1 Spring 2007 Research Log Joseph Djugash

2 The Problem Localize a large network of nodes with the following constraints: Resource Limitation power, communication bandwidth, sensor range, etc. Scalability truly large-scale 's of sensor nodes Robustness accuracy under sub-optimal configurations Efficiency fast convergence and proper resource utilization Node Heterogeneity mobile/static, range/bearing/both Real-time

3 Large Scale Sensor Networks with Mobile Nodes Prior Work and Existing Approaches (Motivation)

4 Preliminary Sensor Networks Approach: MDS Solves multiple constraint equations based on range measurements. Can be formulated as cost minimization Benefits: Relatively simple Provides a single solution even if there are multiple equally likely solution. (reduces confusion) Drawbacks: No filtering of measurements Requires a lot of measurements between nodes Provides a single solution even if there are multiple equally likely solution. (can’t tell how many other solutions there are or if you chose the correct one) Simple Cheap Complex Expensive Est. Type: Cost:

5 Preliminary Robotics Approach Kalman Filters Run individual Kalman filters on each mobile node. Each such KF will maintain a local map of nodes seen by the mobile node The local map will be in its own coordinate frame Each KF follows ideas similar to those presented in my previous SLAM papers. Nodes initialized using a batch algorithm. Inter-node measurements can help improve accuracy of estimate and time to initialize each node. Local map is accurate relative to the robot’s estimated path. This implies that the robot path and map can diverge slowly given sparse distribution of nodes. By combining individual local maps from different KFs a global map can be obtained. When mobile agents explore the same region, their local maps will contain estimates of the same nodes. These overlapping nodes can be used to compute transforms that match the two local maps. Simple Cheap Complex Expensive Est. Type: Cost:

6 Preliminary Robotics Approach Kalman Filters Benefits: Fast, in smaller environments (10’s of nodes). Medium communication overhead. Little memory requirements (state vector + covariance matrix). Drawbacks: Requires the presence of mobile nodes. Complexity of merging maps scales exponentially. Centralized processing – difficult to scale. Need many robots to cover a large region This increases the number of local maps. Thus making the centralized processing even more expensive. Estimate is not a full representation of the state. Represents the state as a mean and ellipse (single modal). Simple Cheap Complex Expensive Est. Type: Cost:

7 Preliminary Robotics Approach Kalman Filters * (black) – true node locations + (magenta) – node estimate in a KF o (green) – combined node estimate global solution  (red) – mobile node – (black) – ground truth path – (red) – estimated path … (blue) – odometry path Simple Cheap Complex Expensive Est. Type: Cost:

8 Parametric Filters Ben Grocholsky’s Method Solves for the full state of the network of nodes within a higher dimensional space. Projections of this manifold back into Euclidean space produces improved representation of the state estimate. Benefits: Highly accurate representation Drawbacks: Computation of simpler motion updates (state diffusion) are much more difficult and requires inversion of a large matrix. Difficult to scale to large scale applications. Simple Cheap Complex Expensive Est. Type: Cost:

9 Parametric Filters Nonlinear Filtering and Estimation Simple Cheap Complex Expensive Est. Type: Cost:

10 Large Scale Sensor Networks with Mobile Nodes Toward a Decentralized (Large Scale) Network Localization Scheme

11 Bayesian Approximation Particle Filter Based Network Localization Initial state is estimated based on current measurements. Two Anchor (arbitrarily chosen) nodes fix the coordinate frame of the local map In practice it is best to choose the nodes with most measurements For other nodes particles are sampled over all measurements If only one range measurement exists, all particles will be sampled over an annulus. This approach ensures that the Multi-Modality within the estimate is maintained. Upon initialization future measurement and motion updates are performed on each node via standard particle filter principles. A single measurement will update the estimates of both nodes that belong to the measurement. Varying Particle count for each node based on its uncertainty allows reduced memory usage. Simple Cheap Complex Expensive Est. Type: Cost:

12 Bayesian Approximation Particle Filter Based Network Localization Simple Cheap Complex Expensive Est. Type: Cost:

13 Bayesian Approximation Particle Filter Based Network Localization Benefits: Fast and accurate initialization. Approximates the full state of the estimate. Multi-Modal Solutions (Non-Gaussian) Does not require the presence of mobile nodes Drawbacks: Scalability is poor. As more and more nodes are estimated within the same local map, the number of particles need to accurately represent each node increases. If the number of particles increases to fit the full uncertainty of multi-modal solutions then computational cost increases. Merging two local maps requires a Combinatorial of the number of particles within the overlapping nodes. Simple Cheap Complex Expensive Est. Type: Cost:

