Multi-sensor target state estimation method, device, apparatus and storage medium

Abstract

The present application relates to the technical field of computer, provide a kind of multi-sensor target state estimation method, device, equipment and storage medium, the method comprises: according to the first observation value of last time to be observed target multi-sensor, the first state estimation of last time to be observed target and the first observation value of current time to be observed target multi-sensor, utilize the first state estimation model to predict and obtain the first state estimation of current time to be observed target;Determine target optimization problem based on edge uncertainty set and preset mapping function, and obtain target mapping function and target probability distribution by solving;Edge uncertainty set is used to represent the possible change in real environment in state estimation process;The second state estimation of to-be-observed target is determined using target mapping function according to the mean of current time to be observed target nominal joint distribution, the covariance of current time to be observed target nominal joint distribution and target probability distribution.The adaptability of multi-sensor target state estimation method is improved.

Description

Technical Field

[0001] The present invention relates to the field of computer technology, and in particular to a multi-sensor target state estimation method, device, equipment and storage medium. Background Art

[0002] Sensor data fusion technology plays a key role in fields such as autonomous driving, aerospace, robot navigation, and security monitoring. Its purpose is to improve the accuracy and reliability of system decisions by integrating data from multiple sensors.

[0003] Core data fusion algorithms include the Kalman filter (KF) and its variants, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). These methods are primarily used for state estimation of linear and nonlinear systems. However, traditional algorithms typically assume that all sensor errors or noise follow a Gaussian distribution and that the system dynamics are known. However, in real environments, environmental conditions and sensors can change rapidly. When these conditions and sensors change rapidly, Kalman filters are less adaptable for target state estimation. Summary of the Invention

[0004] The present invention provides a multi-sensor target state estimation method, device, equipment and storage medium, which are used to solve the defect of poor adaptability of target state estimation in the prior art and improve the adaptability of target state estimation.

[0005] In a first aspect, the present invention provides a multi-sensor target state estimation method, the method comprising the following steps:

[0006] According to the first observation value of the target to be observed by the multiple sensors at the previous moment, the first state estimate of the target to be observed at the previous moment, and the first observation value of the multiple sensors of the target to be observed at the current moment, a first state estimate of the target to be observed at the current moment is predicted using the first state estimation model based on the first observation value of the multiple sensors of the target to be observed at the previous moment;

[0007] Based on the edge uncertainty set and a preset mapping function, a target optimization problem is determined and solved to obtain the target mapping function and target probability distribution; the edge uncertainty set is used to characterize possible changes in the real environment during the state estimation process;

[0008] Utilizing the target mapping function, the second state estimate of the multi-sensor of the target to be observed is determined based on the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation value of the multi-sensor of the target to be observed at the current moment.

[0009] According to a multi-sensor target state estimation method provided by the present invention, the edge uncertainty set includes all probability distributions that satisfy moment constraints; based on the edge uncertainty set and a preset mapping function, a target optimization problem is determined, and the target optimization problem is solved to obtain the target mapping function and target probability distribution, including:

[0010] determining the marginal uncertainty set according to a first estimated value of the target to be observed at a previous moment and fuzzy set parameters of a nominal model corresponding to the first state estimation model;

[0011] Determining the target optimization problem based on the edge uncertainty set and the preset mapping function; the target optimization problem is used to characterize the preset mapping function that is minimized when the probability distribution that satisfies the moment constraint condition is maximized;

[0012] The target optimization problem is solved to obtain the target mapping function and the target probability distribution.

[0013] According to a multi-sensor target state estimation method provided by the present invention, determining the target optimization problem based on the edge uncertainty set and the preset mapping function includes:

[0014] The target optimization problem is determined using the following formula (1):

[0015]

[0016] in, represents the target mapping function, represents the preset mapping function, represents the target probability distribution, represents the marginal uncertainty set, represents the observed value of the target to be observed, Indicates the actual state value of the target to be observed.

[0017] According to a multi-sensor target state estimation method provided by the present invention, solving the target optimization problem to obtain the target mapping function and the target probability distribution includes:

[0018] Determining that an optimal solution to the target optimization problem comprises a Gaussian distribution; the optimal solution is determined based on the target probability distribution;

[0019] Solving the target optimization problem by a convex optimization solver to obtain the target mapping function and the target probability distribution;

[0020] The convex optimization solver includes: a self-dual minimization SeDuMi solver or a semidefinite programming solver SDPT3.

[0021] According to a multi-sensor target state estimation method provided by the present invention, the method comprises: using the target mapping function to determine a second state estimate of the target to be observed according to the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation value of the multi-sensor of the target to be observed at the current moment, including:

[0022] Determining, based on first observation values ​​of the multiple sensors of the target to be observed at a current moment and a first state estimate value of the target to be observed at a current moment, a mean of a nominal joint distribution of the target to be observed at a current moment and a covariance of the nominal joint distribution of the target to be observed at a current moment using the first state estimation model; the first state estimation model is a standard mapping function designed based on a Kalman filter;

[0023] Utilizing the target mapping function, a second standard state estimate of the target to be observed is determined based on the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation values ​​of the multiple sensors of the target to be observed at the current moment.

[0024] According to a multi-sensor target state estimation method provided by the present invention, the method of determining a second state estimate of the target to be observed using the target mapping function according to the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation value of the multi-sensor of the target to be observed at the current moment, includes:

[0025] determining a covariance matrix of the target probability distribution;

[0026] Based on the first observation values ​​of the multiple sensors of the target to be observed at the current moment, the covariance matrix of the target probability distribution and the mean of the nominal joint distribution of the target to be observed at the current moment, the second state estimation value of the target to be observed is obtained using the target mapping function.

[0027] According to a multi-sensor target state estimation method provided by the present invention, before predicting the first state estimate of the target to be observed at the current moment using a first state estimation model based on the first observation value of the multi-sensor of the target to be observed at the previous moment, the first state estimate of the target to be observed at the previous moment, and the first observation value of the multi-sensor of the target to be observed at the current moment, the method further includes:

[0028] According to the first observation values ​​of the multiple sensors of the target to be observed at the last moment, the first state estimation model is used to determine the first state estimation value of the target to be observed at the last moment.

[0029] In a second aspect, the present invention further provides a multi-sensor target state estimation device, which includes the following modules:

[0030] a determination module, configured to predict, based on a first observation value of the target to be observed by multiple sensors at a previous moment, a first state estimate of the target to be observed at a previous moment, and the first observation value of the target to be observed by multiple sensors at a current moment, a first state estimate of the target to be observed at a previous moment, using a first state estimation model; wherein the first state estimate of the target to be observed at a previous moment is predicted using the first state estimation model based on the first observation value of the target to be observed by multiple sensors at a previous moment;

[0031] Based on the edge uncertainty set and a preset mapping function, a target optimization problem is determined and solved to obtain the target mapping function and target probability distribution; the edge uncertainty set is used to characterize possible changes in the real environment during the state estimation process;

[0032] An estimation module is used to use the target mapping function to determine a second state estimate of the multi-sensor of the target to be observed at the current moment according to the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation value of the multi-sensor of the target to be observed at the current moment.

