1. By: Aaron Dyreson (aaron.dyreson@mavs.uta.edu) Supervising Professor: Dr. Ioannis Schizas (schizas@uta.edu)

2. Introduction Topic of Research: The performance of different distributed Kalman Filtering Algorithms in wireless sensor networks What is Kalman Filtering? Brief History Applications Wireless Sensor Networks Centralized Ad Hoc

3. Extended Kalman Filtering (1/2) Data Model Assumptions: A: State transition matrix h: Observation function Noise vectors w k and v k Physical Interpretation w k and v k are zero mean with covariance matrices Q and R respectively

4. Extended Kalman Filtering (2/2) Algorithm Prediction Update: Linearization Kalman Gain Calculation: Measurement Update:

5. Wireless Sensor Networks Topologies to be simulated in research Centralized Ad Hoc

6. Methodology/Procedure Choose system to study Derive physical data model for system Simulations in MATLAB: Wireless sensor network (WSN) with N sensors Trajectory of object according constant velocity model Range and bearing measurements for each sensor Perform extended Kalman filtering in MATLAB to obtain estimates for state of system Calculate localization error between estimate and true

7. Results (1/4) Simulations completed so far: Centralized Extended Kalman Filtering with range and bearing measurments Centralized Extended Kalman filtering with range measurements

8. Results (2/4) Example plots for range and bearing Kalman Filter

9. Results (3/4)

10. Results (4/4) Range and BearingRange Only Number of Sensors Average RMS Error (100 Simulations) Number of Sensors Average RMS Error (100 Simulations) 116.6199 m1434.8799 m 2.5834 m2.8813 m 3.3187 m3.4957 m 4.2496 m4.2301 m 5.2311 m5.2003 m 10.1622 m10.1473 m 25.1104 m25.1036 m

11. Conclusion Still to be researched: Simulation of Ad Hoc topologies Algorithms associated with Ad Hoc topologies More data collection and analysis for centralized distributed Kalman filtering. Any questions?