Sliding window robust adaptive cubature Kalman filtering method and device and medium

Abstract

The invention relates to the technical field of data filtering, and provides a sliding window robust adaptive cubature Kalman filtering method and device and a medium, and the method comprises the steps: obtaining an observation vector of a sensor for a tracked target at a current moment; estimating a current state and an error covariance matrix by using a volume Kalman filtering algorithm based on the observation vector and the previous moment information; performing reverse smoothing on an estimation result at each moment in the sliding window by using a volume Kalman smoother to obtain a state smooth vector and a corresponding matrix; and finally, determining a current noise covariance matrix by variational Bayesian inference based on the information, wherein the current noise covariance matrix is used for correcting a prediction error covariance matrix at the next moment. According to the embodiment of the invention, the sliding window mechanism and the volume Kalman smoother are introduced to carry out reverse smoothing on the historical state, and the variational Bayesian inference is combined to carry out online joint estimation on the time-varying noise covariance matrix, so that the uncertainty of the model and the filtering divergence caused by noise abrupt change can be effectively inhibited, and the state estimation precision and robustness are improved.

Description

Technical Field

[0001] This disclosure relates to the field of data filtering technology, and more specifically, to a sliding window robust adaptive capacitive Kalman filtering method, apparatus, and medium. Background Technology

[0002] Nonlinear state estimation plays a crucial role in engineering fields such as radar target tracking and navigation guidance. Its core task is to recursively estimate the internal state of a dynamic system using noisy observation data. Cumulative Kalman filtering (CKF), as a typical nonlinear filtering method, has attracted widespread attention due to its advantages in multidimensional integral problems.

[0003] However, standard CKF and most of its adaptive variants are typically based on the ideal assumption that the statistical characteristics of process noise and measurement noise are known and constant. In complex real-world applications, such as when a target undergoes sudden maneuvers or the sensor's operating environment changes abruptly, system noise often exhibits significant time-varying characteristics or statistical uncertainty. This can easily lead to a decrease in the estimation accuracy of traditional filters based on fixed noise covariance, or even cause filter divergence.

[0004] To improve the robustness of filtering in uncertain noise environments, related research mainly revolves around two approaches: one is online estimation methods based on covariance matching or maximum likelihood criteria, but these methods either lack theoretical guarantees or are computationally complex and susceptible to initial errors; the other is an adaptive framework based on variational Bayesian inference, which significantly improves the robustness of the estimation by treating the noise covariance matrix as a random variable and performing joint posterior estimation. However, existing variational Bayesian methods still have significant limitations in applications to nonlinear systems: most methods use a pre-set, potentially inaccurate, "nominal" process noise covariance matrix to initialize the iteration at each time step, making their performance extremely sensitive to this prior setting. Summary of the Invention

[0005] This disclosure provides at least one sliding window robust adaptive capacitive Kalman filter method, apparatus, and medium. By introducing a sliding window mechanism and a capacitive Kalman smoother to inversely smooth historical states, and combining variational Bayesian inference to jointly estimate the time-varying noise covariance matrix online, it can effectively suppress filter divergence caused by model uncertainty and noise abrupt changes, and significantly improve the state estimation accuracy and robustness in strongly nonlinear and time-varying noise environments.

[0006] This disclosure provides a sliding window robust adaptive capacitive Kalman filtering method, including: The sensor obtains the observation vector of the tracked target at the current moment; and based on the observation vector, the state estimation vector of the tracked target at the previous moment and the error covariance matrix corresponding to the state estimation vector, the motion state of the tracked target is estimated by the capacitive Kalman filter algorithm to obtain the state estimation vector of the tracked target at the current moment and the estimation error covariance matrix corresponding to the state estimation vector. A capacitive Kalman smoother is used to inversely smooth the state estimation vector and the estimation error covariance matrix corresponding to the state estimation vector at each time step within a sliding window of a preset length, thereby obtaining the state smoothing vector and the smoothing error covariance matrix corresponding to the state smoothing vector at each time step within the sliding window; wherein, the sliding window includes the current time step and multiple consecutive time steps prior to it. Based on the state smoothing vector, smoothing error covariance matrix, and observation vector at each time step within the sliding window, a joint recursive estimation is performed using the variational Bayesian inference method to determine the noise covariance matrix at the current time step; wherein, the noise covariance matrix is ​​used to correct the prediction error covariance matrix during the capacitive Kalman filtering algorithm at the next time step.

[0007] This disclosure provides a sliding window robust adaptive capacitive Kalman filter, comprising: The state estimation module is used to obtain the observation vector of the tracked target by the sensor at the current moment; and based on the observation vector, the state estimation vector of the tracked target at the previous moment and the error covariance matrix corresponding to the state estimation vector, the motion state of the tracked target is estimated by the capacitive Kalman filter algorithm to obtain the state estimation vector of the tracked target at the current moment and the estimation error covariance matrix corresponding to the state estimation vector. The result smoothing module is used to perform inverse smoothing on the state estimation vector and the estimation error covariance matrix corresponding to the state estimation vector at each time step within a sliding window of a preset length using a capacitive Kalman smoother, to obtain the state smoothing vector and the smoothing error covariance matrix corresponding to the state smoothing vector at each time step within the sliding window; wherein, the sliding window includes the current time step and multiple consecutive time steps before it. The matrix determination module is used to determine the noise covariance matrix at the current time by performing joint recursive estimation using the variational Bayesian inference method based on the state smoothing vector, smoothing error covariance matrix and observation vector at each time step within the sliding window; wherein, the noise covariance matrix is ​​used to correct the prediction error covariance matrix during the capacitive Kalman filtering algorithm at the next time step.

[0008] This disclosure provides a computer device including a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the computer device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, they perform the sliding window robust adaptive capacitive Kalman filtering method as described in any of the above possible embodiments.

[0009] This disclosure provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the sliding window robust adaptive capacitive Kalman filtering method as described in any of the possible embodiments above.

[0010] The sliding window robust adaptive capacitive Kalman filtering method, apparatus, and medium provided in this disclosure significantly improve the smoothness and consistency of state estimation by introducing a sliding window mechanism combined with a capacitive Kalman smoother to perform inverse smoothing of historical state estimates. Furthermore, based on the variational Bayesian inference method, the process noise covariance matrix and the measurement noise covariance matrix are jointly recursively estimated within the sliding window, achieving high-precision online identification under conditions where noise statistical characteristics are unknown or time-varying. By feeding the estimated noise covariance matrix back to the capacitive Kalman filtering process at the next time step, the prediction error covariance matrix is ​​corrected in real time, effectively suppressing the accumulation of estimation errors and filter divergence caused by factors such as model mismatch and sudden noise changes.

[0011] To make the above-mentioned objects, features and advantages of this disclosure more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0012] To more clearly illustrate the technical solutions of the embodiments of this disclosure, the accompanying drawings referenced in the embodiments will be briefly described below. These drawings are incorporated in and constitute a part of this specification. They illustrate embodiments conforming to this disclosure and, together with the specification, serve to explain the technical solutions of this disclosure. It should be understood that the following drawings only show some embodiments of this disclosure and should not be considered as limiting the scope. Those skilled in the art can obtain other related drawings based on these drawings without creative effort.

