GPS World, October 2009

Indoor Navigation DEFENSE GOVERNMENT 20 10 0 10 20 30 n 2 INU olny d 100m d 10m d 1m d 01m d 001m σ σ σ σ σ 0 5000 10000 absolute RMS err m 25 20 15 10 5 0 INU Stds dx 02 m dy 02 m dz 0001 m n 4 σ 0 5000 10000 absolute RMS err m σ σ 25 20 15 10 5 0 n 6 0 5000 10000 absolute RMS err m 25 20 15 10 5 0 n 8 0 5000 10000 absolute RMS err m 25 20 15 10 5 0 n 10 0 5000 10000 Frame absolute RMS err m 25 20 15 10 5 0 n 12 0 5000 10000 Frame absolute RMS err m 25 20 15 10 5 0 n 14 0 5000 10000 Frame absolute RMS err m 25 20 15 10 5 0 n 16 0 5000 10000 Frame absolute RMS err m p FIGURE 8 Absolute RMS error reduction is achieved by the distributed EKF multimodal fusion algorithm even as ranging error accuracy varies greatly reduction trends of the multimodal fusion algorithms The relative RMS position error of the collaborating teams using the more aggressive INU noise model grows slowly but remains bounded to about 2 3 meters SEP Likewise a representation of the data from Figure 7 in the style Figure 6 omitted due to space constraints validates that the Teamwork Effect errorscaling law is robust across different INU sensor noise models Effect of Inter Node Ranging Errors While the simulation runs presented above used an RF ranging sensor model with a STD of 1 meter it is interesting to understand how the multimodal fusion algorithm performance changes as the range measurement accuracy changes FIGURE 8 illustrates the performance of the distributed iterative EKF algorithm for 2 to 16 node networks employing ZUPT corrected INU sensors Simulation runs with RF ranging sensor STD varying from 100 down to 001 meters suggest that the multimodal fusion algorithm tolerates large inaccuracies of inter node range constraints while still providing consistent performance In Figure 8 there is an extremely tight grouping of position error estimates for ranging error up to 10 meters and significant system error reduction is achieved even with 100 meter ranging errors FIGURE 9 shows that the distributed iterative EKF fusion algorithm can maintain very accurate relative position estimates even as the ranging accuracy varies significantly Generally speaking the accuracy of inter node ranging sets an average level for relative position estimates while the number of cooperating nodes in the network determines the variation in that error Plotting the absolute error data of Figure 8 in the style of Figure 6 not shown indicates that a strong 1 n continues to hold in agreement with predictions that the Teamwork Effect error scaling law is robust across RF ranging accuracy models Effect of Varying Inter Node Ranging Interval The simulation results presented thus far assume an inter node range measurement rate of 1 Hz That is the entire distributed iterative EKF algorithm executes once per second While the computational and network communication consequences of this rate of execution are reasonable there may be operational reasons for reducing the ranging rate These may include battery power conservation or a desire to maximize low probability ofdetection characteristics by minimizing radio transmissions for ranging and communication FIGURE 10 shows that the sensor fusion algorithms are tolerant to variations in inter node range measurement rate The six curves in 11 A illustrate the absolute position error expected when a team of eight nodes performs inter node ranging at rates varying from 1 per second to 1 per minute The nearly overlapping curves indicate a minimal impact on the absolute system accuracy over the duration of the simulation 11 C shows that the relative position error of the group is affected slightly since the internode ranging constraints are more directly tied to maintaining accurate relative group geometry over the short term 11 B and 11 D show a more detailed view of the absolute and relative error performance by presenting a three minute snapshot of the four hour simulation The curves show that both absolute and relative performance exhibit changes in error dependent on the range measurement interval This behavior illustrates a form of the Reset Effect whereby the individual nodes position error grows at the rate expected of its self contained navigation sensors during the interval between ranging updates where it is effectively operating as a group of size 1 At the instant of the ranging update the position error is reset to the level expected had the nodes been operating together as part of an eight node group all along Validation of the Anchor Effect The multi sensor fusion algorithms described were designed specifically to enable operation of fully mobile nodes with no requirements for external infrastructure However there are advantages to using statically deployed anchor nodes as reference beacons when the operational scenario permits this Even in these cases it is advantageous to minimize the amount of infrastructure required and to permit fl exible operation FIGURE 11 illustrates the effects of using anchor nodes with our distributed EKF multimodal fusion algorithm The growth INS S tds σ 02 m σ 02 m dx dy σ 0001 m dz n 2 INU o lny d 100m d 10m d 1m d 01m σ σ σ σ 0 5000 10000 20 10 0 10 20 30 re lative RMS err m n 4 0 5000 10000 25 20 15 10 5 0 re lative RMS err m 25 20 15 10 5 0 n 6 0 5000 10000 re lative RMS e rr m n 8 0 5000 10000 25 20 15 10 5 0 re lative RMS e rr m 25 20 15 10 5 0 n 10 0 5000 10000 Frame re lative RMS e rr m n 12 0 5000 10000 25 20 15 10 5 0 Frame re lative RMS err m 25 20 15 10 5 0 n 14 0 5000 10000 Frame re lative RMS e rr m n 16 0 5000 10000 25 20 15 10 5 0 Frame re lative RMS e rr m p FIGURE 9 Relative RMS position estimate errors as a function of time network size and RF ranging accuracy www gpsworld com October 2009 GPS World 45