Exact and approximate maximum-likelihood parameter estimation forquasi-synchronous CDMA signals

In order to construct the optimal decorrelator for a quasi-synchronous (QS) code-division multiple-access receiver, it is necessary to estimate the user delays. However, in a QS system, it is shown that delay estimation is equivalent to estimating a parameter vector which is related linearly to the received signal. An exact maximum-likelihood (ML) solution using alternating maximization is first developed for joint estimation of the user delay vectors and amplitudes. Suboptimal recursive least squares (RLS) and least mean square algorithms are then presented which approximate the true ML solution. It is shown that the optimal decorrelator and demodulated symbols are also generated by the RLS algorithm. Simulation and analytical results are presented for the bit-error rate performance of the adaptive receiver, and the average squared error of the estimated delay vectors is compared with the Cramer-Rao bound     

On the robustness of parameter estimation of superimposed signalsby dynamic programming

We analyze a recently proposed dynamic programming algorithm (REDP) for maximum likelihood (ML) parameter estimation of superimposed signals in noise. We show that it degrades gracefully with deviations from the key assumption of a limited interaction signal model (LISMO), providing exact estimates when the LISMO assumption holds exactly. In particular, we show that the deviations of the REDP estimates from the exact ML are continuous in the deviation of the signal model from the LISMO assumption. These deviations of the REDP estimates from the MLE are further quantified by a comparison to an ML algorithm with an exhaustive multidimensional search on a lattice in parameter space. We derive an explicit expression for the lattice spacing for which the two algorithms have equivalent optimization performance, which can be used to assess the robustness of REDP to deviations from the LISMO assumption. The values of this equivalent lattice spacing are found to be small for a classical example of superimposed complex exponentials in noise, confirming the robustness of REDP for this application     

Iterative parameter estimation of multiple chirp signals

The authors propose an algorithm for estimating the parameters of multiple superimposed chirp signals in additive white noise. The algorithm is based on a novel iterative approach that significantly reduces the error propagation effect inherent in many existing techniques. Moreover, it allows the estimation over a wider range of phase parameter values while still maintaining a better estimation accuracy     

Maximum likelihood parameter estimation of superimposed chirpsusing Monte Carlo importance sampling

We address the problem of parameter estimation of superimposed chirp signals in noise. The approach used here is a computationally modest implementation of a maximum likelihood (ML) technique. The ML technique for estimating the complex amplitudes, chirping rates, and frequencies reduces to a separable optimization problem where the chirping rates and frequencies are determined by maximizing a compressed likelihood function that is a function of only the chirping rates and frequencies. Since the compressed likelihood function is multidimensional, its maximization via a grid search is impractical. We propose a noniterative maximization of the compressed likelihood function using importance sampling. Simulation results are presented for a scenario involving closely spaced parameters for the individual signals     

Recursive parameter estimation for noisy autoregressive signals (Corresp.)

The problem of recursively estimating the unknown parameters of a scalar autoregressive (AR) signal observed in additive white noise, including signal power and noise variance, is considered. A state-space model in a canonical but noninnovations form is used to represent the noisy AR signal. An algorithm based on a system identification/parameter estimation technique known as the recursive prediction error method is presented for recursive parameter estimation. Two simulation examples illustrate the effectiveness of the proposed algorithm.     

A reduced-complexity online state sequence and parameter estimatorfor superimposed convolutional coded signals

This paper develops a reduced-complexity online state sequence and parameter estimator for superimposed convolutional coded signals. Joint state sequence and parameter estimation is achieved by iteratively estimating the state sequence via a variable reduced-complexity Viterbi algorithm (VRCVA) and the model parameters via a recursive expectation maximization (EM) approach. The VRCVA is developed from a fixed reduced-complexity Viterbi algorithm (FRCVA). The FRCVA is a special case of the delayed decision-feedback sequence estimation (DDFSE) algorithm. The performance of online versions of the FRCVA, VRCVA, and the standard Viterbi algorithm (VA) are compared when they are used to estimate the state sequence as part of the reduced-complexity online state sequence and parameter estimator     

