616 research outputs found
Bounds for maximum likelihood regular and non-regular DoA estimation in K-distributed noise
We consider the problem of estimating the direction of arrival of a signal embedded in -distributed noise, when secondary data which contains noise only are assumed to be available. Based upon a recent formula of the Fisher information matrix (FIM) for complex elliptically distributed data, we provide a simple expression of the FIM with the two data sets framework. In the specific case of -distributed noise, we show that, under certain conditions, the FIM for the deterministic part of the model can be unbounded, while the FIM for the covariance part of the model is always bounded. In the general case of elliptical distributions, we provide a sufficient condition for unboundedness of the FIM. Accurate approximations of the FIM for -distributed noise are also derived when it is bounded. Additionally, the maximum likelihood estimator of the signal DoA and an approximated version are derived, assuming known covariance matrix: the latter is then estimated from secondary data using a conventional regularization technique. When the FIM is unbounded, an analysis of the estimators reveals a rate of convergence much faster than the usual . Simulations illustrate the different behaviors of the estimators, depending on the FIM being bounded or not
Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental findings and applications
Inferring information from a set of acquired data is the main objective of
any signal processing (SP) method. In particular, the common problem of
estimating the value of a vector of parameters from a set of noisy measurements
is at the core of a plethora of scientific and technological advances in the
last decades; for example, wireless communications, radar and sonar,
biomedicine, image processing, and seismology, just to name a few. Developing
an estimation algorithm often begins by assuming a statistical model for the
measured data, i.e. a probability density function (pdf) which if correct,
fully characterizes the behaviour of the collected data/measurements.
Experience with real data, however, often exposes the limitations of any
assumed data model since modelling errors at some level are always present.
Consequently, the true data model and the model assumed to derive the
estimation algorithm could differ. When this happens, the model is said to be
mismatched or misspecified. Therefore, understanding the possible performance
loss or regret that an estimation algorithm could experience under model
misspecification is of crucial importance for any SP practitioner. Further,
understanding the limits on the performance of any estimator subject to model
misspecification is of practical interest. Motivated by the widespread and
practical need to assess the performance of a mismatched estimator, the goal of
this paper is to help to bring attention to the main theoretical findings on
estimation theory, and in particular on lower bounds under model
misspecification, that have been published in the statistical and econometrical
literature in the last fifty years. Secondly, some applications are discussed
to illustrate the broad range of areas and problems to which this framework
extends, and consequently the numerous opportunities available for SP
researchers.Comment: To appear in the IEEE Signal Processing Magazin
Distributed Bayesian Filtering using Logarithmic Opinion Pool for Dynamic Sensor Networks
The discrete-time Distributed Bayesian Filtering (DBF) algorithm is presented
for the problem of tracking a target dynamic model using a time-varying network
of heterogeneous sensing agents. In the DBF algorithm, the sensing agents
combine their normalized likelihood functions in a distributed manner using the
logarithmic opinion pool and the dynamic average consensus algorithm. We show
that each agent's estimated likelihood function globally exponentially
converges to an error ball centered on the joint likelihood function of the
centralized multi-sensor Bayesian filtering algorithm. We rigorously
characterize the convergence, stability, and robustness properties of the DBF
algorithm. Moreover, we provide an explicit bound on the time step size of the
DBF algorithm that depends on the time-scale of the target dynamics, the
desired convergence error bound, and the modeling and communication error
bounds. Furthermore, the DBF algorithm for linear-Gaussian models is cast into
a modified form of the Kalman information filter. The performance and robust
properties of the DBF algorithm are validated using numerical simulations
Sparsity-Cognizant Total Least-Squares for Perturbed Compressive Sampling
Solving linear regression problems based on the total least-squares (TLS)
criterion has well-documented merits in various applications, where
perturbations appear both in the data vector as well as in the regression
matrix. However, existing TLS approaches do not account for sparsity possibly
present in the unknown vector of regression coefficients. On the other hand,
sparsity is the key attribute exploited by modern compressive sampling and
variable selection approaches to linear regression, which include noise in the
data, but do not account for perturbations in the regression matrix. The
present paper fills this gap by formulating and solving TLS optimization
problems under sparsity constraints. Near-optimum and reduced-complexity
