CN-122019952-A - Noise filtering method and system of sensor

CN122019952ACN 122019952 ACN122019952 ACN 122019952ACN-122019952-A

Abstract

The embodiment of the invention provides a noise filtering method and a noise filtering system of a sensor, wherein the method comprises the steps of modeling noise statistics characteristics of signals of the sensor by adopting Gaussian-Gaussian inverse exponential mixing distribution aiming at the sensor used in an automatic driving scene to obtain a noise model, constructing a joint probability density function of a system state based on a system state equation and a measurement equation, forming the joint probability density function into a joint posterior probability density function by adopting a variable decibel method, solving an optimal approximate probability density function by minimizing KL divergence between the approximate probability density function and the joint posterior probability density function, alternately updating q (x k )、q(y k )、q(π k )、q(λ k ) by utilizing a fixed point iteration method until iteration convergence, and obtaining an optimal estimated value of the system state x k according to the converged approximate probability density function. The fitting degree of noise description is improved from the source, and accurate adaptation and efficient suppression of sensor multi-mode noise are achieved.

Inventors

Cui dongshun
Liu Shede
GAO ZHENYU
OUYANG TINGHUI
LI XIN
ZHANG WEICHAO

Assignees

广智微芯(扬州)有限公司

Dates

Publication Date: 20260512
Application Date: 20251222

Claims (10)

