CN103227623B - The LMS adaptive filter algorithm of variable step size and filter - Google Patents
The LMS adaptive filter algorithm of variable step size and filter Download PDFInfo
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Abstract
The present invention relates to digital signal processing technique field, be specifically related to a kind of LMS adaptive filter algorithm and filter of variable step size.LMS adaptive filter algorithm provided by the present invention and filter, according to the step value of filtering stage change, therefore can obtain convergence rate and less system stability error faster owing to providing simultaneously; Showing as, provide larger step value in the starting stage of adaptive-filtering, thus convergence rate faster can be obtained, at adaptive-filtering close to providing less step value during stable state, thus less steady-state error value can be obtained.
Description
Technical field
The present invention relates to digital signal processing technique field, be specifically related to a kind of LMS(Least Mean Square of variable step size, lowest mean square) adaptive filter algorithm and filter.
Background technology
Sef-adapting filter is one of the study hotspot in signal transacting field always, and through development for many years, it has been widely used in the fields such as digital communication, radar, sonar, seismology, navigation system, biomedicine and Industry Control.
Most widely used in adaptive algorithm is lowest mean square (LMS, Least Mean Square) algorithm, and LMS algorithm is a kind of searching algorithm, and it, by carrying out suitable adjustment to target function, simplifies the calculating to gradient vector.Due to the simplicity that it calculates, LMS algorithm and other associated algorithms have been widely used in the various application of adaptive-filtering.The basic thought of LMS algorithm is the weight coefficient of adjustment filter, makes the mean square error between the output signal of filter and desired signal minimum.In fields such as system identification (namely using an Adaptable System to realize a unknown system convergence), channel equalizations (namely using a transfer function compensating signal to transmit the distortion caused in the channel), LMS algorithm is widely applied.
LMS sef-adapting filter can not change the concrete structure of filter in actual moving process, but filter weight coefficient can carry out iteration renewal according to the difference of parameter, be and obtain desired signal response, filter weight coefficient can adapt to the situation of change of input signal automatically.
The structure of LMS sef-adapting filter of the prior art is as shown in fig. 1:
Wherein, X (k) is primary signal, W (k) is filter weight coefficient matrix, u is the step-length of sef-adapting filter, d (k) is desired signal, y (k) is output signal, and e (k) is desired signal d (k) and the error amount outputing signal y (k), i.e. e (k)=d (k)-y (k).
Its specific works process is: at a time k, primary signal X (k), after a series of delay line transmission, form corresponding different input signal x (0), the x (1) postponed ... x (k); Input signal after difference postpones is multiplied with corresponding filter weight coefficient, and then by the product addition of gained, obtain the output signal y (k) of moment k, i.e. y (k)=x (0) w (0)+... + x (k) w (k)=X (k) W (k); Output signal error amount e (k) is obtained by e (k)=d (k)-y (k), after error amount e (k) is multiplied with step value u, be multiplied with X (k) transient change amount ue (k) X (k) obtained when filter weight coefficient matrix upgrades.When upper once clock signal arrives, the filter weight coefficient matrix value obtained after upgrading is W (k+1)=W (k)+ue (k) X (k), thus completes the adaptive updates process of filter weight coefficient.
But there is following defect in LMS adaptive filter algorithm of the prior art:
In LMS filtering algorithm in the prior art, its algorithm step-size is fixed value, can not obtain good filter converges time and steady state error value simultaneously.Be in particular in, when step-length u arranges larger, filter can reach convergence state fast, if but when filtering is close to stable state, steady state error value can be comparatively large, the error performance of influential system; When step-length u arranges less, filter can obtain less steady state error value, if in the starting stage of adaptive-filtering, convergence time is longer, needs the training sequence length increasing algorithm.
In sum, a kind ofly the adaptive filter algorithm that can realize less steady-state error value while very fast convergence rate can obtained and filter urgently provides.
Summary of the invention
(1) technical problem that will solve
The object of the present invention is to provide a kind of can acquisition very fast convergence rate while, LMS adaptive filter algorithm and the filter of less steady-state error value can be realized.
