CN105403858A - Arrival time difference estimation method - Google Patents

Abstract

The invention provides an arrival time difference estimation method. The method comprises a step of setting of a reference ETDGE algorithm initial value in which an NLMP algorithm is firstly used for arrival time difference rough estimation, an integer place of the arrival time difference truth value is firstly estimated, the numerical value of the integer place serves as the initial value processed by an LMPFTDE algorithm, further fine estimation is then carried out, and the decimal place of the arrival time difference truth value is then estimated.

Description

Step-out time method of estimation

Technical field

The present invention relates to Stochastic signal processing field, more particularly, the present invention relates to the step-out time method of estimation that a kind of precision is higher.

Background technology

Step-out time is estimated to be widely used in the fields such as radiolocation, radar, sonar, seismic survey and biomedicine.Traditional step-out time estimation theory and technology are based on Gaussian distribution and second-order statistic, although this supposition is rational under many circumstances, it meets central limit theorem, the algorithm that step-out time can be made to estimate is tending towards simple, and be convenient to the theoretical analysis carrying out resolving, but there is a large amount of non-Gaussian signals and noise in actual applications.Such as the signal etc. of radar return, underwater sound signal, low-frequency atmospheric, some biomedicine signals and many artificial generations is all non-gaussian distribution.

The non-Gaussian feature of signal and noise, usually causes and supposes that the performance of designed time delay estimator is significantly degenerated based on Gauss, even cisco unity malfunction.Stable distritation is the very important non-Gaussian and random of a class, according to broad sense central limit theorem, Stable distritation is the Limit Distribution that a unique class forms I.i.d. random variables sum, its probability density function exists and continuously, but except little exception, the form that they are not closed.Usually describe with its fundamental function:

φ(t)＝exp{jat-γ|t| ^α[1+jβsgn(t)ω(t,α)]}(1)

In formula (1), $\mathrm{\&omega;}(t,\mathrm{\&alpha;})=\left\{\begin{array}{cc}\tan \left(\mathrm{\&pi;}\mathrm{\&alpha;}/2\right),& \mathrm{\&alpha;}\&NotEqual;1\\ \frac{2}{\mathrm{\&pi;}}\log \left|t\right|,& \mathrm{\&alpha;}=1\end{array}\right.,\mathrm{sgn}\left(t\right)=\left\{\begin{array}{cc}1,& t>0\\ 0,& t=0\\ -1,& t<0\end{array}\right.,$ α ∈ (0,2] be characteristic exponent, represent the thickness of α Stable distritation probability density function hangover, α value is less, and pulse characteristic is more obvious; γ is dispersion coefficient, represents the degree of scatter of α Stable distritation; β is symmetric parameter, is symmetric alpha-stable distribution when β=0, is designated as S α S; A is location parameter, and distribute for S α S, a represents average or the intermediate value of distribution.In four parameters of its fundamental function, most important parameter is characteristic exponent α.When α=2, α Stable distritation is identical with Gaussian distribution.Therefore, α Stable distritation is a kind of Gaussian distribution of broad sense, and it has applicability widely than Gaussian distribution.Think that Gaussian distribution is the special case of α Stable distritation, and claim the situation of 0 < α < 2 to be fractional lower-order α Stable distritation (FLOA distribution).The decay of the probability density function of the attenuation ratio Gaussian process of its probability density function is slow, and thus have thicker hangover, the distinguishing feature of this kind of random signal has more spike than the gaussian signal of routine.So when signal or noise present stronger pulse feature, FLOA distribution is a kind of model preferably.Because FLOA distribution only exists the statistical moment being less than α rank, there is not second order and high-order statistic, fractional lower-order statistics just becomes the important tool that step-out time under non-gaussian α Stable distritation signal noise condition is estimated.

Step-out time algorithm for estimating based on fractional lower-order statistics mainly contains FLOC algorithm, α matching algorithm, the FLOC_WP step-out time method of estimation of nonparametric model class, FLOC_PHAT algorithm, but the step-out time become when this kind of algorithm can not be followed the tracks of; Although AFLC algorithm and LMPTDE can the changes of adaptive tracing step-out time, directly can not estimate non-integer step-out time, must could be obtained the non-integer step-out time of sampling interval by the method for interpolation, improve estimated accuracy.