[0013] Figure 1 A flowchart of a sliding window robust adaptive capacitive Kalman filtering method provided in an embodiment of this disclosure is shown; Figure 2 A flowchart illustrating a method for implementing a capacitive Kalman filter algorithm according to an embodiment of this disclosure is shown. Figure 3 A flowchart is shown illustrating a method for determining a state estimation vector and an estimation error covariance matrix provided in an embodiment of this disclosure; Figure 4 A flowchart of a multiple fading factor calculation method provided by an embodiment of this disclosure is shown; Figure 5 A flowchart of a method for correcting a state prediction vector and prediction error covariance matrix provided in an embodiment of this disclosure is shown; Figure 6 A flowchart of a method for determining a noise covariance matrix provided by an embodiment of this disclosure is shown; Figure 7 A schematic diagram of a sliding window robust adaptive capacitive Kalman filter device provided in an embodiment of this disclosure is shown. Figure 8 A schematic diagram of the structure of a computer device provided in an embodiment of this disclosure is shown. Detailed Implementation

[0014] To make the objectives, technical solutions, and advantages of the embodiments of this disclosure clearer, the technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. The components of the embodiments of this disclosure described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this disclosure provided in the accompanying drawings is not intended to limit the scope of the claimed disclosure, but merely represents selected embodiments of this disclosure. All other embodiments obtained by those skilled in the art based on the embodiments of this disclosure without inventive effort are within the scope of protection of this disclosure.

[0015] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0016] In this document, the term "and / or" merely describes a relationship, indicating that three relationships can exist. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Furthermore, the term "at least one" in this document means any combination of at least two of any one or more elements. For example, including at least one of A, B, and C can mean including any one or more elements selected from the set consisting of A, B, and C.

[0017] Nonlinear state estimation is one of the core technologies in modern information processing, playing an indispensable role in radar target tracking, navigation guidance, robot synchronous localization and mapping, and various industrial control systems. Its fundamental task is to recursively deduce the complete state of a dynamic system—a state that cannot be directly measured—from a series of noisy local observation data. To effectively solve the state estimation problem of nonlinear systems, researchers have developed a series of nonlinear filters based on the classical Kalman filtering (KF) framework. Among them, the Cubature Kalman filter (CKF) has become one of the mainstream methods because it directly approximates the posterior mean and covariance of the state using numerical integration rules, avoiding linearization errors. Furthermore, it exhibits superior accuracy and stability compared to the Extended Kalman Filter (EKF) when dealing with medium- and high-dimensional nonlinear problems.

[0018] However, the standard CKF and most of its derivative algorithms are based on a crucial and often overly idealistic assumption: that the system's process noise covariance matrix (PNCM) and measurement noise covariance matrix (MNCM) are precisely known beforehand and remain constant throughout the filtering process. This assumption is often difficult to hold in practical engineering. For example, when radar tracks high-speed maneuvering targets, unpredictable acceleration changes can cause abrupt changes in the statistical characteristics of process noise; in robot navigation, sensors entering complex environments (such as moving from open ground into jungles or urban canyons with severe multipath effects) can introduce time-varying and uncertain measurement noise. When the fixed noise covariance matrix used in the filter is severely mismatched with the actual noise statistics, it will inevitably lead to a significant decrease in the accuracy of state estimation and may further cause filter divergence, resulting in the failure of the entire tracking or localization system.

[0019] Research has revealed that to address the challenges posed by uncertain noise environments and improve the adaptive and robust performance of filters, various solutions have been proposed in related technologies. Early adaptive methods based on covariance matching and maximum likelihood criteria, while capable of online noise adjustment, generally suffer from insufficient theoretical safeguards, sensitivity to initial conditions, or computational complexity. In recent years, adaptive filtering frameworks based on Variational Bayesian (VB) inference have demonstrated unique advantages. This method treats the unknown noise covariance as a random variable and performs joint posterior estimation based on Bayes' theorem and system state, achieving online learning of noise statistics.

[0020] However, existing nonlinear adaptive methods based on VB still have significant limitations in engineering applications: First, most algorithms heavily rely on a preset "nominal" process noise covariance during iteration, which leads to a significant deterioration in estimation performance when the initial settings deviate significantly from the actual environment; second, traditional single-moment update mechanisms struggle to fully utilize statistical information from historical observation data, have insufficient tracking ability for noise mutations, and converge slowly; furthermore, while some schemes employing Monte Carlo integration techniques can reduce dependence on preset parameters, they impose a heavy computational burden, making it difficult to meet real-time processing requirements.

[0021] Based on the above research, this disclosure provides a sliding window robust adaptive capacitive Kalman filtering method, device, and medium. Specifically, it obtains the observation vector of the sensor on the tracked target at the current moment; estimates the current state and error covariance matrix using a capacitive Kalman filtering algorithm based on the observation vector and information from the previous moment; then, it uses a capacitive Kalman smoother to inversely smooth the estimation results at each moment within the sliding window to obtain the state smoothing vector and the corresponding matrix; finally, it uses variational Bayesian inference to determine the current noise covariance matrix based on this information, which is used to correct the prediction error covariance matrix at the next moment.

[0022] In this embodiment, a sliding window mechanism combined with a capacitive Kalman smoother is introduced to perform inverse smoothing of historical state estimates, significantly improving the smoothness and consistency of state estimates. Furthermore, based on the variational Bayesian inference method, the process noise covariance matrix and the measurement noise covariance matrix are jointly recursively estimated within the sliding window, achieving high-precision online identification under conditions where noise statistical characteristics are unknown or time-varying. By feeding the estimated noise covariance matrix back to the capacitive Kalman filtering process at the next time step, the prediction error covariance matrix is ​​corrected in real time, effectively suppressing the accumulation of estimation errors and filter divergence caused by factors such as model mismatch and sudden noise changes.

[0023] To facilitate understanding of this embodiment, the execution subject of the sliding window robust adaptive capacitive Kalman filtering method provided in this disclosure embodiment will first be described in detail. The execution subject of the sliding window robust adaptive capacitive Kalman filtering method provided in this disclosure embodiment is a computer device. This computer device can be a terminal device or a server. The terminal device can also be a mobile device, a user terminal, a terminal, a handheld device, a computing device, an in-vehicle device, a wearable device, etc. The server can be an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud storage, big data, and artificial intelligence platforms. Optionally, this method can also be applied to an implementation environment composed of computer devices and servers.

[0024] The sliding window robust adaptive capacitive Kalman filtering method provided in the embodiments of this application will be described in detail below with reference to the accompanying drawings. See also Figure 1 The diagram shows a flowchart of a sliding window robust adaptive capacitive Kalman filtering method provided in an embodiment of this disclosure. The method includes the following steps S101 to S103: S101, obtain the observation vector of the target being tracked by the sensor at the current moment; and based on the observation vector, the state estimation vector of the target being tracked at the previous moment and the error covariance matrix corresponding to the state estimation vector, estimate the motion state of the target being tracked by the capacitive Kalman filter algorithm to obtain the state estimation vector of the target being tracked at the current moment and the estimation error covariance matrix corresponding to the state estimation vector.

[0025] As is understandable, sensors are devices used to sense and measure information related to a tracked target. Different types of sensors, based on their working principles, can acquire diverse information about the target. For example, in a radar system, a radar sensor emits electromagnetic waves of specific frequencies and waveforms. When these electromagnetic waves encounter the tracked target, they are reflected. The radar sensor receives these reflected waves and, based on the time delay, frequency changes, and other characteristics of the reflected waves, can accurately calculate key information such as the target's position and velocity. In an optical tracking system, optical sensors, by capturing and analyzing the light reflected or emitted by the target, can acquire information such as the target's shape, color, and coordinates in space.

