A transform-based covariance differencing approach for some classes of parameter estimation problems

Abstract

Abstract-In this paper, we present a method of parameter estimation for a class of problems where the desired signal is embedded in colored noise with unknown covariance. The new algorithm is a variation of the covariance differencing scheme proposed by Paulraj and Kailath. Unlike the previous method, however, the proposed algorithm does not require multiple estimates of the signal covariance matrix. Instead, it uses a priori knowledge of the structure of the noise covariance matrix to transform the array covariance matrix in a way that leaves its noise component unchanged while transforming the signal component in some appropriate manner. We can then eliminate the noise component by forming the difference of the original and transformed covariance matrices. This unique feature of the proposed method allows covariance differencing methods to be applied to a wider class of problems than was previously possible. To illustrate this, we apply the new covariance differencing algorithm to the problems of bearing estimation, resolution of overlapping echos, and transient response analysis. Simulation results are presented for each problem, and the new method's performance is compared to that of conventional methods for solving each respective problem. It is interesting to note that our algorithm eliminates the need for array rotation or translation which is often required for the conventional covariance differencing technique.

Covariance differencing‐based matrix decomposition for coherent sources localisation in bi‐static multiple‐input–multiple‐output radar

“…From another point of view, it implies that when the antenna numbers are fixed, the CD-FBbH method can resolve more coherent sources than CD-FbH and CD-BbH methods. In the third simulation, we validate the effectiveness of proposed methods using another spatially coloured noise model which is a spatial complex AR model of order 2 with coefficients a = [1, −1, 0.2] used in [18]. The parameters are the same with those for 5 coherent sources in the first simulation.…”

“…Then a forward block Toeplitz matrix can be constructed as (18), we find that the construction principle for R Tc2,f p,q is the same with that for R Tc0,f p,q (n) by taking each block matrix in (17) and (18) as an element.…”

Localization of mixed far-field and near-field sources under unknown mutual coupling

“…Note that if (μ, u) is an eigen-pair of R , then (−μ, Ju * ) is also an eigen-pair of R [33,34]. Therefore, by taking the EVD of R , we have…”

Root MUSIC Transform Covariance Differencing for Correlated Sources under Unknown Symmetric Toeplitz Noise

“…And, the proposed method focuses on the case when the unknown noise has its covariance matrix in the symmetric Toeplitz form as in [3], [7]. This happens when the noise field is cylindrical or spherical isotropic around the array elements.…”

“…But in practical situation the covariance noise matrix may be difficult to obtain. To estimate the DOAs under such an unknown noise environment, there are some algorithms proposed [3]- [6] for uncorrelated incident sources. These algorithms are applied under different kinds of unknown noise environments and also they require the number of array elements N must be larger than twice the number of sources K, i.e., N > 2K which increase the computational complexity.…”