Summary of the invention

Technical matters to be solved by this invention is for there is above-mentioned defect in prior art, by the ETDGE algorithm of unbiased esti-mator non-integer step-out time generalization process can have been carried out under Gaussian environment, propose a kind of new method that also can work very well in impulse noise environment.

In order to realize above-mentioned technical purpose, according to the present invention, provide a kind of step-out time method of estimation, comprise: with reference to the setting of ETDGE algorithm initial value, first carry out step-out time rough estimate with NLMP algorithm, thus first estimate the integer-bit of step-out time true value, using the initial value of the numerical value of integer-bit as LMPFTDE algorithm process, and then thin estimation further, thus estimate the decimal place of step-out time true value.

Preferably, the concrete LMPFTDE algorithm process adopted in the present invention comprises the steps:

Adopt formula x ₁(n)=s (n)+v ₁(n) and x ₂(n)=s (n-D)+v ₂n () represents two Received signal strength x ₁(n) and x ₂(n); Wherein s (n) is source signal, and D is non-integer time delay, v ₁(n) and v ₂n () is respectively the ground unrest received, and wherein v ₁(n) and v ₂n () obeys α Stable distritation; And source signal and ground unrest are independently, two-way ground unrest is also mutually independently;

Adopt α norm J=||e (n) of error function || _αrepresent the cost function of time delay estimating system;

Adopt the sinc function of sampling to retrain the coefficient arriving FIR filter in TDOA estimation device, determined the output error e (n) in n moment by following formula:

$\begin{array}{c}e\left(n\right)=x_2\left(n\right)-\hat{g}\left(n\right)x_1\left(n-\hat{D}\left(n\right)\right)\\ =x_2\left(n\right)-\hat{g}\left(n\right)\underset{i=-M}{\overset{M}{\&Sigma;}}\sin c(i-\hat{D}(n\left)\right)x_1(n-i)\end{array};$

In formula for gain is estimated, $\sin c\left(k\right)\stackrel{\mathrm{\&Delta;}}{=}\frac{sin\left(\mathrm{\&pi;}k\right)}{\mathrm{\&pi;}k};$

Thus cost function is expressed as $J=E\left\{\right|e\left(n\right){|}^p\}=f\left(\hat{g}\right(n),\hat{D}(n\left)\right);$

According to the gain of following adaptive iteration formulae discovery:

$\begin{array}{c}\hat{g}\left(n+1\right)=\hat{g}\left(n\right)+{\mathrm{\&mu;}}_g\left(-\widehat{\&dtri;}{J}_{\hat{g}}\left(n\right)\right)\\ =\hat{g}\left(n\right)-{\mathrm{\&mu;}}_g\frac{\&part;{\left|e\left(n\right)\right|}^p}{\&part;\hat{g}\left(n\right)}\\ =\hat{g}\left(n\right)+{\mathrm{p\&mu;}}_g{\left|e\left(n\right)\right|}^{p-1}\mathrm{sgn}\&lsqb;(e\left(n\right)\&rsqb;\underset{i=-M}{\overset{M}{\&Sigma;}}\sin c\left(i-\hat{D}\left(n\right)\right)x_1\left(n-i\right)\end{array};$

According to following adaptive iteration formulae discovery step-out time:

$\begin{array}{c}\hat{D}\left(n+1\right)=\hat{D}\left(n\right)+{\mathrm{\&mu;}}_D\left(-\widehat{\&dtri;}{J}_{\hat{D}}\left(n\right)\right)\\ =\hat{D}\left(n\right)-{\mathrm{\&mu;}}_D\frac{\&part;{\left|e\left(n\right)\right|}^p}{\&part;\hat{D}\left(n\right)}\\ =\hat{D}\left(n\right)+{\mathrm{p\&mu;}}_D{\left|e\left(n\right)\right|}^{p-1}\mathrm{sgn}\&lsqb;(e\left(n\right)\&rsqb;\underset{i=-M}{\overset{M}{\&Sigma;}}f\left(i-\hat{D}\left(n\right)\right)x_1\left(n-i\right)\end{array};$

