Cooperative positioning for low-cost close formation flight based on relative estimation and belief propagation

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Abstract

Cooperative Positioning (CP) is considered to be a promising method for close formation flight, which can fully exploit the navigation information in a network. This work proposes a new CP framework based on relative position estimation and optimized belief propagation (BP), aiming to enhance the absolute positioning accuracy for low-cost UAVs. Relative estimation is used to augment the BP estimation, which can fully exploit the onboard sensors. For BP, it is widely used as a CP estimator. This work proposes an optimized BP based on vectorized message passing and message evaluation, which can make an effective balance between computational load and estimation accuracy. Simulation results show that the proposed CP framework has better estimation accuracy than traditional CP methods, and has lower computational load than the best existing non-parametric BP (NBP) method with equivalent accuracy.

Introduction

Positioning is a fundamental issue in task execution of unmanned aerial vehicle (UAV) [1]. In a close formation flight system, UAV needs accurate and real-time positioning information to conduct collision avoidance, task scheduling and precise control [2]. However, many low-cost or consumer-level UAVs are using an integrated system based on a global navigation satellite system (GNSS) and inertial navigation systems (INS), and their positioning accuracy is not accurate enough for a close formation flight system. To improve the positioning performance of UAVs, one effective way is to enhance the positioning accuracy with a base station, such as the Real Time Kinematic (RTK) system [3], [4]. But this method needs at least one nearby stationary base station that can continuously communicate with all UAVs. Another approach is equipping each UAV with external navigation sensors, such as Lidar, camera, millimeter-wave radar, etc. However, due to limitation of the payload Size, Weight and Power (SWaP) and cost, high-grade sensor configurations may not be suitable for all UAVs in a massive multi-UAV system, especially for low-cost followers with limited payload [5], [6], [7]. Consequently, several leader UAVs equipped with high accuracy navigation sensors can provide good spatial reference information for follower UAVs in a massive formation flight scenario [8], [9], [10].

To improve the overall positioning performance of a multi-UAV system, some researchers have focused on cooperative positioning (CP) algorithms. Compared to traditional sensor fusion methods that only rely on the sensors from a standalone UAV, CP methods can fully exploit the geometrical relationship among all nodes and the observation data from all onboard sensors in a cooperative network, which further improves positioning accuracy [14], [15], [16]. Some researchers focused on non-Bayesian CP methods [11], [12], [13], transforming the CP problem to a least square (LS) problem, which can be iteratively solved by Gauss-Newton or steepest descent methods. However, CP estimation is not always a convex problem, which means it is hard to obtain the global optimum solution for all UAVs. Therefore, these LS-based CP problems need to be relaxed to a cone programing problem [17] or a semi-definite programming problem to get more robust solutions.

The main drawback of non-Bayesian CP methods is the error accumulation caused by deterministic estimation of states; this problem can be solved by the Bayesian CP method. The research in [18] presented a sum-product algorithm for wireless network (SPAWN) based on net-factor graph and net-message passing schedule. The belief propagation (BP) method was applied to estimate the posterior marginal probability density function (PDF) of the agent's position. Simulation results showed that the cooperative scheme largely improves the absolute positioning ability of every single node. However, this method is more suitable for indoor application, the GNSS data is not considered in this algorithm. Research in [19] propose a hybrid SPAWN (H-SPAWN) method which combines the ranging information from neighbor nodes and the GNSS pseudoranges, extend the application of SPAWN to more complex scenarios. Both SPAWN and H-SPAWN are using nonparametric belief propagation (NBP) method to realize CP in wireless sensor networks [20], [21]. The main problem for the NBP is high computational load and heavy communication burden. These methods usually use particle proximation to describe distributions and messages [22], which are usually based on the Monte Carlo integration with importance sampling. BP-based methods are difficult to ensure the real-time performance if there are large numbers of nodes in a cooperative system. To decrease the computational load, the universal cooperative localizer (UCL) [23] was proposed to simplify the sampling process to a generalized linear mixing problem. However, UCL suffers from performance loss caused by the linearization error and the central limit theorem, which has lower estimation accuracy than traditional NBP methods.

Therefore, in this work we propose a CP framework combines the relative position estimation and optimized belief propagation (BP), fusing Ultra-wideband (UWB), GPS and INS information to get robust and precise relative position states, then using optimized BP to enhance the positioning accuracy of low-cost followers, finally improving the navigation performance of whole multi-UAV system. Our main contributions are as follows: (1) Taking advantage of the proposed framework, BP can be conducted via a vectorized message passing process, which converts a multi-dimensional belief propagation problem into a single dimensional one to reduce computation burden. (2) A message evaluation criterion is proposed to screen out the high contribution of the cooperative correction message (CCM), which gives a good tradeoff between computational load and estimation accuracy. (3) Augmentation of double-differenced GNSS pseudorange into a hybrid cooperative framework (such as H-SPAWN).

Also, proposed CP has low dependence on the number of high accurate anchor nodes (the Leader UAVs equipped with expensive high-performance navigation equipment), which decreases the cost of whole system.

Section snippets

Sensor configuration

In this work, the leader UAV carries Real-time kinematic (RTK) module and high accuracy Inertial navigation system (INS) equipment to provide precise absolute navigation estimation, the follower carries low-cost GPS and INS equipment for improved SWaP and cost, albeit sacrificing navigation accuracy. All UAVs carry an ultra-wideband (UWB) transceiver to provide inter-UAV ranging measurements. To realize the cooperative mechanism, all the UAV can communicate their inter-UAV ranging data and

Relative position estimation for inter-node states

The goal of relative position estimation is to achieve accurate and robust real-time inter-node states among all UAVs. To make full use of onboard sensors, this step fuses the double differenced pseudoranges, difference of two UAVs' absolute positioning results and UWB ranging measurements based on an extended Kalman Filter (EKF).

Belief propagation for formation flight

The cooperative localization algorithm based on BP is essentially a message passing method to calculate the posterior marginal probability density function (PDF) of estimated states. This part augments the results of independent Kalman filter estimates to ultimately provide BP-based results that is fed back to the Kalman filter.

Simulation description

Based on the background of close formation flight, a multi-UAV system consists of 1 leader and 30 followers is simulated to verify the proposed CP method (Fig. 8). Assuming that all the UAV can communicate with peers if they are within the working distance of UWB transceiver, which is set as 60 m.

The sensor configuration and the parameters used in the simulation are listed in Table 1. Leader UAV carries the RTK and high-accuracy INS, whereas follower UAV are equipped with low-cost GPS receiver

Conclusions

Based on the background of close formation flight, this paper proposes a cooperative positioning (CP) framework based on relative position estimation and optimized belief propagation (BP). Using the results from relative position estimate, the message passing process for traditional BP can be transformed to a vectorized case. A cooperative correction message (CCM) evaluation method is also proposed to screen out the high contribution message during the message passing process, which largely

Declaration of Competing Interest

No conflict of interest exits in this manuscript, and manuscript is approved by all authors for publication. The described work was original research that has not been published previously.

Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 61673208, 61703208, 61873125), advanced research project of the equipment development (30102080101), The Natural Science Fund of Jiangsu Province (Grant No. BK20181291), the Fundamental Research Funds for the Central Universities (Grant Nos. NP2018108, NZ2018002), Science and Technology on Avionics Integration Laboratory.

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