CN116232282B - Time-varying time delay estimation method, device and system based on adaptive all-pass filter - Google Patents
Time-varying time delay estimation method, device and system based on adaptive all-pass filter Download PDFInfo
- Publication number
- CN116232282B CN116232282B CN202310038779.5A CN202310038779A CN116232282B CN 116232282 B CN116232282 B CN 116232282B CN 202310038779 A CN202310038779 A CN 202310038779A CN 116232282 B CN116232282 B CN 116232282B
- Authority
- CN
- China
- Prior art keywords
- time
- delay
- signal
- value
- representing
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 46
- 230000003044 adaptive effect Effects 0.000 title claims description 44
- 108010076504 Protein Sorting Signals Proteins 0.000 claims description 46
- 238000005070 sampling Methods 0.000 claims description 28
- 230000003111 delayed effect Effects 0.000 claims description 23
- 238000007781 pre-processing Methods 0.000 claims description 20
- 239000011159 matrix material Substances 0.000 claims description 7
- 238000012545 processing Methods 0.000 claims description 6
- 238000004891 communication Methods 0.000 claims description 4
- 238000001914 filtration Methods 0.000 abstract description 3
- 230000006870 function Effects 0.000 description 8
- 230000014509 gene expression Effects 0.000 description 7
- 238000011478 gradient descent method Methods 0.000 description 6
- 230000004044 response Effects 0.000 description 6
- 230000006641 stabilisation Effects 0.000 description 5
- 238000011105 stabilization Methods 0.000 description 5
- 238000010586 diagram Methods 0.000 description 4
- 238000011156 evaluation Methods 0.000 description 4
- 230000008569 process Effects 0.000 description 4
- 238000007476 Maximum Likelihood Methods 0.000 description 2
- 230000008859 change Effects 0.000 description 2
- 238000005457 optimization Methods 0.000 description 2
- 230000002441 reversible effect Effects 0.000 description 2
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000004364 calculation method Methods 0.000 description 1
- 230000001934 delay Effects 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000009826 distribution Methods 0.000 description 1
- 239000003814 drug Substances 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000007613 environmental effect Effects 0.000 description 1
- 230000004927 fusion Effects 0.000 description 1
- 238000012417 linear regression Methods 0.000 description 1
- 230000004807 localization Effects 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000006855 networking Effects 0.000 description 1
- 230000010355 oscillation Effects 0.000 description 1
- 230000000737 periodic effect Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 238000001228 spectrum Methods 0.000 description 1
- 230000003068 static effect Effects 0.000 description 1
- 238000000528 statistical test Methods 0.000 description 1
- 238000005728 strengthening Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 230000001629 suppression Effects 0.000 description 1
- 230000001052 transient effect Effects 0.000 description 1
Classifications
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H21/00—Adaptive networks
- H03H21/0012—Digital adaptive filters
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
- Y02E40/40—Arrangements for reducing harmonics
Abstract
The invention discloses a time-varying time delay estimation method, a time-varying time delay estimation device and a time-varying time delay estimation system based on a self-adaptive all-pass filter, wherein the time-varying time delay estimation method comprises the following steps: receiving an input real-time signal and a delay signal; the filter coefficients are calculated according to the following:calculating a delay estimate according to:the invention realizes quick, stable and accurate estimation of time-varying time delay values among different sensor signals through the self-adaptive all-pass filtering time delay estimator, and improves anti-interference performance while ensuring estimation accuracy and estimation efficiency.
Description
Technical Field
The invention relates to the technical field of intelligent network automobiles, in particular to a time-varying time delay estimation method, device and system based on a self-adaptive all-pass filter.
Background
Time delay estimation (Time Delay Estimation, TDE) is an important research content in numerous fields of acoustics, medicine, light source localization, etc., which enables a more accurate time delay estimation between two or more spatially separated sensor signals without the need for additional hardware.
The rapid development and increasing popularity of low cost sensors in recent years has placed a more stringent demand for fast, accurate, stable time delay estimation techniques. For example, an intelligent network-connected automobile with a plurality of advanced vehicle-mounted sensors, controllers, actuators and other devices realizes unmanned operation through functions such as autonomous fusion positioning, reliable environment sensing, efficient decision planning, robust motion control and the like. The primary goal of motion control is to effectively track a reference path on the premise of ensuring the stability of a vehicle, however, unavoidable vehicle bottom layer delays create a great challenge for the existing motion control algorithm. The vehicle bottom layer time delay mainly comes from CAN communication time delay and actuator time delay, and neglecting the time delay CAN cause inaccurate control model and deteriorated control performance, so that transient response and stability of the system are reduced, and further the phenomena of vehicle steering oscillation, instability and the like occur.
Unmanned vehicle platforms used by many academic institutions reduce the underlying latency by installing a wire control module or new actuators, but this additional high performance hardware will result in increased production costs. Therefore, in the field of intelligent networking automobiles, it is highly desirable to provide a method capable of accurately estimating the time delay.
Disclosure of Invention
It is an object of the present invention to provide a time-varying delay estimation method, device and system based on an adaptive all-pass filter, which overcomes or at least alleviates at least one of the above-mentioned drawbacks of the prior art.
To achieve the above objective, an embodiment of the present invention provides a time-varying delay estimation method based on an adaptive all-pass filter, including:
step 1, receiving an input real-time signal and a delay signal;
step 2, calculating a filter coefficient according to the following formula (14):
where a (k) denotes the filter coefficient value of the current time instant k,wherein n is max The index number representing the largest filter; a (k+1) represents a filter coefficient value at the next time k+1; x is X - (k)＝[x(k-1),...,x(k-n max )] T Represents a backward vector, wherein x (k-1) represents a real-time signal of the last time k-1, and x (k-n) max ) Indicating time k-n max T represents transpose of the matrix; x is X + (k-N τ )＝[x(k+1-N τ ),...,x(k+n max -N τ )] T Represents a forward vector, where x (k+1-N) τ ) A delay signal representing the next time k+1, x (k+n) max -N τ ) Indicating time k+n max Time delay signal of N τ Indicating signal delay N τ A sampling time step dt; epsilon represents a preset positive integer for ensuring that the denominator is not 0; ρ represents a preset adaptive learning rate constant coefficient, 0 < ρ < 2/3; e (k) represents a deviation between a true deviation value of the real-time signal and the delay signal and an estimated deviation value calculated based on the current filter coefficient, and is calculated by the following formula:
step 3, calculating a time delay estimated value according to the following formula (6):
wherein τ represents a delay estimate; a, a n The coefficients of the filter are represented by the coefficients of the filter, n=0, 1, n max The method comprises the steps of carrying out a first treatment on the surface of the dt represents the sampling time step.