[0026] Here, at the current moment, the sensor measures the target being tracked. Based on its operating mode and measurement accuracy, the sensor collects various observable feature data of the target at that moment and integrates this data to form an observation vector. For example, in two-dimensional plane tracking, the observation vector typically includes the target's position coordinates on the x-axis and y-axis. For instance, in a simple two-dimensional plane target tracking experiment, if the target's current position on the x-axis is 3 meters and its position on the y-axis is 4 meters, then the observation vector obtained by the sensor can be represented as [3, 4]. Besides position coordinates, in some cases, the observation vector may also include other information closely related to the target's motion state, such as velocity and acceleration components. If the sensor has the ability to measure the target's velocity and acceleration, and the current target's velocity in the x-axis direction is 1 m / s, its velocity in the y-axis direction is 0.5 m / s, and its acceleration is 0, then the observation vector might expand to [3, 4, 1, 0.5, 0, 0], where the first two elements represent position coordinates, the middle two elements represent velocity components, and the last two elements represent acceleration components.

[0027] Specifically, after obtaining the observation vector at the current moment, it is necessary to combine the state estimation vector of the tracked target at the previous moment and its corresponding error covariance matrix to perform filtering processing on the current state estimation vector of the tracked target and the corresponding estimation error covariance matrix in subsequent steps. The state estimation vector at the previous moment is the estimation result of the tracked target's motion state at the previous moment, which can be the estimated value of key motion parameters such as the target's position, velocity, and acceleration at the previous moment. The error covariance matrix corresponding to the state estimation vector describes the error correlation and magnitude between the elements in the state estimation vector. The error covariance matrix is ​​a symmetric matrix; its diagonal elements represent the variance of each element in the state estimation vector itself, reflecting the dispersion of the estimated value of that element; the off-diagonal elements represent the covariance between different elements, reflecting the correlation of their errors.

[0028] For example, based on the state estimation vector from the previous time step and the corresponding error covariance matrix, the capacitive Kalman filter algorithm can be used to estimate the motion state of the tracked target. Here, the capacitive Kalman filter algorithm is a recursive filtering algorithm based on the capacitive rule. It estimates the target's motion state by sampling the state space using capacitive points and using these sampling points to approximate the posterior probability density function of the nonlinear system.

[0029] Specifically, refer to Figure 2 As shown, when estimating the motion state of the tracked target using the capacitive Kalman filter algorithm, the following steps S201~S204 may be included: S201, Based on the state estimation vector of the tracked target at the previous moment and the error covariance matrix corresponding to the state estimation vector, generate the first set of volume points.

[0030] Here, the state estimation vector contains estimates of the tracked target's position, velocity, and other key motion parameters from the previous moment, while the error covariance matrix describes the error characteristics of these estimates. The process of generating the first set of volume points essentially involves selecting a representative set of points in the state space based on the distribution characteristics determined by the error covariance matrix. The selection of these volume points is not arbitrary but follows specific volume selection rules to ensure they fully reflect the possible distribution of the target's state in the state space. For example, if the state space is a two-dimensional plane, the state estimation vector contains the target's position coordinates on the x-axis and y-axis. The error covariance matrix describes the error range and correlation of these two coordinate estimates. Therefore, the generated first set of volume points will be evenly or weighted within the region defined by the error covariance matrix, centered on the state estimation vector.

[0031] S202, the first set of volume points is propagated through a nonlinear state transition function to obtain the second set of volume points.

[0032] Specifically, the nonlinear state transition function describes the motion of a target from the previous moment to the current moment. It considers various nonlinear factors that may exist during the target's motion, such as air resistance and the nonlinear effects of control inputs. When the first set of volume points passes through this nonlinear state transition function, it is equivalent to simulating the various states that the target may reach at the current moment. For example, if the target is accelerating and there is a nonlinear relationship between acceleration and velocity, then after propagation through the state transition function, the first set of volume points will be transformed into a second set of volume points according to this nonlinear relationship. This new set of volume points represents the set of states that the target may be in at the current moment.

[0033] S203, perform a weighted summation on the second set of volume points to obtain the state prediction vector; and, based on the difference between the second set of volume points and the state prediction vector, determine the prediction error covariance matrix.

[0034] Understandably, the state prediction vector is a preliminary prediction of the target's motion state at the current moment. It integrates the information contained in the second set of volume points. The prediction error covariance matrix is ​​used to describe the error characteristics of the state prediction vector, reflecting the possible deviation range and correlation between the predicted value and the true value.

[0035] Here, since the second set of volume points is obtained after considering the nonlinear characteristics of the target motion, each volume point represents a possible target state, but their contribution to the final state prediction may differ. Therefore, an appropriate weight can be assigned to each volume point. These weights are usually determined based on the generation rules of the volume points and the prior knowledge of the system. For example, if the volume points are generated according to a Gaussian distribution, the weight may be related to the point's position in the distribution; volume points in the central region of the distribution may have larger weights, while those in the peripheral regions may have relatively smaller weights. Multiplying each volume point by its corresponding weight and summing the results yields the state prediction vector.

[0036] Specifically, when determining the prediction error covariance matrix, the first step is to calculate the difference between each volume point and the state prediction vector. This difference reflects the degree of deviation between the target state represented by that volume point and the initial predicted state. Next, these differences can be used to construct the prediction error covariance matrix. This matrix is ​​a symmetric matrix, where each element reflects the error correlation between different dimensions of the state prediction vector and the range of error magnitude.

[0037] S204, based on the noise covariance matrix determined in the previous moment, the observation vector, the state prediction vector at the current moment, and the prediction error covariance matrix, determine the state estimation vector of the tracked target at the current moment, and the estimation error covariance matrix corresponding to the state estimation vector.

[0038] Understandably, the noise covariance matrix includes the process noise covariance matrix and the measurement noise covariance matrix, describing the characteristics of process noise and measurement noise in a target tracking system. Process noise mainly originates from uncertainties in the target's motion, such as sudden interference from unknown external forces or deviations in the execution of control commands. These factors lead to differences between the actual target motion state and the state predicted by the theoretical model. Measurement noise, on the other hand, is caused by factors such as the accuracy limitations of the sensor itself and environmental interference. When the sensor collects target state information, it inevitably introduces certain errors, causing deviations between the measured values ​​and the true values. This noise interferes with the prediction of the target state, making the state prediction vector and the prediction error covariance matrix unable to accurately reflect the target's true state and error situation. By using the noise covariance matrix determined at the previous moment, the state prediction vector can be corrected to be closer to the target's true state, while the prediction error covariance matrix can be adjusted to more accurately reflect the error situation of the corrected state estimate. After this correction process, the current state estimation vector of the tracked target and the corresponding estimation error covariance matrix are finally obtained, which has higher accuracy and reliability, and can provide more solid data support for subsequent target tracking decisions, trajectory planning and other tasks.

[0039] For example, considering that the degree to which different state dimensions of the target are affected by noise may vary during the target's motion, and the noise characteristics may change at different times, since a traditional single fading factor is insufficient to meet the correction requirements in such complex situations, a multiple fading factor method can be used for correction. (Refer to...) Figure 3 As shown, determining the current state estimation vector and estimation error covariance matrix of the tracked target may include the following steps S2041~S2042: S2041, based on the observation vector at the current time, the state prediction vector at the current time, the state estimation vector at the previous time, the estimation error covariance matrix, and the noise covariance matrix, calculate the multiple fading factor.

