
3. Basics of 3-Dimensional Acoustic Target Tracking
3.1. 3-Dimensional Acoustic Target Localization Model
3.2. Geometric Representation of 3-Dimensional Acoustic Target Localization
3.3. Dual Geometric Representation of Acoustic Target Localization
4. Combined Algebraic and Geometric Solution to 3-Dimensional Acoustic Target Localization
4.1. Geometric Properties of Two Sensor Node’s Information
4.2. Demonstrating Geometric Properties of Two Sensor Node’s Information
4.3. An Algebraic Representation of 3-Dimensional Acoustic Target Localization
4.4. Geometric Properties of Three Sensor Node’s Information
4.5. Demonstrating Geometric Properties of Three Sensor Node’s Information
4.6. Geometric Properties of Four Sensor Nodes’ Information
4.7. Demonstrating the Geometric Properties of Four Sensor Node’s Information
4.8. Elimination of the False Positive Answer of 3-Dimensional Acoustic Target Localization
- Case I: If the time of one of the answers say R1 is before the times of the sound sensing by all four sensor nodes and the time of the other answer, R2 is after the time of the sound sensing of at least one of the four sensing nodes, answer R1 is related to past time and answer R2 is related to future time and is the infeasible answer. An example of case I was shown in Figure 7b.
- Case II: If the times of both computed answers R1 and R2 is before the reported times of sound sensing by all sensor nodes, both answers are related to the past and time test cannot help the FCAL method to detect the feasible spatio-temporal information of a target object. Figure 8 shows this case which demonstrates the pitfall of four degree sensing coverage and the FCAL method. In this case we can randomly select one of the answers or we cans or refuse to report any answer. Another approach is to report both answers and assign a 50% confidence degree to each answer. In simulation of this method in Part 5.3, if a redundant set of simultaneous equations with sensing information of different set of sensor nodes is constructed, the application of majority voter increases the probability of selecting the feasible answer. This is because it is probable that other set of simultaneous equations do not fall in case II.
- Case III: If the axis line is tangent to sound broadcasting hypercone of target object intersects with it on a single point, both answers R1 and R2 are the same and both of them are the feasible spatio-temporal information of a target object. The time test method is successful in cases I and III but it cannot detect the correct answer in case II.
5. A Proposed Four Sensing Coverage Based Method
5.1. Four Coverage Axis Line Method for 3-Dimensional Acoustic Target Localization
5.2. Discussion on FCAL Method
5.3. Simulation Model
5.4. Simulation Results
5.5. Elimination Condition for False Positive Answer
6. Five Sensing Coverage Proposed Methods
6.1. Five Coverage Extent Point Method
6.2. Five Coverage Extended Axis Line Method
6.3. Five Coverage Redundant Axis Lines Method
6.4. Application of Proposed Methods in Bayesian Filters
7. Conclusions and Future Work
7.1. Conclusions
7.2. Future work
Acknowledgments
References and Notes
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Pashazadeh, S.; Sharifi, M. A Geometric Modelling Approach to Determining the Best Sensing Coverage for 3-Dimensional Acoustic Target Tracking in Wireless Sensor Networks. Sensors 2009, 9, 6764-6794. https://doi.org/10.3390/s90906764
Pashazadeh S, Sharifi M. A Geometric Modelling Approach to Determining the Best Sensing Coverage for 3-Dimensional Acoustic Target Tracking in Wireless Sensor Networks. Sensors. 2009; 9(9):6764-6794. https://doi.org/10.3390/s90906764
Chicago/Turabian StylePashazadeh, Saeid, and Mohsen Sharifi. 2009. "A Geometric Modelling Approach to Determining the Best Sensing Coverage for 3-Dimensional Acoustic Target Tracking in Wireless Sensor Networks" Sensors 9, no. 9: 6764-6794. https://doi.org/10.3390/s90906764