Noise filtering method and system of sensor

Abstract

The embodiment of the invention provides a noise filtering method and system for a sensor, and the method comprises the steps: carrying out the modeling of the noise statistical characteristics of a signal of the sensor through employing Gaussian-Gaussian-Gaussian inverse index mixed distribution for a sensor used in an automatic driving scene, obtaining a noise model, and carrying out the calculation of the noise model based on a system state equation and a measurement equation, constructing a joint probability density function of a system state, and forming the joint probability density function into a joint posterior probability density function by adopting a variational Bayesian method; solving an optimal approximate probability density function through a KL divergence between a minimum approximate probability density function and a joint posterior probability density function, and alternately updating q (xk), q (yk), q (pi k) and q (lambda k) by using a fixed point iteration method until iteration convergence; and obtaining the optimal estimation value of the system state xk according to the converged approximate probability density function. The fitting degree of noise description is improved from the source, and precise adaptation and efficient suppression of multi-mode noise of the sensor are achieved.

Description

Technical Field

[0001] This invention relates to the field of autonomous driving technology, and more specifically to a noise filtering method and system for sensors. Background Technology

[0002] In existing technologies, sensors are required to acquire different signal data in autonomous driving scenarios to support autonomous driving. However, due to noise and outliers caused by severe weather, signal blockage, and sudden obstacles, the signals of sensors in autonomous driving scenarios are subject to various types of noise, resulting in low state estimation accuracy and poor reliability. Summary of the Invention

[0003] This invention provides a noise filtering method and system for sensors, which can solve the above-mentioned technical problems in the prior art.

[0004] To achieve the above objectives, in one aspect, embodiments of the present invention provide a noise filtering method for a sensor, comprising:

[0005] Step 1: For the sensors used in autonomous driving scenarios, the noise statistical characteristics of the sensor signals are modeled using a Gaussian-Gaussian-Gaussian inverse exponential mixture distribution to obtain a noise model, which is expressed as:

[0006] p GGIE (v k |π)=πN(v k ;0,R k )+(1-π)GIE(v k ;0,R k ,v k (1)

[0007] Wherein, N(v) k ;0,R k ) represents a Gaussian distribution, used to represent the distribution N(v) based on the Gaussian distribution when the sensor signal is normal. k ;0,R k The noise model is constructed as described above, GIE(v) k ;0,R k ,v k ) represents the Gaussian-inverse exponential distribution, used to determine the signal of the sensor when it is disturbed, based on the Gaussian-inverse exponential distribution GIE(v) k ;0,R k ,v k The noise model is constructed as described above;

[0008] v k R represents the noise of the sensor signal at time k. k V represents the measurement noise variance matrix, vk Let π represent the degree of freedom parameter, and let π represent the mixture probability. The mixture probability is modeled as a Beta distribution:

[0009] p(π)=Be(π;e,1-e) (2)

[0010] Where e is the mixed weighting coefficient;

[0011] Combining equations (1) and (2), the noise probability density function of the sensor signal is:

[0012] p(v k )=eN(v k ;0,R k )+(1-e)GIE(v k ;0,R k ,v k (3)

[0013] Step 2: Based on the system state equation and measurement equation, construct the joint probability density function of the system state, where the auxiliary parameter includes x. k y k π k , λ k x k y represents the system state at time k. k Let π represent a Bernoulli random variable. k Let λ represent the mixture probability. k Indicates the mixed parameters;

[0014] Step 3: Using the variational Bayesian method, the joint probability density function is transformed into a joint posterior probability density function p(Θ). k |z 1:k ), and the joint posterior probability density function p(Θ) k |z 1:k Approximately x k y k π k , λ k x k Their respective approximate probability density functions q(x) k ), q(y) k ), q(π) k ), q(λ) k The product of )

[0015] Step 4: Solve for the optimal approximate probability density function by minimizing the KL divergence between the approximate probability density function and the joint posterior probability density function, and alternately update q(x) using the fixed-point iteration method. k ), q(y) k ), q(π) k ), q(λ) kContinue iteratively until convergence;

[0016] Step 5: Obtain the system state x based on the converged approximate probability density function. k The optimal estimate is obtained to filter the sensor signal.

[0017] On the other hand, embodiments of the present invention provide a noise filtering system for a sensor, comprising:

[0018] The noise model construction unit is used to model the noise statistical characteristics of the sensors used in autonomous driving scenarios using a Gaussian-Gaussian-Gaussian inverse exponential mixture distribution to obtain a noise model, which is expressed as:

[0019] p GGIE (v k |π)=πN(v k ;0,R k )+(1-π)GIE(v k ;0,R k ,v k (1)

[0020] Wherein, N(v) k ;0,R k ) represents a Gaussian distribution, used to represent the distribution N(v) based on the Gaussian distribution when the sensor signal is normal. k ;0,R k The noise model is constructed as described above, GIE(v) k ;0,R k ,v k ) represents the Gaussian-inverse exponential distribution, used to determine the signal of the sensor when it is disturbed, based on the Gaussian-inverse exponential distribution GIE(v) k ;0,R k ,v k The noise model is constructed as described above;

[0021] v k R represents the noise of the sensor signal at time k. k V represents the measurement noise variance matrix, v k Let π represent the degree of freedom parameter, and let π represent the mixture probability. The mixture probability is modeled as a Beta distribution:

[0022] p(π)=Be(π;e,1-e) (2)

[0023] Where e is the mixed weighting coefficient;

[0024] Combining equations (1) and (2), the noise probability density function of the sensor signal is:

[0025] p(vk )=eN(v k ;0,R k )+(1-e)GIE(v k ;0,R k ,v k (3)

[0026] The joint probability density function construction unit is used to construct the joint probability density function of the system state based on the system state equation and the measurement equation, wherein the auxiliary parameter includes x. k y k π k , λ k x k y represents the system state at time k. k Let π represent a Bernoulli random variable. k Let λ represent the mixture probability. k Indicates the mixed parameters;

[0027] The transformation unit is used to transform the joint probability density function into a joint posterior probability density function p(Θ) using the variational Bayesian method. k |z 1:k ), and the joint posterior probability density function p(Θ) k |z 1:k Approximately x k y k π k , λ k x k Their respective approximate probability density functions q(x) k ), q(y) k ), q(π) k ), q(λ) k The product of )

[0028] The iterative unit is used to solve for the optimal approximate probability density function by minimizing the KL divergence between the approximate probability density function and the joint posterior probability density function, and to alternately update q(x) using a fixed-point iterative method. k ), q(y) k ), q(π) k ), q(λ) k Continue iteratively until convergence;

[0029] The solver unit is used to obtain the system state x based on the converged approximate probability density function. k The optimal estimate is obtained to filter the sensor signal.

[0030] The above technical solution has the following beneficial effects: The sensor noise filtering method and system of this invention overcomes the limitations of traditional single-distribution modeling. Addressing the dual characteristics of sensor noise in autonomous driving scenarios—that it follows a Gaussian distribution under normal conditions but exhibits heavy-tailed characteristics when disturbed—it constructs a Gaussian-Gaussian-inverse exponential hybrid noise model. By introducing mixed weight coefficients to dynamically balance the contributions of the two distributions, when the sensor is not disturbed, the Gaussian distribution accurately fits the stationary noise, thus ensuring the accuracy of noise modeling under normal conditions. When encountering disturbances such as severe weather, signal obstruction, or sudden obstacles, the Gaussian-inverse exponential distribution (constructed by integrating the Gaussian and inverse exponential distributions) effectively captures the statistical characteristics of heavy-tailed noise (heavy-tailed noise and heavy-tailed characteristics) under disturbance conditions, improving the fit of noise description from the source. This enables accurate characterization of complex noise statistical characteristics, achieving accurate adaptation and efficient suppression of multi-mode sensor noise. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is a flowchart of a noise filtering method for a sensor according to an embodiment of the present invention;

[0033] Figure 2 This is a structural diagram of a noise filtering system for a sensor according to an embodiment of the present invention. Detailed Implementation

[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0035] like Figure 1 As shown, in conjunction with embodiments of the present invention, a noise filtering method for a sensor is provided, comprising:

[0036] Step 1: For the sensors used in autonomous driving scenarios, the noise statistical characteristics of the sensor signals are modeled using a Gaussian-Gaussian-Gaussian inverse exponential mixture distribution to obtain a noise model, which is expressed as:

[0037] p GGIE (v k |π)=πN(v k ;0,R k )+(1-π)GIE(v k ;0,R k ,v k (1)

[0038] Wherein, N(v) k ;0,R k ) represents a Gaussian distribution, used to represent the distribution N(v) based on the Gaussian distribution when the sensor signal is normal. k ;0,R k The noise model is constructed as described above, GIE(v) k ;0,R k ,v k ) represents the Gaussian-inverse exponential distribution, used to determine the signal of the sensor when it is disturbed, based on the Gaussian-inverse exponential distribution GIE(v) k ;0,R k ,v k The noise model is constructed as described above;

[0039] v k R represents the noise of the sensor signal at time k. k V represents the measurement noise variance matrix, v k Let π represent the degree of freedom parameter, and let π represent the mixture probability. The mixture probability is modeled as a Beta distribution:

[0040] p(π)=Be(π;e,1-e) (2)

[0041] Where e is the mixed weighting coefficient;

[0042] Combining equations (1) and (2), the noise probability density function of the sensor signal is:

[0043] p(v k )=eN(v k ;0,R k )+(1-e)GIE(v k ;0,R k ,v k (3)

[0044] Step 2: Based on the system state equation and measurement equation, construct the joint probability density function of the system state, where the auxiliary parameter includes x.k y k π k , λ k x k y represents the system state at time k. k Let π represent a Bernoulli random variable. k Let λ represent the mixture probability. k Indicates the mixed parameters;

[0045] Step 3: Using the variational Bayesian method, the joint probability density function is transformed into a joint posterior probability density function p(Θ). k |z 1:k ), will the joint posterior probability density function p(Θ) k |z 1:k Approximately x k y k π k , λ k x k Their respective approximate probability density functions q(x) k ), q(y) k ), q(π) k ), q(λ) k The product of )

[0046] Step 4: Solve for the optimal approximate probability density function by minimizing the KL divergence between the approximate probability density function and the joint posterior probability density function, and then alternately update q(x) using the fixed-point iterative method. k ), q(y) k ), q(π) k ), q(λ) k Continue iteratively until convergence;

[0047] Step 5: Obtain the system state x based on the converged approximate probability density function. k The optimal estimate is obtained to filter the sensor signal.

[0048] Preferably, step 2 specifically includes:

[0049] According to the measurement equation z k =H k x k +v k The measurement likelihood probability density function is:

[0050] p(z k |x k )=eN(z k H k x k ,R k )+(1-e)GIE(z k H k xk ,R k ,v k (4)

[0051] Where, x k Let z be the system state at time k. The system state includes at least: attitude, velocity, or position. k The measurement value includes at least the location, H. k The measurement matrix is ​​a measurement transition matrix recursively derived from its own measurements and state.

