A method for overflight rapid time-varying self-healing cubature filter based on heterogeneous decoupled coordinate estimation

Abstract

The application discloses a method for overflight rapid change self-healing volume filtering based on heterogeneous decoupling coordinate estimation, and belongs to the technical field of data processing, target tracking and nonlinear state estimation. In view of problems such as coordinate conversion error amplification, fixed model inadaptation to motion, noise mismatch, bias uncompensation and adaptive freezing, the method generates predicted observation by linear prediction of rectangular coordinates and forward mapping of spherical coordinates, directly obtains residual by subtracting the predicted observation from original spherical coordinate observation, and drives state correction; an online adaptive motion is constructed by constructing a residual likelihood driven time-varying transition probability five-order interactive multiple model set; observation and process noise covariance are updated synchronously, low-frequency components of the residual are extracted to estimate and compensate system bias; the autocorrelation coefficient of the residual time sequence is calculated to detect freezing fault and reset the process noise multiplicatively for self-healing. The application is suitable for state estimation of nonlinear dynamic systems such as sensor target tracking, and can be applied to the fields of industrial internet of things information sensing and sensing technology service and industrial information and data processing service.

Description

Technical Field

[0001] This invention belongs to the fields of data processing, sensor target tracking and nonlinear state estimation technology, and relates to an over-the-horizon agile self-healing volumetric filtering method based on heterogeneous decoupled coordinate estimation. Background Technology

[0002] High-speed moving targets are characterized by high flight speed, rapid changes in motion, agile attitude changes during overflight, and significant high-temperature ionization interference, making them a key and challenging target for high-precision sensor tracking. During the overhead phase of a moving target's overflight, problems such as track jitter, tracking lag, path disconnection, and even complete loss of lock-on can easily occur.

[0003] Existing sensor tracking filtering algorithms are mainly divided into two categories: rectangular coordinate filtering and spherical coordinate filtering. Both of them have inherent mechanistic defects.

[0004] The error amplification drawback of rectangular coordinate filtering: EKF, UKF, CKF, and other algorithms in rectangular coordinate systems require the sensor's original spherical coordinate observations to be converted to rectangular coordinate observations in reverse. Taking the x-direction as an example, the total differential error propagation relationship is as follows: The corresponding localization noise variance Angular noise is reduced by the squared distance term. Weighted amplification—During long-distance overflight conditions (r can reach hundreds of kilometers), the equivalent position error of the angle measurement noise is amplified to an unacceptable level, resulting in severe trajectory distortion.

[0005] Numerical singularity drawbacks of spherical coordinate filtering: Spherical coordinate global filtering establishes the state equation in spherical coordinate space, and the state transition contains a large number of fractional nonlinear terms (such as...). When the denominator approaches zero at the singularity point (pitch angle φ→90°), it is easy to cause numerical oscillations, matrix ill-conditioning, or even filter divergence.

[0006] Traditional IMMs with fixed parameters cannot adapt to time-varying motion: The standard IMM-CKF uses fixed Markov transition probabilities and fixed noise parameters, which cannot adapt to the time-varying motion frequency of the moving target. Under strong motion conditions, the model switching lag is significant (approximately 8 frame delay), and the filter exhibits systematic tracking deviation in the initial stage of motion.

[0007] High-temperature ionization interference lacks dedicated compensation: High-temperature ionization interference is generated by the ionization of high-temperature gases on the surface of high-speed moving targets, causing electromagnetic wave refraction and absorption, resulting in a superposition of systematic steady-state bias and time-varying random noise in sensor observations. Traditional filtering algorithms do not have a modular bias compensation mechanism and cannot separate random noise from deterministic energy bias.

[0008] VB adaptive filtering suffers from freeze failure: When the variational Bayesian adaptive filter is in extreme noise mismatch, the NIS amplitude detection is prone to saturation, which causes the adaptive filter to freeze permanently, resulting in the filter losing its parameter iteration ability, the state estimation deviating from the true value and the covariance matrix losing consistency.

[0009] In summary, existing methods lack a mechanism-based solution that simultaneously addresses the contradictions in coordinate systems (i.e., the error amplification of rectangular coordinates and the numerical singularity of spherical coordinates), the contradictions in dynamic adaptation (i.e., fixed parameters not adapting to time-varying motion), the contradictions in noise interference (i.e., the superposition of deterministic bias and time-varying random noise caused by high-temperature ionization interference), and the contradictions in adaptive fault tolerance (i.e., VB freeze failure). This invention provides a systematic solution to these multiple coupled engineering pain points. Summary of the Invention

[0010] One object of the present invention is to solve at least the above-mentioned problems and / or defects, and to provide at least the advantages described below.

[0011] This invention relates to industrial Internet of Things (IoT) information sensing and sensing technology services, industrial information and data processing services, and industrial artificial intelligence network system services. In particular, it relates to a capacitive Kalman filtering method based on a heterogeneous decoupled coordinate estimation architecture, time-varying interactive multi-model, variational Bayesian joint noise adaptation, and time-series fault-tolerant self-healing mechanism, which is suitable for high-precision and stable tracking of high-speed moving targets during the overflight phase.

[0012] The purpose of this invention is to provide a self-healing volumetric filtering method for over-the-horizon agility based on heterogeneous decoupled coordinate estimation. By constructing a heterogeneous decoupled estimation architecture that combines linear prediction in Cartesian coordinates with native updates in spherical coordinates, this method fundamentally eliminates the limitations of traditional Cartesian filtering at the mechanistic level. The divergence problem of over-the-horizon singularities due to angle measurement error amplification and spherical coordinate filtering is addressed by using residual-driven time-varying transition probabilities. The fifth-order interactive multi-model set adapts to the time-varying motion characteristics of the target. It simultaneously suppresses time-varying random noise and steady-state refraction deviation by combining variational Bayesian and RQ adaptive methods with high-temperature ionization interference bias identification and compensation. It detects adaptive freezing faults and performs process noise multiplicative reset self-healing through residual autocorrelation time-series fault tolerance mechanism. It solves the complex engineering problems of rectangular coordinate filtering error amplification, spherical coordinate filtering numerical singularity, traditional IMM fixed parameters not adapting to time-varying motion, lack of dedicated compensation for high-temperature ionization interference, and VB adaptive freezing failure in existing sensor target tracking methods.

[0013] To address the aforementioned problems and achieve the objectives and other advantages of this invention, the following technical solution is provided: a self-healing volumetric filtering method for over-the-horizon agility based on heterogeneous decoupling coordinate estimation, comprising the following steps:

[0014] S1. Acquire the target's native spherical coordinate observation data from the sensor; predict the target's state in a Cartesian coordinate system to obtain predicted state data; transform the predicted state data to the spherical coordinate observation space through a forward mapping to obtain predicted observation data; generate residual data based on the difference between the sensor's native spherical coordinate observation data and the predicted observation data; correct the predicted state data using the residual data to obtain corrected state estimation data.