[0040] Understandably, the state estimation vector and estimation error covariance matrix from the previous time step represent the estimation results and error descriptions of the target state at that time step. By combining this information with the noise covariance matrix from the previous time step, multiple fading factors can be calculated for different state dimensions and different time steps. These multiple fading factors adaptively adjust the degree of correction to the state prediction vector and prediction error covariance matrix based on the characteristics of the noise and changes in the target state. For example, for state dimensions heavily affected by noise, the corresponding multiple fading factors will assign a larger correction weight to more effectively eliminate noise interference; while for dimensions less affected by noise, the correction weight will be reduced accordingly to avoid over-correction leading to distortion of the estimation results.

[0041] For example, refer to Figure 4 As shown, the calculation of multiple fading factors may include the following steps S401~S406: S401, Based on the state estimation vector and the estimation error covariance matrix of the previous time step, generate the third set of volume points.

[0042] Specifically, based on the state estimation vector and estimation error covariance matrix of the previous time step, a specific volume point generation algorithm, such as a Gaussian distribution-based volume point generation method, can be used to generate a representative set of volume points in the state space, namely the third set of volume points. These volume points are uniformly distributed near the state region represented by the state estimation vector, and their distribution characteristics match the estimation error covariance matrix.

[0043] S402, the third set of volume points are propagated through a nonlinear observation function to obtain the propagated observation volume points.

[0044] In practical target tracking systems, sensors often observe target states through nonlinear observation functions. For example, when a radar sensor measures a target's position and velocity, the relationship between its measurements and the target's actual state is nonlinear. Therefore, to simulate the sensor's observation process, a third set of volume points can be substituted into this nonlinear observation function. Through function operations, each volume point is mapped to a new observation space, resulting in corresponding observation volume points. These propagated observation volume points represent the sensor's observation results for different state volume points under ideal conditions, reflecting the nonlinear relationship between the target state and the sensor's observations.

[0045] S403, perform a weighted average of the propagated observation volume points to obtain the predicted observation vector at the current moment; Furthermore, since the third set of volume points were assigned corresponding weights during generation, these weights reflect the contribution of each volume point to the state estimation. After obtaining the propagated observation volume points, a weighted average operation can be performed on them according to these weights to obtain the predicted observation vector at the current time. Specifically, each observation volume point is multiplied by its corresponding weight, and then all the product results are added together. The sum is the predicted observation vector at the current time. This predicted observation vector is the predicted value of the target state that the sensor may observe at the current time based on the data from the previous time step, comprehensively considering the distribution characteristics of the target state and the nonlinear characteristics of sensor observation.

[0046] S404, calculate the innovation sequence based on the observation vector at the current time, the predicted observation vector at the current time, and the noise covariance matrix at the previous time.

[0047] It is understandable that the current observation vector represents the target state information obtained by the sensor during actual measurement, including interference factors such as measurement noise; the current predicted observation vector represents the ideal observation value based on target state estimation and prediction; and the noise covariance matrix of the previous time step describes the statistical characteristics of the measurement noise at the previous time step, reflecting the distribution of measurement noise across different dimensions and the correlation between noise in each dimension. By analyzing and utilizing the noise covariance matrix, we can better understand the degree of influence of measurement noise on the observation and predicted observation vectors, thus allowing for corresponding adjustments and corrections when calculating the innovation sequence. The innovation sequence is the difference between these two vectors, reflecting the deviation between the actual and predicted observation values. This deviation includes not only the influence of measurement noise but may also contain information about the actual changes in the target state. By calculating the innovation sequence, we can quantify the uncertainty of sensor observations and the dynamic changes in the target state, providing crucial data support for subsequent calculations of multiple fading factors.

[0048] S405, calculate the crossover sequence based on the observation vector at the current time, the predicted observation vector at the current time, the propagated observation volume point, and the state prediction vector at the current time.

[0049] Here, the cross sequence establishes the correlation between the current observation vector, the predicted observation vector, the propagated observation volume point, and the state prediction vector. It reflects the interaction between the target state prediction and the actual observation. It not only contains the accuracy information of the target state prediction, but also reflects the potential of the observation information to correct the state prediction. For example, it may fuse different information sources through weighted summation.

[0050] S406, based on the covariance matrix of the new information sequence, the covariance matrix of the crossover sequence, the estimation error covariance matrix of the previous time step, and the noise covariance matrix of the previous time step, the multiple fading factor, which is consistent with the number of dimensions of the state estimation vector, is calculated.

[0051] Specifically, the covariance matrix of the innovation sequence describes the correlation and error magnitude among the elements in the innovation sequence, reflecting the influence of measurement noise and target state changes on the innovation; the covariance matrix of the cross sequence describes the dispersion of the cross sequence and the correlation between its components, reflecting the uncertainty of the interaction between target state prediction and actual observation; the estimation error covariance matrix of the previous time step reflects the error characteristics of the state estimation at the previous time step, and the noise covariance matrix of the previous time step contains information on process noise and measurement noise, describing the impact of noise on target state prediction and observation. By combining these four matrices and using specific mathematical algorithms and models, such as an improved algorithm based on Kalman filtering theory, multiple fading factors consistent with the number of dimensions of the state estimation vector can be calculated. These multiple fading factors can adaptively adjust the degree of correction to the state prediction vector and the prediction error covariance matrix according to different state dimensions and noise characteristics, thereby improving the accuracy and robustness of target state estimation and better adapting to complex and ever-changing target tracking environments.

[0052] S2042, the state prediction vector at the current moment and the prediction error covariance matrix corresponding to the state prediction vector are corrected using the multiple fading factors.

[0053] Here, the role of the multiple fading factor is to dynamically adjust the filtering gain in the state estimation process. In real-world target tracking scenarios, the target state is often abruptly affected by various factors, such as sudden acceleration, turning, or external interference. Simultaneously, the measurement equipment itself contains noise, the magnitude of which may fluctuate with changes in environmental factors. When the target state changes abruptly or the measurement noise is high, traditional state estimation methods may fail to keep up with the changes, leading to significant deviations in the estimation results. In this case, adjusting the fading factor can increase the update amplitude of the state estimation, enabling it to track changes in the target state more quickly and thus reducing estimation errors. Conversely, when the target state is relatively stable and the measurement noise is low, using a large update amplitude for state estimation may lead to overcorrection, causing the estimation results to fluctuate around the true state and reducing accuracy. In this situation, the fading factor keeps the state estimation relatively stable, avoiding overcorrection and ensuring the smoothness and accuracy of the state estimation results.

[0054] For example, when correcting the state prediction vector and prediction error covariance matrix at the current moment, refer to Figure 5 As shown, the steps S501~S503 may be included: S501, calculate the filter gain based on the covariance matrix of the innovation sequence and the covariance matrix of the crossover sequence, and adjust the filter gain using the multiple fading factor to obtain the target correction factor.

[0055] Specifically, by comprehensively considering the covariance matrix of the innovation sequence and the covariance matrix of the crossover sequence, a suitable filtering gain can be calculated. This filtering gain determines the degree to which observation information is utilized during state estimation. Then, by adjusting the filtering gain using multiple fading factors, the target correction factor can be obtained. This adjustment process dynamically optimizes the filtering gain based on changes in the target state and the magnitude of measurement noise, enabling the target correction factor to better adapt to the actual situation, thereby improving the accuracy of state estimation.

[0056] S502, the observation vector at the current moment is corrected based on the target correction factor and the predicted observation vector, and the state estimation vector of the tracked target at the current moment is determined based on the correction result and the state prediction vector.

