Fusion of Multi-Sensor Networks

Teamwork in GPS-Denied Environments

Localization of mobile sensor network nodes in GPS-jammed or GPS-denied areas such as urban, indoor, and subterranean environments will play a key role for civilian and military applications, where teams of people or robots cooperate to perform tactical operations or security, intelligence, and emergency first responder activities. Inertial navigation units (INUs) using three-axis accelerometers, rate sensors, and magnetometers can provide self-contained position estimates for individual entities, but the cumulative drift error associated with all but the largest, most costly, high-performance INUs causes position estimates to exceed useful bounds after even a short time or distance traveled.

Localization based on any number of inter-node distance-measuring techniques can employ static reference beacons and range measurements between mobile nodes. However, the operational flexibility of these solutions is typically limited by infrastructure deployment requirements or by constraints on the number and geometry of participating nodes. Distributed fu sion of multiple independent sensors using the algorithms we present can exploit the complementary nature of each sensor’s behavioral characteristics and errors for overall improvements in system accuracy and operational performance without sacrificing operational flexibility.

We propose a novel approach for estimating both absolute and relative positions for members in a mobile sensor network by continuously fusing pair-wise inter-node range measurements and the position displacement measurements of individual nodes. The range between two members is measured by time-of-arrival (TOA)-based radio frequency (RF) ranging sensors. Position displacement is determined with micro-electromechanical system (MEMS)-based INUs.

We developed centralized and distributed online estimation approaches employing optimization methods and extended Kalman Filter (EKF) frameworks and compared them with an eye toward the implementation of a high-performance, real-time navigation system. Simulations for mobile network mission scenarios four hours in duration with up to 32 nodes show that these methods can successfully localize both the absolute and relative positions of the collaborating nodes to a substantially higher degree of accuracy than can be achieved for non-collaborating nodes.

Our work addresses a class of problems in which initial positions are known. The proposed approaches virtually eliminate ambiguous solutions by continuously fusing current INU measurements and previous fused location estimations as the network topology evolves.

The main underlying assumption of the EKF approach is that the node state can be modeled as a multi-dimensional Gaussian random variable. This assumption is justified by the fact that an INU measurement gives highly peaked unimodal distribution. The final distribution of the state, after considering the ranging constraints, exhibits a dominant mode (the correct solution) close to the INU peak.

Since the range measurement is not a linear function of the locations, we adapt the standard Kalman Filter approach with a distributed iterative EKF formulation that provides excellent accuracy and convergence. In addition, because the INU measures the location offset, which directly corresponds to the velocity, the filter will have very little lag. Furthermore, we make few assumptions on node motion and use a simple constant velocity model for prediction, enabling a flexible implementation that accepts asynchronous sensor inputs.

We propose a novel integration of two practical sensors to estimate both absolute and relative positions of mobile nodes in a manner that greatly improves the performance and operational characteristics of the individual sensors. Specifically, the INUs help the range-based localization to avoid geometric ambiguities that lead to computational difficulties; the range sensors reduce the drift rate of the individual INUs by a factor of =n by providing mutual constraints on possible position estimates of n collaborating nodes. The benefits of collaborative error reduction can be realized without use of anchor reference nodes and with as few as two nodes.

As a benefit of this integration, we can propose a simple but efficient localization algorithm that uses fully distributed processing and nearest-neighbor communications. It is easily extendable to incorporate additional sensor modalities, such as GPS, pressure altimeters, redundant heterogeneous sensors, and so on.

Performance improvements due to collaborative navigation can be described in terms of three error-reduction effects. Simulations show a Teamwork Effect drift-rate reduction that is robust to variations in both INU noise models and inter-node ranging error. We illustrate improvements due to an Anchor Effect using as few as one or two reference nodes deployed in a flexible, mission-dependent manner. The algorithm’s Reset Effect provides immediate, rather than gradual, improvement of the system accuracy as mission conditions change dynamically.

Compared to other sensor-network projects, our algorithms do not require use of anchor nodes, and structural ambiguities are avoided by observations from INUs and previous fused location estimates. Compared to work in robotics and sensor-fusion, our work exploits the collaborative effect of networking in the form of drift reduction of individual nodes enabled by the range constraints. Importantly, the benefits of collaborative navigation can be realized with as few as two nodes.

Performance Predictions

We can make general analytical predictions regarding the error reduction effects expected when multiple nodes collaborate to determine their locations. The following analysis only requires the existence of sufficiently accurate inter-node ranging capabilities and applies more generally beyond the specific multi-sensor fusion frameworks presented.

In Figure 1, r_A and r_B are vectors representing the INU-derived estimates of the locations of nodes A and B, respectively. r_AB is the more accurate RF ranging estimate of the location of node B relative to node A. The location of node A can be estimated by the average of r_A (its own INU) and r_A - r_AB (INU of node B and the location of B relative to A). If r_A and r_B have independent errors of common size σ_INU , and the error of r_AB is negligible compared to it, then this average is statistically optimal and has the reduced error of σ_INU/√2. The location error of B can be reduced similarly.

FIGURE 1. Averaging independent INU drift errors from multiple nodes using accurate relative ranging measurements reduces the error of the final position estimates.

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