Preferably, the filter coefficient value at the initial time is 0.
Preferably, step 1 further comprises: preprocessing an input real-time signal and a delay signal, including:
judging whether the input real-time signal and delay signal are straight-line segment signals or not, if so, executing preprocessing; wherein the preprocessing comprises the following steps: respectively adding a preset noiseless discrete sine signal sequence X to an input real-time signal and a delay signal sin ：
Where A represents the sinusoidal signal amplitude, ω represents the sinusoidal signal frequency, dt represents the sampling time step, and m represents the number of real-time or delayed signals within the window.
Preferably, the method further comprises:
and 4, judging the stability of the calculated time delay estimated value, and outputting an updated time delay estimated value when the updating condition is met, wherein the method comprises the following steps:
obtaining an output delay estimate according to the following equation (17):
wherein,representing the last time obtained delay estimated value; />Representing a currently obtained delay estimated value; thr represents a preset threshold;
wherein MSE last Time delay estimation value representing k-1 timeMean square error index of (2); MSE (mean square error) new Delay estimate representing time k>Mean square error index of (2); m represents the number of sampling time steps dt; x is x 1 (t) a real-time signal sequence representing all signal values; x is x 2 (t) a delayed signal sequence representing all signal values; x is x 1 (i) Representing a real-time signal sequence x 1 The ith signal value in (t), i being an index; />Representing a time-lapse signal sequence x 2 (t)>The value of the signal is then used to determine,is a discrete offset number calculated based on the delay estimation value and the discrete step dt.
The embodiment of the invention provides a time-varying time delay estimation device based on an adaptive all-pass filter, which comprises the following components:
the input module is used for receiving the input real-time signal and the delay signal;
a filter coefficient processing module for calculating filter coefficients according to the following equation (14):
where a (k) denotes the filter coefficient value of the current time instant k,wherein n is max The index number representing the largest filter; a (k+1) represents a filter coefficient value at the next time k+1; x is X - (k)＝[x(k-1),...,x(k-n max )] T Represents a backward vector, wherein x (k-1) represents a real-time signal of the last time k-1, and x (k-n) max ) Indicating time k-n max Real-time signal, T tableTranspose the matrix; x is X + (k-N τ )＝[x(k+1-N τ ),...,x(k+n max -N τ )] T Represents a forward vector, where x (k+1-N) τ ) A delay signal representing the next time k+1, x (k+n) max -N τ ) Indicating time k+n max Time delay signal of N τ Indicating signal delay N τ A sampling time step dt; epsilon represents a preset positive integer for ensuring that the denominator does not represent 0; ρ represents a preset adaptive learning rate constant coefficient, 0 < ρ < 2/3; e (k) represents a deviation between a true deviation value of the real-time signal and the delay signal and an estimated deviation value calculated based on the current filter coefficient, and is calculated by the following formula:
a delay estimation module for calculating a delay estimation value according to the following equation (6):
wherein τ represents a delay estimate; a, a n The coefficients of the filter are represented by the coefficients of the filter, n=0, 1, n max The method comprises the steps of carrying out a first treatment on the surface of the dt represents the sampling time step.
Preferably, the filter coefficient value at the initial time is 0.
Preferably, the apparatus further comprises:
the preprocessing module is used for preprocessing the input real-time signal and the delay signal, and comprises the following steps:
judging whether the input real-time signal and delay signal are straight-line segment signals or not, and if so, executing preprocessing; wherein the preprocessing comprises the following steps: respectively adding a preset noiseless discrete sine signal sequence X to an input real-time signal and a delay signal sin ：
Where A represents the sinusoidal signal amplitude, ω represents the sinusoidal signal frequency, dt represents the sampling time step, and m represents the number of real-time or delayed signals within the window.
Preferably, the apparatus further comprises:
the updating module is used for judging the stability of the time delay estimated value obtained by the time delay estimating module, and outputting the updated time delay estimated value when the updating condition is met, and comprises the following steps:
obtaining an output delay estimate according to the following equation (17):
wherein,representing the last time obtained delay estimated value; />Representing a currently obtained delay estimated value; thr represents a preset threshold;
wherein MSE last Time delay estimation value representing k-1 timeMean square error index of (2); MSE (mean square error) new Delay estimate representing time k>Mean square error index of (2); m represents the number of sampling time steps dt; x is x 1 (t) a real-time signal sequence representing all signal values; x is x 2 (t) a delayed signal sequence representing all signal values; x is x 1 (i) Representing an ith signal value in the real-time signal sequence, i being an index; />Representing the +.sup.th in the delayed signal sequence>Signal value->Is a discrete offset number calculated based on the delay estimation value and the discrete step dt.
The embodiment of the invention provides a time-varying time delay estimation system based on a self-adaptive all-pass filter, which is applied to an intelligent network-connected vehicle and comprises the following components:
the environment sensing device is used for acquiring environment information of the vehicle;
the decision planning device is used for carrying out global track planning according to the environment information and the vehicle state information and outputting planning information to the motion control device;
according to the above embodiment and any optional manner thereof, the time-varying delay estimation device based on the adaptive all-pass filter is configured to estimate a delay value of vehicle bottom layer CAN communication and output the estimated delay value to the motion control device;
and the motion control device is used for calculating a control instruction by combining the planning information and the time delay value to control the vehicle to run.