Performance limitations and error calculations for parameter estimation

Error calculations cannot be carried out precisely when parameters are estimated which affect the observation nonlinearly. This paper summarizes the available approaches to studying performance and compares the resulting answers for a specific case. It is shown that the familiar Cramér-Rao lower bound on rms error yields an accurate answer only for large signal-to-noise ratios (SNR). For low SNR, lower bounds on rms error obtained by Ziv and Zakai give easily calculated and fairly tight answers. Rate distortion theory gives a lower bound on the error achievable with any system. The Barankin lower bound does not appear to give useful information as a computational tool. A technique for approximating the error can be used effectively for a large class of systems. With numerical integration, an upper bound obtained by Seidman gives a fairly tight answer. Recent work by Ziv gives bounds on the bias of estimators but, in general, these appear to be rather weak. Tighter results are obtained for maximum-likelihood estimators with certain symmetry conditions. Applying these techniques makes it possible to locate the threshold level to within a few decibels of channel signal-to-noise ratio. Further, these calculations can be easily carried out for any system.     

Damped sinusoidal signals parameter estimation in frequency domain

Parameter estimation of noisy damped sinusoidal signals in the frequency domain is presented in this paper. The advantage of the frequency domain approach is having the spectral energy concentrated in frequency domain samples. However, the least squares criterion for frequency estimation using frequency domain samples is nonlinear. A low complexity three-sample estimation algorithm (TSEA) for solving the nonlinear problem is proposed. Using the TSEA for initialization, a frequency domain nonlinear least squares (FD-NLS) estimation algorithm is then proposed. In the case of white Gaussian noise, it yields maximum likelihood estimates, verified by simulation results. A time domain NLS (TD-NLS) estimation algorithm is also proposed for comparison.The Cramer-Rao lower bound (CRLB) of the frequency domain estimation algorithms is derived. The theoretical analysis shows that the FD-NLS can yield a near-optimal performance with few energy-concentrated samples. On the other hand, the TD-NLS does not have the energy concentration property and requires more time domain samples to perform satisfactory estimation. Simulation results verify that the frequency domain estimation algorithms provide better tradeoff between computational complexity and estimation accuracy than time domain algorithms.     

伪随机二相码连续波信号参数估计算法

提出了一种伪随机二相码连续波信号参数估计算法。利用倍频法估计出载频和初相,由估计的载频和初相构造相关接收机,根据相关接收机的输出估计码元宽度、码元个数和码序列。     

A parameter estimation scheme for damped sinusoidal signals basedon low-rank Hankel approximation

Most of the existing algorithms for parameter estimation of damped sinusoidal signals are based only on the low-rank approximation of the prediction matrix and ignore the Hankel property of the prediction matrix. We propose a modified Kumaresan-Tufts (MKT) algorithm exploiting both rank-deficient and Hankel properties of the prediction matrix. Computer simulation results demonstrate that compared with the original Kumaresan-Tufts (1982) algorithm and the matrix pencil algorithm, the MKT algorithm has a lower noise threshold and can estimate the parameters of signal with larger damping factors     

Subspace-based parameter estimation of symmetric noncausalautoregressive signals from noisy measurements

Symmetric noncausal auto-regressive signals (SNARS) arise in several, mostly spatial, signal processing applications. We introduce a subspace fitting approach for parameter estimation of SNARS from noise-corrupted measurements. We show that the subspaces associated with a Hankel matrix built from the data covariances contain enough information to determine the signal parameters in a consistent manner. Based on this result, we propose a multiple signal classification (MUSIC)-like methodology for parameter estimation of SNARS. Compared with the methods previously proposed for SNARS parameter estimation, our SNARS-MUSIC approach is expected to possess a better tradeoff between computational and statistical performances     

基于小波变换的跳频信号参数盲估计

本文提出了一种基于小波变换的未知跳频信号参数盲估计方法.该方法利用小波变换在时频域上良好的局部化性质和检测突变点能力,在未知任何先验参数的情况下,能够准确估计出跳频信号的跳变时刻、跳频频率和跳频周期等参数.文中阐述了应用小波变换对跳频信号分析的基本原理,给出了估计跳频信号参数的具体算法步骤,在计算机仿真的基础上对结果进行了性能分析,得到了较为准确的估计结果.     