suboptimum sparse (S-) TLS algorithms are developed to address the perturbed
compressive sampling (and the related dictionary learning) challenge, when
there is a mismatch between the true and adopted bases over which the unknown
vector is sparse. The novel S-TLS schemes also allow for perturbations in the
regression matrix of the least-absolute selection and shrinkage selection
operator (Lasso), and endow TLS approaches with ability to cope with sparse,
under-determined "errors-in-variables" models. Interesting generalizations can
further exploit prior knowledge on the perturbations to obtain novel weighted
and structured S-TLS solvers. Analysis and simulations demonstrate the
practical impact of S-TLS in calibrating the mismatch effects of contemporary
grid-based approaches to cognitive radio sensing, and robust
direction-of-arrival estimation using antenna arrays.Comment: 30 pages, 10 figures, submitted to IEEE Transactions on Signal
Processin
Regularized Covariance Matrix Estimation in Complex Elliptically Symmetric Distributions Using the Expected Likelihood Approach - Part 2: The Under-Sampled Case
In the first part of this series of two papers, we extended the expected likelihood approach originally developed in the Gaussian case, to the broader class of complex elliptically symmetric (CES) distributions and complex angular central Gaussian (ACG) distributions. More precisely, we demonstrated that the probability density function (p.d.f.) of the likelihood ratio (LR) for the (unknown) actual scatter matrix \mSigma_{0} does not depend on the latter: it only depends on the density generator for the CES distribution and is distribution-free in the case of ACG distributed data, i.e., it only depends on the matrix dimension and the number of independent training samples , assuming that . Additionally, regularized scatter matrix estimates based on the EL methodology were derived. In this second part, we consider the under-sampled scenario () which deserves a specific treatment since conventional maximum likelihood estimates do not exist. Indeed, inference about the scatter matrix can only be made in the -dimensional subspace spanned by the columns of the data matrix. We extend the results derived under the Gaussian assumption to the CES and ACG class of distributions. Invariance properties of the under-sampled likelihood ratio evaluated at \mSigma_{0} are presented. Remarkably enough, in the ACG case, the p.d.f. of this LR can be written in a rather simple form as a product of beta distributed random variables. The regularized schemes derived in the first part, based on the EL principle, are extended to the under-sampled scenario and assessed through numerical simulations
Cooperative Position and Orientation Estimation with Multi-Mode Antennas
Robotic multi-agent systems are envisioned for planetary exploration and terrestrial applications. Autonomous operation of robots requires estimations of their positions and orientations, which are obtained from the direction-of-arrival (DoA) and the time-of-arrival (ToA) of radio signals exchanged among the agents. In this thesis, we estimate the signal DoA and ToA using a multi-mode antenna (MMA). An MMA is a single antenna element, where multiple orthogonal current modes are excited by different antenna ports. We provide a first study on the use of MMAs for cooperative position and orientation estimation, specifically exploring their DoA estimation capabilities. Assuming the agents of a cooperative network are equipped with MMAs, lower bounds on the achievable position and orientation accuracy are derived. We realize a gap between the theoretical lower bounds and real-world performance of a cooperative radio localization system, which is caused by imperfect antenna and transceiver calibration. Consequentially, we theoretically analyze in-situ antenna calibration, introduce an algorithm for the calibration of arbitrary multiport antennas and show its effectiveness by simulation. To also improve calibration during operation, we propose cooperative simultaneous localization and calibration (SLAC). We show that cooperative SLAC is able to estimate antenna responses and ranging biases of the agents together with their positions and orientations, leading to considerably better position and orientation accuracy. Finally, we validate the results from theory and simulation by experiments with robotic rovers equipped with software-defined radios (SDRs). In conclusion, we show that DoA estimation with an MMA is feasible, and accuracy can be improved by in-situ calibration and SLAC
Maximum likelihood based estimation of frequency and phase offset in DCT OFDM systems under non-circular transmissions: algorithms, analysis and comparisons
Recently, the advantages of the discrete cosine transform (DCT) based orthogonal frequency-division multiplexing (OFDM) have come to the light. We thus consider DCT- OFDM with non-circular transmission (our results cover circular transmission as well) and present two blind joint maximum- likelihood frequency offset and phase offset estimators. Both our theoretical analysis and numerical comparisons reveal new advantages of DCT-OFDM over the traditional discrete Fourier transform (DFT) based OFDM. These advantages, as well as those already uncovered in the early works on DCT-OFDM, support the belief that DCT-OFDM is a promising multi-carrier modulation scheme
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