Due to the adoption of the technical scheme, the invention has the following advantages:
the invention realizes quick, stable and accurate estimation of time-varying time delay values among different sensor signals through the self-adaptive all-pass filtering time delay estimator, and improves anti-interference performance while ensuring estimation accuracy and estimation efficiency.
Drawings
Fig. 1 is a flow chart of a time-varying delay estimation method based on an adaptive all-pass filter according to an embodiment of the present invention.
Fig. 2 shows a complete flow diagram of a time-varying delay estimation method based on an adaptive all-pass filter according to an embodiment of the present invention.
Fig. 3 shows a schematic structural diagram of a time-varying delay estimation device based on an adaptive all-pass filter according to an embodiment of the present invention.
Fig. 4 shows a schematic structural diagram of a time-varying delay estimation system based on an adaptive all-pass filter according to an embodiment of the present invention.
Detailed Description
In the drawings, the same or similar reference numerals are used to denote the same or similar elements or elements having the same or similar functions. Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
In the description of the present invention, the terms "center", "longitudinal", "lateral", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like indicate an orientation or a positional relationship based on that shown in the drawings, only for convenience of description and simplification of the description, and do not indicate or imply that the apparatus or element to be referred to must have a specific orientation, be configured and operated in a specific orientation, and therefore should not be construed as limiting the scope of protection of the present invention.
In the case of no conflict, the technical features in the embodiments and the implementation modes of the present invention may be combined with each other, and are not limited to the embodiments or implementation modes where the technical features are located.
The existing time delay estimation method mainly comprises the following steps: 1) Generalized correlation method. The principle is that pre-filtering treatment is firstly carried out before cross-correlation is carried out on different sensor signals, which is equivalent to weighting treatment in a frequency domain, thus being beneficial to strengthening spectrum components of source signals in received signals and improving signal to noise ratio, thereby obtaining higher time delay estimation precision, but having poor periodic interference suppression effect on extremely strong correlation, requiring statistic priori knowledge of input signals and noise and having no universality; 2) Maximum likelihood estimation method. The method is characterized in that a conditional probability density function related to time delay is constructed under the assumption of fixed time delay, static data and long observation time, then the time delay is determined by maximizing the value of the density function, and a maximum likelihood estimator is gradually effective when the observation time tends to infinity, but the probability distribution of signals is difficult to obtain in practical application; 3) An adaptive delay estimation method. Compared with other time delay estimation methods, the self-adaptive time delay estimation method does not need statistical priori knowledge of input signals and noise, can continuously adjust the self-adaptive time delay estimation method according to a certain optimal criterion in the self-adaptive process, is suitable for tracking dynamically-changing input environments, is simple in algorithm implementation, can accurately and rapidly estimate time delay, but has slower convergence speed and lower estimation accuracy when the signal-to-noise ratio is low. In addition, there are many other methods in the delay estimation field, such as delay estimation based on linear regression, delay estimation based on hilbert variation, and the like. However, in general, any delay estimation algorithm has its own drawbacks, and further improvements are needed.
The invention will be further described with reference to the drawings and the specific embodiments, it being noted that the technical solution and the design principle of the invention will be described in detail with only one optimized technical solution, but the scope of the invention is not limited thereto.
The embodiment of the invention provides a time-varying time delay estimation method based on an adaptive all-pass filter, which is shown in fig. 1 and comprises the following steps:
step 1, receiving an input real-time signal and a delay signal;
step 2, calculating a filter coefficient according to the following formula (14):
where a (k) denotes the filter coefficient value of the current time instant k,wherein n is max The index number representing the largest filter; a (k+1) represents a filter coefficient value at the next time k+1; x is X - (k)＝[x(k-1),...,x(k-n max )] T Represents a backward vector, wherein x (k-1) represents a real-time signal of the last time k-1, and x (k-n) max ) Indicating time k-n max T represents transpose of the matrix; x is X + (k-N τ )＝[x(k+1-N τ ),...,x(k+n max -N τ )] T Represents a forward vector, where x (k+1-N) τ ) A delay signal representing the next time k+1, x (k+n) max -N τ ) Indicating time k+n max Time delay signal of N τ Indicating signal delay N τ A sampling time step dt; epsilon represents a preset positive integer for ensuring that the denominator does not represent 0; ρ represents a preset adaptive learning rate constant coefficient, 0 < ρ < 2/3; e (k) represents a deviation between a true deviation value of the real-time signal and the delay signal and an estimated deviation value calculated based on the current filter coefficient, and is calculated by the following formula:
step 3, calculating a time delay estimated value according to the following formula (6):
wherein τ represents a delay estimate; a, a n The coefficients of the filter are represented by the coefficients of the filter, n=0, 1, n max The method comprises the steps of carrying out a first treatment on the surface of the dt represents the sampling time step.
Wherein the filter coefficient value at the initial time is 0.
Wherein, step 1 may further comprise: preprocessing an input real-time signal and a delay signal, including:
judging whether the input real-time signal and delay signal are straight-line segment signals or not, if so, executing preprocessing; wherein the preprocessing comprises the following steps: respectively adding a preset noiseless discrete sine signal sequence X to an input real-time signal and a delay signal sin ：
Where A represents the sinusoidal signal amplitude, ω represents the sinusoidal signal frequency, dt represents the sampling time step, and m represents the number of real-time or delayed signals within the window.
Wherein, as shown in fig. 1, the method may further include:
and 4, judging the stability of the calculated time delay estimated value, and outputting an updated time delay estimated value when the updating condition is met, wherein the method comprises the following steps:
obtaining an output delay estimate according to the following equation (17):
wherein,representing the last time obtained delay estimated value; />Representing a currently obtained delay estimated value; thr represents a preset threshold;
wherein MSE last Time delay estimation value representing k-1 timeMean square error index of (2); MSE (mean square error) new Delay estimate representing time k>Mean square error index of (2); m represents the number of sampling time steps dt; x is x 1 (t) a real-time signal sequence representing all signal values; x is x 2 (t) a delayed signal sequence representing all signal values; x is x 1 (i) Representing a real-time signal sequence x 1 The ith signal value in (t), i being an index; />Representing a time-lapse signal sequence x 2 (t)>The value of the signal is then used to determine,is a discrete offset number calculated based on the delay estimation value and the discrete step dt.