[0052] By introducing a Bernoulli-distributed random variable to model the probability mass function, the probability mass function can be expressed as:

[0053] p(y|π)=π y (1-π) 1-y (5)

[0054] Where y represents a discrete value of 0 or 1;

[0055] According to the system state equation x k =F k x k-1 +ω k The one-step prediction probability density function of the system is modeled as a Gaussian distribution.

[0056]

[0057] Among them, F k Let x be the state transition matrix. k-1 ω represents the system state at time k-1. k Represents the state noise matrix;

[0058] z 1:k-1 This represents the measurement sequence from time 1 to k-1. P k|k-1 Let x represent the mean and scaling matrix of the system state, respectively; k For a Gaussian distribution to follow a specific pattern, the mean and scale are two core parameters that determine its probability distribution shape. Together, they characterize the distribution's location and dispersion. The mean is the location parameter of the Gaussian distribution; it determines the position of the axis of symmetry of the probability density curve, which is the center of the distribution. The scale parameter of the Gaussian distribution, usually referring to the standard deviation, determines the "width" of the probability density curve, reflecting the dispersion of the random variable's values.

[0059] Transform the measurement likelihood probability density function as follows:

[0060]

[0061] Among them, y k ,λ k ,πk ,v k The auxiliary parameters are , representing the Bernoulli random variable, mixture parameters, mixture probability, and degrees of freedom parameter, respectively. IE(λ) k ;v k ) represents the inverse exponential distribution, and the expression for the inverse exponential distribution IE(λ; v) is IE(λ k ;v k )=(v k / λ k 2 )exp(-v k / λ k ); p(y k |π k ) and p(π k The probability density function expression for () is as follows:

[0062]

[0063] p(π k ) = Beta(π k ;e,1-e) (9)

[0064] The measurement likelihood probability density function, probability mass function, and prediction probability density function are used as the joint probability density function of the system state.

[0065] Preferably, step 3 includes:

[0066] The variational Bayesian method is introduced to transform the joint probability density function into a joint posterior probability density function p(Θ). k |z 1:k ), and the joint posterior probability density function p(Θ) k |z 1:k Approximately x k , λ k y k π k The product of their respective approximate probability density functions:

[0067] p(Θ k |z 1:k )≈q(x k )q(λ k )q(y k )q(π k (10)

[0068] in, z 1:k Let q(·) be the measurement sequence from time 1 to k, and let q(·) denote the approximate probability density function.

[0069] Preferably, step 4 includes:

[0070] 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; according to Bayes' principle, the optimal solution of equation (10) satisfies:

[0071]

[0072] Where E[·] represents the expectation, θ is any element of Θ, and Θ (-θ) It is the set of all elements in Θ except θ. Represents constant terms related to θ;

[0073] Based on q(x) k ) and q(R) k The variational parameters of (x) are mutually coupled, and the fixed-point iterative method is used to solve for (x). k ), q(y) k ), q(π) k ), q(λ) k );in:

[0074] In the (i+1)th iteration, the approximate posterior probability density distribution of the i-th iteration is used to approximate the expectation. According to equation (1) corresponding to the Gaussian-Gaussian-inverse exponential distribution, the joint posterior probability density function p(Θ) is... k ,z 1:k ) is represented as:

[0075]

[0076] Accordingly, the joint probability density function p(Θ) k ,z 1:k The logarithmic form of ) is

[0077]

[0078] in, Indicates with x k Relevant constants;

[0079] Preferably, step 4 includes:

[0080] Alternately update q(x) using the fixed-point iterative method k ), q(y) k ), q(π) k ), q(λ) k The steps include:

[0081] Let θ = x k ,

[0082]

[0083] q i+1 (xk The posterior probability density function of is:

[0084]

[0085] in, This represents the corrected measurement noise variance matrix at time k+1. Represented as:

[0086]

[0087] in, This represents the corrected measurement noise variance matrix at time k;

[0088] Let θ = y k ,

[0089]

[0090] in, Indicates with y k The relevant constant term, m, represents the dimension of the measurement;

[0091] According to the Bernoulli distribution, q i+1 (y k The posterior probability density function of is:

[0092]

[0093] in, Indicates with y k The irrelevant constant term, exp represents the abbreviation of the exponential function, and tr represents the trace of the matrix being solved;

[0094]

[0095] in, This represents the predicted value of the state in one step. This represents the probability density of a one-step prediction of a state.

[0096] q i+1 (y k Update to Bernoulli distribution:

[0097]

[0098] in, Represents the probability parameters of the Bernoulli distribution:

[0099]

[0100] y k The expectation is:

[0101]

[0102] Let θ = π k Substituting equation (12) into equation (11)

[0103]

[0104] in, Represents π k Relevant constants;

[0105] q (i+1) (π k Updated to Beta distribution:

[0106]

[0107] in, Represented as:

[0108]

[0109] log(π k ) and log(1-π k The expectation is:

[0110]

[0111] Where ψ(·) represents the characteristic function of the variable, and The specific calculation method is given by equation (25);

[0112] Let θ = λ k ,

[0113]

[0114] in, For formula (20), Indicates the relationship with λ k Relevant constants;

[0115] q (i+1) (λ k Updated to a generalized inverse Gaussian distribution:

[0116]

[0117] in,

[0118]

[0119] λ k and log(λ) k The expectation is:

[0120]

[0121] in, This represents a special function for the second type of modified Bessel function.