Wherein μ _gand μ _dconverging factor, 1≤p < α≤2;

To the process that two formula are above normalized, obtain iterative formula

$\hat{g}(n+1)=\hat{g}\left(n\right)+\left\{{\mathrm{p\&mu;}}_g\right|e\left(n\right){|}^{p-1}\mathrm{sgn}\&lsqb;\left(e\right(n)\&rsqb;\underset{i=-M}{\overset{M}{\&Sigma;}}\sin c(i-\hat{D}(n\left)\right)x_1(n-i)\}/|\left|x_1\right|{|}_p^p$

$\hat{D}(n+1)=\hat{D}\left(n\right)-\left\{{\mathrm{p\&mu;}}_D\right|e\left(n\right){|}^{p-1}\mathrm{sgn}\&lsqb;\left(e\right(n)\&rsqb;\underset{i=-M}{\overset{M}{\&Sigma;}}f(i-\hat{D}(n\left)\right)x_1(n-i)\}/|\left|x_1\right|{|}_p^p$

Wherein $\left|\right|x_1|{|}_p^p=x_1{(n+M)}^p+x_1{(n+M-1)}^p+...+x_1{(n-M)}^p;$

Thus cost function is expressed as further $E\left\{{\left|e\left(n\right)\right|}^p\right\}=E\left\{{|x_2\left(n\right)-\hat{g}\left(n\right)\underset{i=-M}{\overset{M}{\&Sigma;}}\sin c(i-\hat{D}(n\left)x_1\right(n-i)|}^p\right\}.$

Preferably, described step-out time method of estimation is used for radiolocation.

Preferably, described step-out time method of estimation is used for radar fix.

Preferably, described step-out time method of estimation is used for radiocoustic position finding.

Preferably, described step-out time method of estimation is used for seismic survey.

Preferably, described step-out time method of estimation is used for biomedical detection.

Accompanying drawing explanation

By reference to the accompanying drawings, and by reference to detailed description below, will more easily there is more complete understanding to the present invention and more easily understand its adjoint advantage and feature, wherein:

Fig. 1 schematically shows the principle schematic of step-out time method of estimation according to the preferred embodiment of the invention.

Fig. 2 schematically shows the experimental result of the ETDGE algorithm under experiment 1.

Fig. 3 schematically shows the experimental result of the NLMPFTDE algorithm process under experiment 1.

Fig. 4 schematically shows the experimental result of the ETDGE algorithm under experiment 2.

Fig. 5 schematically shows the experimental result of the LMPFTDE algorithm process under experiment 2.

Fig. 6 schematically shows the experimental result under experiment 3.

It should be noted that, accompanying drawing is for illustration of the present invention, and unrestricted the present invention.Note, represent that the accompanying drawing of structure may not be draw in proportion.Further, in accompanying drawing, identical or similar element indicates identical or similar label.

Embodiment

In order to make content of the present invention clearly with understandable, below in conjunction with specific embodiments and the drawings, content of the present invention is described in detail.

< least mean p-norm non-integer step-out time method of estimation >

In step-out time estimation problem, supposition two Received signal strength x usually ₁(n) and x ₂n () obeys model below:

x ₁(n)＝s(n)+v ₁(n)(2)

x ₂(n)＝s(n-D)+v ₂(n)(3)

Here s (n) is source signal, and D is non-integer time delay, v ₁(n) and v ₂n () is respectively the ground unrest received, and supposition v ₁(n) and v ₂n () obeys α Stable distritation.Source signal and noise are independently, and two-way noise is also mutually independently.Carry out matching time delay by the FIR filter that a coefficient is the sampling of sinc function, can directly estimate the situation that step-out time true value is non-integer sampling interval like this.