一种新的Costas跳频信号盲参数估计算法

本文以Costas信号为例提出了基于高斯基集的跳频信号自适应分解法，将跳频信号分解为一组高斯基函数的线性叠加。采用遗传算法估计与信号最匹配的高斯基函数。和其它方法相比，该方法具有很高的时频分辨率且无交叉项干扰，参数估计精度高。仿真结果证明了该方法的有效性，适合于低截获概率波形的低信噪比情况。     

Joint state and parameter estimation for a target-directed nonlinear dynamic system model

We present a new approach to joint state and parameter estimation for a target-directed, nonlinear dynamic system model with switching states. The model, recently proposed for representing speech dynamics, is called the hidden dynamic model (HDM). The model parameters, subject to statistical estimation, consist of the target vector and the system matrix (also called "time-constants"), as well as parameters characterizing the nonlinear mapping from the hidden state to the observation. We implement these parameters as the weights of a three-layer feedforward multilayer perceptron (MLP) network. The new estimation approach is based on the extended Kalman filter (EKF), and its performance is compared with the traditional expectation-maximization (EM) based approach. Extensive simulation results are presented using both approaches and under typical HDM speech modeling conditions. The EKF-based algorithm demonstrates superior convergence performance compared with the EM algorithm, but the former suffers from excessive computational loads when adopted for training the MLP weights. In all cases, the simulated model output converges to the given observation sequence. However, only in the case where the MLP weights or the target vector are assumed known do the time-constant parameters converge to their true values. We also show that the MLP weights never converge to their true values, thus demonstrating the many-to-one mapping property of the feedforward MLP. We conclude that, for the system to be identifiable, restrictions on the parameter space are needed.     

Spatial filtering of superimposed convolutional coded signals

In this paper, a method for simultaneously demodulating and estimating the parameters of a number of convolutional coded communication signals incident on an antenna array is presented. The method has the potential to increase the throughput of current multiple-access channel systems, e.g., satellite communications and digital mobile cellular phones, by using an antenna array. The contribution of this paper is the use of sequence estimation combined jointly with parameter estimation in array processing problems. A hidden Markov-model-based technique, the segmental k-means algorithm, is applied to the problem. This algorithm is an iterative procedure with two steps per iteration. The first step involves computing the most likely state sequence for each of the signals (demodulating the signals) given estimates of the signals' parameters. The second step refines the parameter estimates using the signals' mostly likely state sequence estimates. In the simulations presented, it is shown that a significant improvement in the accuracy of the demodulated signals and in the estimation of the signals' angle of arrivals is obtained when compared to a deterministic maximum likelihood estimation method     

A feedback control system for real-time formant estimation. I.Static and dynamic analysis for sinusoidal input signals

A scheme suitable for the real-time estimation of formant frequencies is presented. Formant tracking is based on a feedback technique which uses both the amplitude and phase characteristics of two stagger-tuned bandpass filters to give an improved dynamic behavior. The implementation of the system requires a small number of components, and is practical for low-power applications. An analysis of the static and dynamic behavior is given for sinusoidal input signals. The transient response is independent of the amplitude level of the input signal. The system is designed for second formant detection in a cochlear prosthesis system     

Performance analysis and optimal parameter selection for PYRAMID

Previously, we have proposed PYRAMID, a hierarchical, rule-based scheme for proximity effect correction in electron-beam lithography. In this paper we present a performance analysis of PYRAMID for a variety of different system parameters (resist thickness, substrate composition, etc.). We also discuss the optimal choice of two key correction parameters: global exposure block size and local exposure window size.     

Statistical modeling of cardiovascular signals and parameter estimation based on the extended Kalman filter

Cardiovascular signals such as arterial blood pressure (ABP), pulse oximetry (POX), and intracranial pressure (ICP) contain useful information such as heart rate, respiratory rate, and pulse pressure variation (PPV). We present a novel state-space model of cardiovascular signals and describe how it can be used with the extended Kalman filter (EKF) to simultaneously estimate and track many cardiovascular parameters of interest using a unified statistical approach. We analyze data from four databases containing cardiovascular signals and present representative examples intended to illustrate the versatility, accuracy, and robustness of the algorithm. Our results demonstrate the ability of the algorithm to estimate and track several clinically relevant features of cardiovascular signals. We illustrate how the algorithm can be used to elegantly solve several actively researched and clinically significant problems including heart and respiratory rate estimation, artifact removal, pulse morphology characterization, and PPV estimation.