1. A method of noise filtering of a sensor, comprising: Step 1, modeling noise statistics characteristics of signals of a sensor used in an automatic driving scene by adopting Gaussian-Gaussian reverse-exponential mixing distribution to obtain a noise model, and representing the noise model as: p GGIE (v k |π)＝πN(v k ;0,R k )+(1-π)GIE(v k ;0,R k ,v k ) (1) Wherein N (v k ;0,R k ) represents a gaussian distribution, which is used for constructing and obtaining the noise model based on the gaussian distribution N (v k ;0,R k ) when the signal of the sensor is normal, and GIE (v k ;0,R k ,v k ) represents a gaussian-inverse exponential distribution, which is used for constructing and obtaining the noise model based on the gaussian-inverse exponential distribution GIE (v k ;0,R k ,u k ) when the signal of the sensor is interfered; v k denotes the noise of the signal of the sensor at time k, R k denotes the measurement noise variance matrix, v k denotes the degree of freedom parameter, pi denotes the mixing probability, which is modeled as a Beta distribution: p(π)=Be(π;e,1-e) (2) Wherein e is a mixed weight coefficient; And (2) combining the formula (1) and the formula (2), and enabling a noise probability density function of the signal of the sensor to be as follows: p(v k )＝eN(v k ;0,R k )+(1-e)GIE(v k ;0,R k ,v k ) (3) step 2, constructing a joint probability density function of a system state based on the system state equation and the measurement equation, wherein the auxiliary parameters comprise that x k 、y k 、π k 、λ k ,x k represents the system state at k time, y k represents Bernoulli random variables, pi k represents the mixing probability, and lambda k represents the mixing parameter; Step 3, adopting a variable decibel leaf method, forming a joint posterior probability density function p (Θ k |z 1:k ) by using the joint probability density function, and approximating the joint posterior probability density function p (Θ k |z 1:k ) to the product of the approximate probability density functions q (x k )、q(y k )、q(π k )、q(λ k ) of each x k 、y k 、π k 、λ k ,x k ; Step 4, solving an optimal approximate probability density function by minimizing KL divergence between the approximate probability density function and the joint posterior probability density function, and alternately updating q (x k )、q(y k )、q(π k )、q(λ k ) by using a fixed point iteration method until iteration converges; and step 5, acquiring an optimal estimated value of the system state x k according to the approximate probability density function after convergence, and realizing the filtering of the signals of the sensor.
2. The noise filtering method of a sensor according to claim 1, wherein step 2 comprises: According to the measurement equation z k ＝H k x k +v k , the measurement likelihood probability density function is: p(z k |x k )＝eN(z k ;H k x k ,R k )+(1-e)GIE(z k ;H k x k ,R k ,v k ) (4) Wherein x k is a k moment system state, the system state at least comprises a gesture, a speed or a position, z k is a measurement value, the measurement value at least comprises a position, and H k is a measurement matrix; The probability mass function is modeled by introducing Bernoulli distribution random variables, and the probability mass function is expressed as: p(y|π)=π y (1-π) 1-y (5) Wherein y represents a discrete value of 0 or 1; according to the system state equation x k ＝F k x k-1 +ω k , the one-step predictive probability density function of the system is modeled as a gaussian distribution Wherein F k is a state transition matrix, x k-1 represents a system state at time k-1, and ω k represents a state noise matrix; z 1:k-1 represents the measurement sequence from time 1 to k-1, P k|k-1 represents the mean and scale matrix of the system state, respectively; Transforming the measurement likelihood probability density function into: Wherein y k ,λ k ,π k ,v k is an auxiliary parameter, and represents a bernoulli random variable, a mixing parameter, a mixing probability and a degree of freedom parameter, IE (lambda k ;v k ) represents an inverse exponential distribution, and probability density function expressions of the inverse exponential distribution IE (lambda; v) are IE(λ k ;v k )＝(v k /λ k 2 )exp(-v k /λ k );p(y k |π k ) and p (pi k ) as follows: p(π k )＝Beta(π k ;e,1-e) (9) And taking the measurement likelihood probability density function, the probability quality function and the prediction probability density function as a joint probability density function of the system state.
3. The noise filtering method of a sensor according to claim 2, wherein step 3 comprises: Introducing a variational Bayesian method, forming a joint posterior probability density function p (Θ k |z 1:k ) by using the joint probability density function, and approximating the joint posterior probability density function p (Θ k |z 1:k ) to the product of the approximate probability density functions of x k 、λ k 、y k 、π k respectively: p(Θ k |z 1:k )≈q(x k )q(λ k )q(y k )q(π k ) (10) Wherein, the Z 1:k is the measurement sequence from 1 to k times, q (·) represents the approximate probability density function.
