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Joint Ranging and Phase Offset Estimation for Multiple Drones using ADS-B Signatures

Mostafa Mohammadkarimi, Geert Leus, Raj Thilak Rajan

TL;DR

It is shown that the proposed estimator can jointly estimate the range of multiple drones/aircrafts accurately and a larger number of drones/aircrafts can be supported with higher accuracy by the use of multiple antennas at the receiver.

Abstract

A new method for joint ranging and Phase Offset (PO) estimation of multiple drones/aircrafts is proposed in this paper. The proposed method employs the superimposed uncoordinated Automatic Dependent Surveillance Broadcast (ADS-B) packets broadcasted by drones/aircrafts for joint range and PO estimation. It jointly estimates range and PO prior to ADS-B packet decoding; thus, it can improve air safety when packet decoding is infeasible due to packet collision. Moreover, it enables coherent detection of ADS-B packets, which can result in more reliable multiple target tracking in aviation systems using cooperative sensors for detect and avoid (DAA). By minimizing the Kullback Leibler Divergence (KLD) statistical distance measure, we show that the received complex baseband signal coming from K uncoordinated drones corrupted by Additive White Gaussian Noise (AWGN) at a single antenna receiver can be approximated by an independent and identically distributed Gaussian Mixture (GM) with 2 power K mixture components in the two dimensional (2D) plane. While direct joint Maximum Likelihood Estimation (MLE) of range and PO from the derived GM Probability Density Function (PDF) leads to an intractable maximization, our proposed method employs the Expectation Maximization (EM) algorithm to estimate the modes of the 2D Gaussian mixture followed by a reordering estimation technique through combinatorial optimization to estimate range and PO. An extension to a multiple antenna receiver is also investigated in this paper. While the proposed estimator can estimate the range of multiple drones with a single receive antenna, a larger number of drones can be supported with higher accuracy by the use of multiple antennas at the receiver. The effectiveness of the proposed estimator is supported by simulation results. We show that the proposed estimator can jointly estimate the range of three drones accurately.

Joint Ranging and Phase Offset Estimation for Multiple Drones using ADS-B Signatures

TL;DR

It is shown that the proposed estimator can jointly estimate the range of multiple drones/aircrafts accurately and a larger number of drones/aircrafts can be supported with higher accuracy by the use of multiple antennas at the receiver.

Abstract

A new method for joint ranging and Phase Offset (PO) estimation of multiple drones/aircrafts is proposed in this paper. The proposed method employs the superimposed uncoordinated Automatic Dependent Surveillance Broadcast (ADS-B) packets broadcasted by drones/aircrafts for joint range and PO estimation. It jointly estimates range and PO prior to ADS-B packet decoding; thus, it can improve air safety when packet decoding is infeasible due to packet collision. Moreover, it enables coherent detection of ADS-B packets, which can result in more reliable multiple target tracking in aviation systems using cooperative sensors for detect and avoid (DAA). By minimizing the Kullback Leibler Divergence (KLD) statistical distance measure, we show that the received complex baseband signal coming from K uncoordinated drones corrupted by Additive White Gaussian Noise (AWGN) at a single antenna receiver can be approximated by an independent and identically distributed Gaussian Mixture (GM) with 2 power K mixture components in the two dimensional (2D) plane. While direct joint Maximum Likelihood Estimation (MLE) of range and PO from the derived GM Probability Density Function (PDF) leads to an intractable maximization, our proposed method employs the Expectation Maximization (EM) algorithm to estimate the modes of the 2D Gaussian mixture followed by a reordering estimation technique through combinatorial optimization to estimate range and PO. An extension to a multiple antenna receiver is also investigated in this paper. While the proposed estimator can estimate the range of multiple drones with a single receive antenna, a larger number of drones can be supported with higher accuracy by the use of multiple antennas at the receiver. The effectiveness of the proposed estimator is supported by simulation results. We show that the proposed estimator can jointly estimate the range of three drones accurately.
Paper Structure (19 sections, 1 theorem, 73 equations, 10 figures, 1 table, 1 algorithm)

This paper contains 19 sections, 1 theorem, 73 equations, 10 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Contributions
  4. Notations
  5. System Model
  6. Distribution Approximation
  7. Joint Range and po Estimation
  8. Reordering Estimation
  9. Joint Range and po Estimation
  10. Multiple Antennas Receiver
  11. Maximum Likelihood and em Estimators
  12. Outlier Detection
  13. Computational Complexity Analysis
  14. Simulation
  15. Simulation Setup
  16. ...and 4 more sections

Key Result

Theorem 1

By maximizing the KLD criterion, the elements of the ADS-B packet of the $k$th drone, i.e., ${\bf x}_{k} =[ {x}_{k,0} \ {x}_{k,1} \ \ldots \ {x}_{k,N}]^T= {[} {\bf{0}}_{m_k}^T \ {\bf s}^T \ {\bf d}_k^T \ {\bf{0}}_{M-{m_k}}^T {]}^T$ can be approximated by an iid random variable that are Bernoulli dis where

Figures (10)

  • Figure 1: Range estimation using the asynchronous ADS-B In signatures of the drones at the receiver.
  • Figure 2: An ADS-B packet is composed of a preamble and data in the ppm form.
  • Figure 3: The reception of the ADS-B packets at the receiver. Drones periodically broadcast ADS-B packets. Different colors are used to show the packet of drones.
  • Figure 4: Amplitude of the noisy ADS-B packet after sampling.
  • Figure 5: The in-phase and quadrature components of the received signal for $K=3$ drones at $r_1=r_2=r_3=12$ Km with transmit power of $51$ dBm.
  • ...and 5 more figures

Theorems & Definitions (3)

  • Theorem 1
  • proof
  • proof