Adaptive estimation of HMM transition probabilities

This paper presents new schemes for recursive estimation of the state transition probabilities for hidden Markov models (HMMs) via extended least squares (ELS) and recursive state prediction error (RSPE) methods. Local convergence analysis for the proposed RSPE algorithm is shown using the ordinary differential equation (ODE) approach developed for the more familiar recursive output prediction error (RPE) methods. The presented scheme converges and is relatively well conditioned compared with the previously proposed RPE scheme for estimating the transition probabilities that perform poorly in low noise. The ELS algorithm presented is computationally of order N², which is less than the computational effort of order N⁴ required to implement the RSPE (and previous RPE) scheme, where N is the number of Markov states. Building on earlier work, an algorithm for simultaneous estimation of the state output mappings and the state transition probabilities that requires less computational effort than earlier schemes is also presented and discussed. Implementation aspects of the proposed algorithms are discussed, and simulation studies are presented to illustrate the convergence and convergence rates     

On-line estimation of hidden Markov model parameters based on theKullback-Leibler information measure

Sequential or online hidden Markov model (HMM) signal processing schemes are derived, and their performance is illustrated by simulation. The online algorithms are sequential expectation maximization (EM) schemes and are derived by using stochastic approximations to maximize the Kullback-Leibler information measure. The schemes can be implemented either as filters or fixed-lag or sawtooth-lag smoothers. They yield estimates of the HMM parameters including transition probabilities, Markov state levels, and noise variance. In contrast to the offline EM algorithm (Baum-Welch scheme), which uses the fixed-interval forward-backward scheme, the online schemes have significantly reduced memory requirements and improved convergence, and they can estimate HMM parameters that vary slowly with time or undergo infrequent jump changes. Similar techniques are used to derive online schemes for extracting finite-state Markov chains imbedded in a mixture of white Gaussian noise (WGN) and deterministic signals of known functional form with unknown parameters     

LMS algorithms for tracking slow Markov chains with applications to hidden Markov estimation and adaptive multiuser detection

This paper analyzes the tracking properties of the least mean squares (LMS) algorithm when the underlying parameter evolves according to a finite-state Markov chain with infrequent jumps. First, using perturbed Liapunov function methods, mean-square error estimates are obtained for the tracking error. Then using recent results on two-time-scale Markov chains, mean ordinary differential equation and diffusion approximation results are obtained. It is shown that a sequence of the centered tracking errors converges to an ordinary differential equation. Moreover, a suitably scaled sequence of the tracking errors converges weakly to a diffusion process. It is also shown that iterate averaging of the tracking algorithm results in optimal asymptotic convergence rate in an appropriate sense. Two application examples, analysis of the performance of an adaptive multiuser detection algorithm in a direct-sequence code-division multiple-access (DS/CDMA) system, and tracking analysis of the state of a hidden Markov model (HMM) with infrequent jumps, are presented.     

A new system identification method for fast echo cancelerinitialization

Proposes a new recursive version of an earlier technique for fast initialization of data-driven echo cancelers (DDECs). The speed of convergence and the covariance of the estimate of the proposed technique are comparable to the recursive least squares (RLS) algorithm, however, the computational complexity is no greater than the least mean square (LMS) algorithm. Analysis of computational complexity and the estimation error is also provided. Simulation results based on both floating-point and fixed-point arithmetic illustrate a remarkable improvement in terms of speed of convergence and steady-state error over the computationally comparable LMS algorithm     

Minimum probability of error-based methods for adaptive multiuser detection in multipath DS-CDMA channels

Direct-sequence code-division multiple-access (DS-CDMA) is a popular multiple-access technology for wireless communications. However, its performance is limited by multiple-access interference and multipath distortion. Multiuser detection and space-time processing are two signal processing techniques employed to improve the performance of DS-CDMA. Two minimum probability of error-based space-time multiuser detection algorithms are proposed in this paper. The first algorithm, minimum joint probability of error (MJPOE), aims to minimize the joint probability of error for all users. The second algorithm, minimum conditional probability of error (MCPOE), minimizes the probability of error of each user conditioned on the transmitted bit vector, for each user individually. In both the algorithms, the optimal filter weights are computed adaptively using a gradient descent approach. The MJPOE algorithm is blind and offers a bit-error-rate (BER) performance better than the nonadaptive minimum mean squared error (MMSE) algorithm, at the cost of higher computational complexity. An approach for reducing the computational overheads of MJPOE using Gram-Schmidt orthogonalization is suggested. The BER performance of the MCPOE algorithm is slightly inferior to MMSE, however, it has a computational complexity linear in the number of users. Both blind and training-based implementations for MCPOE are proposed. Both MJPOE and MCPOE have a convergence rate much faster than earlier known adaptive implementations of the MMSE detector, viz. least mean square and recursive least squares. Simulation results are presented for synchronous single path channels as well as asynchronous multipath channels, with multiple antennas employed at the receiver.     

