# Direction Finding Based on Multi-Step Knowledge-Aided Iterative Conjugate Gradient Algorithms

## TL;DR

This paper introduces multi-step knowledge-aided iterative conjugate gradient algorithms for direction-of-arrival estimation, leveraging prior knowledge and covariance matrix structure to improve accuracy in correlated and uncorrelated signal scenarios.

## Contribution

It proposes novel MS-KAI-CG algorithms that exploit prior knowledge and covariance matrix structure, outperforming existing methods in DoA estimation.

## Key findings

- MS-KAI-CG algorithms outperform existing techniques in simulations.
- The MS-KAI-CG-FB variant effectively handles correlated signals.
- Algorithms leverage prior knowledge to enhance covariance matrix estimation.

## Abstract

In this work, we present direction-of-arrival (DoA) estimation algorithms based on the Krylov subspace that effectively exploit prior knowledge of the signals that impinge on a sensor array. The proposed multi-step knowledge-aided iterative conjugate gradient (CG) (MS-KAI-CG) algorithms perform subtraction of the unwanted terms found in the estimated covariance matrix of the sensor data. Furthermore, we develop a version of MS-KAI-CG equipped with forward-backward averaging, called MS-KAI-CG-FB, which is appropriate for scenarios with correlated signals. Unlike current knowledge-aided methods, which take advantage of known DoAs to enhance the estimation of the covariance matrix of the input data, the MS-KAI-CG algorithms take advantage of the knowledge of the structure of the forward-backward smoothed covariance matrix and its disturbance terms. Simulations with both uncorrelated and correlated signals show that the MS-KAI-CG algorithms outperform existing techniques.