Information science and engineering

For array processing, we consider the problem of estimating signals of interest, and their directions of arrival (DOA), in unknown colored noise fields. We develop an estimator that efficiently utilizes a set of noise-only samples and, further, can incorporate prior knowledge of the DOAs with varying degrees of certainty. The estimator is compared with state of the art estimators that utilize noise-only samples, and the Cramér-Rao bound, exhibiting improved performance for smaller sample sets and in poor signal conditions.

We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior inverse-Wishart distributions. The nonconvex problem of jointly estimating the signal of interest and the covariance matrices is tackled by a computationally efficient fixed-point iteration as well as an approximate variational Bayes solution. The statistical performance of estimators is compared numerically to state-ofthe-art estimators from the literature and shown to perform favorably.

Signal parameter estimation and specifically direction of arrival (DOA) estimation for sensor array data is encountered in a number of applications ranging from electronic surveillance to wireless communications. Subspace based methods have shown to provide computationally as well as statistically efficient algorithms for DOA estimation. Estimator performance is ultimately limited by model disturbances such as measurement noise and model errors. Herein, we review a recently proposed framework that allows the derivation of optimal subspace methods taking both finite sample effects (noise) and model perturbations into account. We show how this general estimator reduces to well known techniques for cases when one disturbance dominates completely over the other.

Herein, a novel eigenstructure-based method for direction estimation is presented. The method assumes that the emitter signals are uncorrelated. Ideas from subspace and covariance matching methods are combined to yield a noniterative estimation algorithm when a uniform linear array is employed. The large sample performance of the estimator is analyzed. It is shown that the asymptotic variance of the direction estimates coincides with the relevant Cramér-Rao lower bound (CRB). A compact expression for the CRB is derived for the case when it is known that the signals are uncorrelated, and it is lower than the CRB that is usually used in the array processing literature (assuming no particular structure for the signal covariance matrix). The difference between the two CRB's can be large in difficult scenarios. This implies that in such scenarios, the proposed method has significantly better performance than existing subspace methods such as, for example, WSF, MUSIC, and ESPRIT. Numerical examples are provided to illustrate the obtained results.

Subspace-based methods for parameter identification have received considerable attention in the literature. Starting with a scalar-valued process, it is well known that subspace-based identification of sinusoidal frequencies is possible if the scalar valued data is windowed to form a low-rank vector-valued process. MUSIC and ESPRIT-like estimators have, for some time, been applied to this vector model. In addition, a statistically attractive Markov-like procedure for this class of methods has been proposed. Herein, the Markov-like procedure is reinvestigated. Several results regarding rank, performance, and structure are given in a compact manner. The large sample equivalence with the approximate maximum likelihood method by Stoica et al. is also established.

Estimation of covariance matrices is often an integral part in many signal processing algorithms. In some applications, the covariance matrices can be assumed to have certain structure. Imposing this structure in the estimation typically leads to improved accuracy and robustness (e.g., to small sample effects). In MIMO communications or in signal modelling of EEG data the full covariance matrix can sometimes be modelled as the Kronecker product of two smaller covariance matrices. These smaller matrices may also be structured, e.g., being Toeplitz or at least persymmetric. In this paper we discuss a recently proposed closed form maximum likelihood (ML) based method for the estimation of the Kronecker factor matrices. We also extend the previously presented method to be able to impose the persymmetric constraint into the estimator. Numerical examples show that the mean square errors of the new estimator attains the Cramér-Rao bound even for very small sample sizes.

A characterization of a state of the art pipeline ADC is presented. Measurements are performed on a wide set of frequencies. The integral non linearity (INL) is modeled by high code and low code components, HCF and LCF. The HCF component is to be deprived of any dynamic behavior, and varies piecewise linearly in certain intervals. Hence, the LCF represents the dynamic behavior that should varies the frequency of the test signal. Employement of the method presented in [1] on measured data is performed and complemented with modifications stimulated by the behavior of measured data.

