|
|
马上注册，结交更多好友，享用更多功能，让你轻松玩转社区。
您需要 登录 才可以下载或查看，没有账号？注册
x
Abstract
This thesis deals with three estimation problems motivated by spatial signal
processing using arrays of sensors. All three problems are approached
using tools from estimation theory, including asymptotical analysis of performance
and Cramér-Rao lower bound; Monte Carlo methods are used to
evaluate small sample performance.
The first part of this thesis treats direction of arrival estimation for narrowband
signals. Most algorithms require the noise covariance matrix to be
known or to possess a known structure. In many cases, the noise covariance is
estimated from a separate batch of signal-free samples; in a non-stationary environment
this sample set can be small. By deriving the Cramér-Rao bound
in a form that can be compared to well-known results, we investigate the
combined effects of finite sample sizes, both in the estimated noise covariance
matrix and in the data with signals present. Under the same data model,
we derive the asymptotical covariance of weighted subspace fitting, where the
signal-free samples are used for whitening. The obtained expression suggests
optimal weights that improve performance compared to the standard choice
and that result in an asymptotically efficient estimate. In addition, we propose
a new, asymptotically efficient, method based on the likelihood function.
If the array is uniform and linear, then an iterative search can be avoided. We
propose two such algorithms, based on the two general, iterative, algorithms
discussed. We also treat the detection problem, and provide results that are
useful in a joint detection and estimation algorithm based on the proposed
estimators.
Parameter estimation for the reduced rank linear regression is the second
estimation problem treated in the thesis. It appears in, for example, system
identification and signal processing for communications. We propose a new
method based on instrumental variable principles and we analyze its asymptotical
performance. The new method is asymptotically efficient if the noise is
temporally white, and outperforms previously suggested algorithms when the
noise is temporally correlated. As part of the estimation algorithm, the closest
low rank approximation of a matrix, as measured under a weighted norm,
has to be calculated. This problem lacks solution in the general case. We propose
two new methods that can be computed in fixed time; both methods are
approximate but asymptotically optimal as part of the estimation procedure
in question. We also propose a new algorithm for the related rank detection
problem.
The third problem is that of estimating the covariance matrix of a multivariate
stochastic process. In some applications, the structure of the problem
suggests that the underlying, true, covariance matrix is the Kronecker product
of two matrix factors. The covariance matrix of the channel realizations
in multiple input multiple output (MIMO) communications systems can, under
certain assumptions, have such Kronecker product structure. Moreover,
the factor matrices can sometimes, in turn, be assumed to possess additional
structure. We propose two asymptotically efficient estimators for the case
where the channel realizations can be assumed known. Both estimators can
be computed in fixed time; they differ in their small sample performance and
in their ability to incorporate extra structure in the Kronecker factors. In a
practical MIMO system, the channel realizations have to be estimated from
training data. If the amount of training data is limited, then it is better to
treat the training data, rather than the channel estimates, as inputs to the
channel covariance estimator. We derive and analyze an estimator based on
this new data model. This estimate can be computed in fixed time and the
estimator is also able to optimally use extra structure in the factor matrices. |
|
/2 
eetop公众号
创芯大讲堂
创芯人才网
发表于 2008-1-12 20:41:23