4. The method for noise filtering of a sensor according to claim 3, wherein the step 4 specifically comprises obtaining an optimal approximate probability density function by minimizing KL divergence between the approximate probability density function and the joint posterior probability density function, and the optimal solution of the formula (10) satisfies: Where E [. Cndot. ] represents the expectation that θ is any one element in Θ, Θ (-θ) is the set of all elements in Θ except for θ, A constant term related to θ; The variation parameters based on q (x k ) and q (R k ) are mutually coupled characteristics, and the solution (x k )、q(y k )、q(π k )、q(λ k ) is realized by adopting a fixed point iteration method, wherein: At the i+1th iteration, the approximate posterior probability density distribution of the i-th iteration is used to approximate the expectation, and the joint posterior probability density function p (Θ k ,z 1:k ) is expressed as: correspondingly, the logarithmic form of the joint probability density function p (Θ k ,z 1:k ) is Wherein, the Representing a constant related to x k .
5. The method of noise filtering of a sensor of claim 4, wherein step 4 comprises: The step of alternately updating q (x k )、q(y k )、q(π k )、q(λ k ) using a fixed point iterative method includes: let θ=x k be the number, Q i+1 (x k ) posterior the probability density function is: Wherein, the The measurement noise variance matrix representing the corrected k+1 time is to Expressed as: Wherein, the Representing the corrected measurement noise variance matrix at the k moment; Let θ=y k be the number, Wherein, the Representing a constant term associated with y k , m representing the dimension of the measurement; From the bernoulli distribution, q i+1 (y k ) is: Wherein, the Representing constant terms independent of y k , exp representing a shorthand form of an exponential function, tr representing the trace of the solution matrix; Wherein, the A state one-step predictor is indicated, Representing a state one-step predictive probability density; Update q i+1 (y k ) to bernoulli distribution: Wherein, the Representing bernoulli distribution probability parameters: the expectations of y k are: Let θ=pi k , substituting formula (12) into formula (11) Wherein, the Represents a constant associated with pi k ; update q (i+1) (π k ) to Beta distribution: Wherein, the Expressed as: The expectations of log (pi k ) and log (1-pi k ) are: wherein, psi (·) represents the characteristic function of the variable, And The specific calculation mode is given by the formula (25); let θ=λ k be the sum of, Wherein, the For equation (20), Represents a constant associated with λ k ; update q (i+1) (λ k ) to a generalized inverse gaussian: Wherein, the The expectations of lambda k and log (lambda k ) are: Wherein, the A dedicated function representing a second type of modified bezier function.
6. A noise filtering system for a sensor, comprising: The noise model construction unit is used for modeling the noise statistical characteristics of the signals of the sensors by adopting Gaussian-Gaussian inverse coefficient mixed distribution aiming at the sensors used in the automatic driving scene to obtain a noise model, and the noise model is expressed as: p GGIE (v k |π)＝πN(v k ;0,R k )+(1-π)GIE(v k ;0,R k ,v k ) (1) Wherein N (v k ;0,R k ) represents a gaussian distribution, which is used for constructing and obtaining the noise model based on the gaussian distribution N (v k ;0,R k ) when the signal of the sensor is normal, and GIE (v k ;0,R k ,v k ) represents a gaussian-inverse exponential distribution, which is used for constructing and obtaining the noise model based on the gaussian-inverse exponential distribution GIE (v k ;0,R k ,v k ) when the signal of the sensor is interfered; v k denotes the noise of the signal of the sensor at time k, R k denotes the measurement noise variance matrix, v k denotes the degree of freedom parameter, pi denotes the mixing probability, which is modeled as a Beta distribution: p(π)=Be(π;e,1-e) (2) Wherein e is a mixed weight coefficient; And (2) combining the formula (1) and the formula (2), and enabling a noise probability density function of the signal of the sensor to be as follows: p(v k )＝eN(v k ;0,R k )+(1-e)GIE(v k ;0,R k ,v k ) (3) The system comprises a joint probability density function construction unit, a measurement unit and a control unit, wherein the joint probability density function construction unit is used for constructing a joint probability density function of a system state based on the system state equation and the measurement equation, wherein auxiliary parameters comprise x k 、y k 、π k 、λ k ,x k representing the system state at the moment k, y k representing Bernoulli random variables, pi k representing the mixing probability and lambda k representing the mixing parameters; The conversion unit is used for forming a joint posterior probability density function p (Θ k |z 1:k ) by adopting a variable decibel leaf method, and approximating the joint posterior probability density function p (Θ k |z 1:k ) to the product of the approximate probability density functions q (x k )、q(y k )、q(π k )、q(λ k ) of x k 、y k 、π k 、λ k ,x k respectively; The iteration unit is used for solving the optimal approximate probability density function by minimizing KL divergence between the approximate probability density function and the joint posterior probability density function, and alternately updating q (x k )、q(y k )、q(π k )、q(λ k ) by using a fixed point iteration method until iteration converges; and the solving unit is used for acquiring the optimal estimated value of the system state x k according to the approximate probability density function after convergence, and filtering the signals of the sensor.
