Multi-sensor information fusion estimation method for state-dependent observation loss

Abstract

The invention discloses a multi-sensor information fusion estimation method for state-dependent observation loss, and the method comprises the steps: constructing a system model which is a linear discrete dynamic system model and is used for representing a dynamically changing system state; training an observation loss discriminator, processing a complex observation rejection domain by the observation loss discriminator through a support vector machine, and converting a nonlinear classification problem into a linear convex optimization problem through a kernel function so as to discriminate whether a target state is in the observation rejection domain; and constructing a recursive fusion estimator based on an EM algorithm. According to the invention, the recursive estimator has high robustness and adaptability, can effectively deal with the complex situation of state dependence observation loss in various actual scenes, and significantly improves the precision of system state estimation.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-sensor fusion estimation, and in particular to a multi-sensor information fusion estimation method for state-dependent observation loss. Background Art

[0002] Multi-sensor fusion estimation technology is an important foundational technology in modern intelligent systems, widely used in fields such as autonomous driving, industrial automation, and environmental monitoring. By fusing information acquired by multiple sensors, this technology can provide the system with more accurate and comprehensive state perception and environmental understanding. However, in practical applications, sensors often experience data loss due to environmental interference, hardware failures, or unstable data transmission. In particular, this lost data often depends on the system state, which poses a significant challenge to the accuracy and stability of state estimation. How to construct efficient and robust state estimation methods in the presence of state-dependent observation loss has become a key issue that needs to be addressed in the field of multi-sensor fusion.

[0003] Traditional multi-sensor state estimation methods are usually based on Kalman filtering or its extended forms, relying on the accuracy of the system dynamic model and observation model. However, in real-world scenarios, system models often have errors or biases. In particular, when sensor observations are lost, the estimation performance of these methods is significantly reduced, which in turn affects decision-making and control effects. In addition, state-dependent observation loss further complicates the problem, because traditional methods usually assume that the lost data is independent of the state, an assumption that does not hold true in many real-world scenarios. For example, in unmanned driving scenarios, sensor observations of obstacles may be lost due to the vehicle's motion state and field of view obstruction, and GPS signals may be invalidated due to atmospheric interference. This state dependency makes it more difficult for the estimator to accurately infer the true state of the system. Summary of the Invention

[0004] In order to address the shortcomings of the prior art, the present invention aims to provide a multi-sensor information fusion estimation method for state-dependent observation loss. The recursive estimator has high robustness and adaptability, can effectively cope with the complex situation of state-dependent observation loss in various practical scenarios, and significantly improve the accuracy of system state estimation. In order to achieve the above-mentioned purpose and other advantages of the present invention, a multi-sensor information fusion estimation method for state-dependent observation loss is provided, comprising: Constructing a system model, wherein the system model is a linear discrete dynamic system model for characterizing a dynamically changing system state; Training an observation loss discriminator, which processes complex observation rejection regions through a support vector machine and transforms the nonlinear classification problem into a linear convex optimization problem through a kernel function, thereby determining whether the target state is in the observation rejection region; A recursive fusion estimator is constructed based on the EM algorithm. The recursive fusion estimator is used to process the maximum a posteriori estimation problem containing hidden variables based on observed data and current estimates at each time step using the EM algorithm framework, iteratively update the system state, and ensure that the estimate converges to a stable value.

[0005] Preferably, the observation model corresponding to the linear discrete dynamic system model is used to characterize the observation value of the system state; When receiving signals through remote sensors, the system state may be in the observation rejection domain, resulting in the loss of observations; When the system state Falling into the observation rejection region, the observation data is lost, and the remote sensor can only receive observation noise. The value is 0; otherwise, The value is 1. A binary random variable indicating whether an observation is lost. Preferably, the observation loss discriminator is obtained using a support vector machine A discriminator is used to determine whether the state enters the corresponding observation rejection region or observable region, and each support vector machine regression layer is responsible for predicting the probability that the state is in a certain region.

[0006] Preferably, the observation loss discriminator includes a quadratic kernel function to process the nonlinear feature mapping problem, by mapping the low-dimensional input space to the high-dimensional feature space, the quadratic kernel function is set to ,in Represents the adjustment parameter, which is used to control the flexibility of the kernel function, where Indicates the input status, Represents training samples.

[0007] Preferably, the recursive fusion estimator is specifically implemented as follows: Prediction: Calculate the predicted state and predicted covariance matrix and calculate the predicted information pair; Update: Initialize settings; for each sensor ( ) calculate their weights respectively; calculate the updated information pair and the estimated value, Calculate the estimated value change: Calculate the estimated value change between the previous round and the current round. If the estimated value change is less than the preset threshold or reaches the maximum number of iterations, terminate the algorithm and output the estimated value and covariance matrix.