[0033] In a third aspect, the present invention also provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the multi-sensor target state estimation method as described above is implemented.

[0034] In a fourth aspect, the present invention further provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the multi-sensor target state estimation methods described above.

[0035] In a fifth aspect, the present invention further provides a computer program product, comprising a computer program, which, when executed by a processor, implements any of the multi-sensor target state estimation methods described above.

[0036] The multi-sensor target state estimation method, device, equipment and storage medium provided by the present invention first use a first state estimation model to predict the first state estimate of the target to be observed at the current moment based on the first observation value of the multi-sensor of the target to be observed at the previous moment, the first state estimate of the target to be observed at the previous moment and the first observation value of the multi-sensor of the target to be observed at the current moment; wherein the first state estimate of the target to be observed at the previous moment is predicted based on the first observation value of the multi-sensor of the target to be observed at the previous moment using the first state estimation model; then, based on the marginal uncertainty set and the preset mapping function, the target optimization problem is determined, and the target optimization problem is solved to obtain the target mapping function and the target probability distribution; the marginal uncertainty set is used to characterize the possible changes in the real environment during the state estimation process; further, using the target mapping function, according to the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution and the first observation value of the multi-sensor of the target to be observed at the current moment, the second state estimate of the target to be observed is determined.

[0037] The present invention introduces an edge uncertainty set, which is used to characterize possible changes in the real environment during the state estimation process. This allows the filter to maintain robustness when processing non-Gaussian and unknown noise distributions. Furthermore, the target optimization problem is determined based on the edge uncertainty set and a preset mapping function, and the optimization problem is solved to obtain the target mapping function and the target probability distribution. The target mapping function is used to determine the second state estimate of the target to be observed according to the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution and the first observation value of the multiple sensors of the target to be observed at the current moment, thereby realizing real-time state estimation of the multi-sensor target, providing more accurate state estimation in the presence of model uncertainty and external interference to cope with environmental changes and sensor errors, and improving the adaptability of the multi-sensor target state estimation method. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the technical solutions in the present invention or the prior art, a brief introduction is given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0039] Figure 1This is one of the flow charts of the multi-sensor target state estimation method provided by the present invention.

[0040] Figure 2 This is the second flow chart of the multi-sensor target state estimation method provided by the present invention.

[0041] Figure 3 This is the third flow chart of the multi-sensor target state estimation method provided by the present invention.

[0042] Figure 4 It is a structural diagram of the multi-sensor target state estimation device provided by the present invention.

[0043] Figure 5 It is a structural schematic diagram of the electronic device provided by the present invention. DETAILED DESCRIPTION

[0044] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0045] The terms "first", "second", etc. in the specification and claims of this application are used to distinguish similar objects, and are not used to describe a specific order or sequence. It should be understood that the terms used in this way are interchangeable where appropriate, so that the embodiments of the present application can be implemented in an order other than those illustrated or described herein, and the objects distinguished by "first" and "second" are generally of the same type, and do not limit the number of objects. For example, the first node can be one or more. In addition, "and / or" in the specification and claims represents at least one of the connected objects, and the character " / " generally indicates that the objects associated with each other are in an "or" relationship.

[0046] In order to more clearly understand the various embodiments provided by the present invention, the technical content of the present invention is first introduced as follows:

[0047] To better handle data uncertainty common in real-world applications, covariance intersection (CI) techniques have been developed to synthesize information from different sources without requiring precise knowledge of error correlation statistics. CI is particularly well-suited for situations where sensor error models are unknown or difficult to accurately model. By synthesizing the covariance information from each sensor, CI optimizes the uncertainty of the overall estimate.

[0048] Traditional covariance cross-CI techniques are often combined with Kalman filtering in centralized fusion. The basic assumption of Kalman filtering is that the system dynamics and noise are completely known and follow a Gaussian distribution. It relies on the following system equation for state estimation:

[0049]

[0050] in i Sensor index, t is the time index, x t ∈R n is the state vector, It is a sensor i The measurement vector, is the process noise, It is a sensor i The measurement noise, 、 、 is the nominal system matrix.

[0051] Kalman filter assumption w t and v t is Gaussian white noise, and the initial state x 0、 w t and The correlations between the estimates of different sensors are independent of each other, which requires that the correlations between the estimates of different sensors are completely known. In this case, KF gives the optimal estimate in terms of minimum mean square error (MMSE). When the correlations between the estimates of different sensors are unknown, CI considers all correlations and finds the consistent estimate that minimizes the MSE. That is, for n existing consistent estimates of state x ( x i ，P i )，i=1,… , n， CI considers the following minimization problem to obtain the fused estimate:

[0052]

[0053]

[0054] Traditional covariance intersection (CI) technology is a mainstream solution in the field of multi-sensor data fusion. It is specifically designed to handle uncertainty information fusion when sensor error models are not fully known. CI optimizes the estimated uncertainty by considering the possible correlations between a series of different sensors without relying on a specific error distribution model, thus reducing the reliance on prior knowledge.

[0055] However, although CI technology provides an effective strategy to deal with uncertainty in information fusion, its performance in practical applications is not always ideal. In particular, the performance of CI methods may be limited when faced with highly dynamic environments or non-Gaussian noise conditions.

[0056] (1) Limitations of model and noise assumptions: Although CI technology provides an effective tool to deal with model parameter uncertainty, it still relies on the consistency of sensor noise covariance, which is often difficult to meet when the noise distribution deviates from the nominal distribution.

[0057] (2) Problems in coping with environmental dynamics: Although CI technology can handle a certain degree of dynamic changes, it may be difficult to quickly adapt to drastic changes in environmental conditions in highly dynamic environments, such as autonomous driving or advanced robot navigation systems.

[0058] (3) Complexity of sensor networks: Although CI technology can optimize the fusion of information from multiple sensors, it rarely considers the communication constraints and failure conditions that may exist in sensor networks during its design. In other words, it does not consider the different reliability levels among different sensors. When a single or partial sensor fails, the CI estimate will be overly conservative.

[0059] In summary, while covariance crossover techniques have advantages in handling uncertainty, they still face a series of challenges in practical applications. These challenges highlight the importance of developing new, more efficient, and robust data fusion strategies, especially in application scenarios that require extremely high environmental adaptability and computational efficiency.