[0057] Understandably, the target correction factor reflects the degree of influence of various factors that need to be considered in the target state estimation process. Since the current observation vector contains interference factors such as measurement noise, introducing the target correction factor and the predicted observation vector can eliminate these interferences to some extent, making the corrected observation vector closer to the true state of the target in the observation space. Therefore, the target correction factor can be combined with the predicted observation vector to correct the current observation vector. Then, the corrected observation vector and the state prediction vector are fused using a specific fusion algorithm, such as a Kalman filter-based fusion method, to comprehensively consider the corrected observation information and the state prediction information, thus determining the current state estimation vector of the tracked target. This state estimation vector integrates information from both observation and prediction data, and can more accurately reflect the actual state of the target at the current moment.

[0058] S503, the covariance matrix of the innovation sequence is corrected based on the target correction factor, and the estimation error covariance matrix is ​​determined based on the correction result and the prediction error covariance matrix.

[0059] Specifically, the covariance matrix of the innovation sequence describes the correlation and error magnitude among the elements in the innovation sequence, reflecting the degree of uncertainty in sensor observations. The target correction factor can correct the covariance matrix of the innovation sequence based on the dynamic changes and noise characteristics of the target state. By performing operations, such as multiplication, on the covariance matrix of the innovation sequence with the target correction factor, the element values ​​of the covariance matrix can be adjusted to more accurately reflect the uncertainty of sensor observations at the current moment. Then, the corrected covariance matrix of the innovation sequence is combined with the prediction error covariance matrix, and mathematical models and algorithms, such as update algorithms based on Kalman filtering theory, are used to determine the estimated error covariance matrix. This estimated error covariance matrix can more accurately describe the error characteristics of the current state estimation, providing more reliable information for the subsequent target tracking process and further improving the accuracy and stability of target state estimation.

[0060] S102, the state estimation vector and the estimation error covariance matrix corresponding to the state estimation vector at each time step within a sliding window of a preset length are reverse smoothed using a capacitive Kalman smoother to obtain the state smoothing vector and the smoothing error covariance matrix corresponding to the state smoothing vector at each time step within the sliding window.

[0061] Understandably, a commensurate Kalman smoother is a tool used to further optimize state estimation results. It utilizes information from future moments to improve state estimations from past moments. A sliding window is a time interval encompassing the current moment and several consecutive moments preceding it; its length can be set configurably. For example, if the preset sliding window length is 5 moments, then at the current moment t, the sliding window includes data from moments t, t-1, t-2, t-3, and t-4. Within the sliding window, there are state estimation vectors and corresponding estimation error covariance matrices for each moment. The commensurate Kalman smoother performs inverse smoothing on this data, that is, starting from the last moment of the sliding window, it derives the smoothed state vector and the corresponding smoothing error covariance matrix for each moment in reverse. The smoothed state vector is a more accurate state estimate of the tracked target at the corresponding moment after smoothing, while the smoothing error covariance matrix reflects the error characteristics of the smoothed state estimate. Through this inverse smoothing process, the information within the sliding window can be fully utilized to improve the accuracy of state estimation.

[0062] S103, based on the state smoothing vector, smoothing error covariance matrix and observation vector at each time point within the sliding window, joint recursive estimation is performed using variational Bayesian inference to determine the noise covariance matrix at the current time point.

[0063] Specifically, the variational Bayesian inference method is a statistical inference method based on Bayesian theory and variational principles. This method approximates the true posterior distribution by finding an approximate distribution, thereby estimating unknown parameters. Here, using the state smoothing vector, smoothing error covariance matrix, and observation vector at each time step within the sliding window, a joint recursive estimation using the variational Bayesian inference method can be performed to obtain the noise covariance matrix. After determining the noise covariance matrix at the current time step, it can be used to correct the prediction error covariance matrix during the capacitive Kalman filtering algorithm at the next time step, thereby improving the accuracy of the state estimation at the next time step. This makes the entire filtering method more robust and adaptive, better able to cope with uncertainties and noise interference in the system.

[0064] For example, in practice, the noise covariance matrix is ​​an unknown parameter that needs to be estimated. Therefore, when determining the noise covariance matrix at the current time using the variational Bayesian inference method, reference is made to... Figure 6 As shown, the steps S601 to S605 may be included: S601, the state smoothing vector, smoothing error covariance matrix and observation vector at each time point within the sliding window are taken as known conditions; and the process noise covariance matrix and measurement noise covariance matrix at the current time point are modeled as random variables to be estimated.

[0065] Here, the sliding window mechanism is used to store and process data within a certain time range. After a series of preliminary processing steps, such as filtering and smoothing, the smoothed state vectors at each moment within the sliding window have been obtained, reflecting the relatively smoothed state estimation results of the target within that time period. Simultaneously, the corresponding smoothing error covariance matrix has also been calculated, which describes the error distribution of the smoothed state estimation. The observation vector is the actual data obtained by the sensor measuring the tracked target at the current moment. Since these data have been determined in the previous processing steps, they can be used as known conditions. On the other hand, process noise is the noise introduced by the tracking system during dynamic processes due to various uncertainties (such as model inaccuracies, external interference, etc.), while measurement noise is the noise generated by the sensor during measurement due to its own accuracy, environmental interference, etc. Both types of noise are random, and their covariance matrices are used to quantify the statistical characteristics of the noise. Therefore, modeling the process noise covariance matrix and measurement noise covariance matrix at the current moment as random variables to be estimated aligns with the actual characteristics of noise.

[0066] S602, based on variational Bayesian theory, constructs a joint posterior probability distribution of the process noise covariance matrix and the measurement noise covariance matrix, conditioned on the state smoothing vector, the smoothing error covariance matrix and the observation vector.

[0067] Specifically, variational Bayesian theory is a statistical inference method within the Bayesian framework that approximates the true posterior distribution by finding an approximate distribution. Given the state smoothing vector, the smoothing error covariance matrix, and the observation vector, these data contain a wealth of information about the target state and the observation process. Using these as conditions, a joint posterior probability distribution is constructed for the process noise covariance matrix and the measurement noise covariance matrix. This joint posterior probability distribution describes the probability that the process noise covariance matrix and the measurement noise covariance matrix will take different values ​​given the observation and state smoothing information. From a probabilistic model perspective, it comprehensively considers the effects of prior knowledge and current observation data on the noise covariance matrix. The prior probability distributions of the process noise covariance matrix and the measurement noise covariance matrix are set as inverse Wishart distributions. The inverse-Wishart (IW) distribution is often used as the conjugate prior of the covariance matrix of a Gaussian distribution with a known mean, ensuring that the posterior distribution has the same functional form as the prior distribution. The inverse Wishart distribution can reasonably characterize the prior uncertainty of the covariance matrix, providing an initial probability setting for the noise covariance matrix. Simultaneously, the target state information contained in the current observation data and state smoothing vector will correct and update the prior probability distribution, making the joint posterior probability distribution more accurately reflect the true probability distribution of the noise covariance matrix under the current observation conditions.

[0068] Here, within the time interval Internal state transition function And measuring the likelihood probability density function It can be represented as: ; .