[0015] S2, construct multiple motion models representing the target, calculate the residual likelihood of each model, adjust the transition probabilities between models based on the residual likelihood, and perform multi-model fusion estimation on the corrected state estimation data based on the adjusted transition probabilities to obtain the fused optimal state estimation data;

[0016] S3, perform variational Bayes iteration on the residual data to update the sensor observation noise parameters and process noise parameters of the target; extract the low-frequency components of the residual data to estimate the bias in the sensor observation equation of the target; compensate the sensor measurement data of the target according to the bias to obtain the compensated measurement data and the updated noise parameter estimation data.

[0017] S4, extract the time series of the residual data and calculate the autocorrelation coefficient of the residual time series; determine the VB adaptive freezing fault based on the relationship between the autocorrelation coefficient and the autocorrelation function ACF detection threshold; when a freezing fault is determined to occur, reset the process noise parameters to obtain the optimal state estimation data after self-healing recovery and the reset process noise parameters.

[0018] The final target state estimation data is obtained.

[0019] Preferably, in the above-mentioned over-the-horizon agile self-healing volumetric filtering method based on heterogeneous decoupled coordinate estimation, the heterogeneous decoupled estimation architecture in step S1 only uses the predicted state data through forward mapping. The sensor's native spherical coordinate observation data is converted to spherical coordinate observation space. Without undergoing inverse coordinate transformation, the residual data is generated by directly subtracting the predicted observation data from the original spherical coordinate observation data. ;

[0020] The step of correcting the predicted state data using the residual data specifically involves: using the residual data to drive cross-coordinate state correction through the optimal Kalman gain, wherein the optimal Kalman gain is calculated based on the state-observation cross-covariance and the observation autocovariance.

[0021] Preferably, in the above-mentioned over-the-horizon agile self-healing volumetric filtering method based on heterogeneous decoupling coordinate estimation, the positive geometric mapping relationship is as follows:

[0022]

[0023] The residual data It only includes the sensor's native noise and does not include bias compensation terms. Bias compensation is performed in a separate variational Bayesian adaptive branch and is not deducted from the residual data.

[0024] Preferably, in the above-mentioned agile self-healing volumetric filtering method based on heterogeneous decoupled coordinate estimation, the multiple motion models in step S2 are uniform motion models. Uniform acceleration model accelerometer model Left-hand coordinated turn model And right-hand coordinated turn model Fifth-order model set;

[0025] The transition probability is updated online by calculating the model's posterior probability:

[0026]

[0027] in For the real-time residual likelihood of the j-th model, This represents the posterior model probability at the previous time step.

[0028] Preferably, in the above-ground agile self-healing volumetric filtering method based on heterogeneous decoupled coordinate estimation, the noise parameter in step S3 includes the sensor observation noise covariance of the target. Covariance of process noise The variational Bayes iterative synchronous update and ;

[0029] The variational Bayesian iteration performs fixed-point iteration after each volumetric Kalman filter update, synchronously updating the sensor observation noise covariance. Covariance of process noise The posterior estimate is obtained by a fixed number of iterations, ranging from 3 to 5.

[0030] Preferably, in the above-mentioned over-the-horizon agile self-healing volumetric filtering method based on heterogeneous decoupled coordinate estimation, the bias in step S3 is extracted from the low-frequency components of the residual data through an exponentially weighted moving average:

[0031] ,

[0032] Where α b =0.98 is the bias smoothing coefficient, corresponding to the bias learning rate γ. b =1 α b =0.02, v k The residual data are given; the corrected observation model is... ,in For the sensor measurement data, The target state is defined as follows; the bias compensation is independent of the residual calculation in step S1.

[0033] Preferably, in the above-mentioned agile self-healing volumetric filtering method based on heterogeneous decoupled coordinate estimation, the autocorrelation coefficient in step S4 is the lag-1 sample autocorrelation coefficient based on the Euclidean norm sequence of the residual data:

[0034]

[0035] in For residual vectors The Euclidean norm, Let K be the arithmetic mean of the norms of the K residuals within the window.

[0036] The ACF detection threshold is 0.30, and the sliding window length K = 20 frames; single frame A value >0.30 triggers a reset; autocorrelation detection is paused for 50 frames after the reset.

[0037] Preferably, in the above-described self-healing volumetric filtering method for over-the-horizon agility based on heterogeneous decoupled coordinate estimation, in step S4, when a freezing fault is determined to occur, the process noise covariance Q is multiplicatively amplified and reset. The reset factor increases exponentially with the cumulative number of triggers n, with an initial maximum value of 2.0, a second maximum value of 4.0, and an upper limit of 10.0 for the maximum value of n. The diagonal element of Q does not exceed the initial value and the asymptotic factor. The accumulation of.

[0038] Preferably, in the above-mentioned agile self-healing volumetric filtering method based on heterogeneous decoupled coordinate estimation, step S1 further includes decoupling initialization: the sensor spherical coordinate observation data at the initial moment is used to obtain the initial rectangular position state data through forward geometric mapping; the initial velocity data is estimated through Doppler radial velocity data or the distance difference between adjacent frames; the tangential velocity is initialized with a large covariance.

[0039] This also includes numerical optimization for overflight singularities: when the pitch angle φ approaches the pole, a regularized offset ε is superimposed in the sin(φ) space to correct the ill-conditioned problem of the critical angle, pulling |sin(φ)| back to the safe interval before calculating arcsin. The safe interval is |sin(φ)| ≤ 1. 2ε, when |sin(φ)| > 1 Regularization correction is triggered at ε, pulling |sin(φ)| back to 1. 2ε, where ε = 1 × 10 -4 The pole refers to the pitch angle in spherical coordinate space. near (i.e., positive and negative) The zenith (directly overhead) or nadir direction of the target. Specifically, in the scenario of sensor overflight tracking, this phenomenon occurs when the moving target passes directly above or near the observation station, i.e., when it passes over the top of the target.

[0040] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the above-described methods for over-the-horizon agile self-healing volumetric filtering based on heterogeneous decoupled coordinate estimation.

[0041] The present invention has at least the following beneficial effects:

[0042] This invention, through a heterogeneous decoupled coordinate estimation architecture, fundamentally eliminates the r² angle measurement error amplification problem of traditional Cartesian filtering and the over-the-horizon singularity divergence problem of spherical coordinate filtering at the mechanistic level. This architecture constructs a dual-domain collaborative mechanism of "Cartesian domain linear prediction + spherical domain native update"—the Cartesian coordinate system state transition has no nonlinear fractional terms, ensuring numerical stability throughout the prediction process and fundamentally avoiding spherical coordinate fractional singularities; the spherical domain update only uses the filtered prediction state to complete the forward observation space mapping, and the sensor's native spherical coordinate observation directly differs from the predicted observation to generate residuals without undergoing inverse coordinate transformation, eliminating the inverse transformation link and preventing angle measurement noise from being amplified by r². 2 Weighted amplification, using only forward mapping, stabilizes the numerical values ​​at overshoot singularities. Rigorous theoretical proof demonstrates that this architecture satisfies the unbiasedness and minimum variance estimation criteria. In ablation comparison experiments, using Cartesian coordinates (CKF) with inverse coordinate transformation as a control group, the position RMSE deteriorated by 92.4% compared to DCSH-ICF, verifying that the decoupled architecture is the foundation for stable tracking.

