DOA Tracking Algorithm Using Multi-dimensional Subspace Fitting

In the past 40 years,Direction of Arrival(DOA)estimation has been an important research direction in array signal processing,attracting many researchers' attention.After decades of development,there have been many classic DOA estimation algorithms,such as MUSIC,ESPRIT,ML and so on.In some time-varying application scenarios,we want to obtain the source position at all times.However,due to the constraints of hardware technology,using only traditional DOA estimation algorithm is computationally complex and difficult to implement.At present,some researchers have proposed some adaptive DOA tracking algorithms,such as the PAST algorithm based on Kalman filter.However,when multiple sources are very close and even when these sources have intersections on their trajectory,these algorithms cannot accurately estimate and match the DOA of each source.In order to solve this problem,this thesis proposes a DOA tracking algorithm using multi-dimensional subspace fitting.The thesis introduces in detail the proposed DOA tracking algorithm using multi-dimensional subspace fitting.Firstly,according to the multi-dimensional subspace fitting method,this thesis tracks the signal subspace projection in each time frame.In this thesis,two methods are used to derive the formula and get the same result,which verifies the correctness of the algorithm.Then the Gauss-Newton method is used to optimize the fitting equation to obtain the DOA measured value.Next,a Kalman filter with a validation gate is proposed.The above DOA measured value and the DOA predicted value obtained from the previous time are used as inputs of the Kalman filter to generate a final DOA estimate value.The simulation results show that although the complexity of the proposed algorithm is slightly higher,the estimation performance of the proposed algorithm is much better than that of the PAST algorithm based on Kalman filter.Compared with the PAST algorithm based on Kalman filter,the proposed algorithm has the following three innovations:(1)The PAST algorithm based on Kalman filter is one-dimensional DOA tracking.This algorithm belongs to multi-dimensional DOA tracking.(2)The PAST algorithm based on Kalman filter uses the Newton method to solve the fitting equation.This algorithm constructs the square term in the fitting equation and uses the Gauss-Newton method to find the optimal solution.(3)The PAST algorithm based on Kalman filter simply smooths the measured values using a Kalman filter.The algorithm uses a Kalman filter with a validation gate,which solves the problem that the multi-target source is very close,and can accurately estimate and match the DOA of the multi-target source.