An input-dependent integral nonlinearity (INL) model is developed for pipeline ADC post-correction. The INL model consists of a static and dynamic part. The INL model is subtracted from the ADC digital output for compensation. Static compensation is performed by adjacent sets of gains and offsets. Each set compensates a certain output code range. The frequency content of the INL dynamic component is used to design a set of filter blocks that performs ADC compensation in the time domain. The compensation scheme is applied to measured data of two 12-bit ADCs of the same type (Analog Devices AD9430). Significant performance improvements in terms of spurious free dynamic range (SFDR) are obtained.

We consider the problem of estimating a random state vector when there is information about the maximum distances between its subvectors. The estimation problem is posed in a Bayesian framework in which the minimum mean square error (MMSE) estimate of the state is given by the conditional mean. Since finding the conditional mean requires multidimensional integration, an approximate MMSE estimator is proposed. The performance of the proposed estimator is evaluated in a positioning problem. Finally, the application of the estimator in inequality constrained recursive filtering is illustrated by applying the estimator to a dead-reckoning problem. The MSE of the estimator is compared with two related posterior Cramér-Rao bounds.

The integral nonlinearity (INL) modeling of pipeline analog-digital converters (ADCs) is investigated in this paper. The INL is divided into two distinct entities: a low code frequency component (LCF) and a high code frequency (HCF) component. Two static models are developed to represent the INL data. In both models, the LCF component is represented by a loworder polynomial. The HCF modeling is performed using two different basis functions: sinc and Gaussian. The structure of both HCF models is motivated by the pipeline architecture of the ADC under investigation. The model coefficients are estimated by applying the least-squares method to the measured INL data from two samples of a commercial pipeline ADC. The estimated HCF models are compared to each other and to previous models presented in the existing literature. In addition, the modeling methods are applied to synthetic HCF data generated by a pipeline ADC simulation model constructed in Matlab. The INL models are then used to calibrate the synthetic ADCs, and the improvements in spurious free dynamic range (SFDR) are compared to those obtained when the ADCs are compensated by the INL data. Furthermore, the capability of the HCF modeling to calibrate a given ADC is tested by using the HCF model to compensate a synthetically generated ADC output in which only the measured HCF sequence and noise are added to the quantization process. The results show that the developed HCF models can achieve virtually complete calibration of the considered ADC.

Integral nonlinearity (INL) for pipelined analogdigital converters (ADCs) operating at RF is measured and characterized. A parametric model for the INL of pipelined ADCs is proposed, and the corresponding least-squares problem is formulated and solved. The INL is modeled both with respect to the converter output code and the frequency stimuli, which is dynamic modeling. The INL model contains a static and a dynamic part. The former comprises two 1-D terms in ADC code that are a sequence of zero-centered linear segments and a polynomial term. The 2-D dynamic part consists of a set of polynomials whose parameters are dependent on the ADC input stimuli. The INL modeling methodology is applied to simulated and experimental data from a 12-bit commercial ADC running at 210 mega samples per second. It is demonstrated that the developed methodology is an efficient way to capture the INL of nowadays ADCs running at RF, and it is believed that the methodology is powerful for INL-based ADC postcorrection in wideband applications.

An input-dependent integral nonlinearity (INL) model is developed for pipeline ADC post-correction. The INL model consists of a static and dynamic part. The INL model is subtracted from the ADC digital output for compensation. Static compensation is performed by adjacent sets of gains and offsets. Each set compensates a certain output code range. The frequency content of the INL dynamic component is used to design a set of filter blocks that performs ADC compensation in the time domain. The compensation scheme is applied to measured data of two 12-bit ADCs of the same type (Analog Devices AD9430). Significant performance improvements in terms of spurious free dynamic range (SFDR) are obtained.