In actual applications, the statistical property of signal and noise and its signal to noise ratio (S/N ratio) etc. all likely change in time, the weight coefficient of sef-adapting filter is the binary function of input signal-to-noise ratio and time delay true value, if consider that time delay and signal to noise ratio (S/N ratio) two are because usually carrying out the correction of FIR filter weight coefficient, wave filter is divided into two-stage cascade, one-level is for adapting to the change of signal to noise ratio (S/N ratio), another level is for following the tracks of step-out time, then can make the adaptive process decoupling zero of time delay and signal to noise ratio (S/N ratio), thus improve the performance arriving TDOA estimation.One according to the present invention, based on least mean p-norm criterion, can realize the self-adaptation non-integer step-out time estimator (being called LMPFTDE algorithm process) of step-out time and signal to noise ratio (S/N ratio) decoupling zero as shown in Figure 1 under α Stable distritation noise circumstance.

When processing the step-out time estimation problem under α Stable distritation noise, replace minimum mean square error criterion by minimum dispersion coefficient criterion, can the scope of application of extended method under fractional lower-order α Stable distritation condition.The dispersion coefficient of a α Stable distritation stochastic variable is bounded, the importance and functions of variance when it is equivalent to Gaussian distribution.Therefore, by making minimizing of dispersion coefficient, the average amplitude of evaluated error can be made to reach minimum.New algorithm in this paper adopts α norm J=||e (n) of error function || _αrepresent the cost function of time delay estimating system, avoid the performance degradation caused by lowest mean square criterion.Theoretical by Fractional Lower Order Moments, as long as meet 0 < p < α, the α norm of S α S process is directly proportional to its p rank square.

In step-out time estimator, the sinc function of the coefficient sampling of FIR filter retrains, n moment defeated

Going out error e (n) is:

$\begin{array}{c}e\left(n\right)=x_2\left(n\right)-\hat{g}\left(n\right)x_1\left(n-\hat{D}\left(n\right)\right)\\ =x_2\left(n\right)-\hat{g}\left(n\right)\underset{i=-M}{\overset{M}{\&Sigma;}}\sin c(i-\hat{D}(n\left)\right)x_1(n-i)\end{array}---\left(4\right)$

In formula for gain is estimated, target is herein the average p Norm minimum making error, and namely the p rank square of error is minimum.The cost function of LMPFTDE can be written as this is a two-dimentional nonlinear optimal problem, uses the thought of relaxation method, its decoupling zero is converted into the optimization problem of two one dimensions, carries out iteration, in the hope of optimum solution respectively to gain and step-out time.In certain time delay range, cost function J is unimodal function, has unique minimum value, therefore adopts method of steepest descent, utilizes gradient technique, and substitutes its statistical average with the instantaneous value of error signal.Here, consider directly time delay valuation carry out adaptive iteration, instead of iteration is carried out to the weight vector of wave filter.The gain of LMPFTDE algorithm process and the adaptive iteration formula of step-out time are

$\begin{array}{c}\hat{g}\left(n+1\right)=\hat{g}\left(n\right)+{\mathrm{\&mu;}}_g\left(-\widehat{\&dtri;}{J}_{\hat{g}}\left(n\right)\right)\\ =\hat{g}\left(n\right)-{\mathrm{\&mu;}}_g\frac{\&part;{\left|e\left(n\right)\right|}^p}{\&part;\hat{g}\left(n\right)}\\ =\hat{g}\left(n\right)+{\mathrm{p\&mu;}}_g{\left|e\left(n\right)\right|}^{p-1}\mathrm{sgn}\&lsqb;(e\left(n\right)\&rsqb;\underset{i=-M}{\overset{M}{\&Sigma;}}\sin c\left(i-\hat{D}\left(n\right)\right)x_1\left(n-i\right)\end{array}---\left(5\right)$

$\begin{array}{c}\hat{D}\left(n+1\right)=\hat{D}\left(n\right)+{\mathrm{\&mu;}}_D\left(-\widehat{\&dtri;}{J}_{\hat{D}}\left(n\right)\right)\\ =\hat{D}\left(n\right)-{\mathrm{\&mu;}}_D\frac{\&part;{\left|e\left(n\right)\right|}^p}{\&part;\hat{D}\left(n\right)}\\ =\hat{D}\left(n\right)+{\mathrm{p\&mu;}}_D{\left|e\left(n\right)\right|}^{p-1}\mathrm{sgn}\&lsqb;(e\left(n\right)\&rsqb;\underset{i=-M}{\overset{M}{\&Sigma;}}f\left(i-\hat{D}\left(n\right)\right)x_1\left(n-i\right)\end{array}---\left(6\right)$

Here μ _gand μ _dbe converging factor, get a little positive number, 1≤p < α≤2.

