Abstract—In this paper a modified ESPRIT algorithm based on time subspace (T-ESPRIT) and spatial subspace of estimate 1D-DOA (elevation) of a radiated source to increase the estimation accuracy with low computational load is introduced. Firstly, this algorithm treats with non uniform linear (NULA) array as a multiple sub-uniform linear arrays (ULA) with the common reference point, and the T-ESPRIT method is applied within each sub-ULA. Secondly, in order to increase the estimation accuracy, the estimated DOA is corrected with Doppler frequency (fd) which induced by target movement. Moreover, the proposed algorithm is combined the refined T- ESPRIT method with time differential of arrival (TDOA) technique to form TS-ESPRIT algorithm which calculates an optimum DOA. The estimated results are better than the traditional ESPRIT methods leading to the estimator performance enhancement. Index Terms—DOAE, t-esprit, Doppler frequency, TDOA. I. INTRODUCTION Great efforts have been done to improve DOAE accuracy via applying ESPRIT for uniform linear array (ULA) [1]-[7] and non-uniform linear array (NULA) [8]-[11]. In previous work, the method involved in both the temporal and spatial resolution (TS-ESPRIT) had been introduced to realize subspace approach by combining the S-ESPRIT method with the T-ESPRIT [1] , [2], [12] which realized high estimation accuracy with low computational load due to benefit from the advantages of subspaces and multi-resolution techniques. In this paper a new idea is presented based on spatial subspace concept not on spatial sampling concept which had been used in [1], [8]-[11]. Spatial subspace is realized by divided the NULA to multiple ULAs with the same reference point and compute DOAE by applying T-ESPRIT for each separately, but in parallel with the others. Then, the effect of Doppler frequency on the T-ESPRIT method is explained in order to refine the DOAE. Finally, the TDOA technique [13], [14] is applied and combined the multiple sub-arrays to calculate the optimum DOAE value, which realizes time and space parallel processing, so that it obtains to enhance the estimation accuracy and reduce computational load. Manuscript received June 23, 2015; revised August 25, 2015. Youssef Fayad and Qunsheng Cao are with College of Electronic and Information Engineering, Nanjing University of Aeronautics& Astronautics, Nanjing 210016, China (e-mail: yousseffyad@nuaa.edu.cn, qunsheng@nuaa.edu.cn). Caiyun Wang is with College of Astronautics Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China (e-mail: wangcaiyun@nuaa.edu.cn) II. PROPOSED ALGORITHM A. The Measurement MODEL In this model, the transmission medium and the signals are assumed to be the same as [1], and [12]. Assume there is a number antenna element, and it is divided into L number multiple uniform linear antenna (ULA) each with total N number antenna element in receiving system shown in Fig. 1. And there are K number emitting sources, then the output complex signal z n,l (t) (n=1, 2, …, N，l =1, …, L) at (n, l) sensor at time t can be written as, (1) (2) where stands for the additive white Gaussian noise (AWGN), so that (3) B. Time and Spatial Subspaces Technique Fig. 1 shows the NULA, the displacement for each sub- ULA element from the reference point is computed as follow (4) Fig. 1. Non-uniform linear array. For the Electronic Scanning Beam (ESB) with width Doppler Correction to Improve TS-ESPRIT Algorithm Used in NULA Youssef Fayad, Caiyun Wang, and Qunsheng Cao International Journal of Modeling and Optimization, Vol. 5, No. 4, August 2015 290 DOI: 10.7763/IJMO.2015.V5.476 where S k (t) is the signal of the k th source at time t. is the sensor element response at frequency corresponding to propagation delay between a reference point at (n, l) sensor for the k th wave front impinging on the array from direction θ k , is the displacement of the element in the l th sub-ULA with respect to the reference point (R.P). The receiving model for each l sub-ULA can be written as in matrix form