14 Bayesian Approximation Particle Filter Based Network Localization Simple Cheap Complex Expensive Est. Type: Cost:

15 Particle Filter with MDS Using MDS to reduce particle set… Initialize with the Particle filter Approach. Reduce the particle set to satisfy the MDS solution. Remove particles that are not close to the node estimate from the MDS solution. Benefits: Reduced computation in large networks. Merging local maps is easier. Only a single particle cloud is represented for each node. Reduced particle count and reduced multi-modality makes merging easier. Drawbacks: Full representation of the state is lost. Accuracy of the merged map is questionable, since MDS doesn’t always choose the “correct” solution. In the absence of many measurements, MDS doesn’t produce a solution and in that case drawbacks of the Bayes approach applies. Simple Cheap Complex Expensive Est. Type: Cost:

16 Particle Filter with MDS Using MDS to reduce particle set… Simple Cheap Complex Expensive Est. Type: Cost:

17 Distributed Localization Particle Filter + FastMap Initialization: Identify and form a local map for every “robust quad” (fully connected 4-nodes) in the network. Each local map contains a particle filter estimate of each node within its coordinate frame acquired using the Particle Filter approach. Merging: Given enough connections between local maps, the two LMs can be merged. To merge, use FastMap (a simple triangulation algorithm that produces all possible solutions) to predict possible solutions for the merge. For each solution compute rotation and translation required and store these transformation matrices with each node in the newly merged LM. Note here that no explict transform on the estimate is done to the particles, only the transforms are stored with the original LM. Motion & Measurement Updates Standard methods can be applied here. Except for the nodes that contain a transform (ie. these nodes were merged from another LM). For these nodes, motion update is normal while the measurement updates first determine if the transforms are still valid (using FastMap again) before any update is done. For those transforms that pass the validation, apply the transform to the particles then perform any necessary updates. Simple Cheap Complex Expensive Est. Type: Cost:

18 Distributed Localization Particle Filter + FastMap Simple Cheap Complex Expensive Est. Type: Cost:

19 Distributed Localization Particle Filter + FastMap Benefits: Only a subset of the particles are required to represent the full estimate. Since the transforms store alternate solutions. FastMap gives a easy way to reduce how many possible combinations of “merging” can be done. Merging is a limited operation, if further data is needed, it is computed at that later time. Can be distributed to multiple nodes (not just mobile) Drawbacks: Still requires sharing of a lot of data (ie. not decentralized) Approximation in state representation needs to be proven (although in simulation it seems to work reliably) To Do: Requires an improved control scheme to give way to actively positioning mobile nodes to achieve “merges”. Reduce and plan for what info and in how much detail needs to be shared if implementing a decentralized version. Simple Cheap Complex Expensive Est. Type: Cost:

20 Distributed Localization Particle Filter + FastMap FastMap solution to each local map (robust quad). Ellipses represent fused measurement uncertainty. Stored info: Total of 8 nodes form 3 robust-quad (fully connect 4- node cliques) networks (each colored differently). Simple Cheap Complex Expensive Est. Type: Cost: (a)(b)

21 Distributed Localization Bayes + FastMap FastMap recreation of all possible merges of the three robust quads. Transformed particles representing the full solution that can be acquire from using fig(a) and the transforms from fig(c). Simple Cheap Complex Expensive Est. Type: Cost: (c)(d)

22 Non-Line-Of-Sight Ranging Radios! Exploring New Technology (Not Directly Related to Thesis)

23 Range Statistics in open field

24 Range Statistics in NSH 3 rd Floor Distance Error

25 Tracking w/ Map w/o Odometry

26 Tracking w/ Map & Odometry

27 Room-level Tracking (Geoff’s Pursuit Evasion Algorithm)

28 Density Mapping (The Idea) Errors in observed range measurements (when compared with ground truth) can be used to reconstruct a “map” of environmental noise. Each measurement can produce constraints for all map locations through which the range beam had to travel. Using such constraints we can solve for a “density map” which specifies the “wall noise” in the environment. Analogy: Similar to solving a cross-word puzzle. Range 5 Constraint Range 2 Constraint Combined Constraint

29 Density Mapping NSH A-level

30 Pursuit Evasion Experiments FSR 2007 Results (Geoff’s Research)

31 Panel Town with Non-LOS Parrots