[0043] This invention employs a residual likelihood-driven time-varying Markov transition probability mechanism. It adjusts the transition probability matrix online based on the real-time residual likelihood of each model. Under steady-state conditions, it strengthens the weights of the CV model to ensure smooth trajectory, while under conditions of intense motion, it rapidly increases the weights of higher-order models to eliminate the switching lag inherent in traditional fixed transition probability matrices. The model probability switching latency is reduced from approximately 8 frames to less than 2 frames, and the position and velocity RMSE are reduced by 28.6% and 31.8%, respectively. This solves the problem that traditional IMM with fixed parameters cannot adapt to time-varying motion frequencies.

[0044] This invention employs a synergistic mechanism combining variational Bayesian methods with RQ adaptive filtering and high-temperature ionization bias identification and compensation. It simultaneously estimates the observation noise covariance and process noise covariance online, while using the low-frequency component of the residual to extract a deterministic bias to compensate for systematic biases in the observation equations in real time. This solves the problem of steady-state track drift caused by traditional adaptive filtering that only suppresses noise but does not correct bias. Before bias correction, the average 3D position error was approximately 175m; after correction, the average error was reduced to approximately 23m, a reduction of 87%.

[0045] This invention employs a freeze detection and self-healing mechanism based on the autocorrelation characteristics of residual white noise. It extracts the time-series sequence of the filtered residual to calculate the autocorrelation coefficient. Based on the zero autocorrelation characteristic of white noise, it determines adaptive freeze faults. Under normal operating conditions, the residual is a white noise sequence with zero autocorrelation. Under freeze conditions, the residual loses its white noise characteristic, and the autocorrelation significantly deviates from zero. Upon freeze triggering, a Q-multiplicative reset is performed. The initial reset multiplier is 2.0, and with repeated triggers, the exponent increases to an upper limit of 10.0, breaking the NIS saturation deadlock and restoring the VB adaptive iteration capability. The fault-tolerance mechanism operates silently without precision loss under normal operating conditions. When freeze occurs, the autocorrelation coefficient jumps from near zero to above 0.6, and after triggering the Q-reset, the autocorrelation coefficient quickly falls back to near zero.

[0046] This invention can be widely applied in the fields of industrial IoT and industrial internet, such as industrial IoT information sensing and sensing technology services, industrial information and data processing services, and industrial artificial intelligence network system services.

[0047] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0048] Figure 1 This is a data flow diagram of the DCSH-ICF heterogeneous decoupled coordinate estimation architecture in this embodiment of the invention, consisting of sensor measurement + Cartesian prediction + forward mapping + spherical coordinate residual + IMM fusion + CKF update + VB adaptation + bias compensation + ACF fault tolerance.

[0049] Figure 2 This is a comparison diagram of the rectangular coordinate filtering error amplification mechanism in the embodiments of the present invention and the decoupling scheme of the present invention, showing error amplification vs. original spherical domain residual.

[0050] Figure 3 This is a probability evolution curve of the residual-driven time-varying IMM model in this embodiment of the invention, showing the multi-stage switching of the five models.

[0051] Figure 4 The following is a comparison of 3D position errors before and after high-temperature ionization bias compensation in an embodiment of the present invention: (a) compensation effect and (b) estimated bias tracking.

[0052] Figure 5 The ACF timing fault tolerance detection feature map in the embodiment of the present invention is shown in (a) autocorrelation coefficient change and (b) tr(Q) freeze triggering and self-healing recovery.

[0053] Figure 6 This is a comparison chart of the RMSE positions of DCSH-ICF and EKF / CKF under combined operating conditions such as constant speed / variable speed / atmosphere entry / terminal navigation in an embodiment of the present invention. Detailed Implementation

[0054] The following is combined Figures 1 to 6 The present invention will be further described in detail so that those skilled in the art can implement it based on the description.

[0055] It should be understood that terms such as “having,” “comprising,” and “including” as used herein do not imply the presence or addition of one or more other elements or combinations thereof.

[0056] It should be noted that, unless otherwise specified, the experimental methods described in the following implementation plan are all conventional methods, and the reagents and materials described are all commercially available unless otherwise specified.

[0057] This invention discloses a self-healing volumetric filtering method for overflight agility based on heterogeneous decoupled coordinate estimation, belonging to the field of sensor target tracking and nonlinear state estimation technology. The method includes: constructing a heterogeneous decoupled estimation architecture of linear prediction in Cartesian coordinates and native update in spherical coordinates; replacing the inverse transformation of noisy observations with a forward state mapping, fundamentally eliminating the squared amplification of angle measurement errors and singular coordinate values ​​during overflight conditions; rigorously proving that the architecture satisfies the minimum variance unbiased estimation criterion; and designing residual-driven time-varying transition probabilities CV / CA / Jerk / CT. Left / CT Right A fifth-order interactive multi-model set is used to adjust the Markov transition matrix online according to the time-varying rate of the model probability, adapting to the time-varying motion characteristics of the target. A variational Bayesian joint RQ adaptive mechanism is built, combined with a high-temperature ionization interference bias identification and compensation branch, to simultaneously suppress time-varying random noise and steady-state refraction deviation. A residual autocorrelation time-series fault-tolerant mechanism is introduced, which determines the adaptive freezing fault by detecting the loss of residual white noise characteristics and performs process noise multiplicative reset self-healing. This invention eliminates the traditional Cartesian filtering mechanism from the mechanistic level through a heterogeneous decoupled coordinate architecture. The problems of error amplification and singularity divergence in spherical coordinate filtering were addressed by a four-dimensional collaborative approach of time-varying IMM+VB joint adaptive, bias compensation, and time-series fault tolerance, achieving stable tracking throughout all time periods under the combined conditions of high-speed navigation, strong motion, and high-temperature ionization interference.

[0058] According to one embodiment of the present invention, a self-healing volumetric filtering method for over-the-horizon agility based on heterogeneous decoupling coordinate estimation includes the following steps:

[0059] S1. Acquire the target's native spherical coordinate observation data from the sensor; predict the target's state in a Cartesian coordinate system to obtain predicted state data; transform the predicted state data to the spherical coordinate observation space through a forward mapping to obtain predicted observation data; generate residual data based on the difference between the sensor's native spherical coordinate observation data and the predicted observation data; correct the predicted state data using the residual data to obtain corrected state estimation data.

[0060] S2, construct multiple motion models representing the target, calculate the residual likelihood of each model, adjust the transition probabilities between models based on the residual likelihood, and perform multi-model fusion estimation on the corrected state estimation data based on the adjusted transition probabilities to obtain the fused optimal state estimation data;

[0061] S3, perform variational Bayes iteration on the residual data to update the sensor observation noise parameters and process noise parameters of the target; extract the low-frequency components of the residual data to estimate the bias in the sensor observation equation of the target; compensate the sensor measurement data of the target according to the bias to obtain the compensated measurement data and the updated noise parameter estimation data.

