Digital Signal Processing 24 (2014) 34–41 Contents lists available at ScienceDirect Digital Signal Processing www.elsevier.com/locate/dsp Two-dimensional angle estimation for monostatic MIMO arbitrary array with velocity receive sensors and unknown locations Jianfeng Li ∗ , Xiaofei Zhang College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China article info abstract Article history: Available online 30 August 2013 Keywords: Angle estimation Multi-input multi-output array Velocity sensor Rotational invariance technique In this paper, the problem of two-dimensional angle estimation for monostatic multi-input multi-output (MIMO) array is studied, and an algorithm based on the usage of velocity receive sensors is proposed. The algorithm applies the estimation method of signal parameters via rotational invariance technique (ESPRIT) algorithm to obtain automatically paired two-dimensional angle estimation. By utilizing the relationship within the outputs of velocity sensors, the rotational invariance property of ESPRIT does not depend on the array geometry any more. Hence, the proposed algorithm can provide two-dimensional DOA estimation for the MIMO array without the knowledge of sensor locations in the array. The algorithm requires no peak searches, so it has low complexity. Furthermore, it has better angle estimation performance than propagator method using the same sensor configuration. Error analysis and Cramér– Rao bound (CRB) of angle estimation in MIMO radar are derived. Simulation results verify the usefulness of the algorithm.  2013 Elsevier Inc. All rights reserved. 1. Introduction Multi-input multi-output (MIMO) array systems have been used in radar and sonar systems for target location and detection to overcome fading effect, enhance spatial resolution and improve target detection performance [1–4]. Direction of departure (DOD) and direction of arrival (DOA) estimation for MIMO array is an important issue and has been investigated recently. Maximal likeli- hood method [5] has been used for angle estimation for MIMO ar- ray, but it requires an exhaustive multi-dimensional peak searches, which renders high computational complexity. Capon algorithm [6] and multiple signal classification (MUSIC) algorithms [7–9] can all work well for high-resolution angle estimation with arbitrary ar- ray geometry, but the peak searches with high complexity are also needed. Estimation of signal parameters via rotational invari- ance technique (ESPRIT) algorithm [10], which exploits the invari- ance property in the array, was applied for direction estimation in MIMO radar systems [11–13]. Unitary ESPRIT [14] transforms the complex computations in ESPRIT into real-valued ones to reduce the complexity. Ref. [15] proposed a low-complexity ESPRIT-based method for angle estimation in monostatic MIMO radar and the reduced-dimension transformation can obtain signal to noise ra- tio (SNR) gain. Ref. [16] proposed an ESPRIT-like algorithm which can work well for coherent DOA estimation. Propagator method (PM) was proposed in [17] and was applied for angle estimation in * Corresponding author. E-mail address: lijianfengtin@126.com (J. Li). MIMO array [18,19]. PM utilizes the relationship within the receive data to calculate a propagator matrix and then construct the signal subspace or noise subspace without the eigen-value decomposi- tion (EVD). Hence, it has lower complexity than ESPRIT or MUSIC. Parallel factor analysis (PARAFAC) algorithm has also been used for localization of multiple targets in a MIMO radar system based on the trilinear decomposition [20]. MUSIC and PARAFAC can work well for arbitrary array geometry, but the peak searching and iter- ation will lead to a high complexity. Ref. [21] proposed a method based on the signal subspace to deal with arbitrary arrays without peak searching and iteration, but the knowledge of sensor loca- tions is needed and the maximum number of detectable targets is reduced. The usage of velocity sensor arrays is a key technology of sonar and radar systems [22,23]. Compared to scalar sensor array, ve- locity sensor array has more degrees of freedom. These additional degrees of freedom can enhance spatial resolution, strengthen pa- rameter identifiability and improve target detection performance. By combining the velocity sensor and pressure sensor, an ESPRIT- based method was proposed in [23] to achieve the underwater angle estimation without the knowledge of sensor locations, but an additional pairing was needed. Ref. [24] proposed a successive MUSIC algorithm for angle estimation with velocity receive sensors in MIMO array, and it avoided the two-dimensional peak searching in two-dimensional (2D) MUSIC. Though successive MUSIC algo- rithm can be used for arbitrary array, it requires a priori knowledge of the array geometry. Furthermore, it requires peak searching, which relies on a heavy computational load. 1051-2004/$ – see front matter  2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.dsp.2013.08.005