[0122] like Figure 2 As shown, a noise filtering system for a sensor, according to an embodiment of the present invention, includes:

[0123] The noise model construction unit 21 is used to model the noise statistical characteristics of the sensor signals used in autonomous driving scenarios using a Gaussian-Gaussian-Gaussian inverse exponential mixture distribution to obtain a noise model, which is expressed as:

[0124] p GGIE (v k |π)=πN(v k ;0,R k )+(1-π)GIE(v k ;0,R k ,v k (1)

[0125] Wherein, N(v) k ;0,R k ) represents a Gaussian distribution, used to represent the distribution N(v) based on the Gaussian distribution when the sensor signal is normal. k ;0,R k The noise model is constructed as described above, GIE(v) k ;0,R k ,v k ) represents the Gaussian-inverse exponential distribution, used to determine the signal of the sensor when it is disturbed, based on the Gaussian-inverse exponential distribution GIE(v) k ;0,R k ,v k The noise model is constructed as described above;

[0126] v k R represents the noise of the sensor signal at time k. k V represents the measurement noise variance matrix, v k Let π represent the degree of freedom parameter, and let π represent the mixture probability. The mixture probability is modeled as a Beta distribution:

[0127] p(π)=Be(π;e,1-e) (2)

[0128] Where e is the mixed weighting coefficient;

[0129] Combining equations (1) and (2), the noise probability density function of the sensor signal is:

[0130] p(v k)=eN(v k ;0,R k )+(1-e)GIE(v k ;0,R k ,v k (3)

[0131] Joint probability density function construction unit 22 is used to construct the joint probability density function of the system state based on the system state equation and the measurement equation, wherein the auxiliary parameter includes x. k y k π k , λ k x k y represents the system state at time k. k Let π represent a Bernoulli random variable. k Let λ represent the mixture probability. k Indicates the mixed parameters;

[0132] Transformation unit 23 is used to transform the joint probability density function into a joint posterior probability density function p(Θ) using the variational Bayesian method. k |z 1:k ), and the joint posterior probability density function p(Θ) k |z 1:k Approximately x k y k π k , λ k x k Their respective approximate probability density functions q(x) k ), q(y) k ), q(π) k ), q(λ) k The product of )

[0133] Iteration unit 24 is used to solve for the optimal approximate probability density function by minimizing the KL divergence between the approximate probability density function and the joint posterior probability density function, and to alternately update q(x) using a fixed-point iterative method. k ), q(y) k ), q(π) k ), q(λ) k Continue iteratively until convergence;

[0134] Solver 25 is used to obtain the system state x based on the converged approximate probability density function. k The optimal estimate is obtained to filter the sensor signal.

[0135] Preferably, the joint probability density function construction unit 22 is specifically used for:

[0136] According to the measurement equation z k =Hk x k +v k The measurement likelihood probability density function is:

[0137] 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)

[0138] Where, x k Let z be the system state at time k. The system state includes at least: attitude, velocity, or position. k The measurement value includes at least the location, H. k The measurement matrix is ​​a measurement transition matrix recursively derived from its own measurements and state.

[0139] By introducing a Bernoulli-distributed random variable to model the probability mass function, the probability mass function can be expressed as:

[0140] p(y|π)=π y (1-π) 1-y (5)

[0141] Where y represents a discrete value of 0 or 1;

[0142] According to the system state equation x k =F k x k-1 +ω k The one-step prediction probability density function of the system is modeled as a Gaussian distribution.

[0143]

[0144] Among them, F k Let x be the state transition matrix. k-1 ω represents the system state at time k-1. k Represents the state noise matrix;

[0145] z 1:k-1 This represents the measurement sequence from time 1 to k-1. P k|k-1 These represent the mean and scale matrix of the system state, respectively;

[0146] Transform the measurement likelihood probability density function as follows:

[0147]

[0148] Among them, y k ,λ k ,π k ,v k The auxiliary parameters are , representing the Bernoulli random variable, mixture parameters, mixture probability, and degrees of freedom parameter, respectively. IE(λ) k ;v k ) represents the inverse exponential distribution, and the expression for the inverse exponential distribution IE(λ; v) is IE(λ k ;v k )=(v k / λ k 2 )exp(-v k / λ k ); p(y k |π k ) and p(π k The probability density function expression for () is as follows:

[0149]

[0150] p(π k ) = Beta(π k ;e,1-e) (9)

[0151] The measurement likelihood probability density function, probability mass function, and prediction probability density function are used as the joint probability density function of the system state.

[0152] Preferably, the conversion unit 23 is specifically used for:

[0153] The variational Bayesian method is introduced to transform the joint probability density function into a joint posterior probability density function p(Θ). k |z 1:k ), and the joint posterior probability density function p(Θ) k |z 1:k Approximately x k , λ k y k π k The product of their respective approximate probability density functions:

[0154] p(Θ k |z 1:k )≈q(x k )q(λ k )q(y k )q(π k (10)

[0155] in, z 1:kLet q(·) be the measurement sequence from time 1 to k, and let q(·) denote the approximate probability density function.