(2) technical scheme
Technical solution of the present invention is as follows:
A LMS adaptive filter algorithm for variable step size, comprises step:
S1. the corresponding different input signal postponed is obtained after the delayed process of primary signal;
S2. the product addition of filter weight coefficient corresponding with it for each input signal is obtained the output signal in this moment;
S3. desired signal and described output signal are done difference and obtain error amount;
S4. the product of described error amount and step value and input signal is upgraded described filter weight coefficient as transient change amount;
Described step value is variable.
Preferably, described step-length u (k)=u0+ α | e (k)-e (k-1) |; Wherein, u0 is initial step length, and α is regulatory factor, and e (k) is this computing errors value, and e (k-1) is computing last time errors value.
Preferably, described desired signal is training sequence, and described training sequence selected the training sequence value of regular length before each transmission burst.
Present invention also offers a kind of LMS sef-adapting filter realizing the variable step size of said method:
A LMS sef-adapting filter for variable step size, comprises the delay memory module, adaptive-filtering module and the error generation modules that set gradually; Described delay memory module, adaptive-filtering module and error generation modules are all connected with variable step size generation module;
Described delay memory module comprises some delayers, for carrying out delay disposal to primary signal, obtains the corresponding different input signal postponed;
Described adaptive-filtering module is for upgrading filter weight coefficient and calculating output signal;
Described error generation modules is used for obtaining error amount in conjunction with desired signal and output signal;
Described variable step size generation module is according to step-length u (k)=u0+ α | e (k)-e (k-1) | variable step value is provided; Wherein, u0 is initial step length, and α is regulatory factor, and e (k) is this computing errors value, and e (k-1) is computing last time errors value.
Preferably, described adaptive-filtering module comprises filter weight coefficient updating block and output signal arithmetic element; Described filter weight coefficient updating block and output signal arithmetic element include the multiplier and adder that set gradually.
(3) beneficial effect
LMS adaptive filter algorithm provided by the present invention and filter, because step-length is variable, therefore can obtain convergence rate and less system stability error faster simultaneously; Showing as, provide larger step value in the starting stage of adaptive-filtering, thus convergence rate faster can be obtained, at adaptive-filtering close to providing less step value during stable state, thus less steady-state error value can be obtained.
Accompanying drawing explanation
Fig. 1 is the structural representation of LMS sef-adapting filter in prior art;
Fig. 2 is the model calling schematic diagram of LMS sef-adapting filter in the embodiment of the present invention;
Fig. 3 is the structural representation of LMS sef-adapting filter in the embodiment of the present invention.
Embodiment
Below in conjunction with drawings and Examples, the specific embodiment of the present invention is described further.Following examples only for illustration of the present invention, but are not used for limiting the scope of the invention.
Provide firstly a kind of LMS adaptive filter algorithm of variable step size in the present embodiment, it mainly comprises step:
S1. the corresponding different input signal postponed is obtained after the delayed process of primary signal;
S2. the product addition of filter weight coefficient corresponding with it for each input signal is obtained the output signal in this moment;
S3. desired signal and output signal are done difference and obtain error amount;
S4. the product of error amount and step value and input signal is upgraded filter weight coefficient as transient change amount;
One of greatest improvement point of the present invention is, wherein step value is variable, therefore can obtain convergence rate and less system stability error faster simultaneously; Showing as, provide larger step value in the starting stage of adaptive-filtering, thus convergence rate faster can be obtained, at adaptive-filtering close to providing less step value during stable state, thus less steady-state error value can be obtained.Specifically, the step-length u (k) in the present embodiment=u
0+ α | e (k)-e (k-1) |; Wherein, u
0for initial step length, α is regulatory factor, and e (k) is this computing errors value, and e (k-1) is computing last time errors value.Because step-length can adjust automatically according to the error amount of twice output signal and desired signal, adjustment process can make to provide larger step value u in the starting stage of adaptive-filtering, thus obtain convergence rate faster, at adaptive-filtering close to providing less step value u during stable state, thus obtain less steady-state error value.
Additionally provide a kind of LMS sef-adapting filter realizing the variable step size of said method in the present embodiment, as shown in Figure 2, it mainly comprises the delay memory module, adaptive-filtering module and the error generation modules that set gradually; Postpone memory module, adaptive-filtering module and error generation modules to be all connected with variable step size generation module; Below modules is illustrated respectively.
