GPS-Limited Cooperative Positioning Using Scalable Approximate Decentralized Data Fusion
Steven Dourmashkin, Smead Aerospace Engineering Sciences, University of Colorado Boulder; William Whitacre, Draper; Dennis Akos, Nisar Ahmed, Smead Aerospace Engineering Sciences, University of Colorado Boulder
Decentralized target tracking and localization are very important in many autonomous vehicle system applications, such as autonomous UAV surveillance, spacecraft formation flying, and disaster relief search and rescue. Some of the main advantages of decentralized estimation are (1) information sharing is opportunistic, yielding more informed results than local estimation alone; (2) decentralization enables scalability as vehicles do not have to share all raw measurements back to a centralized server; and (3) vehicles can join the network in an ad-hoc fashion. In turn, there has been a big push for decentralized estimation in systems operating within uncertain environments, in which some vehicles may experience obstructed and/or limited measurements (e.g., denied GPS or limited bandwidth); vehicles can share information among each other to obtain a shared, more accurate solution.
In this paper, we consider the application of two or more vehicles performing cooperative localization using a navigation filter, which estimates the vehicle’s position, IMU error states, and other dynamically-relevant states by running IMU and GPS measurements through a Kalman Filter. By combining these “ownship” estimates with range measurements of each other (e.g., through radio ranging or image processing), vehicles can estimate the location of others in a global coordinate frame. These estimates can then be shared and fused with other vehicles’ local ownship estimates via decentralized cooperative localization such that they can recover from, for example, obstructed GPS measurements, which would otherwise cause vehicles to rely on diverging IMU dead-reckoning estimates. To implement decentralized cooperative localization consistently, however, vehicles must account for the inherent coupling between ownship and target estimates as well as that resulting from fusing other vehicles’ estimates of a common process. This task is nontrivial when vehicles do not share their control inputs and measurements (e.g. their IMU measurements), and when the vehicles do not possess common models of the full set of unknown variables (e.g. other vehicles’ rate gyro biases, or the same tracking dynamics models for common targets or other vehicles).
To fuse state estimates in a decentralized, ad-hoc, scalable fashion, we can implement Decentralized Data Fusion (DDF), a process through which vehicles estimate states of a common process and share those estimates directly with other vehicles in the network rather than the raw sensor measurements used to generate those local estimates. As vehicles fuse and propagate state information throughout the network, localization accuracy at each vehicle becomes consistent with a locally centralized processing approach, without the associated communication bottlenecks or required knowledge of the entire network topology. As such, DDF enables scalability and robustness to changes in network communication topology. To fuse state estimates consistently, however, we must deal with the inherent coupling between ownship and target states. Two common methods for doing so are channel filtering and covariance intersection. We must also handle vehicles having different overlapping definitions of state vectors - that is, the first states are ownship states while the rest are target states, which map differently between vehicles.
This paper provides approximate solutions for dealing with such complex couplings in fused state estimates to prevent overconfidence and in turn diverging errors. Specifically, we describe and provide numerical simulation results for two new methods for performing DDF that use novel loosely integrated IMU-GPS navigation and decentralized kinematic localization filters to exploit information sharing and partial data fusion algorithms for cooperative positioning: the Approximate Channel Filter (ACF) and Factorized Covariance Intersection (FCI). The key idea behind FCI is to significantly reduce the conservativeness associated with approximate DDF techniques (like covariance intersection) for performing state estimate fusion under unknown correlations. The key idea behind ACF is to reduce this conservativeness even further by explicitly constructing and dynamically tracking “sufficiently accurate” approximations to dependent information between vehicle state estimators with respect to a common subset of states (i.e. where sufficiently accurate implies that the common information between estimators for the common subset of states can be well-approximated, even if the local process models at each vehicle use distinct joint target-ownship dynamics).
We demonstrate the approach in simulated cooperative navigation problems for distributed operations with aerial and ground vehicles operating in GPS-limited environments. Our results (which also include evaluations on navigation data from real hardware) show that our decentralized approach is computationally efficient, and provides nearly the same localization performance (in terms of RMSE and estimation error uncertainty) as an ideal centralized localization filter and requires substantially lower communication bandwidth and data rates. The FCI and ACF algorithms also show far less conservativism than traditional covariance intersection algorithms for DDF under unknown correlations, but require significantly lower computationally expense. We also discuss open problems and promising research directions for coping with challenges associated with partial data fusion and event-triggered estimation, including sensitivities to explicit measurement dropouts with unreliable communications, communication latencies, data association, kinematic tracking model selection, and scalability for large networks.