[0060] To address these shortcomings, the present invention provides a multi-sensor target state estimation method. This method aims to enhance the robustness and adaptability of the covariance intersection CI technique in the face of non-Gaussian noise and parameter uncertainty, particularly in highly dynamic environments, by introducing a novel moment-constrained marginal distribution processing strategy. Specifically, the present invention addresses the following key technical issues:

[0061] (1) Uncertainty management of marginal distributions: In practical environments, the statistical characteristics of system noise and dynamics may be unknown or change over time. Existing CI methods cannot effectively handle such uncertainties. This paper introduces a new marginal uncertainty set based on moment constraints to enable the filter to maintain robustness under unknown or changing noise characteristics, thereby improving the overall performance of the system.

[0062] (2) Ability to adapt to dynamic environments: The proposed method can effectively adapt to rapidly changing environmental conditions. By dynamically adjusting the filter's operating parameters to match actual environmental changes, the filter can still provide accurate state estimation when the system model or noise characteristics change.

[0063] (3) Enhance the fault tolerance of the system: Considering that sensors may fail or communication may be interrupted in actual applications, the method of the present invention designs a strategy with high fault tolerance, which can maintain the stability of the system and the accuracy of estimation even when some sensor data is unavailable or there are errors.

[0064] The following combination Figure 1-Figure 5 The present invention describes a multi-sensor target state estimation method, apparatus, device and storage medium.

[0065] Figure 1 This is one of the flow charts of the multi-sensor target state estimation method provided by the present invention, such as Figure 1 As shown, the method includes the following:

[0066] Step 101: Based on the first observation values ​​of the multiple sensors of the target to be observed at the previous moment, the first state estimate of the target to be observed at the previous moment, and the first observation values ​​of the multiple sensors of the target to be observed at the current moment, a first state estimate of the target to be observed at the current moment is predicted using a first state estimation model; wherein the first state estimate of the target to be observed at the previous moment is predicted based on the first observation values ​​of the multiple sensors of the target to be observed at the previous moment using the first state estimation model;

[0067] Specifically, first of all, it should be explained that the execution subject of this embodiment is an electronic device, which is used to enable target state estimation to adapt to rapidly changing environmental conditions, thereby improving the adaptability of target state estimation.

[0068] The specific process of target state estimation in this embodiment can be achieved through the following steps:

[0069] First, obtain the first state estimate of the target to be observed at the previous moment. In this embodiment, the first state estimate of the target to be observed at the previous moment is regarded as a known quantity and can be predicted using a first state estimation model, wherein the first state estimation model is a nominal model, that is, a mapping function of the state estimate that is not optimized. The first state estimate Y of the target to be observed at the previous moment can be obtained based on the first observation value of the multiple sensors of the target to be observed at the previous moment. t-1 .

[0070] Furthermore, the first state estimation model can be used to predict the first state estimation of the target to be observed at the current moment based on the first observation value of the multi-sensor of the target to be observed at the previous moment, the first state estimation of the target to be observed at the previous moment, and the first observation value of the multi-sensor of the target to be observed at the current moment, that is, the preliminary state estimation Y of the target to be observed at the current moment can be achieved using the nominal model. t .

[0071] The first state estimation model (nominal model) performs state estimation according to the following system equation, for example:

[0072]

[0073] Where i is the sensor index, t is the time index, and x t ∈R n is the state vector, is the measurement vector of sensor i at the tth moment, is the process noise, is the measurement noise of sensor i, 、 、 is the nominal system matrix.

[0074] Step 102: Based on the edge uncertainty set and the preset mapping function, determine the target optimization problem, solve the target optimization problem, and obtain the target mapping function and the target probability distribution; the edge uncertainty set is used to characterize the possible changes in the real environment during the state estimation process;

[0075] Specifically, after obtaining the first state estimate of the target at the current moment, we can further construct a marginal uncertainty set. This marginal uncertainty set characterizes the possible changes in the real environment during the state estimation process. In other words, it includes all probability distributions that satisfy the moment constraints. These distributions reflect the possible changes and uncertainties in the real environment.

[0076] Exemplarily, the edge uncertainty set is constructed in the following manner:

[0077]

[0078] Among them, P M represents the moment-based marginal distribution fuzzy set, i represents the i-th sensor, P represents the number of sensors P, Q represents the possible joint distribution of x and y, and F represents the set of distribution density functions of any finite second-order moment of z, where , x represents the state variable, that is, the state variable to be estimated, y i represents the observed variable of the i-th sensor, c x, yi Indicates that Q is in x 、 yi The mean of the marginal distribution of S x, yi Indicates that Q is in x 、 y i The covariance of the marginal distribution of x, yi Denotes the nominal joint distribution P in x 、 y i The mean of the marginal distribution of x, yi Denotes the nominal joint distribution P in x 、 y i The covariance of the marginal distribution of , γ 3,i , γ 2,i , γ 1,i Represents the preset fuzzy set parameters, which are used to control the range of uncertainty and describe the reliability of the edge distribution of each sensor.

[0079] After determining the marginal uncertainty set, that is, the moment-based marginal distribution fuzzy set P M Then, the target optimization problem is further determined based on the edge uncertainty set and the preset mapping function. The preset mapping function is the set of all possible mapping functions, that is, any arrive The set of measurable functions of , where is obtained based on the observed variables, is obtained based on the state variables to be estimated.

[0080] The target optimization problem may be a minimum-maximum optimization problem determined based on an edge uncertainty set, wherein the target optimization problem is used to characterize the predetermined mapping function that is minimized when the probability distribution satisfying the moment constraint is maximized. A filter is subsequently designed based on solving the minimum-maximum optimization problem to ensure that the prediction error is minimized under the most unfavorable conditions.

[0081] Furthermore, by solving the target optimization problem, a target mapping function and a target probability distribution can be obtained, and a filter is involved in state estimation based on the target mapping function and the target probability distribution.

[0082] Step 103: Using the target mapping function, determine the second state estimate of the multiple sensors of the target to be observed based on the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation value of the multiple sensors of the target to be observed at the current moment.

[0083] Specifically, after the target mapping function is obtained, a filter can be designed based on the target mapping function, and then the target state estimation can be achieved based on the filter.

[0084] For example, using the target mapping function, the second state estimate of the target to be observed is determined based on the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation values ​​of multiple sensors of the target to be observed at the current moment.

[0085] In the method provided in this embodiment, the first state estimate of the target to be observed at the current moment is predicted by using a first state estimation model based on the first observation value of the multiple sensors of the target to be observed at the previous moment, the first state estimate of the target to be observed at the previous moment, and the first observation value of the multiple sensors of the target to be observed at the current moment; wherein, the first state estimate of the target to be observed at the previous moment is predicted by using the first state estimation model; then, based on the marginal uncertainty set and the preset mapping function, the target optimization problem is determined, and the target optimization problem is solved to obtain the target mapping function and the target probability distribution; the marginal uncertainty set is used to characterize the possible changes in the real environment during the state estimation process; further, using the target mapping function, the second state estimate of the target to be observed is determined based on the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation value of the multiple sensors of the target to be observed at the current moment.