In order to improve stability and the speed of convergence of algorithm, to the process that formula (5), formula (6) are normalized, there is following iterative formula

$\hat{g}(n+1)=\hat{g}\left(n\right)+\left\{{\mathrm{p\&mu;}}_g\right|e\left(n\right){|}^{p-1}\mathrm{sgn}\&lsqb;\left(e\right(n)\&rsqb;\underset{i=-M}{\overset{M}{\&Sigma;}}\sin c(i-\hat{D}(n\left)\right)x_1(n-i)\}/|\left|x_1\right|{|}_p^p---\left(7\right)$

$\hat{D}(n+1)=\hat{D}\left(n\right)-\left\{{\mathrm{p\&mu;}}_D\right|e\left(n\right){|}^{p-1}\mathrm{sgn}\&lsqb;\left(e\right(n)\&rsqb;\underset{i=-M}{\overset{M}{\&Sigma;}}f(i-\hat{D}(n\left)\right)x_1(n-i)\}/|\left|x_1\right|{|}_p^p---\left(8\right)$

In formula (7), formula (8) $\left|\right|x_1|{|}_p^p=x_1{(n+M)}^p+x_1{(n+M-1)}^p+...+x_1{(n-M)}^p.$

Because cost function in comprise sinc function, so cost function is multimodal, can consider by unimodal by selecting suitable initial value scope in practical application.With reference to the setting of ETDGE algorithm initial value, first carry out step-out time rough estimate with NLMP algorithm, namely first estimate the integer-bit of step-out time true value, using the initial value of this value as LMPFTDE algorithm process, and then thin estimation further, then can estimate the decimal place of step-out time true value.

< Computer Simulation >

Source signal s (n) adopts bpsk signal, carrier frequency f _c=25kHz, sample frequency is f _s=100kHz, element duration is 16T _s, T _s=1/f _s, T _sfor the sampling period.Inhibit signal s (n-D) by source signal s (n) through an impulse response is 61 rank FIR filter produce, setting step-out time difference true value D=1.4T _s.The data length of each experiment is 10000 points.

Experiment 1: the performance of ETDGE algorithm and LMPFTDE algorithm process under this experimental verification Gaussian noise environment.First setting noise item is Gaussian reflectivity mirrors (α=2), two-way noise v ₁(n) and v ₂n () is independently, signal to noise ratio (S/N ratio) iterative initial value ε is a very little number, is to ensure that in iteration, denominator is non-vanishing.Choose the power approximately equal that suitable iteration step length μ value makes two kinds of algorithm evaluated errors in the case respectively, as shown in Figure 3, Figure 4 (the tracking situation (SNR=-3dB) that under Gaussian noise, two kinds of algorithm step-out times are estimated), ETDGE algorithm and NLMPFTDE algorithm all can well be converged in non-integer time delay true value 1.4 to the result of 100 MonteCarlo empirical averages.

Experiment 2: the performance of ETDGE algorithm and LMPFTDE algorithm under this experimental check non-Gaussian noise environment.Mixing signal to noise ratio (S/N ratio) under fractional lower-order S α S partition noise (α=1.5) according to setting, wherein represent the variance of signal, γ _nrepresent the dispersion coefficient of noise item, two-way noise v ₁(n) and v ₂n () is also independently.Iterative initial value the effect of ε is with in experiment 1.First the time delay true value D=0 of setting signal, by regulating converging factor μ to make ETDG algorithm be in critical convergence state, and makes the error power approximately equal that ETDGE algorithm and LMPFTDE algorithm are estimated.If now two kinds of algorithms converging factor is separately the equiconvergence factor.Then, setting time delay true value D=1.4, uses μ value of equal value to carry out adaptive iteration.For the tracking situation (MSNR=0dB that two kinds of algorithm time delays under non-Gaussian noise are estimated, α=1.5), as shown in Figure 4, ETDGE algorithm is in order to ensure convergence, employ very little μ, its speed of convergence is extremely slow, does not still converge to time delay true value 1.4 through the iteration of 10000 times, and as shown in Figure 5, LMPFTDE algorithm can converge to time delay true value 1.4 (carrying out the result of 100 MonteCarlo empirical averages) quickly.

