Decentralized Cooperative Navigation for GPS-Denied Conditions
Cory Schutz, Noam Eshed, and Joel Douglas, Systems & Technology Research
Alternate Number 1
Maintaining accurate navigation in GPS-denied conditions is critical for the U.S. military, particularly as it applies to swarms of unmanned aerial platforms including weapon systems and swarm navigation underground, underwater, or in buildings. The longer that assets must rely on Inertial Measurement Units (IMUs) alone, the larger their state uncertainties become. Making inter-platform measurements and sharing state estimates between multiple cooperating platforms in a swarm has the potential to significantly enhance navigation accuracy, mitigating the loss of GPS. Cooperative navigation must be done in a decentralized framework as high frequency IMU measurements cannot be shared over low-bandwidth communication links, and a centralized approach creates a single point of failure that puts the entire swarm at risk. The decentralized navigation framework introduces a new set of challenges that include correlation of the state estimates of a single platform shared with other platforms and double counting information caused by loops in the communication network. If these challenges are not addressed, the decentralized system generates statistically inconsistent estimates resulting in overly confident platform estimates that are not as accurate as they appear. Therefore, the issue of statistical consistency is critical when developing a decentralized cooperative navigation framework.
We present a novel approach to cooperative navigation using a decentralized pose graph that allows us to rigorously combine all measurements, while using measurement pedigree data to ensure we are not double-counting information. Our decentralized navigation approach uses a set of factor graph estimators on each platform to infer the state variables within a SLAM-based framework. In addition to the range and/or bearing in a standard measurement, cooperative platforms need to share their current state estimate and full state uncertainty. We use a novel Correlation Factor to address overconfidence caused by correlated measurements from a single platform. Instead of treating these measurements as independent, the Correlation Factor connects these measurements in the factor graph to accurately model the measurement correlation. To address loops in the communication network we maintain a tree structure called a Relation Graph that only allows information to flow up the tree, preventing any possibility of double counting information. Given a connected communications graph, which is based on communication range limitations between the platforms in the swarm, we generate a Relation Graph on each platform. For a given platform, the Relation Graph defines (1) which platforms to accept or reject measurements from and (2) the set of estimators to maintain to provide statistically consistent state estimates and uncertainties to be shared with other platforms. When the formation of the swarm changes, causing platforms to come in and out of range of one another, or platforms are lost due to attrition, the Relation Graphs are updated to account for the new communication structure.
The key performance metrics of the system are the accuracy of the platform navigation estimates as compared to the case when no cooperative measurements are available and the statistical consistency of the solution. Navigation performance is dependent upon a range of factors including swarm size, swarm formation, platform trajectories, measurement type and frequency, and sensor quality. We present a five-platform scenario that results in a 50% improvement in navigation accuracy after 60 seconds as compared to dead reckoning using a tactical grade Honeywell HG1700 IMU. For the statistical consistency metric, we run the scenario in a Monte Carlo simulation and compare the sample variance of each state variable to that of the analytic variance computed by the factor graph to demonstrate statistically consistent performance.
This material is based upon work supported by the United States Air Force under Contract No. FA8651-19-C-0046.