[0069] Specifically, those following the IW distribution The form of the 2D symmetric positive definite random matrix B is shown below: ; in, This is represented as the state estimation vector at time j; This is represented as the observation vector at time j; It's about freedom. yes A symmetric positive definite inverse scaling matrix. and Let them represent the traces of the determinant and the matrix, respectively. It is the gamma function of the d variable. The IW distribution has an important property: when... hour, Because the process prediction noise covariance matrix (PECM) Measurement noise covariance matrix MNCM Both are covariance matrices of Gaussian distributions, and in order to jointly estimate... This paper uses the IW distribution as... and The conjugate prior distribution of is: ; ; Based on the characteristics of the IW distribution described above, when Sometimes, ,but: ; in, This represents the PNCM at time k-1; the initial values ​​of the prior parameters are given as follows: ,in It's an adjustment parameter. Substituting the following formula into the above formula yields... The parameter prediction method for PECM is as follows: ; ; Among them, propagation factors This indicates the degree of time fluctuation. For prior information prediction of MNCM, the propagation factor is used. Given a more pronounced approximate posterior distribution, the prior parameter prediction method for MNCM is as follows: ; ; Assume the initial value of MNCM It also follows the IW distribution, that is .Will Set as initial rated MNCM ,but: ; make Then we can obtain .

[0070] Understandably, the joint posterior probability distribution is the foundation for subsequent variational inference and estimation. Subsequent steps will revolve around this joint posterior probability distribution, using variational Bayesian methods to determine a suitable approximate distribution form and continuously optimize the parameters of the approximate distribution, ultimately achieving accurate estimation of the process noise covariance matrix and the measurement noise covariance matrix.

[0071] S603, determine the factor decomposition variational distribution of the process noise covariance matrix and the measurement noise covariance matrix to approximate the joint posterior probability distribution.

[0072] Specifically, since joint posterior probability distributions often have complex mathematical forms, direct calculation and analysis of them are very difficult. Therefore, a relatively simple distribution can be found to approximate them. Here, factor decomposition variational distributions decompose the joint distribution into the product of several relatively simple factors. For example, the joint distribution of the process noise covariance matrix and the measurement noise covariance matrix can be decomposed into the product of factors associated with the process noise covariance matrix and the measurement noise covariance matrix, respectively. This decomposition reduces computational complexity, making subsequent inference and estimation more feasible.

[0073] Here, the factorization variational distribution can be expressed as: ; in, This represents a class of factorized approximate posteriors of the VB hypothesis.

[0074] Thus, by determining a suitable factorization variational distribution, it is possible to handle joint posterior probability distributions more conveniently while ensuring a certain level of approximate accuracy.

[0075] S604, by minimizing the statistical distance between the joint posterior probability distribution and the factor decomposition variational distribution, the distribution parameters of the factor decomposition variational distribution are recursively updated.

[0076] Understandably, statistical distance is used to measure the degree of difference between two probability distributions; commonly used statistical distances include the Kullback-Leibler divergence. By continuously adjusting the distribution parameters of the factorized variational distribution, the statistical distance between it and the joint posterior probability distribution is minimized. Recursive updates mean that in each update step, the estimation result of the previous step is used as the input for the current step. For example, in the first update, the statistical distance is calculated based on the initial factorized variational distribution and the joint posterior probability distribution, and the distribution parameters are adjusted; in the second update, the distribution parameters after the first update are used as a new starting point, and the statistical distance is calculated and adjusted again. In this way, the factorized variational distribution can be gradually made closer to the true joint posterior probability distribution, thereby improving the accuracy of the approximate estimation.

[0077] Here, we can obtain the following by minimizing the Kullback-Leibler divergence (KLD) between the factorial variational distribution and the joint posterior probability distribution: ; in, express and The KLD between. Defines the set of random variables. , express Any element in the factorization variational distribution. The optimal solution of the factorization variational distribution satisfies the following formula: ; in, express Except The set of all external elements, Representing variables Real constants generated during the iteration process.

[0078] Based on the conditional independence property of the Gaussian-IW state-space model and Bayesian theory, the joint posterior probability distribution can be obtained: ; Substituting the above parameterized modeling of random variables, we get: ; make Based on the above formula, the variational distribution can be obtained. The logarithmic form is: ; then It can be used as a degree of freedom. The inverse scaling matrix is The IW distribution is iteratively updated: ; make Variational distribution The logarithmic form is: ; then It can be used as a degree of freedom. The inverse scaling matrix is The IW distribution is iteratively updated: ; make According to the above formula, the variational distribution can be known. The logarithmic form is: .

[0079] then It can be used as an average. The error covariance is Iterative updates using a Gaussian distribution: ; in, and These represent the state smoothing estimate of the sliding window and its PECM, respectively.

[0080] S605, based on the updated distribution parameters of the factor decomposition variational distribution, determine the optimal estimates of the process noise covariance matrix and the measurement noise covariance matrix at the current moment.

[0081] Furthermore, after multiple recursive updates, when the factorization variational distribution sufficiently approximates the joint posterior probability distribution, its distribution parameters contain crucial information about the process noise covariance matrix and the measurement noise covariance matrix. Based on these updated distribution parameters, optimal estimates of the process noise covariance matrix and the measurement noise covariance matrix at the current moment can be determined using appropriate mathematical calculation methods, such as mean calculation and maximum a posteriori estimation. This optimal estimate best reflects the true characteristics of the noise at the current moment, providing accurate noise information for subsequent filtering algorithms, thereby improving the performance and accuracy of the entire target tracking and state estimation system.

[0082] Here, due to random variables There are mutually coupled characteristics between them. Fixed-point iteration is a typical method for solving the above equations; however, using fixed-point iteration leads to a significant increase in computational complexity. Therefore, in order to reduce computational complexity, a sliding window mechanism is used to recursively update the variational parameters.

[0083] Specifically, and The joint posterior probability distribution is transformed into the IW distribution: ; ; The parameter update method is as follows: ; ; in, .

[0084] Calculated using the volume integral rule: ; ; ; .

[0085] here, The parameter update method is as follows: ; ; in, Update using volumetric sampling, as shown below: ; ; ; ; in, , and , They represent and The system smooth state at time t and its corresponding error covariance are calculated as follows: ; ; ; in, Through the Perform volumetric sampling and utilize The propagation sampling points were calculated. Indicates multiple fading factor pairs The correction value, In the form of standard CKF, by express, The definition is as follows: ; ; ; In the above formula for The optimal state estimation vector at time t. for Estimate the state prediction vector at time j.

[0086] According to the above formula, the PNCM can be estimated. The method is as follows: ; MNCM The estimation method is as follows: .

[0087] The sliding window robust adaptive capacitive Kalman filtering method, apparatus, and medium provided in this disclosure significantly improve the smoothness and consistency of state estimation by introducing a sliding window mechanism combined with a capacitive Kalman smoother to perform inverse smoothing of historical state estimates. Furthermore, based on the variational Bayesian inference method, the process noise covariance matrix and the measurement noise covariance matrix are jointly recursively estimated within the sliding window, achieving high-precision online identification under conditions where noise statistical characteristics are unknown or time-varying. By feeding the estimated noise covariance matrix back to the capacitive Kalman filtering process at the next time step, the prediction error covariance matrix is ​​corrected in real time, effectively suppressing the accumulation of estimation errors and filter divergence caused by factors such as model mismatch and sudden noise changes.

[0088] Those skilled in the art will understand that, in the above-described method of the specific implementation, the order in which each step is written does not imply a strict execution order and does not constitute any limitation on the implementation process. The specific execution order of each step should be determined by its function and possible internal logic.

[0089] Based on the same inventive concept, this disclosure also provides a sliding window robust adaptive capacitive Kalman filter device corresponding to the sliding window robust adaptive capacitive Kalman filter method. Since the principle of the device in this disclosure for solving the problem is similar to the sliding window robust adaptive capacitive Kalman filter method described above in this disclosure, the implementation of the device can refer to the implementation of the method, and the repeated parts will not be described again.