The time-varying delay estimation method based on the adaptive all-pass filter provided by the invention is described below through another embodiment. Fig. 2 shows a complete flow diagram of a time-varying delay estimation method based on an adaptive all-pass filter according to an embodiment of the present invention. The method mainly comprises three parts of a window signal processing strategy, an adaptive all-pass filter (an FIR-based all-pass filter+an LMS-based adaptive algorithm) and a time delay estimation stabilization strategy. Updating a signal sequence in a window by using a real-time/time-delay signal, judging whether a stored signal approximates a straight line or not based on the peak value/trough value of the window signal, if so, processing the window signal based on a time-varying sinusoidal signal, inputting the window signal into the real-time/time-delay signal sequence, and outputting the window signal into the processed real-time/time-delay signal sequence; an all-pass filter based on an FIR finite impulse response filter is designed to realize online estimation of time delay, the input is a real-time/time delay signal sequence, and the output is a time delay estimation value; based on the LMS algorithm, the adaptive adjustment of the filter parameters is realized, the convergence of the filter estimation result is ensured, the input is a real-time/delay signal sequence, and the output is a filter coefficient; and designing a delay estimation stabilization strategy based on a mean square error evaluation index, eliminating the error estimation value output by the self-adaptive all-pass filter due to noise interference, inputting the error estimation value as a delay estimation value, and outputting the error estimation value as a processed new delay estimation value.
2.1 adaptive all-pass Filter
The adaptive all-pass filter includes an FIR-based all-pass filter and an LMS-based adaptive algorithm, which are described below.
2.1.1 all-pass filter based on FIR
Constructing a signal channel model:
H(ω)＝e -jτω (1)
wherein: h is the fourier transform of an all-pass filter H, i.e., |h (ω) |=1, j is an imaginary number, ω represents the frequency, and τ is the time delay between the real-time signal and the delayed signal.
With the real-time signal as input and the delayed signal as output, the filter h effects a change in the phase of the signal without changing the amplitude. Since the phase change depends on the delay, the delay value τ can be obtained by estimating the filter h.
The embodiment of the invention constructs an all-pass filter H (omega) based on the ratio of the FIR forward and backward frequency responses:
wherein: p (e) jω ) Is the forward frequency response of the FIR filter P, P (e -jω ) Is the backward frequency response of the FIR filter P.
Let N τ ＝τ/dt，N τ Indicating that the signal is delayed N due to delay characteristics τ The sampling time step dt is a sampling time step, and the value of the sampling time step dt can be flexibly adjusted according to actual needs and preset. k represents the current time, then based on equation (2), the signal at the current time, i.e. the real-time signal x (k) and the delayed signal x (k-N) τ ) Linear treatment gives formula (3), wherein: * For the convolution operator,the formulas representing the sides of the arrow are equivalent, p (k) and p (-k) being forward and reverse expressions of the FIR, respectively, forward being the use of future information and reverse being the use of past information:
setting a support n max FIR, n of individual filter coefficients max For the largest index number of the filter, this value also defines the upper bound τ of the delay estimate max ＝n max * dt, N τ ≤n max Let n represent the index of the filter coefficients, n e [0, n max ]。
The FIR filter response p (n) can be determined by the filter coefficients a n Described as formula (4):
thus, the all-pass filter of equation (3) can be converted to linear expression (5) based on FIR:
in the method, in the process of the invention,the method is characterized in that an all-pass filter expression formula based on convolution is converted into a linear expression based on FIR, high-efficiency expression of the all-pass filter is realized by avoiding complex convolution calculation, and finally, a linear coefficient can be rapidly solved to obtain a time delay estimated value.
When the filter coefficientsWhen equation (1) and equation (2) are derived at ω=0, dH (ω)/dω is calculated, and equation (6) is obtained by equalizing the values of equation (1) and equation (2), so that the delay estimated value τ can be calculated:
the above equations (1) - (6) convert the estimate of the delay value τ into the filter coefficientsIs a function of the estimate of (2). Setting x (k) as the current input real-time signal, x (k-N) τ ) For the current input delay signal, let the filter coefficient a 0 =1, then the linear expression of formula (5) is formula (7):
wherein:X + (k-N τ )＝[x(k+1-N τ ),...,x(k+n max -N τ )] T called forward vector, X - (k)＝[x(k-1),...,x(k-n max )] T Called backward vector, ">Can be expressed as vector +.> Can be expressed as vector +.>
Then the real-time signal x (k) and the delayed signal x (k-N) τ ) Can be further expressed as the following linear formula (8):
due to the real-time signal x (k) and the delayed signal x (k-N) τ ) Let d (k) =x (k-N τ )-x(k)，The delay estimation problem turns into an optimization problem: by minimizing the measurement samples d (k) and by the current filter coefficients +.>The deviation between y (k) is calculated, so that an optimal filter coefficient a is obtained, and then the optimal filter coefficient a is substituted into the formula (6), so that a time delay estimated value tau can be obtained.
The invention iteratively updates the filter coefficient a (k) based on a gradient descent method, wherein a (k) represents the filter coefficient value at the current moment, namely the moment k, and a is the integral expression of the filter coefficient and does not distinguish specific moment. The value of the latest filter coefficient a (k) is used to calculate the delay estimate τ.
The invention defines the deviation between d (k) and y (k) as:
the value is a deviation value defined when calculating the filter coefficient based on a gradient descent method, and specifically represents: the deviation between the real deviation value of the real-time/time-delay signal and the estimated deviation value calculated based on the current filter coefficient defines the performance index function required by the gradient descent method based on the quadratic term of the deviation.
The defined performance index function is expressed as the following formula (10):
J(k)＝|e(k)| 2 (10)
the current gradients may be:
the updated filter coefficients are expressed as equation (12):
wherein: μ is a learning rate parameter of the gradient descent method.