Experiment 3: under this Germicidal efficacy non-Gaussian noise environment, NLMP algorithm is to the estimated performance of non-integer step-out time.The setting of non-Gaussian noise is with experiment 2.For the tracking situation (MSNR=0dB, α=1.5) that NLMP algorithm time delay under non-Gaussian noise is estimated, as shown in Figure 6, NLMP algorithm can not converge to non-integer time delay true value 1.4, but can converge to the integer-bit 1 of time delay true value faster.

Thus, in actual applications, first can carry out the rough estimate of step-out time with NLMP algorithm, the initial value using this estimated value as LMPFTDE algorithm, can ensure that LMPFTDE algorithm convergence is to global optimum like this.

Computerized Numerical Simulation result above shows, according to the LMPFTDE algorithm that fractional lower-order statistics theory proposes, adopt the p norm (1 < p≤α) of error function to represent the cost function of adaptive system, avoid the performance degradation caused by lowest mean square criterion.Its essence has carried out Nonlinear Processing to ensure cost function bounded to error function.This algorithm extends the scope of application of ETDGE algorithm, all can arrive by direct estimation decimal preferably, improve the estimated accuracy time difference under gaussian sum fractional lower-order α Stable distritation noise.

In sum, the invention provides based on the step-out time method of the estimation degree of precision of Alpha Gaussian distribution and the application in radiolocation thereof.

In addition, it should be noted that, unless stated otherwise or point out, otherwise the term " first " in instructions, " second ", " the 3rd " etc. describe only for distinguishing each assembly, element, step etc. in instructions, instead of for representing logical relation between each assembly, element, step or ordinal relation etc.

Be understandable that, although the present invention with preferred embodiment disclose as above, but above-described embodiment and be not used to limit the present invention.For any those of ordinary skill in the art, do not departing under technical solution of the present invention ambit, the technology contents of above-mentioned announcement all can be utilized to make many possible variations and modification to technical solution of the present invention, or be revised as the Equivalent embodiments of equivalent variations.Therefore, every content not departing from technical solution of the present invention, according to technical spirit of the present invention to any simple modification made for any of the above embodiments, equivalent variations and modification, all still belongs in the scope of technical solution of the present invention protection.

Claims (7)

1. a step-out time method of estimation, it is characterized in that comprising: with reference to the setting of ETDGE algorithm initial value, first step-out time rough estimate is carried out with NLMP algorithm, thus first estimate the integer-bit of step-out time true value, using the initial value of the numerical value of integer-bit as LMPFTDE algorithm process, and then thin estimation further, thus estimate the decimal place of step-out time true value.

2. step-out time method of estimation according to claim 1, is characterized in that LMPFTDE algorithm process comprises the steps:

Adopt formula x ₁(n)=s (n)+v ₁(n) and x ₂(n)=s (n-D)+v ₂n () represents two Received signal strength x ₁(n) and x ₂(n); Wherein s (n) is source signal, and D is non-integer time delay, v ₁(n) and v ₂n () is respectively the ground unrest received, and wherein v ₁(n) and v ₂n () obeys α Stable distritation; And source signal and ground unrest are independently, two-way ground unrest is also mutually independently;

Adopt α norm J=||e (n) of error function || _αrepresent the cost function of time delay estimating system;

Adopt the sinc function of sampling to retrain the coefficient arriving FIR filter in TDOA estimation device, by under

State the output error e (n) that formula determines the n moment:

$\begin{array}{c}e\left(n\right)=x_2\left(n\right)-\hat{g}\left(n\right)x_1\left(n-\hat{D}\left(n\right)\right)\\ =x_2\left(n\right)-\hat{g}\left(n\right)\underset{i=-M}{\overset{M}{\&Sigma;}}\sin c\left(i-\hat{D}\left(n\right)\right)x_1\left(n-i\right)\end{array};$

In formula for gain is estimated, $\sin c\left(k\right)\stackrel{\mathrm{\&Delta;}}{=}\frac{sin\left(\mathrm{\&pi;}k\right)}{\mathrm{\&pi;}k};$