[0090] Reference Figure 7 The diagram shown is a schematic of a sliding window robust adaptive capacitive Kalman filter device 700 provided in an embodiment of this disclosure. The device includes: The state estimation module 701 is used to obtain the observation vector of the tracked target by the sensor at the current moment; and based on the observation vector, the state estimation vector of the tracked target at the previous moment and the error covariance matrix corresponding to the state estimation vector, the motion state of the tracked target is estimated by the capacitive Kalman filter algorithm to obtain the state estimation vector of the tracked target at the current moment and the estimation error covariance matrix corresponding to the state estimation vector. The result smoothing module 702 is used to perform inverse smoothing on the state estimation vector and the estimation error covariance matrix corresponding to the state estimation vector at each time step within a sliding window of a preset length using a capacitive Kalman smoother, to obtain the state smoothing vector and the smoothing error covariance matrix corresponding to the state smoothing vector at each time step within the sliding window; wherein, the sliding window includes the current time step and multiple consecutive time steps before it. The matrix determination module 703 is used to determine the noise covariance matrix at the current time by performing joint recursive estimation using the variational Bayesian inference method based on the state smoothing vector, smoothing error covariance matrix and observation vector at each time step within the sliding window; wherein, the noise covariance matrix is ​​used to correct the prediction error covariance matrix during the capacitive Kalman filtering algorithm at the next time step.

[0091] In some possible embodiments, the state estimation module 701 is specifically used for: Based on the state estimation vector of the tracked target at the previous moment and the error covariance matrix corresponding to the state estimation vector, the first set of volume points is generated. The first set of volume points is propagated through a nonlinear state transition function to obtain the second set of volume points; The second set of volume points is weighted and summed to obtain the state prediction vector; and the prediction error covariance matrix is ​​determined based on the difference between the second set of volume points and the state prediction vector. Based on the noise covariance matrix determined at the previous moment, the observation vector, the state prediction vector at the current moment, and the prediction error covariance matrix, the state estimation vector of the tracked target at the current moment and the estimation error covariance matrix corresponding to the state estimation vector are determined.

[0092] In some possible embodiments, the state estimation module 701 is further configured to: Based on the observation vector at the current moment, the state prediction vector at the current moment, the state estimation vector at the previous moment, the estimation error covariance matrix, and the noise covariance matrix, calculate the multiple fading factor; The state prediction vector at the current moment and the prediction error covariance matrix corresponding to the state prediction vector are corrected using the multiple fading factors.

[0093] In some possible embodiments, the state estimation module 701 is further configured to: Based on the state estimation vector and the estimation error covariance matrix of the previous time step, a third set of volume points is generated; The third set of volume points is propagated through a nonlinear observation function to obtain the propagated observation volume points; The predicted observation vector at the current moment is obtained by weighting the propagated observation volume points; The innovation sequence is calculated based on the observation vector at the current time, the predicted observation vector at the current time, and the noise covariance matrix at the previous time. Calculate the crossover sequence based on the observation vector at the current moment, the predicted observation vector at the current moment, the propagated observation volume point, and the state prediction vector at the current moment; The multiple fading factor, which is consistent with the number of dimensions of the state estimation vector, is calculated based on the covariance matrix of the new information sequence, the covariance matrix of the crossover sequence, the estimation error covariance matrix of the previous time step, and the noise covariance matrix of the previous time step.

[0094] In some possible embodiments, the state estimation module 701 is further configured to: The filter gain is calculated based on the covariance matrix of the innovation sequence and the covariance matrix of the crossover sequence, and the filter gain is adjusted using the multiple fading factor to obtain the target correction factor. The observation vector at the current moment is corrected based on the target correction factor and the predicted observation vector, and the state estimation vector of the tracked target at the current moment is determined based on the correction result and the state prediction vector. The covariance matrix of the innovation sequence is corrected based on the target correction factor, and the estimation error covariance matrix is ​​determined based on the correction result and the prediction error covariance matrix.

[0095] In some possible embodiments, the noise covariance matrix includes a process noise covariance matrix and a measurement noise covariance matrix; the matrix determination module 703 is specifically used for: The state smoothing vector, smoothing error covariance matrix, and observation vector at each time point within the sliding window are taken as known conditions; and the process noise covariance matrix and measurement noise covariance matrix at the current time point are modeled as random variables to be estimated. Based on variational Bayesian theory, a joint posterior probability distribution of the process noise covariance matrix and the measurement noise covariance matrix is ​​constructed, conditioned on the state smoothing vector, the smoothing error covariance matrix, and the observation vector. Determine the factor decomposition variational distribution of the process noise covariance matrix and the measurement noise covariance matrix to approximate the joint posterior probability distribution; The distribution parameters of the factor decomposition variational distribution are recursively updated by minimizing the statistical distance between the joint posterior probability distribution and the factor decomposition variational distribution. Based on the updated distribution parameters of the factorization variational distribution, determine the optimal estimates of the process noise covariance matrix and the measurement noise covariance matrix at the current moment.

[0096] In some possible embodiments, the prior probability distributions of the process noise covariance matrix and the measurement noise covariance matrix are defined as inverse Wishart distributions.

[0097] Based on the same technical concept, this disclosure also provides a computer device. (See also...) Figure 8 The diagram shows the structure of a computer device 800 provided in this embodiment of the present disclosure, including a processor 801, a memory 802, and a bus 803. The memory 802 stores execution instructions and includes a main memory 8021 and an external memory 8022. The main memory 8021, also called internal memory, is used to temporarily store computational data in the processor 801 and data exchanged with external memory 8022 such as a hard disk. The processor 801 exchanges data with the external memory 8022 through the main memory 8021.

[0098] In this embodiment, the memory 802 is specifically used to store application code that executes the solution of this application, and its execution is controlled by the processor 801. That is, when the computer device 800 is running, the processor 801 communicates with the memory 802 through the bus 803, so that the processor 801 executes the application code stored in the memory 802, and then executes the method described in any of the foregoing embodiments.

[0099] The memory 802 may be, but is not limited to, random access memory (RAM), read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), etc.

[0100] Processor 801 may be an integrated circuit chip with signal processing capabilities. The aforementioned processor can be a general-purpose processor, including a Central Processing Unit (CPU), a Network Processor (NP), etc.; it can also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this invention. The general-purpose processor can be a microprocessor or any conventional processor.

[0101] It is understood that the structures illustrated in the embodiments of this application do not constitute a specific limitation on the computer device 800. In other embodiments of this application, the computer device 800 may include more or fewer components than illustrated, or combine some components, or split some components, or have different component arrangements. The illustrated components may be implemented in hardware, software, or a combination of software and hardware.

[0102] This disclosure also provides a computer-readable storage medium storing a computer program that, when executed by a processor, performs the steps of the sliding window robust adaptive capacitive Kalman filtering method described in the above-described method embodiments. The storage medium can be volatile or non-volatile computer-readable storage.

[0103] This disclosure also provides a computer program product carrying program code. The program code includes instructions that can be used to execute the steps of the sliding window robust adaptive capacitive Kalman filtering method described in the above method embodiments. For details, please refer to the above method embodiments, which will not be repeated here.

[0104] The aforementioned computer program product can be implemented through hardware, software, or a combination thereof. In one optional embodiment, the computer program product is specifically embodied in a computer storage medium; in another optional embodiment, the computer program product is specifically embodied in a software product, such as a software development kit (SDK), etc.

[0105] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems and devices described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here. In the several embodiments provided in this disclosure, it should be understood that the disclosed systems and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division; in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Another point is that the displayed or discussed mutual coupling or direct coupling or communication connection may be through some communication interfaces; the indirect coupling or communication connection of devices or units may be electrical, mechanical, or other forms.