2.1.2 LMS-based adaptive algorithm
The invention obtains a time-varying learning rate parameter mu based on an LMS algorithm, is used for ensuring error convergence in an optimization process, and finally realizes an Adaptive All-pass Filter (AAPF) for estimating time delay. The set adaptive learning rate is formula (13):
in combination with the adaptive learning rate μ, equation (12) becomes:
wherein: ρ is an adaptive learning rate constant coefficient, 0 < ρ < 2/3; epsilon is a very small positive integer used to ensure that the denominator is not 0.
In the present invention, the filter coefficient values at the initial time may be arbitrary values, and may be set to 0 in all, for example. All initial values of 0 are set in the concrete implementation, and the coefficient value of the filter can be quickly converged to a proper value when the coefficient is updated by a gradient descent method.
2.2 delay estimation stabilization strategy
When the output of the adaptive all-pass filter is simulated and verified based on real-time and time delay signal data, the phenomenon that the output result is changed between different values at high frequency due to noise interference exists, and even false estimated values such as negative numbers appear, so that the result of the time delay estimation is unstable.
In the embodiment of the invention, a delay estimation stabilization strategy is designed based on the mean square error evaluation index, so that the stability of a delay estimation result is improved and the error estimation value is eliminated.
The main idea of the delay estimation stabilization strategy is to use statistical tests. Setting: there is a real-time signal sequence x containing all signal values within M sample time steps dt 1 (t) and delay signal sequence x 2 (t) the range of values of the delay estimate is [ tau ] min ,τ max ]I.e. the upper bound is τ max The lower bound is τ min . Time delay estimated value based on last time (k-1 time)And delay estimate at the current time (time k)>Calculating MSE using (15) last Delay estimate representing time k-1 +.>MSE is calculated using equation (16) new Delay estimate representing time k>Mean square error index of (2):
wherein x is 1 (i) Representing an ith signal value in the real-time signal sequence, i being an index;representing the +.sup.th in the delayed signal sequence>Signal value->Is a discrete offset number calculated based on the delay estimation value and the discrete step dt.
In essence, the evaluation index may be obtained by using the MSE mean square error provided by formulas (15) - (16), or may be obtained by calculating other evaluation criteria such as variance or standard deviation.
Based on the MSE index, the delay estimation updating strategy provided by the invention is shown in the following formula (17):
wherein: τ (k) represents the estimated value of time delay at time k, thr 1 The threshold value is updated for time delay estimation, and the value can be flexibly set in advance according to actual needs, for example Thr is set 1 =0.2. By comparing the variances of the estimated values of adjacent moments to the real-time and delay signals in the same window, when the variance between the two is not large, the result of delay estimation is assumed to be unreliable, the estimated value of the last moment is reserved at the moment, otherwise, the delay result is carried outUpdating and outputting the result of the time delay estimation at the current moment.
2.3 Window Signal processing strategy
Because the filter coefficient a (k) is iteratively updated based on the gradient descent method in the embodiment of the invention, if the real-time and time-delay signal sequences stored in the current time window are both approximate to straight line segments, the performance index function tends to 0, so that the currently calculated gradient value tends to 0, namely the gradient vanishes phenomenon, as shown in the formula (18):
wherein: 0 is zero matrix. The "gradient vanishes" makes the iteratively updated filter coefficient a (k+1) approximately equal to the filter coefficient value a (k) at the previous time, as shown in equation (19). If the window signal sequence is always approximate to a straight line segment within a period of time, the time delay estimated value is always unchanged, and the time delay estimated error is greatly increased.
Embodiments of the present invention contemplate real-time signals x (k) and delayed signals x (k-N) within a window τ ) An ideal signal component is superimposed on the basis of the above, and the signal component meets the characteristics of amplitude time variation, uncorrelation with window signals and no noise, so that the generated new window signal sequence is ensured not to be approximate to a straight line segment all the time, and the original time delay and noise characteristics between signals are not changed.
Therefore, the embodiment of the invention judges whether the signal stored in the window approximates a straight line or not based on the wave crest/wave trough value of the window signal, and introduces a time-varying and noiseless discrete signal with any amplitude to process the window signal, thereby effectively avoiding larger estimation errors caused by the gradient vanishing phenomenon when the LMS algorithm dynamically adjusts the filter coefficient.
Specifically, the embodiment of the invention introduces a noise-free discrete sine signal sequence X sin ：
X sin ＝A·[sin(1·ω·dt),sin(2·ω·dt),...,sin(m·ω·dt)] (20)
Wherein: dt is the sampling time step length, A is the sine signal amplitude, omega is the sine signal frequency, and m is the number of real-time or delayed signals in a window; x (k) is the real-time signal sequence in the current k moment window, X (k) max 、X(k) min Respectively the peak value and the trough value, X (k-N τ ) For delaying signal sequences within the current k-time window, X (k-N τ ) max 、X(k-N τ ) min Respectively the wave crest and wave trough values, X '(k) and X' (k-N) τ ) Respectively updated real-time and time-delay signal sequences Thr 2 For signal update threshold, in one example of the present invention, a=1, ω=1, m=50, thr is set 2 ＝10 -4 It can also be flexibly set to other values according to actual needs, which is not limited herein.
The embodiment of the invention provides a time-varying time delay estimation method based on a self-adaptive all-pass filter, which realizes rapid, stable and accurate estimation of time-varying time delay values among different sensor signals, ensures estimation accuracy and estimation efficiency and improves anti-interference performance.