[0062] S4, extract the time series of the residual data and calculate the autocorrelation coefficient of the residual time series; determine the VB adaptive freezing fault based on the relationship between the autocorrelation coefficient and the autocorrelation function ACF detection threshold; when a freezing fault is determined to occur, reset the process noise parameters to obtain the optimal state estimation data after self-healing recovery and the reset process noise parameters.

[0063] The final target state estimation data is obtained.

[0064] This embodiment eliminates the limitations of traditional Cartesian coordinate filtering at the mechanistic level through a heterogeneous decoupled coordinate estimation architecture. To address the issues of angle measurement error amplification and numerical divergence at singular points in traditional spherical coordinate filtering, linear prediction in rectangular coordinates ensures numerical stability throughout the prediction process. Native observation updates in the spherical domain eliminate the inverse transformation link, preventing angle measurement noise from being weighted by the squared distance term. A time-varying transition probability mechanism driven by residual likelihood allows model switching to adapt to the time-varying characteristics of the target's motion frequency. In steady-state conditions, lower-order model weights are strengthened to ensure smooth trajectory, while in high-motion conditions, higher-order model weights are rapidly increased to eliminate switching lag. Through a collaborative architecture of variational Bayesian joint updates and bias compensation, random noise covariance and deterministic bias are estimated online and compensated in real-time, enabling parallel processing of random noise suppression and steady-state deviation correction. A residual autocorrelation time-series fault-tolerant detection and a process noise reset self-healing mechanism are employed, based on the zero autocorrelation characteristic of white noise, to determine adaptive freezing faults and automatically restore the filter's iterative capability after a fault occurs. The entire four-step architecture forms a complete closed-loop processing chain. The functions of each step are decoupled and cooperate with each other, which can solve the multiple coupling engineering problems faced by existing sensor target tracking methods under complex conditions such as overhead flight, strong motion and high temperature ionization interference, and finally output high-precision and high-continuity target state estimation results.

[0065] According to one embodiment of the present invention, in the over-the-horizon agile self-healing volumetric filtering method based on heterogeneous decoupled coordinate estimation, preferably, the heterogeneous decoupled estimation architecture in step S1 uses only the predicted state data through forward mapping. The sensor's native spherical coordinate observation data is converted to spherical coordinate observation space. Without undergoing inverse coordinate transformation, the residual data is generated by directly subtracting the predicted observation data from the original spherical coordinate observation data. ;

[0066] The step of correcting the predicted state data using the residual data specifically involves: using the residual data to drive cross-coordinate state correction through the optimal Kalman gain, wherein the optimal Kalman gain is calculated based on the state-observation cross-covariance and the observation autocovariance.

[0067] This embodiment features a Cartesian coordinate system with no nonlinear fractional terms in the state transition, ensuring numerical stability throughout the prediction process and fundamentally avoiding the singularity of spherical coordinate fractions. The spherical domain update uses only filtered predicted states to complete the forward observation space mapping. The sensor's native spherical coordinate observations are directly subtracted from the predicted observation data to generate residuals without inverse coordinate transformation, eliminating the inverse transformation link and preventing angle measurement noise from being amplified by the distance squared term. This architecture achieves synergy between stable Cartesian domain prediction and high-precision spherical domain correction, completely avoiding the inherent defects of both coordinate systems.

[0068] According to one embodiment of the present invention, in the over-the-horizon agile self-healing volumetric filtering method based on heterogeneous decoupling coordinate estimation, preferably, the forward geometric mapping relationship is as follows:

[0069]

[0070] The residual data It only includes the sensor's native noise and does not include bias compensation terms. Bias compensation is performed in a separate variational Bayesian adaptive branch and is not deducted from the residual data.

[0071] The residuals contain only the sensor's native noise, ensuring that the Kalman gain calculation is unaffected by bias estimation errors, and maintaining the optimal state correction direction for the filter. Bias compensation is performed in an independent variational Bayesian adaptive branch, achieving functional decoupling between bias identification and noise suppression; random noise and deterministic bias are handled by different mechanisms. Forward mapping involves only algebraic operations, and numerical stability is unaffected by pitch angle changes, maintaining stable output even near overflight singularities.

[0072] According to one embodiment of the present invention, in the over-the-horizon agile self-healing volumetric filtering method based on heterogeneous decoupled coordinate estimation, preferably, the plurality of motion models in step S2 are uniform motion models. Uniform acceleration model accelerometer model Left-hand coordinated turn model And right-hand coordinated turn model Fifth-order model set;

[0073] The transition probability is updated online by calculating the model's posterior probability:

[0074]

[0075] in For the real-time residual likelihood of the j-th model, This represents the posterior model probability at the previous time step.

[0076] The model switching speed adapts to the time-varying characteristics of the target motion frequency. Under steady-state conditions, the uniform velocity model maintains a high probability to ensure a smooth trajectory, while under strong motion conditions, the probability of higher-order models increases rapidly to eliminate switching lag. The posterior probabilities of each model are updated online based on real-time residual likelihood, eliminating the need for a fixed prior transition probability matrix. This ensures that the multi-model fusion estimation results always favor the dynamic model that best matches the current motion state. The complete coverage of the fifth-order model set provides corresponding models to support the filter under different conditions such as steady-state uniform velocity, normal motion, high-order sharp turns, and coordinated turns, avoiding model mismatch problems caused by insufficient coverage of a single model or multiple model sets.

[0077] According to one embodiment of the present invention, in the over-the-horizon agile self-healing volumetric filtering method based on heterogeneous decoupled coordinate estimation, preferably, the noise parameter in step S3 includes the sensor observation noise covariance of the target. Covariance of process noise The variational Bayes iterative synchronous update and ;

[0078] The variational Bayesian iteration performs fixed-point iteration after each volumetric Kalman filter update, synchronously updating the sensor observation noise covariance. Covariance of process noise The posterior estimate is obtained by a fixed number of iterations, ranging from 3 to 5.

[0079] The observation noise covariance and process noise covariance are updated synchronously in the same iteration process, and the estimated results of the two noise parameters match each other, avoiding the parameter mismatch problem caused by single-parameter updates. The number of fixed-point iterations is fixed at three to five times, ensuring convergence accuracy while keeping the computational cost within an acceptable range. The synchronously updated observation noise covariance can adapt to the time-varying measurement noise fluctuations caused by high-temperature ionization interference, and the synchronously updated process noise covariance can adapt to the time-varying motion intensity caused by the target's over-range agility. Together, they ensure that the Kalman gain remains in the optimal computational state at each sampling time.

