The intra-pulse phase change caused by frequency difference of arrival (FDOA) is very little and even omitted due to extremely short duration of emitter pulses that the joint location using time difference of arrival (TDOA) and FDOA cannot be realised. To solve this problem, a multi-pulse coherent accumulation algorithm of direct position determination (DPD) using the TDOA and FDOA is proposed in this study. Through establishing coherent signal model of short pulses which is deterministic but unknown, the maximum likelihood estimator for localisation of a stationary emitter using multiple moving receivers is derived by taking the DPD approach under additive Gaussian white noise environment. This study also derives a signal-specific Cramer–Rao lower bound (CRLB) of DPD, modelling the signal as a deterministic unknown. The CRLB is more applicable to some specific (non-stationary, non-Gaussian) signals, especially electromagnetic signals. Simulation results show that the proposed method achieves a significant performance improvement in locating accuracy over the existing methods and its accuracy is close to the CRLB in normal signal-to-noise ratio.

References

1. 1)
  - 1. Yalu, C., Li, P., Jinzhou, L., et al: ‘A new iterative algorithm for geolocating a known altitude target using TDOA and FDOA measurements in the presence of satellite location uncertainty’, Chin. J. Aeronaut., 2015, 28, (5), pp. 1510–1528.
2. 2)
  - 19. Pourhomayoun, M., Flower, M.L.: ‘Spatial sparsity based emitter localization’. The 46th Annual Conf. Information Sciences and Systems (CISS), Princeton, NJ, 2012, pp. 1–4.
3. 3)
  - 17. Cevher, V., Duarte, M.F., Baraniuk, R.G.: ‘Distributed target localization via spatial sparsity’. Sixteenth European Signal Processing Conf., Switzerland, 2008, pp. 25–29.
4. 4)
  - 20. Weiss, A.J.: ‘Direct geolocation of wideband emitters based on delay and Doppler’, IEEE Trans. Signal Process., 2011, 59, (6), pp. 2513–2521.
5. 5)
  - 2. Kim, Y.H., Kim, D.G., Kim, H.N.: ‘Two-step estimator for moving emitter geolocation using time difference of arrival/frequency difference of arrival measurements’, IET Radar Sonar Navig., 2015, 9, (7), pp. 881–887.
6. 6)
  - 15. Wax, M., Kailath, T.: ‘Decentralized processing in sensor arrays’, IEEE Trans. Acoust., Speech, Signal Process, 1985, 33, pp. 1123–1129.
7. 7)
  - 11. Yeredor, A.: ‘Eyal Angel. Joint TDOA and FDOA estimation: a conditional bound and its use for optimally weighted localization’, IEEE Trans. Signal Process., 2011, 59, (4), pp. 1612–1623.
8. 8)
  - 7. Ulman, R.: ‘Wideband TDOA-FDOA processing using summation of short-time CAF's’, IEEE Trans. Signal Process., 1999, 47, (12), pp. 3193–3200.
9. 9)
  - 18. Ke, W., Wang, T.T., Wu, L.N.: ‘Multi-target direct localization via approximate l0 norm minimization’, Electron. Lett., 2012, 48, (23), pp. 1498–1500.
10. 10)
  - 21. Vankayalapati, N., Kay, S., Ding, Q.: ‘TDOA based direct positioning maximum likelihood estimator and Cramer–Rao bound’, IEEE Trans. Aerosp. Electron. Syst., 2014, 50, (3), pp. 1616–1635.
11. 11)
  - 10. Ho, K.C., Xu, W.: ‘An accurate algebraic solution for moving source location using TDOA and FDOA measurements’, IEEE Trans. Signal Process., 2004, 52, (9), pp. 2453–2463.
12. 12)
  - 4. Yu, H., Huang, G., Gao, J., et al: ‘Approximate maximum likelihood algorithm for moving source localization using TDOA and FDOA measurements’, Chin. J. Aeronaut., 2012, 25, (4), pp. 593–597.
13. 13)
  - 16. Ivan, P.P., Vucic, D., Okiljevic, P.: ‘Direct position determination of wideband signals: coherent and noncoherent approach’. The 11th Int. Conf. Telecommunication in Modern Satellite, Cable and Broadcasting Services (TESIKS), Nis, October 2013, pp. 77–80.
14. 14)
  - 5. Stein, S.: ‘Algorithms for ambiguity function processing’, IEEE Trans. Acoust. Speech Signal Process., 1981, 29, (2), pp. 588–599.
15. 15)
  - 8. Quazi, A.H.: ‘An overview on the time delay estimate in active and passive systems for target localization’, IEEE Trans. Acoust. Speech Signal Process., 1981, 4, (ASSP-29), pp. 527–533.
16. 16)
  - 22. Kay, S.M.: ‘Fundamentals of statistical signal processing: estimation theory’ (Prentice-Hall, Upper Saddle River, NJ, 1993).
17. 17)
  - 6. Stein, S.: ‘Differential delay/Doppler ML estimation with unknown signals’, IEEE Trans. Signal Process., 1993, 41, pp. 2717–2719.
18. 18)
  - 9. Jinzhou, L., Fucheng, G., wenli, J.: ‘Source localization and calibration using TDOA and FDOA measurements in the presence of sensor location uncertainty’, Sci. China Inf. Sci., 2014, 57, pp. 1–12.
19. 19)
  - 12. Weiss, A., Amar, A.: ‘Direct geolocation of stationary wideband radio signal based on time delays and Doppler shifts’. IEEE/SP 15th Workshop Statistical Signal Processing (SSP ‘09), August 2009, pp. 101–104.
20. 20)
  - 3. Zhou, K., Roumeliotis, S.I.: ‘Multirobot active target tracking with combinations of relative observations’, IEEE Trans. Robot., 2011, 27, (4), pp. 678–695.
21. 21)
  - 13. Amar, A., Weiss, A.J.: ‘Advances in direct position determination’. Sensor Array and Multichannel Signal Processing Workshop Proceedings, 2004, pp. 584–588.
22. 22)
  - 14. Weiss, A.J.: ‘Direct position determination of narrowband radio frequency transmitters’, IEEE Signal Process. Lett., 2004, 11, (5), pp. 513–516.

Direct positioning maximum likelihood estimator using TDOA and FDOA for coherent short-pulse radar

References

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