7. The noise filtering system of a sensor according to claim 6, wherein the joint probability density function construction unit is specifically configured to: According to the measurement equation z k ＝H k x k +v k , the measurement likelihood probability density function is: p(z k |x k )＝eN(z k ;H k x k ,R k )+(1-e)GIE(z k ;H k x k ,R k ,v k ) (4) Wherein x k is a k moment system state, the system state at least comprises a gesture, a speed or a position, z k is a measurement value, the measurement value at least comprises a position, and H k is a measurement matrix; The probability mass function is modeled by introducing Bernoulli distribution random variables, and the probability mass function is expressed as: p(y|π)=π y (1-π) 1-y (5) Wherein y represents a discrete value of 0 or 1; according to the system state equation x k ＝F k x k-1 +ω k , the one-step predictive probability density function of the system is modeled as a gaussian distribution Wherein F k is a state transition matrix, x k-1 represents a system state at time k-1, and ω k represents a state noise matrix; z 1:k-1 represents the measurement sequence from time 1 to k-1, P k|k-1 represents the mean and scale matrix of the system state, respectively; Transforming the measurement likelihood probability density function into: Wherein y k ,λ k ,π k ,v k is an auxiliary parameter, and represents a bernoulli random variable, a mixing parameter, a mixing probability and a degree of freedom parameter, IE (lambda k ;v k ) represents an inverse exponential distribution, and probability density function expressions of the inverse exponential distribution IE (lambda; v) are IE(λ k ;v k )＝(v k /λ k 2 )exp(-v k /λ k );p(y k |π k ) and p (pi k ) as follows: p(π k )＝Beta(π k ;e,1-e) (9) And taking the measurement likelihood probability density function, the probability quality function and the prediction probability density function as a joint probability density function of the system state.
8. The noise filtering system of a sensor according to claim 7, wherein the conversion unit is specifically configured to: Introducing a variational Bayesian method, forming a joint posterior probability density function p (Θ k |z 1:k ) by using the joint probability density function, and approximating the joint posterior probability density function p (Θ k |z 1:k ) to the product of the approximate probability density functions of x k 、λ k 、y k 、π k respectively: p(Θ k |z 1:k )≈q(x k )q(λ k )q(y k )q(π k ) (10) Wherein, the Z 1:k is the measurement sequence from 1 to k times, q (·) represents the approximate probability density function.
9. The noise filtering system of a sensor according to claim 8, wherein the iteration unit is specifically configured to: The optimal approximate probability density function can be obtained by minimizing the KL divergence between the approximate probability density function and the joint posterior probability density function, and the optimal solution of equation (10) satisfies according to Bayes theory: Where E [. Cndot. ] represents the expectation that θ is any one element in Θ, Θ (-θ) is the set of all elements in Θ except for θ, A constant term related to θ; The variation parameters based on q (x k ) and q (R k ) are mutually coupled characteristics, and the solution (x k )、q(y k )、q(π k )、q(λ k ) is realized by adopting a fixed point iteration method, wherein: At the i+1th iteration, the approximate posterior probability density distribution of the i-th iteration is used to approximate the expectation, and the joint posterior probability density function p (Θ k ,z 1:k ) is expressed as: correspondingly, the logarithmic form of the joint probability density function p (Θ k ,z 1:k ) is Wherein, the Representing a constant related to x k .
10. The noise filtering system of a sensor according to claim 9, wherein the iteration unit is specifically configured to: The step of alternately updating q (x k )、q(y k )、q(π k )、q(λ k ) using a fixed point iterative method includes: let θ=x k be the number, Q i+1 (x k ) posterior the probability density function is: Wherein, the The measurement noise variance matrix representing the corrected k+1 time is to Expressed as: Wherein, the Representing the corrected measurement noise variance matrix at the k moment; Let θ=y k be the number, Wherein, the Representing a constant term associated with y k , m representing the dimension of the measurement; From the bernoulli distribution, q i+1 (y k ) is: Wherein, the Representing constant terms independent of y k , exp representing a shorthand form of an exponential function, tr representing the trace of the solution matrix; Wherein, the A state one-step predictor is indicated, Representing a state one-step predictive probability density; Update q i+1 (y k ) to bernoulli distribution: Wherein, the Representing bernoulli distribution probability parameters: the expectations of y k are: Let θ=pi k , substituting formula (12) into formula (11) Wherein, the Represents a constant associated with pi k ; update q (i+1) (π k ) to Beta distribution: Wherein, the Expressed as: The expectations of log (pi k ) and log (1-pi k ) are: wherein, psi (·) represents the characteristic function of the variable, And The specific calculation mode is given by the formula (25); let θ=λ k be the sum of, Wherein, the For equation (20), Represents a constant associated with λ k ; update q (i+1) (λ k ) to a generalized inverse gaussian: Wherein, the The expectations of lambda k and log (lambda k ) are: Wherein, the A dedicated function representing a second type of modified bezier function.

