# Applications of Optimal Subspace Estimation

#### Abstract

Optimal Subspace Estimation (OSE) is a technique for estimating the signal subspace of a noisy data matrix or covariance matrix using a specific structure known as shift-invariance to generate an accurate estimate. For the applications in this thesis, the datasets are generated using a line array of sensors and multiple snapshots to produce data which should have the desired structure. The OSE algorithm exploits this structure in the data matrix in order to generate an estimate of the underlying noise-free signal subspace. Two applications have been chosen where the covariance matrices of the signal data should exhibit this desired structure. The applications are common signal processing subjects known as Adaptive Beamforming and Space-Time Adaptive Processing (STAP).^ OSE is an ideal estimation method for the application of Adaptive Beamforming. It is capable of achieving performance better than a commonly used algorithm known as Dominant Mode Rejection (DMR) while using orders of magnitude fewer snapshots. The OSE algorithm stands out in its ability to quickly approach the Cramer-Rao bound with many fewer snapshots of data. This is especially true when the line array of sensors is able to be carefully calibrated. Results are obtained by multiple simulations that outline the overall performance of theoretical data and test the robustness of the chosen algorithms.^ The application of Space-Time Adaptive Beamforming is chosen because it is essentially a two-dimensional adaptation of the Adaptive Beamforming example. The data matrix now contains angle and timing information which becomes increasingly difficult to generate a good estimate as real world physics are applied to the model. Processing this data quickly becomes computationally inefficient and requires a modified OSE algorithm know as Subspace Averaging (SSA) was needed. With theoretical data a lower bound is quickly approached but like the algorithms used for comparison, practical results are not easily achieved with simple processing.^

#### Subject Area

Electrical engineering

#### Recommended Citation

Christopher Grayson,
"Applications of Optimal Subspace Estimation"
(2016).
*Dissertations and Master's Theses (Campus Access).*
Paper AAI10245557.

http://digitalcommons.uri.edu/dissertations/AAI10245557