[0086] The present invention introduces an edge uncertainty set, which is used to characterize possible changes in the real environment during the state estimation process. This allows the filter to maintain robustness when processing non-Gaussian and unknown noise distributions. Furthermore, the target optimization problem is determined based on the edge uncertainty set and a preset mapping function, and the optimization problem is solved to obtain the target mapping function and the target probability distribution. The target mapping function is used to determine the second state estimate of the target to be observed according to the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution and the first observation value of multiple sensors of the target to be observed at the current moment, thereby realizing real-time state estimation of the target. It can provide more accurate state estimation in the presence of model uncertainty and external interference to cope with environmental changes and sensor errors, thereby improving the adaptability of the multi-sensor target state estimation method.

[0087] According to a multi-sensor target state estimation method provided by the present invention, the edge uncertainty set includes all probability distributions that satisfy moment constraints; based on the edge uncertainty set and a preset mapping function, a target optimization problem is determined and solved, and the target mapping function and target probability distribution are obtained, including:

[0088] Determine a marginal uncertainty set based on a first observation value of the multi-sensor of the target to be observed at a previous moment, a first observation value of the multi-sensor of the target to be observed at a current moment, and a first state estimate of the target to be observed at a current moment;

[0089] Based on the edge uncertainty set and the preset mapping function, a target optimization problem is determined; the target optimization problem is used to characterize the preset mapping function that is minimized when the probability distribution that satisfies the moment constraint condition is maximized;

[0090] Solve the target optimization problem and obtain the target mapping function and target probability distribution.

[0091] Specifically, in some embodiments, the marginal uncertainty set includes all probability distributions that satisfy moment constraints.

[0092] Correspondingly, step 102 can be implemented by the following steps:

[0093] First, the marginal uncertainty set is determined based on the first estimated value of the target to be observed at the previous moment and the fuzzy set parameters of the nominal model corresponding to the first state estimation model. Exemplarily, the marginal uncertainty set is constructed, for example, in the following manner:

[0094]

[0095] Among them, P M represents the moment-based marginal distribution fuzzy set, i represents the i-th sensor, P represents the number of sensors P, Q represents the possible joint distribution of x and y, and F represents the set of distribution density functions of any finite second-order moment of z, where , x represents the state variable, that is, the state variable to be estimated, y i represents the observed variable of the i-th sensor, c x, yi Indicates that Q is in x 、 y i The mean of the marginal distribution of S x, yi Indicates that Q is in x 、 y i The covariance of the marginal distribution of x, yi Denotes the nominal joint distribution P in x 、 y i The mean of the marginal distribution of x, yi Denotes the nominal joint distribution P in x 、 y i The covariance of the marginal distribution of , γ 3,i , γ 2,i , γ 1,i Represents the preset fuzzy set parameters, which are used to control the range of uncertainty and describe the reliability of the edge distribution of each sensor.

[0096] Further, based on the edge uncertainty set and a preset mapping function, a target optimization problem is determined; the target optimization problem is used to represent the minimum preset mapping function under the condition that the probability distribution of the moment constraint condition is maximum.

[0097] The target optimization problem is used to represent the minimum preset mapping function under the condition that the probability distribution of the moment constraint condition is maximum, and the original problem is converted into a minimax problem, that is, into solving the minimum preset mapping function under the condition that the probability distribution of the moment constraint condition is maximum.

[0098] Further, the target optimization problem is solved to obtain a target mapping function and a target probability distribution. For example, a convex optimization solver is used to solve the target mapping function and the target probability distribution, which facilitates subsequent design of a filter based on the target mapping function to achieve target state estimation.

[0099] Exemplarily, Figure 2 is a flowchart of a second embodiment of the multi-sensor target state estimation method provided by the application, as shown in Figure 2 as shown in Figure 2 The method comprises the following steps.

[0100] In step 201, an original minimization problem is obtained.

[0101] In step 202, the target optimization problem is converted into a minimax problem.

[0102] In step 203, it is proved that the optimal solution of the target optimization problem contains a Gaussian.

[0103] In step 204, the target optimization problem is equivalent to a convex nonlinear semi-definite programming problem.

[0104] The method provided in this embodiment first determines a marginal uncertainty set based on the first observation value of the multi-sensor target to be observed at the previous moment, the first observation value of the multi-sensor target to be observed at the current moment, and the first state estimate of the target to be observed at the current moment; then, based on the marginal uncertainty set and the preset mapping function, a target optimization problem is determined; the target optimization problem is used to characterize the preset mapping function that is minimized when the probability distribution that satisfies the moment constraint is maximized; then, the target optimization problem is solved to obtain the target mapping function and the target probability distribution. In the present invention, by introducing a marginal uncertainty set, the marginal uncertainty set is used to characterize the possible changes in the real environment during the state estimation process, and then, based on the marginal uncertainty set and the preset mapping function, the target optimization problem is determined, and the optimization problem is solved to obtain the target mapping function and the target probability distribution, which facilitates the subsequent use of the target mapping function and the target probability distribution to design a filter, and then perform target state estimation based on the designed filter. This can provide more accurate state estimation in the presence of model uncertainty and external interference to cope with environmental changes and sensor errors, thereby improving the adaptability of the multi-sensor target state estimation method.

[0105] According to a multi-sensor target state estimation method provided by the present invention, based on an edge uncertainty set and a preset mapping function, a target optimization problem is determined, including:

[0106] The target optimization problem is determined using the following formula (1):

[0107]

[0108] in, represents the target mapping function, Represents the preset mapping function, represents the target probability distribution, represents the marginal uncertainty set, represents the observed value of the target to be observed, Indicates the actual state value of the target to be observed.

[0109] Specifically, in some embodiments, based on the edge uncertainty set and the preset mapping function, the specific implementation process of determining the target optimization problem may include the following steps:

[0110] For example, the target optimization problem is determined using the following formula (1):

[0111] (1)

[0112] in, Represents the target mapping function, that is, the mapping function to be obtained, the estimation equation from observation y to state x, represents the preset mapping function, that is, the set of all possible mapping functions, represents the target probability distribution, that is, the possible joint distribution of x and y, represents the marginal uncertainty set, represents the observed value of the target to be observed, Indicates the actual state value of the target to be observed.

[0113] In other words, in this embodiment, the original minimization problem is converted into a minimum-maximum problem, that is, a preset mapping function is obtained that is minimized when the probability distribution that satisfies the moment constraint condition is maximized.

[0114] The method provided in this embodiment constructs a minimum-maximum optimization problem of a marginal uncertainty set with moment constraints. The present invention can not only theoretically guarantee performance under the most unfavorable conditions, but also adaptively adjust the filtering process to cope with environmental changes and sensor errors. The adaptability of the multi-sensor target state estimation method is relatively high.