Description

Noise filtering method and system of sensor Technical Field The invention relates to the technical field of automatic driving, in particular to a noise filtering method and system of a sensor. Background In the prior art, under an automatic driving scene, a sensor is required to acquire different signal data to provide support for automatic driving, but the signal of the sensor under the automatic driving scene has various different noises due to noise and wild value influence caused by bad weather, signal shielding, sudden obstacle and the like, so that the problems of low state estimation precision and poor reliability are solved. Disclosure of Invention The embodiment of the invention provides a noise filtering method and a noise filtering system for a sensor, which can solve the technical problems in the prior art. In order to achieve the above object, in one aspect, an embodiment of the present invention provides a noise filtering method of a sensor, including: Step 1, modeling noise statistics characteristics of signals of a sensor used in an automatic driving scene by adopting Gaussian-Gaussian reverse-exponential mixing distribution to obtain a noise model, and representing the noise model as: pGGIE(vk|π)＝πN(vk;0,Rk)+(1-π)GIE(vk;0,Rk,vk) (1) Wherein N (v k;0,Rk) represents a gaussian distribution, which is used for constructing and obtaining the noise model based on the gaussian distribution N (v k;0,Rk) when the signal of the sensor is normal, and GIE (v k;0,Rk,vk) represents a gaussian-inverse exponential distribution, which is used for constructing and obtaining the noise model based on the gaussian-inverse exponential distribution GIE (v k;0,Rk,vk) when the signal of the sensor is interfered; v k denotes the noise of the signal of the sensor at time k, R k denotes the measurement noise variance matrix, v k denotes the degree of freedom parameter, pi denotes the mixing probability, which is modeled as a Beta distribution: p(π)=Be(π;e,1-e) (2) Wherein e is a mixed weight coefficient; And (2) combining the formula (1) and the formula (2), and enabling a noise probability density function of the signal of the sensor to be as follows: p(vk)＝eN(vk;0,Rk)+(1-e)GIE(vk;0,Rk,vk) (3) step 2, constructing a joint probability density function of a system state based on the system state equation and the measurement equation, wherein the auxiliary parameters comprise that x k、yk、πk、λk,xk represents the system state at k time, y k represents Bernoulli random variables, pi k represents the mixing probability, and lambda k represents the mixing parameter; Step 3, adopting a variable decibel leaf method, forming a joint posterior probability density function p (Θ k|z1:k) by using the joint probability density function, and approximating the joint posterior probability density function p (Θ k|z1:k) to the product of the approximate probability density functions q (x k)、q(yk)、q(πk)、q(λk) of each x k、yk、πk、λk,xk; Step 4, solving an optimal approximate probability density function by minimizing KL divergence between the approximate probability density function and the joint posterior probability density function, and alternately updating q (x k)、q(yk)、q(πk)、q(λk) by using a fixed point iteration method until iteration converges; and step 5, acquiring an optimal estimated value of the system state x k according to the approximate probability density function after convergence, and realizing the filtering of the signals of the sensor. In another aspect, an embodiment of the present invention provides a noise filtering system of a sensor, including: The noise model construction unit is used for modeling the noise statistical characteristics of the signals of the sensors by adopting Gaussian-Gaussian inverse coefficient mixed distribution aiming at the sensors used in the automatic driving scene to obtain a noise model, and the noise model is expressed as: pGGIE(vk|π)＝πN(vk;0,Rk)+(1-π)GIE(vk;0,Rk,vk) (1) Wherein N (v k;0,Rk) represents a gaussian distribution, which is used for constructing and obtaining the noise model based on the gaussian distribution N (v k;0,Rk) when the signal of the sensor is normal, and GIE (v k;0,Rk,vk) represents a gaussian-inverse exponential distribution, which is used for constructing and obtaining the noise model based on the gaussian-inverse exponential distribution GIE (v k;0,Rk,vk) when the signal of the sensor is interfered; v k denotes the noise of the signal of the sensor at time k, R k denotes the measurement noise variance matrix, v k denotes the degree of freedom parameter, pi denotes the mixing probability, which is modeled as a Beta distribution: p(π)=Be(π;e,1-e) (2) Wherein e is a mixed weight coefficient; And (2) combining the formula (1) and the formula (2), and enabling a noise probability density function of the signal of the sensor to be as follows: p(vk)＝eN(vk;0,Rk)+(1-e)GIE(vk;0,Rk,vk) (3) The system comprises a joint probability density function construction unit, a measur