Abstract
The ultra-wideband (UWB) system, which transmits information using nanosecond or even sub-nanosecond pulses, has been widely applied in precise positioning. In this paper, we investigate the problem of the time of arrival (TOA) estimation and the direction of arrival (DOA) estimation in the UWB systems with antenna array and propose a joint TOA and DOA estimation algorithm with doubled frequency sample points and extended number of clusters. Specifically, the proposed algorithm uses two antennas to receive impinging signals and utilizes the conjugate symmetry characteristic of the delay matrices to extend the sample points as well as the number of clusters. Moreover, in order to obtain TOA estimates with low computational complexity, the proposed algorithm transforms the two-dimensional (2D) spectral search to one-dimensional (1D) searches. The DOA estimates can then be achieved by using the TOA estimation results and the geometric information. Simulation results are given to testify the performance of the proposed algorithm.
Highlights
One of the basic problems in the UWB positioning system is the time of arrival (TOA) estimation
Estimation algorithms can be divided into two categories: one is the traditional algorithms based on the time domain, and the other is the high-resolution algorithms based on the frequency domain. e former mainly includes the coherent detection method using pulse template matched filter [8] and the incoherent TOA estimation algorithm based on threshold or energy detection [9,10,11]. e coherent algorithm based on matched filter can obtain TOA estimates with high accuracy but at the same time with high sampling rate, complex receiver structure, and expensive equipment cost. e incoherent TOA estimation algorithm has the advantages of low sampling rate, fast convergence speed, and low hardware resource occupation rate
Due to the multipath effect and the nonline-of-sight (NLOS) condition, direct path (DP) may not be the Mathematical Problems in Engineering strongest path; the algorithm resolution declines. erefore, super-resolution estimation algorithms based on frequency-domain processing are proposed [12,13,14,15,16,17,18]. ese algorithms, such as the multiple signal classification (MUSIC) algorithm [12, 13], the propagator method (PM) [14], the estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm [15, 16], and the matrix pencil algorithm [17, 18], model the channel impulse response in frequency domain and realize the TOA estimation using the orthogonality between the signal subspace and the noise subspace, which can achieve high estimation resolution
Summary
According to the Saleh–Valenzuela (SV) model [23], we consider that the transmit signal produces multiple multipath components after passing through the channel, and these multipath components arrive at the receiver in the form of clusters. L 1 where α(l k) is kth cluster, the channel fading which obeys the factor of Rayleigh the lth path in the distribution. According to the basic theory of the digital signal processing, the received signal of the kth cluster in the time domain can be expressed as [23]. Β(Lk)]T contains the complex channel fading factor of the kth cluster and wk [W(k)(ω0), W(k)(ω1), . According to (7), the received signal of the two antennas in the frequency domain can be expressed as [23]. E estimation of the two channel impulse responses in the frequency domain can be achieved by
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