1. Spatial Signal Processing with Emphasis on Emitter Localization
Anthony J. Weiss
28 July 2019
Spatial Signal Processing

2. Spatial Signal Processing
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.
28 July 2019
Spatial Signal Processing

3. Spatial Signal Processing
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
28 July 2019
Spatial Signal Processing

4. Spatial Signal Processing
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
28 July 2019
Spatial Signal Processing

5. Spatial Signal Processing
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
28 July 2019
Spatial Signal Processing

6. Spatial Signal Processing
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
28 July 2019
Spatial Signal Processing