Analog-digital converter (ADC) integral nonlinearity (INL) modeling is investigated. The model is comprised of two entities: a low code frequency (LCF) component modeled by an L-order polynomial, and a static high code frequency component (HCF), modeled by P linear disjoint segments centered around zero. Both model components are functions of the ADC output code k. A methodical way of estimating the LCF polynomial order L and the set of segments (number of and their borders), is suggested. The method computes the polynomial order L and the set of segments (number and borders) that minimizes the root mean square (RMS) distance between the INL data and its model. The method is applied to measured INL sequences of a 12-bit Analog Devices pipeline ADC (AD9430).

A dynamic characterization of analog-digital converter integral nonlinearity (INL) is considered. When using a plurality of test frequencies in the measurement set-up, the dynamic errors of the converter are characterized. The INL is modeled by low and high code components -LCF and HCF, respectively. The LCF and HCF are parameterized and a least squares method is derived for the estimation of the parameter values from obtained measurements. A closed form solution to the estimation problem is derived and its performance is illustrated by a numerical example. The proposed method is believed to be fruitful in wide-band characterization of analog-digital converters at radio frequency, and thus of importance for the evaluation of modern and future wireless communication systems.

This paper describes a novel and a low-cost calibration approach to estimate the relative transformation between an inertial measurement unit (IMU) and a camera, which are rigidly mounted together. The calibration is performed by fusing the measurements from the IMU-camera rig moving in front of a planar mirror. To construct the visual observations, we select a set of key features attached to the visual inertial rig where the 3D positions of the key features are unknown. During calibration, the system is navigating in front of the planar mirror while the vision sensor observes the reflections of the key features in the mirror, and the inertial sensor measures the system's linear accelerations and rotational velocities over time. Our first contribution in this paper is studying the observability properties of IMUcamera calibration parameters. For this visual inertial calibration problem, we derive its time-varying nonlinear state-space model and study its observability properties using the Lie derivative rank condition test. We show that the calibration parameters and the 3D position of the key features are observable. As our second contribution, we propose an approach for estimating the calibration parameters along with the 3D position of the key features and the dynamics of the analyzed system. The estimation problem is then solved in the unscented Kalman filter framework. We illustrate the findings of our theoretical analysis using both simulations and experiments. The achieved performance indicates that our proposed method can conveniently be used in consumer products like visual inertial based applications in smartphones for localization, 3D reconstruction, and surveillance applications.

Electronic warfare systems for use against military communication sources include direction-finding. The considered direction-finding electronic-warfare system uses two intercept receivers which is eavesdropping on the transmitted signal with no knowledge of the waveform used, or its origin. Down-conversion to baseband is required in order to digitize the received signal. This can be done using a superheterodyne receiver where an oscillator is used to mix the signal-of-interest to baseband. Errors in frequency and phase between the oscillators degrade the performance. Because of this error, the performance derived in previous work by the authors will not apply since the used model no longer is applicable. The extended model presented here considers the oscillator errors. The performance using the extended model is determined numerically and the result is compared to the Cramér-Rao lower bound for the ideal system using a typical signal waveform.

An electronic warfare (EW) system with two spatially separated intercept receivers, targeting military communication systems is considered. The EW system estimates the direction-of-arrival via a correlation-based time-difference-of-arrival (TDOA) method without any prior knowledge of the signals-ofinterest.

Direction-finding of radio transmitters is considered and in particular correlation-based time-difference-ofarrival (TDOA) estimation between a pair of intercept receivers. In the target application, the received and down-converted signals are corrupted by a frequency error due to a receiver frequency tuning offset which degrades the performance of the TDOA estimation. Traditionally, the cross-ambiguity function (CAF) is used in a 2D scheme for joint TDOA and frequency error estimation. In this paper, sequential 1D frequency error and TDOA estimators are introduced and compared to the 2D method. The 2D method attains the CRLB for both the TDOA and frequency error estimates, but have high computational and memory complexity. The proposed frequency error estimator is outperformed by the 2D method. However, the main objective is to estimate the TDOA and the proposed TDOA estimator have a performance similar to that of the 2D method. The main advantage of the proposed method is a reduction in both computational and memory complexity.