We consider the problem of tracking the direction of arrivals (DOA) of multiple moving targets in monostatic multipleinput multipleoutput (MIMO) radar. A lowcomplexity DOA tracking algorithm in monostatic MIMO radar is proposed. The proposed algorithm obtains DOA estimation via the difference between previous and current covariance matrix of the reduceddimension transformation signal, and it reduces the computational complexity and realizes automatic association in DOA tracking. Error analysis and CramérRao lower bound (CRLB) of DOA tracking are derived in the paper. The proposed algorithm not only can be regarded as an extension of arraysignalprocessing DOA tracking algorithm in (Zhang et al. (2008)), but also is an improved version of the DOA tracking algorithm in (Zhang et al. (2008)). Furthermore, the proposed algorithm has better DOA tracking performance than the DOA tracking algorithm in (Zhang et al. (2008)). The simulation results demonstrate effectiveness of the proposed algorithm. Our work provides the technical support for the practical application of MIMO radar.
Multipleinput multipleoutput (MIMO) radar employs multiple antennas to simultaneously transmit diverse waveforms and utilizes multiple antennas to receive the reflected signals [
DOA tracking for array antenna has been investigated for a long time, which contains projection approximation and subspace tracking (PAST) algorithm [
DOA tracking for MIMO radar is to track the DOA of the moving targets. PARAFAC adaptive algorithms [
In this paper, we reference the arraysignalprocessing DOA tracking idea in [
There are some differences between the work in [
The reminder of this paper is structured as follows. Section
We consider a monostatic MIMO radar system equipped with both uniform linear arrays (ULAs) for the transmit/receive array, in which
The array structure of monostatic MIMO radar.
The DOA tracking algorithm of array signal processing in [
Then we define
The covariance matrix of
The direction matrix in the reduceddimension signal in (
We assume that
We define
Then we can obtain [
We assume that the noise covariance matrix at time
Using the Vandermonde characteristic of the matrices
where
Then
Considering that
According to (
Equation (
From (
Using the method of least square, we get
Through the above analysis, the angles at time of
For the finite samples, the covariance matrix in (
Till now, we show the major steps of DOA tracking algorithm for monostatic radar as follows.
Use reduceddimension matrix
Get covariance matrix
We compute
We estimate
Repeat Steps
In this paper, the number of targets in MIMO radar is assumed to be preknown. If we have no knowledge about it, we may use the existing sourcenumber estimation technique in [
The initial angles in DOA tracking are obtained by ESPRIT algorithm or other DOA algorithms. The initial DOA is
We assume that the noise covariance matrices of adjacent time are approximately equal. The noise component in (
The proposed algorithm works well in condition of small value of
Since the reduceddimension matrix is sparse, its transformation adds less computational load. The proposed algorithm does not require eigenvalue decomposition of the covariance matrix and avoids an extra data association. For the proposed algorithm, the calculation of the covariance matrix requires
Complexity comparison.
Algorithm  Computational complexity 

PAST [ 

PASTd [ 

The proposed algorithm 

Complexity comparison with
The advantages of the proposed algorithm can be presented as follows.
The proposed algorithm does not require eigenvalue decomposition of the covariance matrix and has lower complexity than the conventional DOA tracking algorithms including PAST and PASTd.
The proposed algorithm can implement automatic association of DOA for monostatic MIMO radar.
The proposed algorithm has much better DOA tracking performance than the DOA tracking algorithm in [
In this section, we derive the variance of DOA tracking and CRLB. We assume that the observation noise variances are almost the same at adjacent time. When computing
According to (
According to (
And we have
We define that
According to [
According to [
Then we can define the average CRLB as follows:
The Monte Carlo simulations are adopted to assess DOA tracking performance of the proposed algorithm. We suppose that there are three moving targets. We define rootmean square error (RMSE) as
Figure
DOA tracking results of the proposed algorithm at SNR = 15 dB (Scene 1).
Figures
DOA tracking results of the proposed algorithm at SNR = 15 dB (Scene 2).
DOA tracking results of the proposed algorithm at SNR = 15 dB (Scene 3).
Figure
DOA tracking performance comparison with
Figure
DOA tracking with different values of
Figures
DOA tracking with different values of
DOA tracking with different values of
Figure
DOA tracking performance with different angle spacing.
In this paper we have presented the DOA tracking of multiple moving targets for monostatic MIMO radar. The proposed algorithm obtains DOA estimation of the target via the difference in previous and current covariance matrix of the reduceddimension transformation signals, and the proposed algorithm reduces the computational complexity and realizes automatic association of DOA. Error analysis and CRLB of DOA tracking are derived in the paper. The simulation results demonstrate effectiveness and robustness of the proposed algorithm. Our research provides technical support for the practical application of MIMO radar.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported by China NSF Grants (61371169, 61301108, and 61071164), Jiangsu Planned Projects for Postdoctoral Research Funds (1201039C), China Postdoctoral Science Foundation (2012M521099 and 2013M541661), Open Project of Key Laboratory of Modern Acoustic of Ministry of Education (Nanjing University), Aeronautical Science Foundation of China (20120152001), Qing Lan Project, Priority Academic Program Development of Jiangsu High Education Institutions, and Fundamental Research Funds for the Central Universities (NS2013024, kfjj130114, and kfjj130115).