2014年度课件自适应滤波器ch1

1、22:32Adaptive Filter Theory朱国富电子工程研究所 新体制雷达研究室M： O：73459-80422:32Adaptive Filter TheoryChapter 1: IntroductionChapter 1: Introduction1.1.The Filtering Problem1.2.Adaptive Filter1.3.Linear filter structure1.4.Approaches to the development of linear adaptive filtering algorithm1.5.Adaptive Beamforming

2、1.6.Applications1.7.Some historical notes1.1.The Filtering ProblemThe term filter is often used to describe a device in the form of a piece of physical hardware or software that is applied to a set of noisy data in order to extract information about a prescribed quantity of interest.For radar: MTI:

3、Pulse CancellerGMTI: DPCA, STAP1.Filtering2.Smoothing3.PredictingFilters three basic information-processing tasks: 1.Filtering 2.Smoothing 3.PredictingLinear optimal filter:Filter may be classified into Linear and Nonlinear.Those optimal Filter requires a priori information about the statistics of t

4、he dataCost Function Minimum (Mean-Square-Error)To Stationary process: Wiener filter To Non- stationary process: Kalman filter1.2.Adaptive FilterThe Design of a Wiener Filter requires a priori information about the statistics of the data to be present. In fact, this information is not known complete

5、ly. Estimation and plug into is used as filter.However, Adaptive filter may be a more efficient method. By such a device we mean one that is self-designing in that the adaptive filter relies for its operation on a recursive algorithm. Adaptive filter is determined by one or more the following factor

6、s: 1.Rate of convergence 2.Mis-adjustment 3.Tracking 4.Robustness putational requirement 6.Structure 7.Numerical properties.1.3.Linear filter structureThe operation of a Linear adaptive filtering algorithm involves two basic processes: 1.A filtering process-Structure 2.An adaptive process -Algorithm

7、1.3.Linear filter structure FIR IIRFIR:Transversal FilterLattice PredictorSystolic ArrayStructure:1.FIR Transversal FilterCharacteristics:All-zeros filter StableLinear phase shift2.Lattice predictorCharacteristics:Modular structure StableLinear phase shift3.Systolic array a parallel computing networ

8、k ideally suited for mapping a number of important linear algebra computations, such as Matrix multiplication, triangularization, and back substitution.ModularityLocal interconnectionsPipelined Synchronized parallel processing 1.4.Approaches to the development of linear adaptive filtering algorithm.

9、 There is no unique solution to the linear adaptive filtering problem. Basically, We may identify two distinct approaches for deriving recursive algorithms.1) Stochastic Gradient Approach Principle: Cost function=Mean-Squared Error-Second-order function of weight-Minimum-Point-corresponding weight i

10、s the optimum Wiener Solution.Method of steepest descentLMS, Least-mean-square2) Least-Squares Estimation Principle: Cost function=Sum of weight error squares.Block estimation: the input data stream is arranged in the form of blocks of equal length.Recursive estimation: the input data is updated on

11、a sample-by-sample basis. RLS: Recursive least-squares Standard RLS Algorithm: Matrix inversion lemma Square-root RLS algorithm: QR position Fast RLS algorithm: order-recursive adaptive filters fast transversal filters How to choose an adaptive filterWhatever the choice, it has to be cost-effective.

12、Three important issues: computational cost performance and robustness1.5.Adaptive BeamformingTime form of Adaptive filterSpatial form of Adaptive filter Used in radar, sonar, communications, geophysical exploration, astrophysical exploration, and biomedical signal processing. A number of independent

13、 sensors are placed at different point in space to “listen” to the received signal.-The sensors provide a means of sampling the received signal in space. The beamformer has to satisfy two requirements: A steering capability The effect of sources of interference are minimized. Algorithm that minimize

14、s the variance of the beamformer output, subject to this constraint, is therefore referred to as the Minimum-Variance Distortionless Response(MVDR) beamforming algorithm.1.6. ApplicationsThe ability of an adaptive filter to operate satisfactorily in an unknown environments and track time variations

15、of input statistics make the adaptive filter a powerful device for signal processing and control application.The function of the four basic classes of adaptive filter application depicted herein are as following:IdentificationInverse modelingPredictionInterference cancelingIdentificationInverse mode

16、lingPredictionInterference cancelingTable:Applications of adaptive filterClass of adaptive filteringApplication1IdentificationSystem identificationLayered earth modeling2InverseAdaptive equalizationBlind equalization3PredictionLinear predictive codingAdaptive differential pulse-code modulationAutore

17、gressive spectrum analysisSignal detection4Interference cancelingAdaptive noise cancelingEcho cancellationAdaptive beamforming2. Linear Adaptive FilterStochastic Gradient Algorithms:In 1959, Widrow and Hopf devised the Least-Mean-Square Algorithm in their study a pattern recognition scheme. The LMS

18、Algorithm was a simple and yet effective algorithm for the operation of adaptive transversal filter.In 1980s and 1990s, Sayed and Rupp have shown that LMS algorithm is indeed optimal and robust.Recursive Least-Square AlgorithmThe original paper on the standard RLS alg. appears to be that of Plackett

19、(1950).In 1974, Godard used Kalman filter theory to derive a variant of the RLS algorithm.Sayed and Kailath published an expository paper, in which the exact relationship between the RLS algorithm and Kalman filter theory delineated for the first time.In 1981, Gentleman and Kung introduced a numeric

20、ally robust method, that is Systolic Array, based on the position of matrix algebra for solving the RLS problem.3. Adaptive signal-processing ApplicationsAdaptive EqualizationCoding of SpeechSpectrum AnalysisAdaptive Noise CancellationAdaptive BeamformingAdaptive noise cancellation:The initial work

21、on adaptive echo cancellers started around 1965, it appears that Kelly of Bell Telephone Lab, was the first to propose the use of an adaptive filter for echo cancellation.The adaptive line enhancer was originated by Widrow and his co-workers at Stanford University in 1965.Adaptive BeamformingIn the

22、late 1950s, Howells invented the intermediate frequency sidelobe canceller. Howells published his paper in the 1976 Special Issue of the IEEE trans. on AP.The second major contribution to adaptive array antennas was made by Applebaum in 1966. He derived the control law governing the operation of an adapti