Postpone memory module and mainly comprise a series of delayer, it is mainly used in carrying out corresponding delay disposal to primary signal, obtains the corresponding different input signal postponed, upgrades for subsequent filter weight coefficient.
Adaptive-filtering module is for upgrading filter weight coefficient and calculating output signal; In the present embodiment, adaptive-filtering module mainly comprises filter weight coefficient updating block and output signal arithmetic element two large divisions; Filter weight coefficient updating block is made up of the adder set gradually and multiplier, can produce the filter weight coefficient of a new round according to input signal values x (k), variable step size value u (k) and corresponding moment output error value e (k), its filter weight coefficient more new formula is w (k+1)=w (k)+u (k) e (k) x (k); Output signal arithmetic element comprises the adder and multiplier that set gradually equally, and it can calculate the output signal y (k) of corresponding moment k according to filter weight coefficient matrix W (k) and input signal matrix X (k).
Error generation modules is used for obtaining error amount in conjunction with desired signal and output signal, and its computing formula is e (k)=d (k)-y (k).
Variable step size generation module, be mainly used according to the real-time output error e(k of filter) size and relevant parameter arrange adjustment sef-adapting filter step-length u(k), show as according to step-length u (k)=u0+ α | e (k)-e (k-1) | variable step value is provided; Wherein, u0 is initial step length, and α is regulatory factor, and e (k) is this computing errors value, and e (k-1) is computing last time errors value.Thus make sef-adapting filter provide larger step-length can produce very fast convergence rate at initial operating stage, the steady-state error value that less step-length can provide less is provided when sef-adapting filter is stable.
Below in conjunction with Fig. 3, the calculating process of the LMS sef-adapting filter of above-mentioned variable step size is illustrated:
K at any one time, input signal X (k) forms burst x (0), the x (1) of a series of difference delay through postponing memory module ... x (k) is as the input of follow-up adaptive-filtering module; Delayer in this module and unit period signal clk are synchronous operation.
Output signal y (k) is made difference with corresponding moment expected signal value d (k) and can be outputed signal error amount e (k), i.e. e (k)=d (k)-y (k).In the present embodiment, expected signal value d (k) training sequence replaces, and training sequence can send and select the known training sequence value of regular length before each transmission burst.In variable step size generation module, under clock cycle signal clk effect, obtain corresponding moment variable step size value u (k)=u
0+ α | e (k)-e (k-1) |.Wherein u
0for system initial step length, generally select smaller value, α is regulatory factor.In the system cloud gray model starting stage, system output signal y (k) is larger with desired signal d (k) error e (k), and adjacent moment error signal relative difference is comparatively large, therefore larger step value can be produced, thus accelerate the convergence of sef-adapting filter.In the system run all right stage, systematic error signal e (k) is less, and the relative error magnitudes of adjacent moment error is less, therefore can produce less step value, thus makes system obtain less steady-state error value.
Adaptive-filtering module comprises filter weight coefficient updating block and output signal arithmetic element, and function as described above.The input signal sequence of generation and variable step size value u (k) is utilized to carry out the renewal synchronous with unit period signal clk to filter weight coefficient.Meanwhile, output signal arithmetic element utilizes the filter weight coefficient after upgrading and input signal sequence to calculate the output signal y (k) of sef-adapting filter, and its computing formula is y (k)=X (k) W (k).
The LMS adaptive filter algorithm of variable step size provided by the present invention and filter are through experimental verification, only increase by two adders in enforcement complexity after, and good steady-state error value can be provided while the convergence rate significantly increasing adaptive-filtering, higher performance is provided.
Above execution mode is only for illustration of the present invention; and be not limitation of the present invention; the those of ordinary skill of relevant technical field; without departing from the spirit and scope of the present invention; can also make a variety of changes and modification, therefore all equivalent technical schemes also belong to protection category of the present invention.
Claims (4)
1. a LMS adaptive filter algorithm for variable step size, comprises step:
S1. the corresponding different input signal postponed is obtained after the delayed process of primary signal;
S2. the product addition of filter weight coefficient corresponding with it for each input signal is obtained the output signal in this moment;
S3. desired signal and described output signal are done difference and obtain error amount;
S4. the product of described error amount and step value and input signal is upgraded described filter weight coefficient as transient change amount;
It is characterized in that, described step value is variable;
Described step-length u (k)=u
0+ α | e (k)-e (k-1) |; Wherein, u
0for initial step length, α is regulatory factor, and e (k) is this computing errors value, and e (k-1) is computing last time errors value.