[0008] Compared with existing technologies, the present invention offers the following advantages: It proposes a recursive estimation method based on the expectation-maximization algorithm to address the problem of state-dependent observation loss in multi-sensor fusion estimation. This method aims to effectively recover the system state under complex conditions of state-dependent observation loss and noise interference by optimizing the posterior probability distribution. To achieve this goal, the present invention builds on the maximum a posteriori (MAP) optimization framework and constructs an expectation-maximization (EM) algorithm framework. This algorithm treats the observation loss variable as a hidden variable and iteratively solves the state estimation problem, thereby improving the accuracy of state estimation. Specifically, by incorporating support vector machine (SVM) technology, the state-dependent observation loss problem is transformed into a convex optimization problem, improving the algorithm's computational efficiency. Secondly, by iteratively executing the expectation step (E-step) and maximization step (M-step), the state estimate gradually converges to a global or local optimum. In summary, the proposed recursive estimator exhibits high robustness and adaptability, effectively addressing the complex state-dependent observation loss situation in various practical scenarios and significantly improving the accuracy of system state estimation. This method has broad application prospects in the fields of intelligence and automation, and provides reliable support for their applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 This is a schematic diagram of the system model structure of the multi-sensor information fusion estimation method for state-dependent observation loss according to the present invention. The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0010] Reference Figure 1 , a multi-sensor information fusion estimation method for state-dependent observation loss, including: Construct a system model. The system model is a linear discrete dynamic system model used to characterize the dynamically changing system state. The system state includes unmanned driving, stock price fluctuations, and weather changes. The mathematical expression of the model is:

[0011] in, and Respectively represent the system Moment and The state value at the moment, express The system noise at the moment is subject to the mean , the variance is Gaussian distributed random variables, matrix is a symmetric positive definite matrix that satisfies , represents the state transition matrix. Indicates that the length of the real number field is Vector collection of Represents the size of the real number field A collection of matrices.

[0012] The observation model corresponding to the linear discrete dynamic system model is used to represent the observed value of the system state. During the observation process, noise may be mixed in. The mathematical expression of this model is:

[0013] in, Indicates the system The observed value of the state value at the moment, express The observation noise at the moment is subject to the mean , the variance is A Gaussian distributed random variable, are all symmetric positive definite matrices, satisfying , A binary random variable indicating whether the observation is missing, represents the observation matrix. represents the field of real numbers, Indicates that the length of the real number field is Vector collection of and Respectively represent the size of the real number field and size A collection of matrices.

[0014] When receiving signals from remote sensors, the system state may be in the observation rejection region, resulting in the loss of observations. The observation rejection region of a sensor is , define the set of observation rejection regions as

[0015] The observable region is defined as , which is the complement of the total space for all observed rejection regions.

[0016] When the system state falls into the observation rejection region, that is, When the observation data is lost, the remote sensor can only receive observation noise. The value is 0; otherwise, The value is 1, that is

[0017] in, represents a nonlinear function that maps states from the state space to the observation rejection space.

[0018] System noise at different times and observation noise are independent of each other and meet

[0019] Different observation rejection regions do not overlap with each other, satisfying .

[0020] use express The system state of the time series is expressed as express The observations of the time series.

[0021] Furthermore, an observation loss discriminator is trained. The observation loss discriminator processes the complex observation rejection domain through a support vector machine and transforms the nonlinear classification problem into a linear convex optimization problem through a kernel function, thereby determining whether the target state is in the observation rejection domain. The present invention uses a support vector machine to obtain A discriminator is used to determine whether the state enters the corresponding observation rejection domain or observable region. At the same time, the quadratic kernel function is introduced to deal with the nonlinear feature mapping problem, and the classification ability and accuracy are improved by mapping the low-dimensional input space to the high-dimensional feature space. Through this strategy, the discrimination accuracy of each sensor can be effectively improved. Among them, each support vector machine regression layer is responsible for predicting the probability that the state is in a certain region, and the region The discriminant function of the corresponding support vector machine regression layer is expressed as:

[0022] in, Indicates the input status, represents the training sample, represents the weight, represents the bias term, Represents the kernel function, which is used to map the input state to the high-dimensional feature space. In the present invention, the quadratic kernel function is set to ,in Represents a tuning parameter that controls the flexibility of the kernel function. The goal of the support vector machine regression layer is to minimize the objective function of the following optimization problem:

[0023]

[0024]

[0025] in, represents the regularization coefficient, Indicates the By solving the above optimization problem, the parameters of the support vector machine regression layer can be obtained 、 and , so the discriminant function is written in the following matrix form:

[0026] The coefficient of the quadratic term is ; The linear coefficient is ; The constant coefficient is .