The embodiment of the invention also provides a time-varying delay estimation device based on the adaptive all-pass filter, as shown in fig. 3, which comprises:
an input module 31 for receiving an input real-time signal and a delay signal;
a filter coefficient processing module 32 for calculating filter coefficients according to the following equation (14):
where a (k) denotes the filter coefficient value of the current time instant k,wherein n is max The index number representing the largest filter; a (k+1) represents the nextFilter coefficient values at time k+1; x is X - (k)＝[x(k-1),...,x(k-n max )] T Represents a backward vector, wherein x (k-1) represents a real-time signal of the last time k-1, and x (k-n) max ) Indicating time k-n max T represents transpose of the matrix; x is X + (k-N τ )＝[x(k+1-N τ ),...,x(k+n max -N τ )] T Represents a forward vector, where x (k+1-N) τ ) A delay signal representing the next time k+1, x (k+n) max -N τ ) Indicating time k+n max Time delay signal of N τ Indicating signal delay N τ A sampling time step dt; epsilon represents a preset positive integer for ensuring that the denominator does not represent 0; ρ represents a preset adaptive learning rate constant coefficient, 0 < ρ < 2/3; e (k) represents a deviation between a true deviation value of the real-time signal and the delay signal and an estimated deviation value calculated based on the current filter coefficient, and is calculated by the following formula:
a delay estimation module 33, configured to calculate a delay estimation value according to the following equation (6):
wherein τ represents a delay estimate; a, a n The coefficients of the filter are represented by the coefficients of the filter, n=0, 1, n max The method comprises the steps of carrying out a first treatment on the surface of the dt represents the sampling time step.
Wherein the filter coefficient value at the initial time is 0.
Wherein the apparatus may further comprise:
a preprocessing module 34, configured to preprocess the input real-time signal and the delay signal, including:
judging whether the input real-time signal and delay signal are straight-line segment signals or not, if so, executing preprocessing; wherein the preprocessing comprises the following steps: respectively adding a preset noiseless discrete sine signal sequence X to an input real-time signal and a delay signal sin ：
Where A represents the sinusoidal signal amplitude, ω represents the sinusoidal signal frequency, dt represents the sampling time step, and m represents the number of real-time or delayed signals within the window.
Wherein the apparatus may further comprise:
the updating module 35 is configured to perform stability judgment on the delay estimation value obtained by the delay estimation module, and output an updated delay estimation value when the update condition is satisfied, where the updating module includes:
obtaining an output delay estimate according to the following equation (17):
wherein,representing the last time obtained delay estimated value; />Representing a currently obtained delay estimated value; thr represents a preset threshold;
wherein MSE last Time delay estimation value representing k-1 timeMean square error index of (2); MSE (mean square error) new Delay estimate representing time k>Mean square error index of (2); m represents the number of sampling time steps dt;x 1 (t) a real-time signal sequence representing all signal values; x is x 2 (t) a delayed signal sequence representing all signal values; x is x 1 (i) Representing a real-time signal sequence x 1 The ith signal value in (t), i being an index; />Representing a time-lapse signal sequence x 2 (t)>The value of the signal is then used to determine,is a discrete offset number calculated based on the delay estimation value and the discrete step dt.
The embodiment of the invention also provides a time-varying time delay estimation system based on the adaptive all-pass filter, which is applied to an intelligent network-connected vehicle, as shown in fig. 4, and comprises the following steps:
an environment sensing device 41 for acquiring environment information of the vehicle;
decision planning means 42 for performing global trajectory planning based on the environmental information and the vehicle state information, and outputting the planning information to motion control means 44;
the time-varying time delay estimating device 43 based on the adaptive all-pass filter is configured to estimate a time delay value of the vehicle bottom layer CAN communication and output the time delay value to the motion control device 44;
the motion control device 44 is used for calculating control instructions to control the vehicle to run in combination with the planning information and the time delay value.
The embodiment of the invention provides a time-varying time delay estimation device and a time-varying time delay estimation system based on a self-adaptive all-pass filter, which realize rapid, stable and accurate estimation of time-varying time delay values among different sensor signals, ensure estimation accuracy and estimation efficiency and improve anti-interference performance.
Finally, it should be pointed out that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting. Those of ordinary skill in the art will appreciate that: the technical schemes described in the foregoing embodiments may be modified or some of the technical features may be replaced equivalently; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (9)
1. A time-varying delay estimation method based on an adaptive all-pass filter, comprising:
step 1, receiving an input real-time signal and a delay signal;
step 2, calculating a filter coefficient according to the following formula (14):
where a (k) denotes the filter coefficient value of the current time instant k,wherein n is max The index number representing the largest filter; a (k+1) represents a filter coefficient value at the next time k+1; x is X - (k)＝[x(k-1),...,x(k-n max )] T Represents a backward vector, wherein x (k-1) represents a real-time signal of the last time k-1, and x (k-n) max ) Indicating time k-n max T represents transpose of the matrix; x is X + (k-N τ )＝[x(k+1-N τ ),...,x(k+n max -N τ )] T Represents a forward vector, where x (k+1-N) τ ) A delay signal representing the next time k+1, x (k+n) max -N τ ) Indicating time k+n max Time delay signal of N τ Indicating signal delay N τ A sampling time step dt; epsilon represents a preset positive integer for ensuring that the denominator is not 0; ρ represents a preset adaptive learning rate constant coefficient, 0 < ρ < 2/3; e (k) represents a deviation between a true deviation value of the real-time signal and the delay signal and an estimated deviation value calculated based on the current filter coefficient, and is calculated by the following formula:
step 3, calculating a time delay estimated value according to the following formula (6):
wherein τ represents a delay estimate; a, a n The coefficients of the filter are represented by the coefficients of the filter, n=0, 1, n max The method comprises the steps of carrying out a first treatment on the surface of the dt represents the sampling time step.
2. The adaptive all-pass filter-based time-varying delay estimation method of claim 1, wherein the filter coefficient value at the initial time is 0.
3. The adaptive all-pass filter-based time-varying delay estimation method of claim 1, wherein step 1 further comprises: preprocessing an input real-time signal and a delay signal, including:
judging whether the input real-time signal and delay signal are straight-line segment signals or not, and if so, executing preprocessing; wherein the preprocessing comprises the following steps: respectively adding a preset noiseless discrete sine signal sequence X to an input real-time signal and a delay signal sin ：
X sin ＝A·[sin(1·ω·dt),sin(2·ω·dt),...,sin(m·ω·dt)]，
Where A represents the sinusoidal signal amplitude, ω represents the sinusoidal signal frequency, dt represents the sampling time step, and m represents the number of real-time or delayed signals within the window.