[0115] According to a multi-sensor target state estimation method provided by the present invention, a target optimization problem is solved to obtain a target mapping function and a target probability distribution, including:

[0116] Determining that the optimal solution of the target optimization problem contains a Gaussian distribution; the optimal solution is determined based on the target probability distribution;

[0117] The target optimization problem is solved by a convex optimization solver to obtain the target mapping function and target probability distribution;

[0118] Among them, the convex optimization solver includes: self-dual minimization SeDuMi solver or semidefinite programming solver SDPT3.

[0119] Specifically, in some embodiments, the specific implementation process of solving the determined target optimization problem to obtain the target mapping function and the target probability distribution includes the following steps:

[0120] First, we need to determine whether the optimal solution to the target optimization problem contains a Gaussian distribution. This optimal solution is determined based on the target probability distribution. Furthermore, we need to solve the target optimization problem to obtain the target mapping function, which is also known as the state estimation function of the filter.

[0121] The objective optimization problem (minimization problem) can be equivalent to a convex nonlinear semidefinite programming problem. Convex nonlinear semidefinite programming problems are a special type of optimization problem that combines the characteristics of convex optimization and semidefinite programming while introducing nonlinear factors. This type of problem plays an important role in the field of mathematical programming because it has applications in many engineering and scientific fields, such as optimal control, structural design, and economics and finance.

[0122] Specifically, a typical convex nonlinear semi-positive definite programming problem can be expressed as:

[0123] Minimize f ( x )

[0124] subjectto G ( x )⪯0

[0125] in, f :R n →R is a convex function, G :R n → Sm is a smooth function that maps real vectors to symmetric matrix space, S m represents the m-order real symmetric matrix space, ⪯ represents the semi-negative definite partial order, that is, A ⪯ B express A − B is a negative semidefinite matrix.

[0126] The difficulty of this type of problem lies in dealing with convexity, nonlinearity, and positive semidefiniteness at the same time. This requires the algorithm design to ensure the efficiency of convex optimization while also dealing with the complexity brought by nonlinearity and positive semidefinite constraints. Methods for solving this type of problem include augmented Lagrange method, primal-dual interior point method, sequential semidefinite programming method, etc.

[0127] Furthermore, this embodiment can solve the target optimization problem using a convex optimization solver to obtain a target mapping function and a target probability distribution. The convex optimization solver includes a self-dual minimization SeDuMi solver or a semidefinite programming solver SDPT3.

[0128] SeDuMi is a Matlab / GNU Octave package for solving convex optimization problems. It handles linear equations and inequalities, quadratic constraints, and semidefinite constraints (linear matrix inequalities). SeDuMi stands for Self-Dual-Minimization. The package was originally developed by Jos F. Sturm, who tragically passed away in 2003. It was subsequently maintained and developed by the Advanced Optimization Lab at McMaster University. Currently, SeDuMi is hosted and maintained by the CORAL Laboratory in the Department of Industrial and Systems Engineering at Lehigh University. SeDuMi's primary focus is solving optimization problems, particularly those involving cones of symmetry. It includes precompiled MATLAB and Octave MEX files for Windows, Linux, and macOS (including Intel and Apple Silicon). Installing SeDuMi typically involves downloading the compressed archive, adding it to Matlab's search path, and then running the installation script. An example of using SeDuMi involves defining an optimization problem and calling the sedumi function to solve it. The basic form of this function is [x, y, info] = sedumi(A, b,c, K, params), where A, b, c, and K represent the coefficient matrix, constraint vector, objective function vector, and constraint type of the defined model, respectively. params is a structure used to set the algorithm's parameters and termination conditions. SeDuMi is widely used for optimization problems in fields such as signal processing, machine learning, and financial mathematics. For example, in signal recovery, SeDuMi can be used to implement LASSO regression or sparse representation. It is also often used in conjunction with data analysis and machine learning libraries. For example, in MATLAB's Statistics and Machine Learning Toolbox, SeDuMi is a key component for solving the optimization problems underlying certain models. Overall, SeDuMi is a powerful toolbox specifically designed for solving linear, quadratic, and semidefinite programming problems. Its efficiency and robustness have led to its widespread use in teaching and research.

[0129] SDPT3 is a MATLAB package for solving semidefinite programming (SDP) problems. It handles linear equations and inequalities, quadratic constraints, and semidefinite constraints (linear matrix inequalities). The following are some of the key features and capabilities of SDPT3:

[0130] 1. Algorithms: SDPT3 implements an infeasible path-following algorithm (sqlp.m) for solving convex optimization problems involving semidefinite cone, second-order, and linear cone constraints. It also includes a path-following algorithm (HSDsqlp.m) for solving the 3-parameter homogeneous self-dual reconstruction form of SQLP.

[0131] 2. New features: SDPT3 can handle free variables, determinant maximization problems, SDPs with complex data, MATLAB 7.3 on 64-bit machines, and the 3-parameter homogeneous self-dual model of SQLP.

[0132] 3. Data format: SDPT3 can call data files stored in SDPA format and SeDuMi format.

[0133] 4. Optimization problem type: SDPT3 is designed to solve cone programming problems whose constraint cones are semidefinite cones, second-order cones, non-negative orthogonal bodies, and products of Euclidean spaces. Its objective function is the sum of a linear function associated with the constraint cone and a logarithmic obstacle term.

[0134] 5. Performance and Efficiency: SDPT3 performs faster on large sparse problems, is able to solve problems of larger sizes, and is more robust when dealing with unrestricted variables.

[0135] SDPT3 is a powerful tool for solving convex optimization problems, especially those involving symmetric cones. It is widely used in teaching and research due to its efficiency and robustness.

[0136] The method provided in this embodiment solves the target optimization problem through a convex optimization solver to obtain a target mapping function and a target probability distribution. The advantages of using a convex optimization solver to solve the problem are high efficiency and robustness, which facilitates the subsequent use of the target mapping function and the target probability distribution to design a filter, and then perform target state estimation based on the designed filter. It can provide more accurate state estimation in the presence of model uncertainty and external interference to cope with environmental changes and sensor errors, thereby improving the adaptability of the multi-sensor target state estimation method.

[0137] According to a multi-sensor target state estimation method provided by the present invention, a target mapping function is used to determine a second state estimate of the target to be observed based on the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation values ​​of the multiple sensors of the target to be observed at the current moment, including:

[0138] Determining the mean and covariance of the nominal joint distribution of the target to be observed at the current moment using a first state estimation model based on first observation values ​​of multiple sensors of the target to be observed at the current moment and a first state estimation value of the target to be observed at the current moment; the first state estimation model is a standard mapping function designed based on a Kalman filter;

[0139] The target mapping function is used to determine the second state estimate of the target to be observed according to the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation values ​​of the multiple sensors of the target to be observed at the current moment.

