An adaptive notch filter for frequency estimation of a periodic signal

Online frequency estimation of a pure sinusoidal signal is a classical problem that has many practical applications. Recently an ANF with global convergence property has been developed for this purpose. There exist some practical applications in which signals are not pure sinusoidal and contain harmonics. Therefore, online frequency estimation of periodic but not necessarily sinusoidal signals espoused by such applications becomes quite important. This note presents an alternative stability analysis for a modified ANF that permits the presence of harmonics in the incoming signal. Also, this stability analysis is simpler and alleviates the problem complexity even in the case of pure sinusoidal signal. Simulation results confirm theoretical issues.     

Self-tuning adaptive frequency tracker

An automatic gain tuning algorithm is proposed for a recently introduced adaptive notch filter. Theoretical analysis and simulations show that, under Gaussian random-walk type assumptions, the proposed extension is capable of adjusting adaptation gains of the filter so as to minimize the mean-squared frequency tracking error without prior knowledge of the true frequency trajectory. A simplified one degree of freedom version of the filter, recommended for practical applications, is proposed as well.     

Stochastic averaging analysis of a steepest-descent-type adaptive time-delay estimation algorithm

In this paper stochastic averaging analysis tools are used to study an adaptive time-delay estimation algorithm. Analyzing such an algorithm is very difficult because of its nonlinear, infinite-dimensional, and time-variant nature. By stochastic averaging analysis, we show that for the time-invariant delay case, the adaptive algorithm output converges weakly to the solution of an ordinary differential equation. Local convergence is demonstrated by showing that the solution of this differential equation converges exponentially to the true delay under reasonable initial conditions. Implementation of the algorithm is also discussed. Guided by the averaging results, a modified algorithm is proposed to eliminate the bias of the delay estimation. Second-order analysis is carried out and the results provide a theoretical justification of the observations made by other researchers with simulation and heuristic argument. Computer simulations are also included to support the analysis.     

On periodic solutions of adaptive systems in the presence of periodic forcing terms

We consider a discrete-time system consisting of a linear plant and a periodically forced feedback controller whose parameters are slowly adapted. Using degree theory, we give sufficient conditions for the existence of periodic solutions. Using linearization methods, we give sufficient conditions for their (in)stability provided the adaptation is slow enough. We then study when the degree theoretic conditions for the existence are satisfied byd-steps-ahead adaptive controllers in the presence of unmodeled dynamics and a persistently exciting periodic reference output.     

Generalized adaptive notch filters with frequency debiasing for tracking of polynomial phase systems

Generalized adaptive notch filters are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. For general patterns of frequency variation the generalized adaptive notch filtering algorithms yield biased frequency estimates. We show that when system frequencies change slowly in a smooth way, the estimation bias can be substantially reduced by means of post-filtering of the frequency estimates. The modified (debiased) algorithm has better tracking capabilities than the original algorithm.     

自适应混合滤波算法在微型飞行器姿态估计中的应用

针对低成本惯性测量单元(IMU)存在漂移和噪声干扰等问题,提出了一种具有自适应参数调节的混合滤波算法。采用四元数法进行系统模型的描述,用梯度下降法对加速度计测得的数据进行处理,再通过互补滤波器将其与陀螺仪测量值进行融合,形成混合滤波算法。同时,考虑到飞行姿态的复杂性,进行参数λ的自适应调节,因而改进后的混合滤波算法,能保证各种飞行姿态变化情况下实时姿态的最优估算。实际系统在线实时性能测试表明,提出的算法简单,估计精度高,易于在嵌入式系统中实现,具有较高推广应用价值。     

Diagnosis of broken rotor bars in induction motors based on harmonic analysis of fault components using modified adaptive notch filter and discrete wavelet transform

This paper proposes a method for fast and accurate detection of broken rotor bars (BRBs) in a three-phase squirrel cage induction motor. The fundamental component of the stator current signal is extracted using a linear time-invariant filter. The resultant residual signal which contains the harmonic components of the current is then used to detect the BRBs, by means of discrete wavelet transform (DWT). Since in experiment it is not possible to break the rotor bars while the motor is under load, finite element method and MATLAB/Simulink are employed to accurately demonstrate the behavior of the running machine as the BRB happens. To get more accuracy, differential evolution (DE) optimization algorithm is used to obtain the corresponding fault impedance for the rotor external circuit of the MATLAB model. Detail coefficients (DCs) of the wavelet decomposition are employed as the new fault indicators. Simulation results show that using DCs of the harmonic component signal rather than the actual current signal, leads to more distinctive fault signatures in the wavelet decomposition. The obtained results suggest that the proposed fault detection scheme can be employed as a highly reliable technique for diagnosing rotor bar failures in running machines.     