[0156] Preferably, the iteration unit 24 is specifically used for:

[0157] 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; according to Bayes' principle, the optimal solution of equation (10) satisfies:

[0158]

[0159] Where E[·] represents the expectation, θ is any element of Θ, and Θ (-θ) It is the set of all elements in Θ except θ. Represents constant terms related to θ;

[0160] Based on q(x) k ) and q(R) k The variational parameters of (x) are mutually coupled, and the fixed-point iterative method is used to solve for (x). k ), q(y) k ), q(π) k ), q(λ) k );in:

[0161] In the (i+1)th iteration, the approximate posterior probability density distribution of the i-th iteration is used to approximate the expectation. According to equation (1) corresponding to the Gaussian-Gaussian-inverse exponential distribution, the joint posterior probability density function p(Θ) is... k ,z 1:k ) is represented as:

[0162]

[0163] Accordingly, the joint probability density function p(Θ) k ,z 1:k The logarithmic form of ) is

[0164]

[0165]

[0166] in, Indicates with x k Relevant constants;

[0167] Preferably, the iteration unit 24 is specifically used for:

[0168] Alternately update q(x) using the fixed-point iterative method k ), q(y) k ), q(π) k ), q(λ)k The steps include:

[0169] Let θ = x k ,

[0170]

[0171] q i+1 (x k The posterior probability density function of is:

[0172]

[0173] in, This represents the corrected measurement noise variance matrix at time k+1. Represented as:

[0174]

[0175] in, This represents the corrected measurement noise variance matrix at time k;

[0176] Let θ = y k ,

[0177]

[0178] in, Indicates with y k The relevant constant term, m, represents the dimension of the measurement;

[0179] According to the Bernoulli distribution, q i+1 (y k The posterior probability density function of is:

[0180]

[0181] in, Indicates with y k The irrelevant constant term, exp represents the abbreviation of the exponential function, and tr represents the trace of the matrix being solved;

[0182]

[0183]

[0184] in, This represents the predicted value of the state in one step. This represents the probability density of a one-step prediction of a state.

[0185] q i+1 (y k Update to Bernoulli distribution:

[0186]

[0187] in, Represents the probability parameters of the Bernoulli distribution:

[0188]

[0189] y k The expectation is:

[0190]

[0191] Let θ = π k Substituting equation (12) into equation (11)

[0192]

[0193] in, Represents π k Relevant constants;

[0194] q (i+1) (π k Updated to Beta distribution:

[0195]

[0196] in, Represented as:

[0197]

[0198] log(π k ) and log(1-π k The expectation is:

[0199]

[0200] Where ψ(·) represents the characteristic function of the variable, and The specific calculation method is given by equation (25);

[0201] Let θ = λ k ,

[0202]

[0203] in, For formula (20), Indicates the relationship with λ k Relevant constants;

[0204] q (i+1) (λ k Updated to a generalized inverse Gaussian distribution:

[0205]

[0206] in,

[0207]

[0208] λ k and log(λ) k The expectation is:

[0209]

[0210] in, This represents a special function for the second type of modified Bessel function.

[0211] The beneficial technical effects achieved by the embodiments of the present invention are as follows:

[0212] The sensor noise filtering method and system of this invention overcomes the limitations of traditional single-distribution modeling. Addressing the dual characteristics of sensor noise in autonomous driving scenarios—that it follows a Gaussian distribution under normal conditions but exhibits heavy-tailed characteristics when disturbed—the method constructs a Gaussian-Gaussian-inverse exponential hybrid noise model. This model dynamically balances the contributions of the two distributions by introducing hybrid weighting coefficients. Specifically, when the sensor is undisturbed, the Gaussian distribution accurately fits the stationary noise, ensuring the accuracy of noise modeling under normal conditions. When encountering disturbances such as severe weather, signal obstruction, or sudden obstacles, the Gaussian-inverse exponential distribution (constructed by integrating the Gaussian and inverse exponential distributions) effectively captures the statistical characteristics of heavy-tailed noise (heavy-tailed noise and heavy-tailed characteristics) under disturbed conditions, improving the fit of the noise description from the source. This enables accurate characterization of complex noise statistical characteristics, achieving precise adaptation and efficient suppression of multi-mode sensor noise.

[0213] This invention constructs a joint probability density function for system state and auxiliary parameters by introducing Bernoulli, Beta, and generalized inverse Gaussian distributions. Using a variational Bayesian method, it obtains an approximate posterior probability density function by minimizing the KL divergence. The optimal estimates of key parameters such as system state, mixed parameters, and mixed probabilities are then obtained using a fixed-point iterative method, enabling accurate filtering of disturbed sensor data. This invention effectively suppresses the influence of noise and outliers caused by severe weather, signal obstruction, and sudden obstacles, improving the robustness and accuracy of state estimation in autonomous driving systems and providing reliable data support for path planning and decision control.

[0214] It should be understood that the specific order or hierarchy of steps in the disclosed process is an example of an exemplary method. Based on design preferences, it should be understood that the specific order or hierarchy of steps in the process may be rearranged without departing from the scope of this disclosure. The appended method claims provide elements of various steps in an exemplary order and are not intended to limit the scope to the specific order or hierarchy described.

[0215] In the above detailed description, various features are combined together in a single embodiment to simplify this disclosure. This approach to disclosure should not be construed as reflecting an intention that embodiments of the claimed subject matter require more features than are explicitly stated in each claim. Rather, as reflected in the appended claims, the invention is presented with fewer features than all of the features of the single disclosed embodiment. Therefore, the appended claims are hereby explicitly incorporated into the detailed description, wherein each claim stands alone as a preferred embodiment of the invention.

[0216] The disclosed embodiments have been described above to enable any person skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be applied to other embodiments without departing from the spirit and scope of this disclosure. Therefore, this disclosure is not limited to the embodiments given herein, but is consistent with the broadest scope of the principles and novel features disclosed in this application.