Adaptive power techniques for blind channel estimation in CDMA systems

The problem of blind adaptive channel estimation in code-division multiple access (CDMA) systems is considered. Motivated by the iterative power method, which is used in numerical analysis for estimating singular values and singular vectors, we develop recursive least squares (RLS) and least mean squares (LMS) subspace-based adaptive algorithms in order to identify the impulse response of the multipath channel. The schemes proposed in this paper use only the spreading code of the user of interest and the received data and are therefore blind. Both versions (RLS and LMS) exhibit rapid convergence combined with low computational complexity. With the help of simulations, we demonstrate the improved performance of our methods as compared with the already-existing techniques in the literature.     

Autoregressive State Prediction Model Based on Hidden Markov and the Application

Considering the inaccuracies of the traditional Hidden Markov Model (HHM) in the dynamic processes that are close relatively related before and after characterization, an autoregressive state prediction model based on Hidden Markov with Autoregressive model and the coefficient of AR is proposed, which takes the coefficient of AR as the observations of the continuous HHM. Taking the recognition and prediction of heavy vehicle driving states as the research object, a two-layer HMM model is set up to describe the state of the whole steering process of the vehicle. The AR model is for the features extracting of the observations in a short period of time, and the coefficient of AR is extracted as the observed sequence of the lower HMM model library. The upper HMM is used to identify and predict the overall state of the vehicle during steering. The proposed model makes the state sequence with the highest probability on-line predicted in the observed sequence by the Viterbi algorithm, and calculates the state transition law to predict the state of the vehicle in a certain period of time in the future using the Markov prediction algorithm. Combining the double lane change and hook steering to train the parameters of the model, the online identification and prediction of heavy vehicle rollover states can be achieved. The results show that the proposed model can accurately identify the driving state of the vehicle with good real-time performance, and the good prediction on the trend of heavy vehicle driving conditions is verified.     

Numeric Variable Forgetting Factor RLS Algorithm for Second-Order Volterra Filtering

Nonlinear adaptive filtering techniques for system identification (based on the Volterra model) are widely used for the identification of nonlinearities in many applications. In this correspondence, the improved tracking capability of a numeric variable forgetting factor recursive least squares (NVFF-RLS) algorithm is presented for first-order and second-order time-varying Volterra systems under a nonstationary environment. The nonlinear system tracking problem is converted into a state estimation problem of the time-variant system. The time-varying Volterra kernels are governed by the first-order Gauss–Markov stochastic difference equation, upon which the state-space representation of this system is built. In comparison to the conventional fixed forgetting factor recursive least squares algorithm, the NVFF-RLS algorithm provides better channel estimation as well as channel tracking performance in terms of the minimum mean square error (MMSE) for first-order and second-order Volterra systems. The NVFF-RLS algorithm is adapted to the time-varying signals by using the updating prediction error criterion, which accounts for the nonstationarity of the signal. The demonstrated simulation results manifest that the proposed method has good adaptability in the time-varying environment, and it also reduces the computational complexity.     

A new family of concurrent algorithms for adaptive Volterra andlinear filters

A novel idea for introducing concurrency in least squares (LS) adaptive algorithms by sacrificing optimality has been proposed. The resultant class of algorithms provides schemes to fill the wide gap in the convergence rates of LS and stochastic gradient (SG) algorithms. It will be particularly useful in the real time implementations of large-order linear and Volterra filters for which both the LS and SG algorithms are unsuited     

Linearly constrained block adaptive filtering algorithm withoptimum convergence factors