基于极大后验估计的自适应容积卡尔曼滤波器

针对标准的容积卡尔曼滤波器(CKF) 设计需要精确已知噪声先验统计知识的问题, 提出一种自适应CKF 算法. 该算法在滤波过程中, 利用Sage-Husa 极大后验估值器对噪声的统计特性进行在线估计和修正, 有效地提高了CKF 的估计精度和数值稳定性. 在某些情况下, 噪声协方差估计会出现异常现象使得滤波发散, 进而提出了相应的改进方法. 仿真结果表明了自适应CKF 算法的可行性和有效性, 且明显改善了标准CKF 算法的滤波效果.     

低信噪比下的跳频信号参数估计

针对基于时频分布的跳频信号参数估计存在信噪比阈值的问题,提出了一种参数估计的算法。该算法首先基于粒子群优化,利用匹配追踪算法对信号进行自适应分解,获取匹配原子;然后基于原子参数对跳频信号进行参数估计。仿真结果表明,该方法不仅解决了匹配追踪算法运算量巨大的问题,而且克服了跳频信号各参数估计误差的相互影响,同时在低信噪比下参数估计的方差也比较小,更加适应于实际的电子战环境。     

State of charge estimation for lithium-ion batteries: An adaptive approach

State of charge (SoC) estimation is of key importance in the design of battery management systems. An adaptive SoC estimator, which is named AdaptSoC, is developed in this paper. It is able to estimate the SoC in real time when the model parameters are unknown, via joint state (SoC) and parameter estimation. The AdaptSoC algorithm is designed on the basis of three procedures. First, a reduced-complexity battery model in state-space form is developed from the well-known single particle model (SPM). Then a joint local observability/identifiability analysis of the SoC and the unknown model parameters is performed. Finally, the SoC is estimated simultaneously with the parameters using the iterated extended Kalman filter (IEKF). Simulation and experimental results exhibit the effectiveness of the AdaptSoC.     

Set-based adaptive estimation for a class of nonlinear systems with time-varying parameters

In this paper, an adaptive estimation technique is proposed for the estimation of time-varying parameters for a class of continuous-time nonlinear system. A set-based adaptive estimation is used to estimate the time-varying parameters along with an uncertainty set. The proposed method is such that the uncertainty set update is guaranteed to contain the true value of the parameters. Unlike existing techniques that rely on the use of polynomial approximations of the time-varying behaviour of the parameters, the proposed technique does require a functional representation of the time-varying behaviour of the parameter estimates. A simulation example and a building systems estimation example are considered to illustrate the developed procedure and ascertain the theoretical results.     

Normalized estimation of fundamental frequency and measurement of harmonics/interharmonics

An adaptive notch filter is presented to estimate the fundamental frequency and measure both harmonics and interharmonics of an almost periodic signal with unknown time-variant fundamental frequency, which has the robustness that the convergence speed is determined by neither amplitude nor frequency of fundamental component. The algorithm forms a one-dimensional slow adaptive integral manifold whose existence and stability are proved by averaging method and Lyapunov stability theorem. The local exponential stability and the ultimate boundedness of fundamental frequency estimation are proved. The local exponential stability makes sure that the fundamental frequency, the harmonic and interharmonic components can be all fast tracked. The principle for adjusting the parameters with their influences on transient and steady-state performance is investigated and decreasing parameters can improve noise characteristic. The validity is verified by simulation results.     

窄带音频信号时差估计算法

研究定位中的窄带音频信号时差估计问题,给出时差估计的信号模型,在研究传统广义相关时差估计算法及基于希尔伯特变换时差估计算法基础上,提出基于接收信号分数阶希尔伯特变换的时差估计算法。通过仿真实验,得到不同变换阶数下归一化后的时差估计均方误差曲线,在最优时差估计域下,与广义相关法及希尔伯特变换时差估计算法相比,提出的算法具有较好的估计性能。     

一种新的线性调频信号数字产生方法

线性调频信号是雷达中常采用的一种脉冲压缩信号。提出了一种新的线性调频信号数字产生方法,该方法是利用两个二阶无限脉冲响应滤波器进行计算产生信号;分析和评价了用该方法产生带宽为15 MHz、脉宽为20 µs的线性调频信号,并进行了幅度误差补偿。实验结果及分析表明：该产生方法具有计算复杂度低、无需大容量存储器且实现容易的特点。     

Impulsive noise suppression in the case of frequency estimation by exploring signal sparsity

The frequency estimation problem is addressed in this work in the presence of impulsive noise. Two typical scenarios are considered; that is, the received data are assumed to be uniformly sampled, i.e., without data missing for the first case and data are randomly missed for the second case. The main objective of this work is to explore the signal sparsity in the frequency domain to perform frequency estimation under the impulsive noise. Therefore, to that end, a DFT-like matrix is created in which the frequency sparsity is provided. The missing measurements are modeled by a sparse representation as well, where missing samples are set to be zeros. Based on this model, the missing pattern represented by a vector is indeed sparse since it only contains zeros and ones. The impulsive noise is remodeled as a superposition of a unknown sparse vector and a Gaussian vector because of the impulsive nature of noise. By utilizing the sparse property of the vector, the impulsive noise can be treated as a unknown parameter and hence it can be canceled efficiently. By exploring the sparsity obtained, therefore, a joint estimation method is devised under optimization framework. It renders one to simultaneously estimate the frequency, noise, and the missing pattern. Numerical studies and an application to speech denoising indicate that the joint estimation method always offers precise and consistent performance when compared to the non-joint estimation approach.     