[0217] The foregoing description includes examples of one or more embodiments. It is certainly impossible to describe all possible combinations of components or methods in order to describe the above embodiments, but those skilled in the art will recognize that further combinations and arrangements of the various embodiments are possible. Therefore, the embodiments described herein are intended to cover all such changes, modifications, and variations that fall within the scope of the appended claims. Furthermore, the term "comprising" as used in the specification or claims is interpreted in a manner similar to the term "including," as interpreted when used as a conjunction in the claims. Additionally, the use of any term "or" in the specification of the claims is intended to mean "non-exclusive or."

[0218] Those skilled in the art will also understand that the various illustrative logical blocks, units, and steps listed in the embodiments of the present invention can be implemented by electronic hardware, computer software, or a combination of both. To clearly demonstrate the interchangeability of hardware and software, the functions of the various illustrative components, units, and steps described above have been generally described. Whether such functionality is implemented through hardware or software depends on the specific application and the overall system design requirements. Those skilled in the art can implement the described functions using various methods for each specific application, but such implementation should not be construed as exceeding the scope of protection of the embodiments of the present invention.

[0219] The various illustrative logic blocks or units described in the embodiments of this invention can be implemented or operate the described functions using a general-purpose processor, digital signal processor, application-specific integrated circuit (ASIC), field-programmable gate array or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof. The general-purpose processor can be a microprocessor; alternatively, it can be any conventional processor, controller, microcontroller, or state machine. The processor can also be implemented using a combination of computing devices, such as a digital signal processor and a microprocessor, multiple microprocessors, one or more microprocessors combined with a digital signal processor core, or any other similar configuration.

[0220] The steps of the methods or algorithms described in the embodiments of this invention can be directly embedded in hardware, a software module executed by a processor, or a combination of both. The software module can be stored in RAM, flash memory, ROM, EPROM, EEPROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium in the art. Exemplarily, the storage medium can be connected to the processor so that the processor can read information from and write information to the storage medium. Optionally, the storage medium can also be integrated into the processor. The processor and storage medium can be housed in an ASIC, which can be housed in a user terminal. Optionally, the processor and storage medium can also be housed in different components of the user terminal.

[0221] In one or more exemplary designs, the functions described in the embodiments of the present invention can be implemented in hardware, software, firmware, or any combination of these three. If implemented in software, these functions can be stored on a computer-readable medium or transmitted on a computer-readable medium in the form of one or more instructions or code. Computer-readable media include computer storage media and communication media that facilitate the transfer of computer programs from one place to another. Storage media can be any available media that can be accessed by a general-purpose or special-purpose computer. For example, such computer-readable media can include, but is not limited to, RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store program code in the form of instructions or data structures and other forms that can be read by a general-purpose or special-purpose computer, or a general-purpose or special-purpose processor. Furthermore, any connection can be suitably defined as a computer-readable medium, for example, if the software is transmitted from a website, server or other remote resource via a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL) or wirelessly, such as infrared, wireless and microwave, it is also included in the defined computer-readable medium. The disks and discs mentioned include compressed disks, laser discs, optical discs, DVDs, floppy disks, and Blu-ray discs. Disks typically copy data magnetically, while disks typically copy data optically using lasers. Combinations of the above can also be contained in computer-readable media.

[0222] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A noise filtering method for a sensor, characterized in that, include: Step 1: For the sensors used in autonomous driving scenarios, the noise statistical characteristics of the sensor signals are modeled using a Gaussian-Gaussian-Gaussian inverse exponential mixture distribution to obtain a noise model, which 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, used to represent the distribution N(v) based on the Gaussian distribution when the sensor signal is normal. k ;0,R k The noise model is constructed as described above, GIE(v) k ;0,R k ,v k ) represents the Gaussian-inverse exponential distribution, used to determine the signal of the sensor when it is disturbed, based on the Gaussian-inverse exponential distribution GIE(v) k ;0,R k ,u k The noise model is constructed as described above; v k R represents the noise of the sensor signal at time k. k V represents the measurement noise variance matrix, v k Let π represent the degree of freedom parameter, and let π represent the mixture probability. The mixture probability is modeled as a Beta distribution: p(π)=Be(π;e,1-e) (2) Where e is the mixed weighting coefficient; Combining equations (1) and (2), the noise probability density function of the sensor signal is: p(v k )=eN(v k ;0,R k )+(1-e)GIE(v k ;0,R k ,in k ) (3) Step 2: Based on the system state equation and measurement equation, construct the joint probability density function of the system state, where the auxiliary parameter includes x. k y k π k , λ k x k y represents the system state at time k. k Let π represent a Bernoulli random variable. k Let λ represent the mixture probability. k Indicates the mixed parameters; Step 3: Using the variational Bayesian method, the joint probability density function is transformed into a joint posterior probability density function p(Θ). k |z 1:k ), and the joint posterior probability density function p(Θ) k |z 1:k Approximately x k y k π k , λ k x k Their respective approximate probability density functions q(x) k ), q(y) k ), q(π) k ), q(λ) k The product of ) Step 4: Solve for the optimal approximate probability density function by minimizing the KL divergence between the approximate probability density function and the joint posterior probability density function, and then alternately update q(x) using the fixed-point iterative method. k ), q(y) k ), q(π) k ), q(λ) k (This continues until the iteration converges;) Step 5: Obtain the system state x based on the converged approximate probability density function. k The optimal estimate is obtained to filter the sensor signal.