[0027] These parameters can be obtained through offline training and used by the recursive estimator online.

[0028] Furthermore, a recursive fusion estimator is constructed based on the EM algorithm. The recursive fusion estimator is used to process the maximum a posteriori estimation problem involving hidden variables at each time step based on the observed data and the current estimate using the EM algorithm framework, iteratively update the system state, and ensure that the estimate converges to a stable value.

[0029] The designed recursive fusion estimator based on the EM algorithm is as follows: At the moment , the current observation value is known , the estimated value at the previous moment is known and the covariance matrix , known parameters ,in They represent the quadratic coefficient, linear coefficient and constant coefficient of the support vector machine discriminant function respectively, Represents the total number of sensors. The execution algorithm is as follows: Prediction step [P] Compute the forecast state and forecast covariance matrix: ; .

[0030] Calculate the predicted information pair: .

[0031] .

[0032] Update step [U] (1) Initialization: Set the number of iterations ; Set the initial estimate .

[0033] (2) Expected Step [E] For each sensor ( ) calculate their weights respectively: , Represents the last estimated value in the state The probability that no observation is lost under the condition .

[0034] (3) Maximization step [M] Calculate the updated information pair: ; .

[0035] Calculate the estimate: .

[0036] judge Area , if it is located at The observation rejection region corresponding to the sensor is recorded as ; If it is not in any observation rejection region, it is recorded as . Also remember the number of this area is .

[0037] if , then solve the equation , where the function is: .

[0038] And update the information again: ; .

[0039] And calculate the estimate again: .

[0040] Otherwise, proceed directly to the next step.

[0041] (4) Calculate the change in estimated value Calculate the change in estimate between the previous round and the current round: .

[0042] If the change in the estimated value is less than the preset threshold or the maximum number of iterations is reached, the algorithm is terminated and the estimated value and covariance matrix are output: ; .

[0043] Otherwise, jump to (2).

[0044] The number of devices and processing scales described herein are intended to simplify the description of the present invention, and the application, modification, and variation of the present invention will be apparent to those skilled in the art. Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiment. They can be applied to various fields suitable for the present invention. For those skilled in the art, additional modifications can be easily implemented. Therefore, the present invention is not limited to the specific details and illustrations shown and described herein without departing from the general concept defined by the claims and their equivalents.

Claims

1. A multi-sensor information fusion estimation method for state-dependent observation loss, characterized in that: include: Constructing a system model, wherein the system model is a linear discrete dynamic system model for characterizing a dynamically changing system state; Training an observation loss discriminator, which processes complex observation rejection regions through a support vector machine and transforms the nonlinear classification problem into a linear convex optimization problem through a kernel function, thereby determining whether the target state is in the observation rejection region; A recursive fusion estimator is constructed based on the EM algorithm. The recursive fusion estimator is used to process the maximum a posteriori estimation problem containing hidden variables based on observed data and current estimates at each time step using the EM algorithm framework, iteratively update the system state, and ensure that the estimate converges to a stable value.

2. A multi-sensor information fusion estimation method for state-dependent observation loss according to claim 1, characterized in that: The observation model corresponding to the linear discrete dynamic system model is used to represent the observation value of the system state; When receiving signals through remote sensors, the system state may be in the observation rejection domain, resulting in the loss of observations; When the system state Falling into the observation rejection region, the observation data is lost, and the remote sensor can only receive observation noise. The value is 0; otherwise, The value is 1. A binary random variable indicating whether an observation is missing.

3. A multi-sensor information fusion estimation method for state-dependent observation loss according to claim 1, characterized in that: The observation loss discriminator is obtained by using support vector machine A discriminator is used to determine whether the state enters the corresponding observation rejection region or observable region, and each support vector machine regression layer is responsible for predicting the probability that the state is in a certain region.

4. A multi-sensor information fusion estimation method for state-dependent observation loss according to claim 3, characterized in that: The observation loss discriminator includes a quadratic kernel function to process the nonlinear feature mapping problem, by mapping the low-dimensional input space to the high-dimensional feature space, and the quadratic kernel function is set to ,in Represents the adjustment parameter, which is used to control the flexibility of the kernel function, where Indicates the input status, Represents training samples.

5. The multi-sensor information fusion estimation method for state-dependent observation loss according to claim 1, characterized in that: The recursive fusion estimator is specifically implemented as follows: Prediction: Calculate the predicted state and predicted covariance matrix and calculate the predicted information pair; Update: Initialize settings; for each sensor ( ) calculate their weights respectively; Calculate the updated information pair and the estimated value, Calculate the estimated value change: Calculate the estimated value change between the previous round and the current round. If the estimated value change is less than the preset threshold or reaches the maximum number of iterations, terminate the algorithm and output the estimated value and covariance matrix.

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