[0106] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0107] In addition, the functional units in the various embodiments of this disclosure can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0108] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a processor-executable, non-volatile, computer-readable storage medium. Based on this understanding, the technical solution of this disclosure, in essence, or the part 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 to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this disclosure. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0109] Finally, it should be noted that the above-described embodiments are merely specific implementations of this disclosure, used to illustrate the technical solutions of this disclosure, and not to limit it. The protection scope of this disclosure is not limited thereto. Although this disclosure has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features, within the scope of the technology disclosed in this disclosure. Such modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this disclosure, and should all be covered within the protection scope of this disclosure. Therefore, the protection scope of this disclosure should be determined by the protection scope of the claims.

Claims

1. A sliding window robust adaptive capacitive Kalman filtering method, characterized in that, include: Obtain the sensor's observation vector of the tracked target at the current moment; Based on the observation vector, the state estimation vector of the tracked target at the previous time step, and the error covariance matrix corresponding to the state estimation vector, the motion state of the tracked target is estimated by the capacitive Kalman filter algorithm to obtain the state estimation vector of the tracked target at the current time step and the estimation error covariance matrix corresponding to the state estimation vector. A capacitive Kalman smoother is used to inversely smooth the state estimation vector and the estimation error covariance matrix corresponding to the state estimation vector at each time step within a sliding window of a preset length, thereby obtaining the state smoothing vector and the smoothing error covariance matrix corresponding to the state smoothing vector at each time step within the sliding window; wherein, the sliding window includes the current time step and multiple consecutive time steps prior to it. Based on the state smoothing vector, smoothing error covariance matrix, and observation vector at each time step within the sliding window, a joint recursive estimation is performed using the variational Bayesian inference method to determine the noise covariance matrix at the current time step; wherein, the noise covariance matrix is ​​used to correct the prediction error covariance matrix during the capacitive Kalman filtering algorithm at the next time step.

2. The method according to claim 1, characterized in that, The estimation of the motion state of the tracked target using the capacitive Kalman filter algorithm includes: Based on the state estimation vector of the tracked target at the previous moment and the error covariance matrix corresponding to the state estimation vector, the first set of volume points is generated. The first set of volume points is propagated through a nonlinear state transition function to obtain the second set of volume points; The second set of volume points is weighted and summed to obtain the state prediction vector; and the prediction error covariance matrix is ​​determined based on the difference between the second set of volume points and the state prediction vector. Based on the noise covariance matrix determined at the previous moment, the observation vector, the state prediction vector at the current moment, and the prediction error covariance matrix, the state estimation vector of the tracked target at the current moment and the estimation error covariance matrix corresponding to the state estimation vector are determined.

3. The method according to claim 2, characterized in that, The process of determining the state estimation vector of the tracked target at the current moment and the estimation error covariance matrix corresponding to the state estimation vector, based on the noise covariance matrix determined at the previous moment, the observation vector, the state prediction vector at the current moment, and the prediction error covariance matrix, includes: Based on the observation vector at the current moment, the state prediction vector at the current moment, the state estimation vector at the previous moment, the estimation error covariance matrix, and the noise covariance matrix, calculate the multiple fading factor; The state prediction vector at the current moment and the prediction error covariance matrix corresponding to the state prediction vector are corrected using the multiple fading factors.

4. The method according to claim 3, characterized in that, The calculation of the multiple fading factor includes: Based on the state estimation vector and the estimation error covariance matrix of the previous time step, a third set of volume points is generated; The third set of volume points is propagated through a nonlinear observation function to obtain the propagated observation volume points; The predicted observation vector at the current moment is obtained by weighting the propagated observation volume points; The innovation sequence is calculated based on the observation vector at the current time, the predicted observation vector at the current time, and the noise covariance matrix at the previous time. Calculate the crossover sequence based on the observation vector at the current moment, the predicted observation vector at the current moment, the propagated observation volume point, and the state prediction vector at the current moment; The multiple fading factor, which is consistent with the number of dimensions of the state estimation vector, is calculated based on the covariance matrix of the new information sequence, the covariance matrix of the crossover sequence, the estimation error covariance matrix of the previous time step, and the noise covariance matrix of the previous time step.

5. The method according to claim 4, characterized in that, The step of correcting the current state prediction vector and the prediction error covariance matrix corresponding to the state prediction vector using the multiple fading factors includes: The filter gain is calculated based on the covariance matrix of the innovation sequence and the covariance matrix of the crossover sequence, and the filter gain is adjusted using the multiple fading factor to obtain the target correction factor. The observation vector at the current moment is corrected based on the target correction factor and the predicted observation vector, and the state estimation vector of the tracked target at the current moment is determined based on the correction result and the state prediction vector. The covariance matrix of the innovation sequence is corrected based on the target correction factor, and the estimation error covariance matrix is ​​determined based on the correction result and the prediction error covariance matrix.

6. The method according to claim 1, characterized in that, The noise covariance matrix includes the process noise covariance matrix and the measurement noise covariance matrix; The method of determining the noise covariance matrix at the current time through joint recursive estimation using variational Bayesian inference includes: The state smoothing vector, smoothing error covariance matrix, and observation vector at each time point within the sliding window are taken as known conditions; and the process noise covariance matrix and measurement noise covariance matrix at the current time point are modeled as random variables to be estimated. Based on variational Bayesian theory, a joint posterior probability distribution of the process noise covariance matrix and the measurement noise covariance matrix is ​​constructed, conditioned on the state smoothing vector, the smoothing error covariance matrix, and the observation vector. Determine the factor decomposition variational distribution of the process noise covariance matrix and the measurement noise covariance matrix to approximate the joint posterior probability distribution; The distribution parameters of the factor decomposition variational distribution are recursively updated by minimizing the statistical distance between the joint posterior probability distribution and the factor decomposition variational distribution. Based on the updated distribution parameters of the factorization variational distribution, determine the optimal estimates of the process noise covariance matrix and the measurement noise covariance matrix at the current moment.

7. The method according to claim 6, characterized in that, The prior probability distributions of the process noise covariance matrix and the measurement noise covariance matrix are defined as inverse Wishart distributions.

8. A sliding window robust adaptive capacitive Kalman filter, characterized in that, include: The state estimation module is used to obtain the sensor's observation vector of the tracked target at the current moment; Based on the observation vector, the state estimation vector of the tracked target at the previous time step, and the error covariance matrix corresponding to the state estimation vector, the motion state of the tracked target is estimated by the capacitive Kalman filter algorithm to obtain the state estimation vector of the tracked target at the current time step and the estimation error covariance matrix corresponding to the state estimation vector. The data smoothing module is used to perform inverse smoothing on the state estimation vector and the estimation error covariance matrix corresponding to the state estimation vector at each time step within a sliding window of a preset length using a capacitive Kalman smoother, to obtain the state smoothing vector and the smoothing error covariance matrix corresponding to the state smoothing vector at each time step within the sliding window; wherein, the sliding window includes the current time step and multiple consecutive time steps prior to it. The matrix determination module is used to determine the noise covariance matrix at the current time by performing joint recursive estimation using the variational Bayesian inference method based on the state smoothing vector, smoothing error covariance matrix and observation vector at each time step within the sliding window; wherein, the noise covariance matrix is ​​used to correct the prediction error covariance matrix during the capacitive Kalman filtering algorithm at the next time step.

9. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 7.

10. A computer device, comprising a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method of any one of claims 1 to 7.

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