An adaptive unscented Kalman filter approach to secure state estimation for wireless sensor networks

Wireless sensor networks are vulnerable to false data injection attacks, which may mislead the state estimation. To solve this problem, this paper presents a chi-square test-based adaptive secure state estimation (CTASSE) algorithm for state estimation and attack detection. Taking advantage of Kalman filters, attack signal together with process noise or measurement noise are described as total white Gaussian noise with uncertain covariance matrix. The chi-square test method is used in the adaptation of the total noise covariance and attack detection. Then, a standard adaptive unscented Kalman filter (UKF) is used for the state estimation. Finally, simulation results show that the proposed CTASSE algorithm performs better than other UKFs in state estimation and is also effective in real-time attack detection.     

Kalman filter for adaptive learning of look-up tables with application to automotive battery resistance estimation

In online automotive applications, look-up tables are often used to model nonlinearities in component models that are to be valid over large operating ranges. If the component characteristics change with ageing or wear, these look-up tables must be updated online. Here, a method is presented where a Kalman filter is used to update the entire look-up table based on local estimation at the current operating conditions. The method is based on the idea that the parameter changes observed as a component ages are caused by physical phenomena having effect over a larger part of the operating range that may have been excited. This means that ageing patterns at different operating points are correlated, and these correlations are used to drive a random walk process that models the parameter changes. To demonstrate properties of the method, it is applied to estimate the ohmic resistance of a lithium–ion battery. In simulations the complete look-up table is successfully updated without problems of drift, even in parts of the operating range that are almost never excited. The method is also robust to uncertainties, both in the ageing model and in initial parameter estimates.     

Analysis of an identification algorithm arising in the adaptive estimation of Markov chains

We investigate an algorithm applied to the adaptive estimation of partially observed finite-state Markov chains. The algorithm utilizes the recursive equation characterizing the conditional distribution of the state of the Markov chain, given the past observations. We show that the process “driving” the algorithm has a unique invariant measure for each fixed value of the parameter, and following the ordinary differential equation method for stochastic approximations, establish almost sure convergence of the parameter estimates to the solutions of an associated differential equation. The performance of the adaptive estimation scheme is analyzed by examining the induced controlled Markov process with respect to a long-run average cost criterion. This research was supported in part by the Air Force Office of Scientific Research under Grant AFOSR-86-0029, in part by the National Science Foundation under Grant ECS-8617860 and in part by the DoD Joint Services Electronics Program through the Air Force Office of Scientific Research (AFSC) Contract F49620-86-C-0045.     

基于粒子群算法的跳频信号参数估计*

针对基于时频分布的参数估计存在信噪比阈值和低信噪比下方差大的问题,提出了一种基于多峰优化粒子群算法的跳频信号参数估计新算法。该算法首先将跳频信号分解为时频原子的线性组合,然后由匹配原子获取跳频信号的参数估计。仿真结果表明,基于改进的物种形成粒子群算法能够搜索到与跳频信号分量相匹配的原子,与平滑伪魏格纳分布相比,提出的参数估计算法在低信噪比下具有较小的估计方差,更加适宜于电子战的实际应用。     

An alternative Kalman innovation filter approach for receiver position estimation based on GPS measurements

This article presents an alternative Kalman innovation filter approach for receiver position estimation, based on pseudorange measurements of the global positioning system. First, a dynamic pseudorange model is represented as an ARMAX model and a pseudorange state-space innovation model suitable for both parameter identification and state estimation. The Kalman gain in the pseudorange coordinates is directly calculated from the identified parameters without prior knowledge of the noise properties and the receiver parameters. Then, the pseudorange state-space innovation model is transformed into the receiver state-space innovation model for optimal estimation of the receiver position. Hence, the proposed approach overcomes the drawbacks of the classical Kalman filter approach since it does not require prior knowledge of the noise properties, and the receiver's dynamic model to calculate the Kalman gain. In addition, due to its simplicity, it can be easily implemented in any receiver. To demonstrate the effectiveness of the approach, it is utilized to estimate the position of a stationary receiver and its performance is compared against two versions of the classical Kalman filter approach. The results show that the proposed approach yields consistently good estimation of the receiver position and outperforms the other methods.