2. The noise filtering method for a sensor according to claim 1, characterized in that, Step 2 includes: 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) Where, x k Let z be the system state at time k. The system state includes at least: attitude, velocity, or position. k The measurement value includes at least the location, H. k For measurement matrix; By introducing a Bernoulli-distributed random variable to model the probability mass function, the probability mass function can be expressed as: p(y|π)=π y (1-π) 1-y (5) Where 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 prediction probability density function of the system is modeled as a Gaussian distribution. Among them, F k Let x be the state transition matrix. k-1 ω represents the system state at time k-1. k Represents the state noise matrix; z 1:k-1 This represents the measurement sequence from time 1 to k-1. P k|k-1 These represent the mean and scale matrix of the system state, respectively; Transform the measurement likelihood probability density function as follows: Among them, y k ,λ k ,π k ,v k The auxiliary parameters are , representing the Bernoulli random variable, mixture parameters, mixture probability, and degrees of freedom parameter, respectively. IE(λ) k ;v k ) represents the inverse exponential distribution, and the expression for the inverse exponential distribution IE(λ; v) is IE(λ k ;v k )=(v k / λ k 2 )exp(-v k / λ k ); p(y k |π k ) and p(π k The probability density function expression for () is as follows: p(π k )=Beta(π k ;e,1-e) (9) The measurement likelihood probability density function, probability mass function, and prediction probability density function are used as the joint probability density function of the system state.

3. The noise filtering method for the sensor according to claim 2, characterized in that, Step 3 includes: The variational Bayesian method is introduced to transform the joint probability density function into a joint posterior probability density function p(Θ). k |z 1:k ), and the joint posterior probability density function p(Θ) k |z 1:k Approximately x k , λ k y k π k The product of their respective approximate probability density functions: p(Θ k |z 1:k )≈q(x k )q(λ k )q(y k )q(π k ) (10) in, z 1:k Let q(·) be the measurement sequence from time 1 to k, and let q(·) denote the approximate probability density function.

4. The noise filtering method for the sensor according to claim 3, characterized in that, Step 4 specifically includes: minimizing the KL divergence between the approximate probability density function and the joint posterior probability density function to obtain the optimal approximate probability density function; according to Bayes' principle, the optimal solution of equation (10) satisfies: Where E[·] represents the expectation, θ is any element of Θ, and Θ (-θ) It is the set of all elements in Θ except θ. Represents constant terms related to θ; Based on q(x) k ) and q(R k The variational parameters of (x) are mutually coupled, and the fixed-point iterative method is used to solve for (x). k ), q(y) k ), q(π) k ), q(λ) k );in: In the (i+1)th iteration, the approximate posterior probability density distribution of the i-th iteration is used to approximate the expectation. According to equation (1) corresponding to the Gaussian-Gaussian-inverse exponential distribution, the joint posterior probability density function p(Θ) is... k ,z 1:k ) is represented as: Accordingly, the joint probability density function p(Θ) k ,z 1:k The logarithmic form of ) is in, Indicates with x k Relevant constants.

5. The noise filtering method for a sensor according to claim 4, characterized in that, Step 4 includes: Alternately update q(x) using the fixed-point iterative method k ), q(y) k ), q(π) k ), q(λ) k The steps include: Let θ = x k , q i+1 (x k The posterior probability density function of is: in, This represents the corrected measurement noise variance matrix at time k+1. Represented as: in, This represents the corrected measurement noise variance matrix at time k; Let θ = y k , in, Indicates with y k The relevant constant term, m, represents the dimension of the measurement; According to the Bernoulli distribution, q i+1 (y k The posterior probability density function of is: in, Indicates with y k The irrelevant constant term, exp represents the abbreviation of the exponential function, and tr represents the trace of the matrix being solved; in, This represents the predicted value of the state in one step. This represents the probability density of a one-step prediction of a state. q i+1 (y k Update to Bernoulli distribution: in, Represents the probability parameters of the Bernoulli distribution: y k The expectation is: Let θ = π k Substituting equation (12) into equation (11) in, Represents π k Relevant constants; q (i+1) (π k Updated to Beta distribution: in, Represented as: log(π k ) and log(1-π k The expectation is: Where ψ(·) represents the characteristic function of the variable, and The specific calculation method is given by equation (25); Let θ = λ k , in, For formula (20), Indicates the relationship with λ k Relevant constants; q (i+1) (λ k Updated to a generalized inverse Gaussian distribution: in, λ k and log(λ) k The expectation is: in, This represents a special function for the second type of modified Bessel function.

6. A noise filtering system for a sensor, characterized in that, include: The noise model construction unit is used to model the noise statistical characteristics of the sensors used in autonomous driving scenarios using a Gaussian-Gaussian-Gaussian inverse exponential mixture distribution to obtain a noise model, which 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, used to represent the distribution N(v) based on the Gaussian distribution when the sensor signal is normal. k ;0,R k The noise model is constructed as described above, GIE(v) k ;0,R k ,v k ) represents the Gaussian-inverse exponential distribution, used to determine the signal of the sensor when it is disturbed, based on the Gaussian-inverse exponential distribution GIE(v) k ;0,R k ,v k The noise model is constructed as described above; v k R represents the noise of the sensor signal at time k. k V represents the measurement noise variance matrix, v k Let π represent the degree of freedom parameter, and let π represent the mixture probability. The mixture probability is modeled as a Beta distribution: p(π)=Be(π;e,1-e) (2) Where e is the mixed weighting coefficient; Combining equations (1) and (2), the noise probability density function of the sensor signal is: p(v k )=eN(v k ;0,R k )+(1-e)GIE(v k ;0,R k ,in k ) (3) The joint probability density function construction unit is used to construct the joint probability density function of the system state based on the system state equation and the measurement equation, wherein the auxiliary parameter includes x. k y k π k , λ k x k y represents the system state at time k. k Let π represent a Bernoulli random variable. k Let λ represent the mixture probability. k Indicates the mixed parameters; The transformation unit is used to transform the joint probability density function into a joint posterior probability density function p(Θ) using the variational Bayesian method. k |z 1:k ), and the joint posterior probability density function p(Θ) k |z 1:k Approximately x k y k π k , λ k x k Their respective approximate probability density functions q(x) k ), q(y) k ), q(π) k ), q(λ) k The product of ) The iterative unit is used to solve for the optimal approximate probability density function by minimizing the KL divergence between the approximate probability density function and the joint posterior probability density function, and to alternately update q(x) using a fixed-point iterative method. k ), q(y) k ), q(π) k ), q(λ) k (This continues until the iteration converges;) The solver unit is used to obtain the system state x based on the converged approximate probability density function. k The optimal estimate is obtained to filter the sensor signal.