2. LMS adaptive filter algorithm according to claim 1, is characterized in that, described desired signal is training sequence, and described training sequence selected the training sequence value of regular length before each transmission burst.
3. a LMS sef-adapting filter for variable step size, is characterized in that, comprises the delay memory module, adaptive-filtering module and the error generation modules that set gradually; Described delay memory module, adaptive-filtering module and error generation modules are all connected with variable step size generation module;
Described delay memory module comprises some delayers, for carrying out delay disposal to primary signal, obtains the corresponding different input signal postponed;
Described adaptive-filtering module is for upgrading filter weight coefficient and calculating output signal;
Described error generation modules is used for obtaining error amount in conjunction with desired signal and output signal;
Described variable step size generation module is according to step-length u (k)=u
0+ α | e (k)-e (k-1) | variable step value is provided; Wherein, u
0for initial step length, α is regulatory factor, and e (k) is this computing errors value, and e (k-1) is computing last time errors value.
4. LMS sef-adapting filter according to claim 3, is characterized in that, described adaptive-filtering module comprises filter weight coefficient updating block and output signal arithmetic element; Described filter weight coefficient updating block and output signal arithmetic element include the multiplier and adder that set gradually.
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| CN104283528A (en) * | 2014-09-18 | 2015-01-14 | 河海大学 | Variable-step LMS adaptive filtering method |
| CN107210986B (en) * | 2015-02-16 | 2020-01-03 | 华为技术有限公司 | Method and apparatus for processing signals |
| CN105656570A (en) * | 2015-12-30 | 2016-06-08 | 南方科技大学 | Transmit power calibration method, transmit power calibration system, and radio frequency system |
| CN106998229B (en) * | 2016-12-14 | 2019-02-15 | 吉林大学 | A kind of mode division multiplexing system Deplexing method based on variable step without constraint FD-LMS |
| CN106919808B (en) * | 2017-02-28 | 2019-06-14 | 哈尔滨工业大学深圳研究生院 | Gene identification system based on change step length least mean square error sef-adapting filter |
| CN107395158A (en) * | 2017-07-14 | 2017-11-24 | 歌尔科技有限公司 | Data calibration method and device |
| CN110649912A (en) * | 2018-06-27 | 2020-01-03 | 深圳光启尖端技术有限责任公司 | Modeling method of spatial filter |
| CN109217844B (en) * | 2018-10-30 | 2022-02-25 | 哈尔滨理工大学 | Hyper-parameter optimization method based on pre-training random Fourier feature kernel LMS |
| CN109884596B (en) * | 2019-01-24 | 2020-11-03 | 北京海兰信数据科技股份有限公司 | GPS filtering system and filtering method of marine navigation radar |
| CN110429921B (en) * | 2019-07-30 | 2021-01-01 | 西安电子科技大学 | Variable-step LMS adaptive filtering method and storage medium thereof |
| CN112054782B (en) * | 2020-08-20 | 2022-11-18 | 中国人民解放军陆军勤务学院 | Variable step size factor construction method for LMS adaptive filtering |
| CN112039498B (en) * | 2020-08-27 | 2023-11-14 | 重庆邮电大学 | Self-adaptive signal processing method and medium based on polymorphic variable step-length least mean square |
| CN114063649A (en) * | 2021-11-17 | 2022-02-18 | 国网天津市电力公司电力科学研究院 | Novel variable-step-size transformer robot fish obstacle avoidance device and method |
| CN114861134B (en) * | 2022-07-08 | 2022-09-06 | 四川大学 | Step length determination method for calculating water drop motion track and storage medium |
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| KR100603202B1 (en) * | 2004-06-28 | 2006-07-24 | 삼성전자주식회사 | Method and apparatus for auto selecting step size of LMS type equalizer |
| CN101252559A (en) * | 2007-10-12 | 2008-08-27 | 电子科技大学中山学院 | Method of training sequence time change step length least mean square |
| CN102394593B (en) * | 2011-09-19 | 2014-06-25 | 北京东方联星科技有限公司 | Integrated least-mean-square (LMS) adaptive filter and method |
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