4. The adaptive all-pass filter-based time-varying delay estimation method of claim 1, further comprising:
and 4, judging the stability of the calculated time delay estimated value, and outputting an updated time delay estimated value when the updating condition is met, wherein the method comprises the following steps:
obtaining an output delay estimate according to the following equation (17):
wherein,representing the last time obtained delay estimated value; />Representing a currently obtained delay estimated value; thr represents a preset threshold;
wherein MSE last Time delay estimation value representing k-1 timeMean square error index of (2); MSE (mean square error) new Delay estimate representing time k>Mean square error index of (2); m represents the number of sampling time steps dt; x is x 1 (t) a real-time signal sequence representing all signal values; x is x 2 (t) a delayed signal sequence representing all signal values; x is x 1 (i) Representing a real-time signal sequence x 1 The ith signal value in (t), i being an index; />Representing a time-lapse signal sequence x 2 (t)>The value of the signal is then used to determine,is a discrete offset number calculated based on the delay estimation value and the discrete step dt.
5. A time-varying delay estimation device based on an adaptive all-pass filter, comprising:
the input module is used for receiving the input real-time signal and the delay signal;
a filter coefficient processing module for calculating filter coefficients according to the following equation (14):
where a (k) denotes the filter coefficient value of the current time instant k,wherein n is max The index number representing the largest filter; a (k+1) represents a filter coefficient value at the next time k+1; x is X - (k)＝[x(k-1),...,x(k-n max )] T Represents a backward vector, wherein x (k-1) represents a real-time signal of the last time k-1, and x (k-n) max ) Indicating time k-n max T represents transpose of the matrix; x is X + (k-N τ )＝[x(k+1-N τ ),...,x(k+n max -N τ )] T Represents a forward vector, where x (k+1-N) τ ) A delay signal representing the next time k+1, x (k+n) max -N τ ) Indicating time k+n max Time delay signal of N τ Indicating signal delay N τ A sampling time step dt; epsilon represents a preset positive integer for ensuring that the denominator does not represent 0; ρ represents a preset adaptive learning rate constant coefficient, 0 < ρ < 2/3; e (k) represents the true deviation value of the real-time signal and the delay signal and is based on the current filter coefficientThe deviation between the calculated estimated deviation values is calculated by the following formula:
a delay estimation module for calculating a delay estimation value according to the following equation (6):
wherein τ represents a delay estimate; a, a n The coefficients of the filter are represented by the coefficients of the filter, n=0, 1, n max The method comprises the steps of carrying out a first treatment on the surface of the dt represents the sampling time step.
6. The adaptive all-pass filter-based time-varying delay estimation device of claim 5, wherein the filter coefficient value at the initial time is 0.
7. The adaptive all-pass filter-based time-varying delay estimation device of claim 5, further comprising:
the preprocessing module is used for preprocessing the input real-time signal and the delay signal, and comprises the following steps:
judging whether the input real-time signal and delay signal are straight-line segment signals or not, and if so, executing preprocessing; wherein the preprocessing comprises the following steps: respectively adding a preset noiseless discrete sine signal sequence X to an input real-time signal and a delay signal sin ：
X sin ＝A·[sin(1·ω·dt),sin(2·ω·dt),...,sin(m·ω·dt)]，
Where A represents the sinusoidal signal amplitude, ω represents the sinusoidal signal frequency, dt represents the sampling time step, and m represents the number of real-time or delayed signals within the window.
8. The adaptive all-pass filter-based time-varying delay estimation device of claim 5, further comprising:
the updating module is used for judging the stability of the time delay estimated value obtained by the time delay estimating module, and outputting the updated time delay estimated value when the updating condition is met, and comprises the following steps:
obtaining an output delay estimate according to the following equation (17):
wherein,representing the last time obtained delay estimated value; />Representing a currently obtained delay estimated value; thr represents a preset threshold;
wherein MSE last Time delay estimation value representing k-1 timeMean square error index of (2); MSE (mean square error) new Delay estimate representing time k>Mean square error index of (2); m represents the number of sampling time steps dt; x is x 1 (t) a real-time signal sequence representing all signal values; x is x 2 (t) a delayed signal sequence representing all signal values; x is x 1 (i) Representing an ith signal value in the real-time signal sequence, i being an index; />Representing the +.sup.th in the delayed signal sequence>Signal value->Is a discrete offset number calculated based on the delay estimation value and the discrete step dt.