7. The noise filtering system for the sensor according to claim 6, characterized in that, The joint probability density function construction unit is specifically used for: 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) Where, x k Let z be the system state at time k. The system state includes at least: attitude, velocity, or position. k The measurement value includes at least the location, H. k For measurement matrix; By introducing a Bernoulli-distributed random variable to model the probability mass function, the probability mass function can be expressed as: p(y|π)=π y (1-π) 1-y (5) Where 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 prediction probability density function of the system is modeled as a Gaussian distribution. Among them, F k Let x be the state transition matrix. k-1 ω represents the system state at time k-1. k Represents the state noise matrix; z 1:k-1 This represents the measurement sequence from time 1 to k-1. P k|k-1 These represent the mean and scale matrix of the system state, respectively; Transform the measurement likelihood probability density function as follows: Among them, y k ,λ k ,π k ,v k The auxiliary parameters are , representing the Bernoulli random variable, mixture parameters, mixture probability, and degrees of freedom parameter, respectively. IE(λ) k ;v k ) represents the inverse exponential distribution, and the expression for the inverse exponential distribution IE(λ; v) is IE(λ k ;v k )=(v k / λ k 2 )exp(-v k / λ k ); p(y k |π k ) and p(π k The probability density function expression for () is as follows: p(π k )=Beta(π k ;e,1-e) (9) The measurement likelihood probability density function, probability mass function, and prediction probability density function are used as the joint probability density function of the system state.

8. The noise filtering system for the sensor according to claim 7, characterized in that, The conversion unit is specifically used for: The variational Bayesian method is introduced to transform the joint probability density function into a joint posterior probability density function p(Θ). k |z 1:k ), and the joint posterior probability density function p(Θ) k |z 1:k Approximately x k , λ k y k π k The product of their respective approximate probability density functions: p(Θ k |z 1:k )≈q(x k )q(λ k )q(y k )q(π k ) (10) in, z 1:k Let q(·) be the measurement sequence from time 1 to k, and let q(·) denote the approximate probability density function.

9. The noise filtering system for the sensor according to claim 8, characterized in that, The iterative unit is specifically used for: 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; according to Bayes' principle, the optimal solution of equation (10) satisfies: Where E[·] represents the expectation, θ is any element of Θ, and Θ (-θ) It is the set of all elements in Θ except θ. Represents constant terms related to θ; Based on q(x) k ) and q(R) k The variational parameters of (x) are mutually coupled, and the fixed-point iterative method is used to solve for (x). k ), q(y) k ), q(π) k ), q(λ) k );in: In the (i+1)th iteration, the approximate posterior probability density distribution of the i-th iteration is used to approximate the expectation. According to equation (1) corresponding to the Gaussian-Gaussian-inverse exponential distribution, the joint posterior probability density function p(Θ) is... k ,z 1:k ) is represented as: Accordingly, the joint probability density function p(Θ) k ,z 1:k The logarithmic form of ) is in, Indicates with x k Relevant constants.

10. The noise filtering system for the sensor according to claim 9, characterized in that, The iterative unit is specifically used for: Alternately update q(x) using the fixed-point iterative method k ), q(y) k ), q(π) k ), q(λ) k The steps include: Let θ = x k , q i+1 (x k The posterior probability density function of is: in, This represents the corrected measurement noise variance matrix at time k+1. Represented as: in, This represents the corrected measurement noise variance matrix at time k; Let θ = y k , in, Indicates with y k The relevant constant term, m, represents the dimension of the measurement; According to the Bernoulli distribution, q i+1 (y k The posterior probability density function of is: in, Indicates with y k The irrelevant constant term, exp represents the abbreviation of the exponential function, and tr represents the trace of the matrix being solved; in, This represents the predicted value of the state in one step. This represents the probability density of a one-step prediction of a state. q i+1 (y k Update to Bernoulli distribution: in, Represents the probability parameters of the Bernoulli distribution: y k The expectation is: Let θ = π k Substituting equation (12) into equation (11) in, Represents π k Relevant constants; q (i+1) (π k Updated to Beta distribution: in, Represented as: log(π k ) and log(1-π k The expectation is: Where ψ(·) represents the characteristic function of the variable, and The specific calculation method is given by equation (25); Let θ = λ k , in, For formula (20), Indicates the relationship with λ k Relevant constants; q (i+1) (λ k Updated to a generalized inverse Gaussian distribution: in, λ k and log(λ) k The expectation is: in, This represents a special function for the second type of modified Bessel function.

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