A new linearly constrained adaptive filtering algorithm, the linearly constrained optimum block adaptive (LCOBA) algorithm, is presented. The LCOBA algorithm processes data in blocks and uses variable convergence factors which are optimised in a least square sense. It is superior to Frost's linearly constrained least mean squares algorithm at achieving the conflicting goals of fast convergence with little steady-state error. In addition, its computational requirements generally tend to be smaller than that of the Frost algorithm, as the block length is increased     

A hidden Markov model-based algorithm for fault diagnosis withpartial and imperfect tests

We present a hidden Markov model (HMM) based algorithm for fault diagnosis in systems with partial and imperfect tests. The HMM-based algorithm finds the most likely state evolution, given a sequence of uncertain test outcomes over time. We also present a method to estimate online the HMM parameters, namely, the state transition probabilities, the instantaneous probabilities of test outcomes given the system state and the initial state distribution, that are fundamental to HMM-based adaptive fault diagnosis. The efficacy of the parameter estimation method is demonstrated by comparing the diagnostic accuracies of an algorithm with complete knowledge of HMM parameters with those of an adaptive one. In addition, the advantages of using the HMM approach over a Hamming-distance based fault diagnosis technique are quantified. Tradeoffs in computational complexity versus performance of the diagnostic algorithm are also discussed     

Total least mean squares algorithm

Widrow (1971) proposed the least mean squares (LMS) algorithm, which has been extensively applied in adaptive signal processing and adaptive control. The LMS algorithm is based on the minimum mean squares error. On the basis of the total least mean squares error or the minimum Raleigh quotient, we propose the total least mean squares (TLMS) algorithm. The paper gives the statistical analysis for this algorithm, studies the global asymptotic convergence of this algorithm by an equivalent energy function, and evaluates the performances of this algorithm via computer simulations     

On the Application of the Fast Kalman Algorithm to Adaptive Deconvolution of Seismic Data

The application of a recently proposed fast implementation of the recursive least squares algorithm, called the Fast Kalman Algorithm (FKA) to adaptive deconvolution of seismic data is discussed. The newly proposed algorithm does not require the storage and updating of a matrix to calculate the filter gain, and hence is computationally very efficient. Furthermore, it has an interesting structure yielding both the forward and backward prediction residuals of the seismic trace and thus permits the estimation of a ?smoothed residual? without any additional computations. The paper also compares the new algorithm with the conventional Kalman algorithm (CKA) proposed earlier [3] for seismic deconvolution. Results of experiments on simulated as well as real data show that while the FKA is a little more sensitive to the choice of some initial parameters which need to be selected carefully, it can yield comparable performance with greatly reduced computational effort.     

Averaged stochastic gradient algorithms for adaptive blindmultiuser detection in DS/CDMA systems

In this paper, we present a blind adaptive gradient (BAG) algorithm for code-aided suppression of multiple-access interference (MAI) and narrow-band interference (NBI) in direct-sequence/code-division multiple-access (DS/CDMA) systems. This BAG algorithm is based on the concept of accelerating the convergence of a stochastic gradient algorithm by averaging. This ingenious concept of averaging was invented by Polyak and Juditsky (1992)-this paper examines its application to blind multiuser detection and NBI suppression in DS/CDMA systems. We prove that BAG has identical convergence and tracking properties to recursive least squares (LMS) but has a computational cost similar to the least mean squares (LMS) algorithm-i.e., an order of magnitude lower computational cost than RLS. Simulations are used to compare our averaged gradient algorithm with the blind LMS and LMS schemes     

Adaptive noncoherent DFE for MDPSK signals transmitted over ISIchannels

A novel noncoherent decision-feedback equalization (NDFE) scheme for M-ary differential phase shift-keying signals transmitted over intersymbol interference channels is presented. A suboptimum version with lower computational complexity and a noncoherent linear equalizer (NLE) are derived from the original NDFE scheme. Furthermore, the relation of the novel NLE to a previously proposed NLE is investigated. In contrast to known NDFE schemes, the novel scheme can approach the performance of coherent minimum mean-squared error decision-feedback equalization. For adaptation of the feedforward and feedback filters, efficient novel modified least mean-square and recursive least squares algorithms are presented. Finally, it is shown that the proposed adaptive NDFE scheme is robust against frequency offset     

用神经网络实现VBR视频通信量的在线预测

VBR(Varible Bit Rate)视频信号具有时变性、非线性和突发性等特点,实现该信号通信量的高精度预测难度较大.针对以上问题,本文提出了一种用于VBR视频通信量预测的自适应神经网络模型,网络训练采用离线与在线相结合的方式,同时通过删除不重要的权重,以优化网络的拓扑结构,提高网络的推广能力,降低网络在线学习的计算复杂度;对VBR视频通信量预测的模拟结果表明该模型具有高的预测精度,并能满足通信系统对预测实时性的要求.     

