GPS World, October 2009

DEFENSE GOVERNMENT Indoor Navigation Centralized nNodes 8 nMCRs 50 INU dx 02m dy 02m dz 0001m d 1 T 1 T 5 T 10 T 15 T 30 T 60 Δ Δ Δ Δ Δ Δ 2000 4000 6000 8000 10000 12000 14000 8 6 4 2 0 absolute RMS err m σ 56 54 52 5 48 σ σ σ 6800 6850 6900 6950 7000 absolute RMS err m 2000 4000 6000 8000 10000 12000 14000 3 25 2 15 1 05 0 relative RMS err m Frame Measurement Instance 3 25 2 15 1 05 0 6800 6850 6900 6950 7000 relative RMS err m Frame p FIGURE 10 Varying the inter node range measurement rate shows minimal long term impact on system accuracy Short term error behavior follows Reset Effect predictions of absolute RMS error over time is displayed for network sizes varying from two to 16 nodes where zero one or two anchor nodes are deployed at the start of the mission Even using only one anchor node improves absolute position accuracy by an additional factor of approximately three for small networks approaching a factor of two for the larger network sizes When we also introduce a second anchor node at the start of the mission we see that the absolute position error is bounded to a low level of about 1 or 2 meters SEP Figure 11 s results indicate the predicted Anchor Effect Inter node range constraints provide accurate relative position geometry due to the Teamwork Effect while absolute position accuracy is still permitted to grow albeit at a lower rate over time Compared to classical uses of reference beacons requiring many more anchor points to be effective we see drastic improvements with minimal numbers of anchors Validation of the Reset Effect The continual refinement of position estimates from the multi sensor fusion algorithms can produce performance that improves rather than degrades over time The accumulated position estimates of mobile nodes are reset to a lower level in the middle of a mission in a manner that provides immediate rather than gradual improvement of the estimate accuracy This Reset Effect is demonstrable under a number of conditions A mobile node whose position error has grown establishes contact with a stationary anchor node The mobile nodes position estimate and its confidence in accuracy of that estimate will improve A mobile node whose position error has grown establishes contact with another mobile with a better location certainty An individual or a small group of mobile nodes merges with another group of mobile nodes forming a larger group This allows for collectively better error performance for example due to the Teamwork Effect The first two instances are rather intuitive and follow directly from the manner in which node position estimates are weighted and combined by the sensor fusion algorithms The position estimate of a node mobile or anchor that is known to a high degree of confidence will be weighted more heavily when the positions are averaged by the fusion process The third is less intuitive but follows from the earlier Reset Effect prediction FIGURE 12 illustrates the first case where the mobile nodes operate as teams for the initial portion of the simulation their own position errors bounded only by the Teamwork Effect After one hour the group makes contact with one or two anchor nodes that provide an immediate reset in error level to a lower value The error reduction is coupled with the Anchor Effect where the number of mobile nodes and anchor nodes determines the extent of the error reduction When the system is lightly constrained by just one anchor node the error reset is less drastic and the absolute error continues to grow over time albeit at a reduced rate When constrained by two anchor nodes absolute error is capped to a low nearly constant level In the third case the Reset Effect enables teams of nodes that split into subgroups and merge some time later to regain the same level of positioning performance as if they had not split The Reset Effect is immediately evident in the simulation results illustrated in FIGURE 13 which presents absolute and relative position error for three scenarios Curves representing the expected error performance of four and eight node teams working together from start to finish are shown for reference As expected the error of the four node team grows at a slightly higher rate to levels that exceed those of the eight node team for the duration of the simulation A third curve shows the absolute error of an eight node team that works together for the first third of the simulation At that point the team splits into two smaller four node teams whose members can only perform inter node range measurements within their group As expected the average position error begins to increase at the 25 20 15 10 5 0 n 2 inu only dist w o anchor dist w 1 anchor dist w 2 anchors 0 5000 10000 Frame absolute RMS err m 25 20 15 10 5 0 n 4 nMCRs 50 INU dx 02 m dy 02 m dz 0001 m MSSI D 1 m 0 5000 10000 Frame absolute RMS err m σ σ σ σ 25 20 15 10 5 0 n 6 0 5000 10000 Frame absolute RMS err m 25 20 15 10 5 0 n 8 0 5000 10000 Frame 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 Unaided ins only Operation 1 Anchor 2 Anchors RF aided Operation p FIGURE 11 Simulation validation of the Anchor Effect Use of just one anchor reference beacon can improve absolute position accuracy by a factor of two to three while two anchor nodes bounds absolute error to a low constant level less than 1 2 meters GPS World October 2009 www gpsworld com 46