Unscented Transformation based array interpolation

It is impossible to enforce exact responses for each sensor involved in an antenna array. Important signal processing techniques such as Estimation of Signal Parameters via Rotational Invariance (ESPRIT), Forward Backward Average (FBA) and Spatial Smoothing (SPS) rely on sensor arrays with Vandermonde or centro-hermitian responses. To achieve such responses array interpolation is often necessary. In this work a novel way of performing array interpolation while minimizing the transformation error using the Unscented Transformation (UT) is presented. The UT provides a different method for mapping interpolated regions and also exhibits a new insight into array interpolation and its current limitations. A set of numerical simulations presents promising results for array interpolation employing the UT.

[1]  M. S. Babtlett.  Smoothing Periodograms from Time-Series with Continuous Spectra , 1948, Nature.

[2]  R. O. Schmidt,et al.  Multiple emitter location and signal Parameter estimation , 1986 .

[3]  Buon Kiong Lau,et al.  An improved array interpolation approach to DOA estimation in correlated signal environments , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[4]  Josef A. Nossek,et al.  A signal adaptive array interpolation approach with reduced transformation bias for DOA estimation of highly correlated signals , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[5]  L.R.A.X. de Menezes,et al.  A New Procedure for Assessing the Sensitivity of Antennas Using the Unscented Transform , 2010, IEEE Transactions on Antennas and Propagation.

[6]  C. Christopoulos,et al.  The use of Unscented Transforms for statistical analysis in EMC , 2008, 2008 International Symposium on Electromagnetic Compatibility - EMC Europe.

[7]  Buon Kiong Lau,et al.  Data-adaptive array interpolation for DOA estimation in correlated signal environments , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[8]  Marius Pesavento,et al.  Virtual array design for array interpolation using differential geometry , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[9]  Jeffrey K. Uhlmann,et al.  New extension of the Kalman filter to nonlinear systems , 1997, Defense, Security, and Sensing.

[10]  Björn E. Ottersten,et al.  Analysis of subspace fitting and ML techniques for parameter estimation from sensor array data , 1992, IEEE Trans. Signal Process..

[11]  Geovany A. Borges,et al.  Modeling device manufacturing uncertainty in Electromagnetic Simulations , 2008, 2008 IEEE MTT-S International Microwave Symposium Digest.

[12]  Benjamin Friedlander,et al.  The root-MUSIC algorithm for direction finding with interpolated arrays , 1993, Signal Process..

[13]  Arthur Jay Barabell,et al.  Improving the resolution performance of eigenstructure-based direction-finding algorithms , 1983, ICASSP.

[14]  M. Haardt,et al.  Enhanced Model Order Estimation using Higher-Order Arrays , 2007, 2007 Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers.

[15]  P. Stoica,et al.  Novel eigenanalysis method for direction estimation , 1990 .

[16]  T. P. Bronez.  Sector interpolation of non-uniform arrays for efficient high resolution bearing estimation , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[17]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[18]  Thomas Kailath,et al.  ESPIRT-estimation of signal parameters via rotational invariance techniques , 1989 .

[19]  Michael I. Miller,et al.  Maximum-likelihood narrow-band direction finding and the EM algorithm , 1990, IEEE Trans. Acoust. Speech Signal Process..

[20]  Z. Luo,et al.  Robust array interpolation using second-order cone programming , 2002, IEEE Signal Processing Letters.

[21]  Thomas Kailath,et al.  Detection of signals by information theoretic criteria , 1985, IEEE Trans. Acoust. Speech Signal Process..

[22]  A. Weiss,et al.  The interpolated ESPRIT algorithm for direction finding , 1991, 17th Convention of Electrical and Electronics Engineers in Israel.

[23]  Florian Roemer,et al.  Multi-dimensional model order selection , 2011, EURASIP J. Adv. Signal Process..

[24]  Alfred O. Hero,et al.  Space-alternating generalized expectation-maximization algorithm , 1994, IEEE Trans. Signal Process..

[25]  André Lima Férrer de Almeida,et al.  Multidimensional Array Interpolation Applied to Direction of Arrival Estimation , 2015, WSA.

[26]  Marius Pesavento,et al.  A new approach to array interpolation by generation of artificial shift invariances: interpolated ESPRIT , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[27]  B. Friedlander,et al.  Direction finding using spatial smoothing with interpolated arrays , 1992 .

[28]  T. Moon.  The expectation-maximization algorithm , 1996, IEEE Signal Process. Mag..

[29]  Geovany Araujo Borges,et al.  Efficient computation of stochastic electromagnetic problems using unscented transforms , 2008 .

[30]  André Quinquis,et al.  A New Method for Estimating the Number of Harmonic Components in Noise with Application in High Resolution Radar , 2004, EURASIP J. Adv. Signal Process..

[31]  Bjorn Ottersten,et al.  Exact and Large Sample ML Techniques for Parameter Estimation and Detection in Array Processing , 1993 .

[32]  James E. Evans,et al.  Application of Advanced Signal Processing Techniques to Angle of Arrival Estimation in ATC Navigation and Surveillance Systems , 1982 .

[33]  Yoram Bresler,et al.  Exact maximum likelihood parameter estimation of superimposed exponential signals in noise , 1986, IEEE Trans. Acoust. Speech Signal Process..

[34]  Josef A. Nossek,et al.  The Extended Invariance Principle for Signal Parameter Estimation in an Unknown Spatial Field , 2011, IEEE Transactions on Signal Processing.

[35]  S. Unnikrishna Pillai,et al.  Forward/backward spatial smoothing techniques for coherent signal identification , 1989, IEEE Trans. Acoust. Speech Signal Process..