[0140] Specifically, in some embodiments, after solving the target optimization problem to obtain the target mapping function and the target probability distribution, the process of using the target mapping function to estimate the target state can be implemented as follows:

[0141] First, the first state estimation model is a standard mapping function designed based on the Kalman filter. According to the first observation values ​​of the multi-sensor of the target to be observed at the current moment and the first state estimation value of the target to be observed at the current moment, the first state estimation model is used to determine the mean of the nominal joint distribution of the target to be observed at the current moment, for example, the mean μ of the marginal distribution of the nominal joint distribution P at time t at x x,t , the mean μ of the marginal distribution of the nominal joint distribution P on y at time t y,t , and the covariance of the nominal joint distribution of the target to be observed at the current moment, for example, the covariance of the nominal joint distribution P at time t.

[0142]

[0143]

[0144] Among them, μ t represents the mean of the joint distribution of the nominal joint distribution P at time t in x and y, ∑t represents the covariance of the nominal joint distribution P at time t, F t-1 represents fixed parameters set according to the motion model, H t represents fixed parameters set according to the observation model, G represents the estimated value of x at time t based on the observations from time 0 to time t. t-1 represents fixed parameters set according to the motion model, Q t-1 represents the covariance of the process noise w at time t-1, R t represents the covariance of the observation noise v at time t.

[0145] Furthermore, the target mapping function is used to determine the second state estimate of the target to be observed based on the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation values ​​of the multiple sensors of the target to be observed at the current moment.

[0146] The method provided in this embodiment uses the target mapping function and the target probability distribution to design a filter, and then performs target state estimation based on the designed filter. It can provide more accurate state estimation in the presence of model uncertainty and external interference to cope with environmental changes and sensor errors, thereby improving the adaptability of the multi-sensor target state estimation method.

[0147] According to a multi-sensor target state estimation method provided by the present invention, a target mapping function is used to determine a second state estimate of the target to be observed based on the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation values ​​of the multiple sensors of the target to be observed at the current moment, including:

[0148] Determine the covariance matrix of the target probability distribution;

[0149] Based on the first observation values ​​of the multiple sensors of the target to be observed at the current moment, the covariance matrix of the target probability distribution and the mean of the nominal joint distribution of the target to be observed at the current moment, the second state estimation value of the target to be observed is obtained using the target mapping function.

[0150] Specifically, in some embodiments, determining the second state estimate of the target to be observed using the target mapping function according to the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation values ​​of the multiple sensors of the target to be observed at the current moment includes:

[0151] First, the covariance matrix of the target probability distribution is determined. Then, based on the first observation values ​​of the multiple sensors of the target to be observed at the current moment, the covariance matrix of the target probability distribution, and the mean of the nominal joint distribution of the target to be observed at the current moment, the target mapping function is used to obtain the second state estimate of the target to be observed.

[0152] Exemplarily, the process of determining the second state estimate of the target to be observed is as follows:

[0153]

[0154] in, represents the estimated value of x at time t based on the observations from time 0 to time t, represents the mean of the marginal distribution of the nominal joint distribution P at time t, and S represents the covariance of the target probability distribution Q, where

[0155]

[0156] Here y is the measurement of all p sensors, which can be expanded to:

[0157]

[0158]

[0159] The method provided in this embodiment uses the target mapping function and the target probability distribution to design a filter, and then performs target state estimation based on the designed filter. It can provide more accurate state estimation in the presence of model uncertainty and external interference to cope with environmental changes and sensor errors, thereby improving the adaptability of the multi-sensor target state estimation method.

[0160] According to a multi-sensor target state estimation method provided by the present invention, before using a first state estimation model to predict a first state estimate of a target to be observed at a current moment based on first observation values ​​of the multi-sensors of the target to be observed at a previous moment, a first state estimate of the target to be observed at a previous moment, and the first observation values ​​of the multi-sensors of the target to be observed at a current moment, the method further includes:

[0161] According to the first observation values ​​of the multiple sensors of the target to be observed at the last moment, a first state estimation value of the target to be observed at the last moment is determined by using a first state estimation model.

[0162] Specifically, in some embodiments, before step 101 , the method further includes determining a first state estimation value of the target to be observed at the previous moment.

[0163] For example, the nominal model first state estimation model is used to determine the first state estimation value of the target to be observed at the last moment according to the first observation value of the multiple sensors of the target to be observed at the last moment using the first state estimation model.

[0164] The method provided in this embodiment uses a first state estimation model to determine the first state estimation value of the target to be observed at the previous moment based on the first observation value of multiple sensors of the target to be observed at the previous moment. Afterwards, the first state estimation value of the target to be observed at the previous moment is used as a known quantity to realize the subsequent target mapping function determination, thereby realizing target state estimation.

[0165] Figure 3 This is the third flow chart of the multi-sensor target state estimation method provided by the present invention, such as Figure 3 As shown, the method includes:

[0166] Step 301: Input the state estimate at time t-1.

[0167] Step 302: Make a prediction based on the nominal model to obtain a state estimate at time t.

[0168] Step 303: Determine the target optimization problem based on the edge uncertainty set, solve the target optimization problem, and obtain the target mapping function and target probability distribution.

[0169] Step 304: Output the state estimate at time t according to the target mapping function and the target probability distribution.

[0170] The multi-sensor target state estimation device provided by the present invention is described below. The multi-sensor target state estimation device described below and the multi-sensor target state estimation method described above can refer to each other.

[0171] Figure 4 This is a schematic diagram of the structure of the multi-sensor target state estimation device provided by the present invention. Figure 4 As shown, the multi-sensor target state estimation device 400 includes the following modules:

[0172] Determining module 410 is configured to predict, based on the first observation values ​​of the multiple sensors of the target to be observed at the previous moment, the first state estimate of the target to be observed at the previous moment, and the first observation values ​​of the multiple sensors of the target to be observed at the current moment, a first state estimate of the target to be observed at the current moment using a first state estimation model; wherein the first state estimate of the target to be observed at the previous moment is predicted using the first state estimation model based on the first observation values ​​of the multiple sensors of the target to be observed at the previous moment;

[0173] Based on the edge uncertainty set and a preset mapping function, a target optimization problem is determined and solved to obtain the target mapping function and target probability distribution; the edge uncertainty set is used to characterize possible changes in the real environment during the state estimation process;

[0174] The estimation module 420 is used to use the target mapping function to determine the second state estimate of the multi-sensor of the target to be observed at the current moment according to the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation value of the multi-sensor of the target to be observed at the current moment.

