Spatial Signal Processing with Emphasis on Emitter Localization

Spatial Signal Processing with Emphasis on Emitter Localization Anthony J. Weiss 27 October 2020 Spatial Signal Processing 1

What to expect? • The course covers the important theory developments associated with Emitter Location from 1939. • We will try to obtain detailed understanding of the results • We will not discuss in detail “existing systems” • After the course you should be able to: – Recommend a localization technique – Evaluate a theoretical Lower bound on performance – Estimate the localization performance as a function of sensors-source geometry, SNR, observation time, signal parameters (bandwidth, center frequency), model errors, localization technique, etc. 27 October 2020 Spatial Signal Processing 2

Contents • • • Introduction Understanding Geographic Coordinates Complex representation of RF Signals Complex Random variables and vectors - probability density function and the complex gradient operator Lower Bounds on Parameter Estimation Errors Statistical Theory of Passive Location Systems (CEP, GDOP, uncertainty ellipse) DOA Estimation of Single Signal – MLE – Deterministic Unknown Signal – MLE – Known Signal – MLE – Gaussian Signal – CRLB - Deterministic Unknown Signal – CRLB – Known Signal – CRLB – Gaussian Signal Beam-forming Capon’s Beam-former Null Steering Diversely Polarized Signals and Antennas 27 October 2020 Spatial Signal Processing 3

Contents • • DOA Estimation Multiple Signals – MLE – Deterministic Unknown Signals – MLE – Known Signals – MLE – Gaussian Signals – CRLB - Deterministic Unknown Signals – CRLB – Known Signals – CRLB – Gaussian Signals – MUSIC Algorithm – Beam space MUSIC – Root MUSIC – IQML – ESPRIT – Weighted Subspace Fitting – EM Algorithm – Alternating Projection – MODE (optional) – Mono-pulse (optional) Detection of Signal Subspace Dimension 27 October 2020 Spatial Signal Processing 4

Contents • • • DOA Based Localization – MLE and CRLB – Stansfield’s Algorithm – DOA GDOP – DOA CEP TOA/DTOA Measurements – Methods (generalized CC, Leading Edge) – Lower bounds (CRLB, Modified Ziv-Zakai) Localization based on TDOA/TOA – Maximum Likelihood – DPD – Closed form solutions Received Signal Strength Measurements Localization based on RSS DDOP Measurements DDOP Localization DDOP+DTOA Localization DPD (Direct Position Determination) Outliers 27 October 2020 Spatial Signal Processing 5

Contents • • • Calibration of time, location, gain, phase array orientation Model Errors Localization of nodes in Sensors network Single Site Location Robust Estimator (M estimator, L estimators, p-norm) Employment of sparsity for outliers removal 27 October 2020 Spatial Signal Processing 6