Thus cost function is expressed as $J=E\left\{\right|e\left(n\right){|}^p\}=f\left(\hat{g}\right(n),\hat{D}(n\left)\right);$

According to the gain of following adaptive iteration formulae discovery:

$\begin{array}{c}\hat{g}\left(n+1\right)=\hat{g}\left(n\right)+{\mathrm{\&mu;}}_g\left(-\widehat{\&dtri;}{J}_{\hat{g}}\left(n\right)\right)\\ =\hat{g}\left(n\right)-{\mathrm{\&mu;}}_g\frac{\&part;|e\left(n\right){|}^p}{\&part;\hat{g}\left(n\right)}\\ =\hat{g}\left(n\right)+{\mathrm{p\&mu;}}_g|e\left(n\right){|}^{p-1}\mathrm{sgn}\&lsqb;(e\left(n\right)\&rsqb;\underset{i=-M}{\overset{M}{\&Sigma;}}\sin c\left(i-\hat{D}\left(n\right)\right)x_1\left(n-i\right)\end{array};$

According to following adaptive iteration formulae discovery step-out time:

$\begin{array}{c}\hat{D}\left(n+1\right)=\hat{D}\left(n\right)+{\mathrm{\&mu;}}_D\left(-\widehat{\&dtri;}{J}_{\hat{D}}\left(n\right)\right)\\ =\hat{D}\left(n\right)-{\mathrm{\&mu;}}_D\frac{\&part;|e\left(n\right){|}^p}{\&part;\hat{D}\left(n\right)}\\ =\hat{D}\left(n\right)-{\mathrm{p\&mu;}}_D|e\left(n\right){|}^{p-1}\mathrm{sgn}\&lsqb;(e\left(n\right)\&rsqb;\underset{i=-M}{\overset{M}{\&Sigma;}}f\left(i-\hat{D}\left(n\right)\right)x_1\left(n-i\right)\end{array};$

Wherein μ _gand μ _dconverging factor, 1≤p < α≤2;

To the process that two formula are above normalized, obtain iterative formula

$\hat{g}(n+1)=\hat{g}\left(n\right)+\left\{{\mathrm{p\&mu;}}_g\right|e\left(n\right){|}^{p-1}\mathrm{sgn}\&lsqb;\left(e\right(n)\&rsqb;\underset{i=-M}{\overset{M}{\&Sigma;}}\sin c(i-\hat{D}(n\left)\right)x_1(n-i)\}/|\left|x_1\right|{|}_p^p$

$\hat{D}(n+1)=\hat{D}\left(n\right)-\left\{{\mathrm{p\&mu;}}_D\right|e\left(n\right){|}^{p-1}\mathrm{sgn}\&lsqb;\left(e\right(n)\&rsqb;\underset{i=-M}{\overset{M}{\&Sigma;}}f(i-\hat{D}(n\left)\right)x_1(n-i)\}/|\left|x_1\right|{|}_p^p$

Wherein $\left|\right|x_1|{|}_p^p=x_1{\left(n+M\right)}^p+x_1{\left(n+M-1\right)}^p+...+x_1{\left(n-M\right)}^p;$

Thus cost function is expressed as further $E\left\{\right|e\left(n\right){|}^p\}=E\{|x_2\left(n\right)-\hat{g}\left(n\right)\underset{i=-M}{\overset{M}{\&Sigma;}}\sin c(i-\hat{D}\left(n\right)x_1(n-i\left)\right){|}^p\}.$

3. step-out time method of estimation according to claim 1 and 2, is characterized in that, described step-out time method of estimation is used for radiolocation.

4. step-out time method of estimation according to claim 1 and 2, is characterized in that, described step-out time method of estimation is used for radar fix.

5. step-out time method of estimation according to claim 1 and 2, is characterized in that, described step-out time method of estimation is used for radiocoustic position finding.

6. step-out time method of estimation according to claim 1 and 2, is characterized in that, described step-out time method of estimation is used for seismic survey.

7. step-out time method of estimation according to claim 1 and 2, is characterized in that, described step-out time method of estimation is used for biomedical detection.