[0175] The device provided in this embodiment includes a determination module 410 and an estimation module 420, wherein the determination module 410 is used to predict the first state estimate of the target to be observed at the current moment based on the first observation value of the multiple sensors of the target to be observed at the previous moment, the first state estimate of the target to be observed at the previous moment, and the first observation value of the multiple sensors of the target to be observed at the current moment using a first state estimation model; wherein the first state estimate of the target to be observed at the previous moment is predicted based on the first observation value of the multiple sensors of the target to be observed at the previous moment using the first state estimation model; then, the estimation module 420 is used to determine the target optimization problem based on the marginal uncertainty set and the preset mapping function, and solve the target optimization problem to obtain the target mapping function and the target probability distribution; the marginal uncertainty set is used to characterize the possible changes in the real environment during the state estimation process; further, using the target mapping function, according to the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation value of the multiple sensors of the target to be observed at the current moment, determine the second state estimate of the multiple sensors of the target to be observed.

[0176] The present invention introduces an edge uncertainty set, which is used to characterize possible changes in the real environment during the state estimation process. This allows the filter to maintain robustness when processing non-Gaussian and unknown noise distributions. Furthermore, the target optimization problem is determined based on the edge uncertainty set and a preset mapping function, and the optimization problem is solved to obtain the target mapping function and the target probability distribution. The target mapping function is used to determine the second state estimation of the multi-sensor to be observed target according to the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution and the first observation value of the multi-sensor to be observed target at the current moment, thereby realizing real-time state estimation of the multi-sensor target, providing more accurate state estimation in the presence of model uncertainty and external interference to cope with environmental changes and sensor errors, and improving the adaptability of the multi-sensor target state estimation method.

[0177] According to a multi-sensor target state estimation device 400 provided by the present invention, the marginal uncertainty set includes all probability distributions that satisfy moment constraints;

[0178] The determining module 410 is specifically configured to:

[0179] determining the marginal uncertainty set according to a first estimated value of the target to be observed at a previous moment and fuzzy set parameters of a nominal model corresponding to the first state estimation model;

[0180] Determining the target optimization problem based on the edge uncertainty set and the preset mapping function; the target optimization problem is used to characterize the preset mapping function that is minimized when the probability distribution that satisfies the moment constraint condition is maximized;

[0181] The target optimization problem is solved to obtain the target mapping function and the target probability distribution.

[0182] According to a multi-sensor target state estimation device 400 provided by the present invention, the determination module 410 is further configured to:

[0183] The target optimization problem is determined using the following formula (1):

[0184]

[0185] in, represents the target mapping function, represents the preset mapping function, represents the target probability distribution, represents the marginal uncertainty set, represents the observed value of the target to be observed, Indicates the actual state value of the target to be observed.

[0186] According to a multi-sensor target state estimation device 400 provided by the present invention, the determination module 410 is further configured to:

[0187] Determining that an optimal solution to the target optimization problem comprises a Gaussian distribution; the optimal solution is determined based on the target probability distribution;

[0188] Solving the target optimization problem by a convex optimization solver to obtain the target mapping function and the target probability distribution;

[0189] The convex optimization solver includes: a self-dual minimization SeDuMi solver or a semidefinite programming solver SDPT3.

[0190] According to a multi-sensor target state estimation device 400 provided by the present invention, the estimation module 420 is specifically configured to include:

[0191] Determining, based on first observation values ​​of the multiple sensors of the target to be observed at a current moment and a first state estimate value of the target to be observed at a current moment, a mean of a nominal joint distribution of the target to be observed at a current moment and a covariance of the nominal joint distribution of the target to be observed at a current moment using the first state estimation model; the first state estimation model is a standard mapping function designed based on a Kalman filter;

[0192] Utilizing the target mapping function, a second standard state estimate of the target to be observed is determined based on the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation values ​​of the multiple sensors of the target to be observed at the current moment.

[0193] According to a multi-sensor target state estimation device 400 provided by the present invention, the estimation module 420 is further configured to include:

[0194] determining a covariance matrix of the target probability distribution;

[0195] Based on the first observation values ​​of the multiple sensors of the target to be observed at the current moment, the covariance matrix of the target probability distribution and the mean of the nominal joint distribution of the target to be observed at the current moment, the second state estimation value of the target to be observed is obtained using the target mapping function.

[0196] According to a multi-sensor target state estimation device 400 provided by the present invention, the determination module 410 is further configured to:

[0197] According to the first observation values ​​of the multiple sensors of the target to be observed at the last moment, the first state estimation model is used to determine the first state estimation value of the target to be observed at the last moment.

[0198] Figure 5 An example of a physical structure diagram of an electronic device is shown below. Figure 5 As shown, the electronic device may include: a processor 510, a communication interface 520, a memory 530, and a communication bus 540, wherein the processor 510, the communication interface 520, and the memory 530 communicate with each other via the communication bus 540. The processor 510 may call the logic instructions in the memory 530 to execute the multi-sensor target state estimation method, which includes:

[0199] According to the first observation value of the target to be observed by the multiple sensors at the previous moment, the first state estimate of the target to be observed at the previous moment, and the first observation value of the multiple sensors of the target to be observed at the current moment, a first state estimate of the target to be observed at the current moment is predicted using the first state estimation model based on the first observation value of the multiple sensors of the target to be observed at the previous moment;

[0200] Based on the edge uncertainty set and a preset mapping function, a target optimization problem is determined and solved to obtain the target mapping function and target probability distribution; the edge uncertainty set is used to characterize possible changes in the real environment during the state estimation process;

[0201] Utilizing the target mapping function, the second state estimate of the multi-sensor of the target to be observed is determined based on the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation value of the multi-sensor of the target to be observed at the current moment.

[0202] Furthermore, the logic instructions in the aforementioned memory 530 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a mobile hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0203] On the other hand, the present invention further provides a computer program product, which includes a computer program. The computer program can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can perform the multi-sensor target state estimation method provided by the above methods, which includes:

[0204] According to the first observation value of the target to be observed by the multiple sensors at the previous moment, the first state estimate of the target to be observed at the previous moment, and the first observation value of the multiple sensors of the target to be observed at the current moment, a first state estimate of the target to be observed at the current moment is predicted using the first state estimation model based on the first observation value of the multiple sensors of the target to be observed at the previous moment;

[0205] Based on the edge uncertainty set and a preset mapping function, a target optimization problem is determined and solved to obtain the target mapping function and target probability distribution; the edge uncertainty set is used to characterize possible changes in the real environment during the state estimation process;

[0206] Utilizing the target mapping function, the second state estimate of the multi-sensor of the target to be observed is determined based on the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation value of the multi-sensor of the target to be observed at the current moment.