Spectrum and energy efficiency of cooperative spectrum prediction in cognitive radio networks

In this paper, the spectrum and energy efficiency of cooperative spectrum prediction (CSP) in cognitive radio networks are investigated. In addition, the performance of cooperative spectrum prediction is evaluated using a hidden Markov model (HMM) and a multilayer perceptron (MLP) neural network. The cooperation between secondary users in predicting the next channel status employs AND, OR and majority rule fusion schemes. These schemes are compared for HMM and MLP predictors as a function of channel occupancy in term of prediction error, spectrum efficiency and energy efficiency. The impact of busy and idle state prediction errors on the spectrum efficiency is also investigated. Simulation results are presented which show a significant improvement in the spectrum efficiency of the secondary users CSP with the majority rule at the cost of a small degradation in energy efficiency compared to single spectrum prediction and traditional spectrum sensing.

     

Adaptive space-time reduced-rank estimation based on diversity-combined decimation and interpolation applied to interference suppression in CDMA systems

An adaptive low-complexity space-time reduced-rank processor is proposed for interference suppression in asynchronous DS code division multiple access (CDMA) systems based on a diversity-combined decimation and interpolation method. The novel design approach for the processor employs an iterative procedure to jointly optimise the interpolation, decimation and estimation tasks for reduced-rank parameter estimation. Joint iterative least squares design parameter estimators are described and low-complexity adaptive recursive least squares (RLS) algorithms for the proposed structure are developed. To design the decimation unit, the optimal decimation scheme based on the counting principle is presented and lowcomplexity decimation structures are proposed. Linear space-time receivers with antenna arrays based on the proposed reduced-rank processor are then presented and investigated to mitigate multi-access interference and intersymbol interference in an asynchronous DS-CDMA system uplink scenario. An analysis of the convergence properties of the proposed space-time processor is carried out and analytical expressions are derived to predict the mean squared error performance of the proposed processor with RLS algorithms. Simulations show that the proposed processor outperforms the best known reduced-rank schemes at substantially lower complexity.     

基于马尔可夫过程的卫星移动信道模型及长期预测方法

卫星移动信道可被描述为基于有限状态马尔可夫过程的衰落模型,该文分析了卫星信道的可预测性,然后基于加权预测思想提出了一种卫星移动信道长期预测方法,该方法在当前信道采样的基础上进行二次采样,采样频率大于马尔可夫状态转移速率的2倍,利用信道状态的相关性和信道状态转移概率信息来加权预测未来长期内的信道状态,并依据自回归预测模型给出信道预测输出值,仿真结果表明,采用此方法对卫星信道未来的信道状态进行预测,在信噪比较高时均方误差能够达到10-2量级,在自适应传输过程中可以降低系统平均误比特率,且能够提高系统吞吐量性能,这对卫星移动通信系统的自适应传输和自适应资源分配都具有一定的指导意义。     

Adaptive Reduced-Rank Processing Based on Joint and Iterative Interpolation, Decimation, and Filtering

We present an adaptive reduced-rank signal processing technique for performing dimensionality reduction in general adaptive filtering problems. The proposed method is based on the concept of joint and iterative interpolation, decimation and filtering. We describe an iterative least squares (LS) procedure to jointly optimize the interpolation, decimation and filtering tasks for reduced-rank adaptive filtering. In order to design the decimation unit, we present the optimal decimation scheme and also propose low-complexity decimation structures. We then develop low-complexity least-mean squares (LMS) and recursive least squares (RLS) algorithms for the proposed scheme along with automatic rank and branch adaptation techniques. An analysis of the convergence properties and issues of the proposed algorithms is carried out and the key features of the optimization problem such as the existence of multiple solutions are discussed. We consider the application of the proposed algorithms to interference suppression in code-division multiple-access (CDMA) systems. Simulations results show that the proposed algorithms outperform the best known reduced-rank schemes with lower complexity.