[0080] According to one embodiment of the present invention, in the over-the-horizon agile self-healing volumetric filtering method based on heterogeneous decoupled coordinate estimation, preferably, the bias in step S3 is extracted from the low-frequency components of the residual data by exponentially weighted moving average:

[0081] ,

[0082] Where α b =0.98 is the bias smoothing coefficient, corresponding to the bias learning rate γ. b =1 α b =0.02, v k The residual data are given; the corrected observation model is... ,in For the sensor measurement data, The target state is defined as follows: the bias compensation is independent of the residual calculation in step S1. The bias estimation is based on the low-frequency components of the residuals rather than directly on the original measurement data. High-frequency random noise is effectively filtered out, making the bias estimation purer and more stable. The 0.98 smoothing coefficient makes the bias estimation sensitive to medium- and long-term trends but insensitive to instantaneous disturbances, avoiding misjudging random noise as systematic bias. The bias compensation is independent of the main residual calculation path, the bias estimation error does not pollute the Kalman gain, and the main filtering path is decoupled from the bias identification branch. The corrected observation model separates the deterministic bias from the random noise model, enabling online identification and real-time compensation of systematic deviations, solving the problem of traditional adaptive filtering only suppressing noise without correcting deviations, leading to steady-state track deviations.

[0083] According to one embodiment of the present invention, in the over-range agile self-healing volumetric filtering method based on heterogeneous decoupled coordinate estimation, preferably, the autocorrelation coefficient in step S4 is the lag-1 sample autocorrelation coefficient based on the Euclidean norm sequence of the residual data:

[0084]

[0085] in For residual vectors The Euclidean norm, Let K be the arithmetic mean of the norms of the K residuals within the window.

[0086] The ACF detection threshold is 0.30, and the sliding window length K = 20 frames; single frame A threshold of >0.30 triggers a reset; autocorrelation detection is paused for a 50-frame cooldown period after the reset. The detection principle based on the zero autocorrelation characteristic of white noise fundamentally distinguishes between normal filtering and frozen failure states, and is not limited by residual amplitude saturation. The autocorrelation coefficient based on the residual norm eliminates sign cancellation interference between vector components, improving detection sensitivity. The calculation of the autocorrelation coefficient for a lag sample requires only a first-order lag, making it simple to calculate and quick to respond, suitable for real-time processing systems. The 0.30 threshold achieves a reasonable balance between detection sensitivity and resistance to false triggering; the 20-frame window length achieves a reasonable balance between detection reliability and latency; and the 50-frame cooldown period avoids repeated triggering after the reset, ensuring the stable recovery process of the filter. The entire detection and reset mechanism operates silently under normal working conditions without introducing accuracy loss, only actively intervening when a freeze occurs, achieving fault-tolerant self-healing of adaptive filtering.

[0087] According to one embodiment of the present invention, in the over-the-horizon agile self-healing volumetric filtering method based on heterogeneous decoupled coordinate estimation, preferably, in step S4, when a freezing fault is determined to occur, the process noise covariance Q is multiplicatively amplified and reset. The reset factor increases exponentially with the cumulative number of triggers n, with an initial maximum value of 2.0, a second maximum value of 4.0, and an upper limit of 10.0 for the maximum value of n. The diagonal element of Q does not exceed the initial value and the asymptotic factor. The reset rate adaptively adjusts with the cumulative number of triggers. Occasional faults are handled with gentle resets to avoid disturbances, while recurring faults are handled with forceful resets to effectively break saturation deadlocks. The progressively increasing reset rate eliminates the time overhead of repeatedly trying the optimal reset strength, ensuring each reset is performed within a reasonable strength range. A cap of 10.0 prevents unbounded amplification of process noise, guaranteeing the filter's basic stability under extreme conditions. Diagonal element constraints ensure the positive definiteness of the covariance matrix is ​​maintained, avoiding numerical ill-conditioning caused by excessive resets. This mechanism executes automatically after a freeze trigger, requiring no manual intervention or parameter adjustments, achieving automatic self-healing recovery of the adaptive filter.

[0088] Optionally, steps S1) to S4) constitute a high-temperature ionization interference bias-noise-motion joint adaptive closed loop: the output of the bias compensation step S3) is used as the input step S1) for residual calculation; the model probability output of the time-varying IMM step S2) modulates the forgetting factor of the variational Bayes iteration step S3); and the reset result of the ACF fault-tolerant step S4) is fed back to the model probability initialization of the time-varying IMM step S2). This enables the four functional modules of bias estimation, noise adaptation, model switching, and fault-tolerant self-healing to form a coordinated adjustment to jointly adapt to the time-varying interference characteristics of high-temperature ionization interference.

[0089] According to one embodiment of the present invention, in the over-the-horizon agile self-healing volumetric filtering method based on heterogeneous decoupled coordinate estimation, preferably, step S1 further includes decoupled initialization: the sensor spherical coordinate observation data at the initial moment is used to obtain the initial rectangular position state data through positive geometric mapping; the initial velocity data is estimated through Doppler radial velocity data or the distance difference between adjacent frames; the tangential velocity is initialized with a large covariance.

[0090] This also includes numerical optimization for overflight singularities: when the pitch angle φ approaches the pole, a regularized offset ε is superimposed in the sin(φ) space to correct the ill-conditioned problem of the critical angle, pulling |sin(φ)| back to the safe interval before calculating arcsin. The safe interval is |sin(φ)| ≤ 1. 2ε, when |sin(φ)| > 1 Regularization correction is triggered at ε, pulling |sin(φ)| back to 1. 2ε, where ε = 1 × 10 -4The pole refers to the pitch angle in spherical coordinate space. near (i.e., positive and negative) The zenith (directly overhead) or nadir direction of the target. Specifically, in the scenario of sensor overflight tracking, this phenomenon occurs when the moving target passes directly above or near the observation station, i.e., when it passes over the top of the target.

[0091] The position of the first frame is obtained through forward mapping, avoiding the initial error amplification of traditional reverse conversion. Radial velocity is obtained based on Doppler measurement or range difference, with a clear physical basis. Tangential velocity is initialized with a large covariance, enabling the filter to learn tangential velocity progressively from subsequent measurements without forcibly pre-setting inaccurate initial values. Regularized offset at the overrun singularity eliminates numerical ill-conditioning at critical angles, allowing the filter to maintain stable state estimation even when the pitch angle is close to the extreme. Decoupled initialization of position and velocity assigns different initial confidence levels to each state component according to its degree of information certainty; higher information certainty results in a smaller initial covariance, while higher uncertainty results in a larger initial covariance, conforming to the theoretical principle of optimal estimation.

[0092] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the over-the-horizon agile self-healing volumetric filtering method based on heterogeneous decoupled coordinate estimation as described in any one of the claims.

[0093] According to one embodiment of the present invention, a self-healing volumetric filtering method for over-the-horizon agility based on heterogeneous decoupled coordinate estimation includes the following steps:

[0094] S1. Construct a heterogeneous decoupled estimation architecture that combines linear prediction in Cartesian coordinates with native updates in spherical coordinates. The target state is linearly predicted in Cartesian coordinates, and sensor spherical coordinate observations are updated in native spherical coordinate space through positive state mapping. The state correction is driven by the spherical coordinate residuals between the predicted and actual observations.

[0095] S2, Constructing the residual-driven time-varying transition probability A fifth-order interactive multi-model set is used to adjust the Markov transition probability matrix online based on the real-time residual likelihood of each model. Steady-state enhancement of CV model weights ensures smooth trajectory, while rapid motion increases the weights of higher-order models to eliminate switching lag.

[0096] S3, A variational Bayesian joint RQ adaptive mechanism is constructed to simultaneously estimate the observation noise covariance online. Covariance of process noise Simultaneously, the high-temperature ionization bias identification compensation branch is used to extract the low-frequency component of the residual to compensate for the systematic bias of the observation equation in real time.

[0097] S4 extracts the time series of the filtered residuals and calculates the autocorrelation coefficient. Based on the zero autocorrelation characteristic of white noise, it determines the adaptive freeze fault and triggers a multiplicative reset to restore the adaptive iterative capability of VB. The reset factor increases exponentially with the number of triggers (2.0 for the first time, 4.0 for the second time, and 10.0 for the upper limit). The Q diagonal element does not exceed the product of the initial value and the increment factor to avoid excessive amplification that could cause track jitter.

[0098] Optionally, in the method, the heterogeneous decoupling estimation architecture described in S1 uses only the forward state mapping. h(x̂_{k|k-1}) maps the predicted state to the spherical coordinate observation space. The sensor's spherical coordinate observations are directly subtracted from the predicted observations without inverse coordinate transformation to generate residuals, thus eliminating angular noise from the squared distance term. The error amplification effect of weighted amplification.

[0099] Optionally, in the method, the forward geometric mapping relationship is:

[0100]

[0101] The residual Only sensor native noise is included (bias compensation is performed through a separate VB adaptive branch and is not deducted from the CKF update residual, thus avoiding bias estimation error from polluting the Kalman gain calculation).

[0102] Optionally, in the method, the time-varying transition probability in S2 is obtained by using the model posterior probability. Online updates, including The Markov transition probability matrix, representing the posterior model probability of the previous frame, participates in the generation of the mixed prior of each model through the state mixing step, thereby realizing information exchange between models.

[0103] Optionally, in the method described, the high-temperature ionization bias identification and compensation in S3 is extracted using the residual low-frequency component EMA: , where α b =0.98 is the bias smoothing coefficient (corresponding to the bias learning rate γ). b =1-α b =0.02), ν k This represents the current residual.

[0104] Optionally, in the method, the autocorrelation coefficient in S4 is the lag-1 sample autocorrelation coefficient based on the Euclidean norm sequence of the residual vector, and the calculation formula is:

[0105]

[0106] in For residual vectors The Euclidean norm, The autocorrelation coefficient is the arithmetic mean of the K residual norms within the window. The reason the autocorrelation coefficient is calculated based on the residual norms rather than directly on the residual vectors is that norm operations condense vector information into a single positive scalar, eliminating the interference of sign cancellation between vector components on autocorrelation estimation, making the lag-1 autocorrelation more sensitive to the detection of correlation in the residual sequence. When the ACF detection threshold is exceeded, it is determined to be an adaptive freeze fault. After being triggered, it enters a cooldown period for silent detection to avoid repeated triggering.

[0107] Optionally, in the method, the process noise is multiplicatively reset to... The diagonal element of Q does not exceed the initial Q and the asymptotic multiplier. The product, n, is the cumulative number of triggers, with a maximum of 2 times for the first trigger, 4 times for the second, and 10 times for the third and above. The NIS saturation deadlock is broken by forcibly increasing the process noise, and the VB adaptive iteration is restored.

[0108] Optionally, in the method, S1 further includes decoupling initialization: the initial rectangular position state is obtained by the sensor spherical coordinate observation of the first frame through forward geometric mapping, and the initial velocity is estimated by Doppler radial velocity or distance difference between adjacent frames. The tangential velocity absorbs uncertainty with large covariance, avoiding the amplification of initial error in traditional single-frame reverse conversion.

[0109] Optionally, the method further includes numerical optimization of overshoot singularities: when the pitch angle φ approaches the pole, a regularization offset ε is applied in the sin(φ) space to correct the critical angle ill-conditioning, pulling |sin(φ)| back to the safe range and avoiding numerical abrupt changes caused by arcsin input saturation; the safe range is... The derivative of arcsin exist The time-to-infinity property leads to numerical ill-conditionedness. A safe interval constrains the upper bound of the derivative to a finite value to ensure numerical stability; where ε = 1 × 10⁻⁶. -4 Corresponding trigger threshold Safety upper limit .

[0110] According to one embodiment of the present invention, a self-healing volumetric filtering method for over-the-horizon agility based on heterogeneous decoupled coordinate estimation includes the following steps:

[0111] S1, Construction of heterogeneous decoupled coordinate estimation architecture.

[0112] Construct a heterogeneous, decoupled estimation architecture that combines linear prediction in Cartesian coordinates with native updates in spherical coordinates:

[0113] Cartesian domain linear prediction: target state vector In a rectangular coordinate system, the state transition equation is defined as follows: It is a linear form, and the state transition in the rectangular coordinate system has no nonlinear fractional terms, ensuring numerical stability throughout the prediction process and avoiding the singularity of spherical coordinate fractions from the root.

[0114] Spherical Native Update: Sensor native observations are in spherical coordinate form Forward observation space mapping is completed using only filtered prediction states. Where h(·) represents the positive geometric mapping from rectangular coordinates to spherical coordinates:

[0115]

[0116] Constructing the residuals of native sensor observations and predicted observations The residual contains only the sensor's native noise, with no Amplified distortion. Optimal Kalman gain. Complete cross-coordinate state correction: .

[0117] This architecture achieves stable prediction in the Cartesian domain and high-precision correction in the spherical domain, completely avoiding the inherent defects of the two types of coordinate systems: (i) the inverse transformation link is eliminated, and angle measurement noise is not affected. (ii) Using only the forward mapping, the architecture is numerically stable at the singularity. Rigorous theoretical proof demonstrates that the architecture satisfies the unbiasedness and minimum variance estimation criteria.

[0118] S2, residual-driven construction of time-varying transition probability IMM multi-model set.

[0119] Construct CV (constant velocity) / CA (constant acceleration) / Jerk (jerk) acceleration. (Turn left) (Right turn) A set of five-order dynamic models, adapted for steady-state uniform velocity, normal motion, high-order sharp turns, and coordinated turning conditions. A time-varying Markov transition probability matrix driven by residual likelihood is designed. :

[0120]

[0121] in For the real-time residual likelihood of the j-th model, The probability is the posterior model probability of the previous frame. Under steady-state conditions, the CV model probability is close to 1.0, ensuring a smooth trajectory; under strong motion conditions, the CA / Jerk / CT model probability increases rapidly, and the model switching delay is reduced from about 8 frames in the traditional fixed TPM to less than 2 frames.

[0122] S3, VB combined with RQ adaptive and high-temperature ionization bias compensation.

[0123] (a) VB Joint RQ Adaptive: Constructing a variational Bayesian two-parameter joint adaptive architecture to synchronously iteratively update the observation noise covariance. Covariance of process noise Steady-state convergence. To suppress noise disturbances, adaptive lifting is implemented under strong motion conditions. To strengthen the weight of observation residuals.

[0124] (b) High-temperature ionization bias identification and compensation: Design a bias identification and compensation branch to extract deterministic bias through the residual low-frequency component EMA. (α) b =0.98), real-time compensation for observation equation bias, solving the problem of steady-state track drift caused by traditional adaptive filtering that only suppresses noise but does not correct bias. The corrected observation model is as follows: This enables decoupled modeling of random noise and deterministic bias.

[0125] S4, ACF timing fault-tolerant self-healing mechanism.

[0126] Extract the time series sequence of the filtered residuals and calculate the autocorrelation coefficient:

[0127]

[0128] Based on the zero autocorrelation characteristic of white noise: Under normal operating conditions, the residual is a white noise sequence with zero autocorrelation. Under frozen conditions, the residual loses the white noise characteristic, and the autocorrelation deviates significantly from zero, indicating an adaptive freeze fault. After freeze is triggered, a Q-multiplicative reset is performed. (The upper limit of the diagonal element of Q is the initial Q×min(10, 2)) n (where n is the cumulative number of triggers), by forcibly increasing the process noise, the NIS saturation deadlock is broken, and the VB adaptive iteration capability is restored.

[0129] S5, decoupling initialization and numerical optimization of overrunning singularities.

[0130] A decoupled initialization strategy is adopted, in which the first frame spherical coordinate observation is forward mapped to obtain the rectangular position, and the initial velocity is estimated by Doppler radial velocity or distance difference between adjacent frames, thus avoiding the initial error amplification problem of traditional single-frame reverse transformation. For the numerical singular case of passing over the top of the flight φ→90°, sin(φ) spatial regularization offset is introduced to correct the ill-conditioned problem of the critical angle.

[0131] System Model

[0132] Constructing a composite flight condition for a high-speed moving target: initial target position [10000 m, 10000 m, 8000 m], initial velocity [-300 m / s, -250 m / s, 180 m / s], total duration 100 s. Steady-state uniform velocity from 0 to 60 s, followed by a high-order strong motion and sharp turn from 60 to 80 s. High-temperature ionization interference time-varying noise and steady-state bias are superimposed throughout the entire process, and the flight path covers the singularity region of the flight path.

[0133] Sensor measurement model: Among them, the actual ranging noise Angular noise Initial value of high temperature ionization bias The initial value of the filter observation noise covariance is set to be conservatively large. (i.e. σr) init =25m, σa init =12mrad), which converges online to the true noise level via the VB adaptive mechanism.

[0134] In another approach, the heterogeneous decoupling coordinate estimation is implemented as follows:

[0135] Initialization: A decoupled initialization strategy is adopted. The initial Cartesian position state is obtained through forward geometric mapping of the sensor's spherical coordinate observation in the first frame, supplemented by Doppler radial velocity or distance difference estimation between adjacent frames to estimate the initial velocity, where the tangential velocity has a large covariance σ²=10. 7 m² / s² absorbs uncertainty and avoids the amplification of initial error in traditional single-frame reverse conversion.

[0136] Prediction step (Cartesian domain): In the Cartesian coordinate system, based on the current IMM model... The state transition matrix F completes the linear prediction:

[0137]

[0138] The state transition in the rectangular coordinate system has no nonlinear fractional terms, ensuring the stability of the predicted values ​​throughout the process.

[0139] Update step (spherical domain): Generate 2 using the CKF third-order spherical radial volume rule. x Each volume point is propagated to the spherical coordinate observation space via a forward geometric mapping.

[0140] Volume point construction: Let To predict the state mean, To predict the covariance matrix, Its Cholesky decomposition factor ( ), for The Column, then n x The number of equal-weighted volumetric points is:

[0141] x

[0142]

[0143] in This is the radial scaling factor for the sphere (corresponding to third-order precision). The position component of each volume point is obtained through a positive geometric mapping. Propagation to spherical coordinate observation space:

[0144] x

[0145] The predicted observation mean is calculated by equal weighting:

[0146]

[0147] State dimension in this application (3D position + 3D velocity) generation There are 1 volumetric points, each with equal weight. .

[0148] Calculate the spherical coordinate residuals: The offset compensation is performed through a separate VB branch and is not deducted from the CKF update residual. This residual is directly based on the difference between the sensor's native spherical coordinate observation and the predicted observation, without any inverse transformation step, and the angle measurement noise is not amplified by r².

[0149] Calculate the Kalman gain and perform cross-coordinate state correction.

[0150] In another approach, the specific implementation method of the time-varying IMM is as follows:

[0151] Model sets: Maintain CV (6-dimensional uniform velocity), CA (6-dimensional pseudo-acceleration heuristic, with the F matrix containing velocity increment terms to simulate acceleration-inertial effects), and Jerk (6-dimensional higher-order implicit modeling of rapid turning motion with high process noise intensity). (6-dimensional left-hand coordinated turn, including the actual turning kinematics F matrix) (6-dimensional right-hand coordinated turn) Five dynamic models. CV / CA / Jerk share the DWNA (Discrete White Noise Acceleration) framework (only the process noise intensity differs). Includes sin / cos turning kinematics terms. Each model's CKF sub-filter runs independently for prediction and updates.

[0152] All five models uniformly adopt a 6-dimensional state vector. State transition matrices for each model Process noise covariance The definition is as follows:

[0153] (a) CV (uniform velocity model):

[0154]

[0155] (b) CA (pseudo-accelerometer heuristic): shares the F matrix structure with CV, but the velocity diagonal elements contain auto-incrementing terms. ( , Simulates acceleration-inertial effects to prevent excessively rapid regression to CV priors:

[0156]

[0157] (c) Jerk (higher-order implicit): The F matrix is ​​the same as the CV ( ), with high process noise spectral density ( Implicit modeling of higher-order dynamics of rapid rotation.

[0158] The CV / CA / Jerk models share the DWNA process noise covariance, only the spectral density is shared. different:

[0159]

[0160] (d) CT / CT (Coordinated Turn): Uniform circular motion in a plane Axis-independent CV. Let The turning angular rate (for left turns) Turn right ),definition ,but The planar sub-block is:

[0161]

[0162] Axle block is The process noise covariance is the same. form( , (rad / s).

[0163] Time-varying transition probabilities: The transition probability matrix is ​​updated each frame based on the residual likelihood of each model. The diagonal elements (model retention probabilities) are adaptively adjusted according to the model likelihood: the model retention probability is increased to above 0.90 for high likelihood models and decreased to below 0.60 for low likelihood models. Row normalization ensures the validity of the probabilities.

[0164] Model probability update and fusion: The posterior model probability is updated according to Bayesian rules, and the weighted output is the globally optimal trajectory.

[0165] In another approach, the specific implementation method of the ACF timing fault tolerance is as follows:

[0166] Detection parameters: sliding window length K = 20 frames, autocorrelation hysteresis τ = 1, ACF detection threshold. Reset coefficient .

[0167] Detection logic: Maintain a 20-frame residual history sequence

[0168] (a) Calculate the autocorrelation coefficient with lag 1;

[0169] (b) If > 0.30, determined to be a freeze fault (a reset is performed on the first trigger, and silent detection is performed during the 50-frame cooldown period after the reset to avoid repeated triggers).

[0170] (c) Triggering Q-multiplicative reset: The upper limit of the diagonal elements of Q is the initial Q×min(10, 2). n ), where n is the cumulative number of triggers, with a maximum of 2 times for the first trigger, 4 times for the second, and 10 times for the third and subsequent triggers;

[0171] (d) ACF detection is silent during the 50-frame cooldown period after reset to avoid repeated triggering.

[0172] In another approach, the recommended values ​​for the parameters are shown in Table 1.

[0173] Table 1

[0174]

[0175] The embodiments of the present invention can be applied to the fields of industrial Internet of Things information sensing and sensing technology services, industrial information and data processing services, and industrial artificial intelligence network system services, providing high-precision state estimation and data fusion support for industrial intelligent manufacturing service platforms.

[0176] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, other modifications can be easily made. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details.

Claims

1. A self-healing volumetric filtering method for over-the-horizon agility based on heterogeneous decoupling coordinate estimation, characterized in that, Includes the following steps: S1. Acquire the target's native spherical coordinate observation data from the sensor; predict the target's state in a Cartesian coordinate system to obtain predicted state data; transform the predicted state data to the spherical coordinate observation space through a forward mapping to obtain predicted observation data; generate residual data based on the difference between the sensor's native spherical coordinate observation data and the predicted observation data; correct the predicted state data using the residual data to obtain corrected state estimation data. S2, construct multiple motion models representing the target, calculate the residual likelihood of each model, and adjust the transition probabilities between models based on the residual likelihood; Based on the adjusted transition probabilities, multi-model fusion estimation is performed on the corrected state estimation data to obtain the fused optimal state estimation data. S3, perform variational Bayes iteration on the residual data to update the sensor observation noise parameters and process noise parameters of the target; extract the low-frequency components of the residual data to estimate the bias in the sensor observation equation of the target; Based on the sensor measurement data of the bias compensation target, the compensated measurement data and the updated noise parameter estimation data are obtained. S4, extract the time series sequence of the residual data and calculate the autocorrelation coefficient of the residual time series sequence; The VB adaptive freeze fault is determined based on the relationship between the autocorrelation coefficient and the autocorrelation function (ACF) detection threshold. When a freezing fault is detected, the process noise parameters are reset to obtain the optimal state estimation data after self-healing recovery and the reset process noise parameters. The final target state estimation data is obtained.

2. The over-the-horizon self-healing volumetric filtering method based on heterogeneous decoupling coordinate estimation as described in claim 1, characterized in that, The heterogeneous decoupling estimation architecture described in step S1 uses only the predicted state data through forward mapping. The sensor's native spherical coordinate observation data is converted to spherical coordinate observation space. Without undergoing inverse coordinate transformation, the residual data is generated by directly subtracting the predicted observation data from the original spherical coordinate observation data. ; The predicted state data is corrected by means of the residual data, specifically by using the residual data to drive cross-coordinate state correction through the optimal Kalman gain, which is calculated based on the state-observation cross-covariance and the observation autocovariance.

3. The over-the-horizon agile self-healing volumetric filtering method based on heterogeneous decoupling coordinate estimation as described in claim 2, characterized in that, The positive geometric mapping relationship is as follows: ； The residual data It only includes sensor native noise, and bias compensation is performed in a separate variational Bayesian adaptive branch.

4. The over-the-horizon agile self-healing volumetric filtering method based on heterogeneous decoupling coordinate estimation as described in claim 1, characterized in that, The multiple motion models mentioned in step S2 are uniform motion models. Uniform acceleration model accelerometer model Left-hand coordinated turn model And right-hand coordinated turn model Fifth-order model set; The transition probability is updated online by calculating the model's posterior probability: ； in For the real-time residual likelihood of the j-th model, This represents the posterior model probability at the previous time step.

5. The over-the-horizon agile self-healing volumetric filtering method based on heterogeneous decoupling coordinate estimation as described in claim 1, characterized in that, The noise parameters mentioned in step S3 include the sensor observation noise covariance of the target. Covariance of process noise The variational Bayes iterative synchronous update and ; Variational Bayesian iteration performs fixed-point iteration after each volumetric Kalman filter update, synchronously updating the sensor observation noise covariance. Covariance of process noise The posterior estimate is obtained by a fixed number of iterations, ranging from 3 to 5.

6. The over-the-horizon self-healing volumetric filtering method based on heterogeneous decoupling coordinate estimation as described in claim 1, characterized in that, The bias mentioned in step S3 is extracted from the low-frequency components of the residual data using an exponentially weighted moving average: ， Where α b =0.98 is the bias smoothing coefficient, corresponding to the bias learning rate γ. b =1 α b =0.02, v k The residual data are given; the corrected observation model is... ,in For the sensor measurement data, The target state is defined as follows; the bias compensation is independent of the residual calculation in step S1.

7. The over-the-horizon self-healing volumetric filtering method based on heterogeneous decoupling coordinate estimation as described in claim 1, characterized in that, The autocorrelation coefficient mentioned in step S4 is the lag-1 sample autocorrelation coefficient based on the Euclidean norm sequence of the residual data: ； in For residual vectors The Euclidean norm, Let K be the arithmetic mean of the norms of the K residuals within the window; The ACF detection threshold is 0.30, and the sliding window length is K=20 frames; a single frame >0.30 will trigger a reset; after the reset, autocorrelation detection will be paused for a 50-frame cooldown period.

8. The over-the-horizon self-healing volumetric filtering method based on heterogeneous decoupling coordinate estimation as described in claim 1, characterized in that, In step S4, when a freeze fault is detected, the process noise covariance Q is multiplicatively amplified and reset. The reset factor increases exponentially with the cumulative number of triggers n, with an initial maximum value of 2.0, a second maximum value of 4.0, and an upper limit of 10.0 for the maximum value of n. The diagonal element of Q does not exceed the initial value and the asymptotic factor. The accumulation of.

9. The over-the-horizon agile self-healing volumetric filtering method based on heterogeneous decoupling coordinate estimation as described in claim 1, characterized in that, Step S1 also includes decoupling initialization: the sensor spherical coordinate observation data at the initial moment is used to obtain the initial rectangular position state data through forward geometric mapping; the initial velocity data is estimated through Doppler radial velocity data or the distance difference between adjacent frames; the tangential velocity is initialized with a large covariance. This also includes numerical optimization for overflight singularities: when the pitch angle φ approaches the pole, a regularized offset ε is superimposed in the sin(φ) space to correct the ill-conditioned problem of the critical angle, pulling |sin(φ)| back to the safe interval before calculating arcsin. The safe interval is |sin(φ)| ≤ 1. 2ε, when |sin(φ)| > 1 Regularization correction is triggered at ε, pulling |sin(φ)| back to 1. 2ε.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the over-the-horizon agile self-healing volumetric filtering method based on heterogeneous decoupled coordinate estimation as described in any one of claims 1 to 9.

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