[0207] In another aspect, the present invention further provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to perform the multi-sensor target state estimation method provided by the above methods, the method comprising:

[0208] According to the first observation value of the target to be observed by the multiple sensors at the previous moment, the first state estimate of the target to be observed at the previous moment, and the first observation value of the multiple sensors of the target to be observed at the current moment, a first state estimate of the target to be observed at the current moment is predicted using the first state estimation model based on the first observation value of the multiple sensors of the target to be observed at the previous moment;

[0209] Based on the edge uncertainty set and a preset mapping function, a target optimization problem is determined and solved to obtain the target mapping function and target probability distribution; the edge uncertainty set is used to characterize possible changes in the real environment during the state estimation process;

[0210] Utilizing the target mapping function, the second state estimate of the multi-sensor of the target to be observed is determined based on the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation value of the multi-sensor of the target to be observed at the current moment.

[0211] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0212] Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented using software plus a necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the essence of the above technical solution, or the portion that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, or an optical disk, and includes a number of instructions for causing a computer device (such as a personal computer, server, or network device) to execute the methods described in each embodiment or certain portions of the embodiments.

[0213] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A multi-sensor target state estimation method, characterized in that: include: According to the first observation value of the target to be observed by the multiple sensors at the previous moment, the first state estimate of the target to be observed at the previous moment, and the first observation value of the multiple sensors of the target to be observed at the current moment, a first state estimate of the target to be observed at the current moment is predicted using the first state estimation model based on the first observation value of the multiple sensors of the target to be observed at the previous moment; Based on the edge uncertainty set and a preset mapping function, a target optimization problem is determined and solved to obtain a target mapping function and a target probability distribution; the edge uncertainty set is used to characterize possible changes in the real environment during the state estimation process; Utilizing the target mapping function, the second state estimate of the multi-sensor of the target to be observed is determined according to the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation value of the multi-sensor of the target to be observed at the current moment; the mean of the nominal joint distribution of the target to be observed at the current moment and the covariance of the nominal joint distribution of the target to be observed at the current moment are determined based on the first state estimate value of the target to be observed at the current moment.

2. The multi-sensor target state estimation method according to claim 1, characterized in that: The edge uncertainty set includes all probability distributions that satisfy the moment constraint conditions; based on the edge uncertainty set and the preset mapping function, the target optimization problem is determined, and the target optimization problem is solved to obtain the target mapping function and the target probability distribution, including: determining the marginal uncertainty set according to a first estimated value of the target to be observed at a previous moment and fuzzy set parameters of a nominal model corresponding to the first state estimation model; Determining the target optimization problem based on the edge uncertainty set and the preset mapping function; the target optimization problem is used to characterize the preset mapping function that is minimized when the probability distribution that satisfies the moment constraint condition is maximized; The target optimization problem is solved to obtain the target mapping function and the target probability distribution.

3. The multi-sensor target state estimation method according to claim 2, characterized in that: The determining the target optimization problem based on the edge uncertainty set and the preset mapping function includes: The target optimization problem is determined using the following formula (1): （1） in, represents the target mapping function, represents the preset mapping function, represents the target probability distribution, represents the marginal uncertainty set, represents the observed value of the target to be observed, Indicates the actual state value of the target to be observed.

4. The multi-sensor target state estimation method according to claim 2, characterized in that: The step of solving the target optimization problem to obtain the target mapping function and the target probability distribution includes: Determining that an optimal solution to the target optimization problem comprises a Gaussian distribution; the optimal solution is determined based on the target probability distribution; Solving the target optimization problem by a convex optimization solver to obtain the target mapping function and the target probability distribution; The convex optimization solver includes: a self-dual minimization SeDuMi solver or a semidefinite programming solver SDPT3.

5. The multi-sensor target state estimation method according to claim 1, characterized in that: Determining a second state estimate of the multi-sensor of the target to be observed by using the target mapping function according to a mean of the nominal joint distribution of the target to be observed at a current moment, a covariance of the nominal joint distribution of the target to be observed at a current moment, the target probability distribution, and a first observation value of the multi-sensor of the target to be observed at a current moment includes: Determining, based on first observation values ​​of the multiple sensors of the target to be observed at a current moment and a first state estimate value of the target to be observed at a current moment, a mean of a nominal joint distribution of the target to be observed at a current moment and a covariance of the nominal joint distribution of the target to be observed at a current moment using the first state estimation model; the first state estimation model is a standard mapping function designed based on a Kalman filter; Utilizing the target mapping function, a second standard state estimate of the target to be observed is determined based on the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation values ​​of the multiple sensors of the target to be observed at the current moment.

6. The multi-sensor target state estimation method according to claim 1, characterized in that: Determining a second state estimate of the multi-sensor of the target to be observed using the target mapping function according to a mean of the nominal joint distribution of the target to be observed at a current moment, a covariance of the nominal joint distribution of the target to be observed at a current moment, the target probability distribution, and a first observation value of the multi-sensor of the target to be observed at a current moment includes: determining a covariance matrix of the target probability distribution; Based on the first observation values ​​of the multiple sensors of the target to be observed at the current moment, the covariance matrix of the target probability distribution and the mean of the nominal joint distribution of the target to be observed at the current moment, the second state estimation value of the target to be observed is obtained using the target mapping function.

7. The multi-sensor target state estimation method according to any one of claims 1 to 6, characterized in that: Before obtaining the first state estimate of the target to be observed at the current moment by using the first state estimation model to predict based on the first observation value of the target to be observed by the multiple sensors at the previous moment, the first state estimate of the target to be observed at the previous moment, and the first observation value of the target to be observed by the multiple sensors at the current moment, the method further includes: According to the first observation values ​​of the multiple sensors of the target to be observed at the last moment, the first state estimation model is used to determine the first state estimation value of the target to be observed at the last moment.

8. A multi-sensor target state estimation device, characterized in that: include: a determination module, configured to predict, based on a first observation value of the target to be observed by multiple sensors at a previous moment, a first state estimate of the target to be observed at a previous moment, and the first observation value of the target to be observed by multiple sensors at a current moment, a first state estimate of the target to be observed at a previous moment, using a first state estimation model; wherein the first state estimate of the target to be observed at a previous moment is predicted using the first state estimation model based on the first observation value of the target to be observed by multiple sensors at a previous moment; Based on the edge uncertainty set and a preset mapping function, a target optimization problem is determined and solved to obtain a target mapping function and a target probability distribution; the edge uncertainty set is used to characterize possible changes in the real environment during the state estimation process; An estimation module is used to determine a second state estimate of the multi-sensor of the target to be observed by using the target mapping function according to the mean of the nominal joint distribution of the target to be observed at the current moment, the covariance of the nominal joint distribution of the target to be observed at the current moment, the target probability distribution, and the first observation value of the multi-sensor of the target to be observed at the current moment; the mean of the nominal joint distribution of the target to be observed at the current moment and the covariance of the nominal joint distribution of the target to be observed at the current moment are determined based on the first state estimate value of the target to be observed at the current moment.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the multi-sensor target state estimation method according to any one of claims 1 to 7 is implemented.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the multi-sensor target state estimation method according to any one of claims 1 to 7 is implemented.

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