9. A time-varying delay estimation system based on an adaptive all-pass filter, applied to an intelligent network-connected vehicle, comprising:
the environment sensing device is used for acquiring environment information of the vehicle;
the decision planning device is used for carrying out global track planning according to the environment information and the vehicle state information and outputting planning information to the motion control device;
the apparatus according to any one of claims 5-8, configured to estimate a latency value of vehicle under-layer CAN communication and output the estimated latency value to the motion control apparatus;
and the motion control device is used for calculating a control instruction by combining the planning information and the time delay value to control the vehicle to run.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310038779.5A CN116232282B (en) | 2023-01-12 | 2023-01-12 | Time-varying time delay estimation method, device and system based on adaptive all-pass filter |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310038779.5A CN116232282B (en) | 2023-01-12 | 2023-01-12 | Time-varying time delay estimation method, device and system based on adaptive all-pass filter |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN116232282A CN116232282A (en) | 2023-06-06 |
| CN116232282B true CN116232282B (en) | 2023-12-19 |
Family
ID=86577905
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202310038779.5A Active CN116232282B (en) | 2023-01-12 | 2023-01-12 | Time-varying time delay estimation method, device and system based on adaptive all-pass filter |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116232282B (en) |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6430295B1 (en) * | 1997-07-11 | 2002-08-06 | Telefonaktiebolaget Lm Ericsson (Publ) | Methods and apparatus for measuring signal level and delay at multiple sensors |
| KR101321290B1 (en) * | 2012-05-22 | 2013-10-28 | 연세대학교 원주산학협력단 | Holter system with atrial fibrillation waveform extraction and therof method |
| CN106603036A (en) * | 2016-11-24 | 2017-04-26 | 北京理工大学 | Adaptive time delay estimation method based on low-order interpolation filter |
| CN108284841A (en) * | 2017-12-11 | 2018-07-17 | 江苏大学 | A kind of distributed-driving electric automobile transport condition adaptive iteration method of estimation |
| CN110531777A (en) * | 2019-08-13 | 2019-12-03 | 北京理工大学 | Quadrotor attitude control method and system based on Auto Disturbances Rejection Control Technique |
| CN110909863A (en) * | 2019-10-12 | 2020-03-24 | 西安理工大学 | Artificial neural network-based estimation method for time delay of sky and earth waves of Roland |
| CN115143954A (en) * | 2022-09-05 | 2022-10-04 | 中国电子科技集团公司第二十八研究所 | Unmanned vehicle navigation method based on multi-source information fusion |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8063824B2 (en) * | 2008-08-26 | 2011-11-22 | Soneticom, Inc. | Magnitude-squared coherence filtering in a time difference of arrival (TDOA) or group delay interferometric geolocation system |
| CN105940445B (en) * | 2016-02-04 | 2018-06-12 | 曾新晓 | A kind of voice communication system and its method |
-
2023
- 2023-01-12 CN CN202310038779.5A patent/CN116232282B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6430295B1 (en) * | 1997-07-11 | 2002-08-06 | Telefonaktiebolaget Lm Ericsson (Publ) | Methods and apparatus for measuring signal level and delay at multiple sensors |
| KR101321290B1 (en) * | 2012-05-22 | 2013-10-28 | 연세대학교 원주산학협력단 | Holter system with atrial fibrillation waveform extraction and therof method |
| CN106603036A (en) * | 2016-11-24 | 2017-04-26 | 北京理工大学 | Adaptive time delay estimation method based on low-order interpolation filter |
| CN108284841A (en) * | 2017-12-11 | 2018-07-17 | 江苏大学 | A kind of distributed-driving electric automobile transport condition adaptive iteration method of estimation |
| CN110531777A (en) * | 2019-08-13 | 2019-12-03 | 北京理工大学 | Quadrotor attitude control method and system based on Auto Disturbances Rejection Control Technique |
| CN110909863A (en) * | 2019-10-12 | 2020-03-24 | 西安理工大学 | Artificial neural network-based estimation method for time delay of sky and earth waves of Roland |
| CN115143954A (en) * | 2022-09-05 | 2022-10-04 | 中国电子科技集团公司第二十八研究所 | Unmanned vehicle navigation method based on multi-source information fusion |
Non-Patent Citations (3)
| Title |
|---|
| An Adaptive All-Pass Filter for Time-Varying Delay Estimation;Beth Jelfs等;IEEE Signal Processing Letters;第28卷;628 - 632 * |
| 基于神经网络方法的可变分数延迟FIR滤波器设计;李晓东, 何松柏, 赵辉, 虞厥邦;信号处理(第05期);525-527 * |
| 通信导航一体化波形设计与接收方法优化;许笑笑;中国优秀硕士学位论文全文数据库;40-60 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN116232282A (en) | 2023-06-06 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Hu et al. | Gain-constrained recursive filtering with stochastic nonlinearities and probabilistic sensor delays | |
| CN107561503B (en) | Adaptive target tracking filtering method based on multiple fading factors | |
| Lázaro-Gredilla et al. | Adaptively biasing the weights of adaptive filters | |
| CN105891810B (en) | A kind of quick self-adapted joint delay time estimation method | |
| CN108490396B (en) | Ultra-short baseline positioning method based on underwater acoustic signal Kalman filtering | |
| US20140269887A1 (en) | Equalizer and detector arrangement employing joint entropy-based calibration | |
| WO2006008611A1 (en) | Multiple hypothesis channel estimation and prediction for ofdm systems | |
| CN111950711A (en) | Second-order hybrid construction method and system of complex-valued forward neural network | |
| CN106059531B (en) | A kind of non-negative sef-adapting filter | |
| CN116232282B (en) | Time-varying time delay estimation method, device and system based on adaptive all-pass filter | |
| CN114157345B (en) | Unmanned aerial vehicle cluster collaborative airspace anti-interference method based on data assistance | |
| CN110266388B (en) | PMD (polarization mode dispersion) equalization method and device, electronic equipment and storage medium | |
| CN109061686B (en) | Self-adaptive multipath estimation method based on recursive generalized maximum mutual entropy | |
| CN106603036A (en) | Adaptive time delay estimation method based on low-order interpolation filter | |
| CN107070825B (en) | Wavelet weighted multi-mode blind equalization method based on simulated annealing wolf pack optimization | |
| CN117240666A (en) | Neural network underwater acoustic channel estimation method based on cluster self-attention mechanism | |
| CN107330468B (en) | Multi-sensor distributed data fusion method based on Cherenov fusion criterion | |
| CN107018104B (en) | Wavelet weighted multi-mode blind equalization method based on mixed monkey swarm optimization | |
| CN109474258B (en) | Nuclear parameter optimization method of random Fourier feature kernel LMS (least mean square) based on nuclear polarization strategy | |
| CN105388471A (en) | Adaptive electromagnetic field time delay estimation method and device | |
| Zhang et al. | Robust transmitted waveform and received filter design for cognitive radar in the presence of signal-dependent interference | |
| Berkhoff et al. | Parallel fast-array recursive least squares filters for active noise control with on-line system identification | |
| CN109861937B (en) | Underwater acoustic channel estimation method and system based on MSASSWOMP algorithm | |
| Rani et al. | Adaptive synchronization and linear channel parameter estimation using adaptive filtering | |
| Wang et al. | Research on model fusion algorithm based on CSI fingerprint localization |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |