A method for estimating the motion state of a spatial non-cooperative target

Abstract

The present disclosure relates to a motion state estimation method of a space non-cooperative target, and relates to the technical field of aerospace. The method comprises the following steps: inputting a current state estimation value into a disturbance force prediction model to obtain a current disturbance force prediction value of the space non-cooperative target at a current time; determining an average observation value of the space non-cooperative target at a next time corresponding to the current time according to the current state estimation value and a current covariance estimation value, and determining a predicted state estimation value and a predicted covariance estimation value of the space non-cooperative target at the next time according to the current disturbance force prediction value; determining a target state estimation value of the space non-cooperative target at the next time based on the average observation value, the predicted state estimation value and the predicted covariance estimation value, and estimating a motion state of the space non-cooperative target at the next time based on the target state estimation value. The present disclosure improves the accuracy of the estimated motion state.

Description

Technical Field

[0001] This disclosure relates to the field of aerospace technology, and more specifically, to a method for estimating the motion state of a non-cooperative space target. Background Technology

[0002] During flight, non-cooperative targets in space are subjected to various types of unmodeled, nonlinear external disturbances, including air drag, solar radiation pressure, and geomagnetic forces. These dynamics pose significant challenges to accurately calculating the motion of non-cooperative targets. Traditionally, the unmodeled portion of target dynamics has been treated as generalized noise and filtered and eliminated using a low-pass filter. However, this method is only applicable to constant disturbances.

[0003] However, in reality, the interference force is related to the motion state of non-cooperative targets in most cases, and is therefore time-varying. As a result, the estimated interference force obtained by using a low-pass filter has a phase difference with the actual interference force. If the estimated interference force is substituted into the motion estimator, it will introduce a significant error, ultimately reducing the estimation effect of the service satellite on the state of non-cooperative targets; that is, the accuracy of the estimated motion state is low.

[0004] It should be noted that the information in the background section above is only used to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this disclosure is to provide a method for estimating the motion state of a non-cooperative target in space, thereby overcoming, at least to some extent, the problem of low accuracy in estimating the motion state due to limitations and defects in related technologies.

[0006] According to one aspect of this disclosure, a method for estimating the motion state of a non-cooperative target in space is provided, comprising:

[0007] Establish the state space equations for the non-cooperative space target and the observation equations for the non-cooperative space target by the serving satellite, and create a state filter based on the state space equations and the observation equations;

[0008] The current state estimate and current covariance estimate of the non-cooperative space target at the current moment are determined based on the state filter, and the current state estimate is input into the interference force prediction model to obtain the current interference force prediction value of the non-cooperative space target at the current moment.

[0009] Based on the current state estimate and the current covariance estimate, the average observation value of the non-cooperative space target at the next time corresponding to the current time is determined, and based on the current disturbance force prediction value, the predicted state estimate and the predicted covariance estimate of the non-cooperative space target at the next time are determined.

[0010] Based on the average observed value, the predicted state estimate, and the predicted covariance estimate, the target state estimate of the non-cooperative space target at the next time step is determined, and the motion state of the non-cooperative space target at the next time step is estimated based on the target state estimate.

[0011] In one exemplary embodiment of this disclosure, the interference force prediction model is obtained in the following manner:

[0012] The first historical state estimate, the first historical covariance estimate, and the first historical residual value of the non-cooperative spatial target at time k-1 are determined based on the state filter.

[0013] The first historical residual value is subjected to amplitude limiting and recursive averaging filtering to obtain the first deviation filter value; wherein, the timestamp of the median value of the average filtering queue is denoted as M;

[0014] Read the second historical state estimate corresponding to the timestamp M from the state filter, and input the second historical state estimate into the neural network model to be trained to obtain the deviation prediction result;

[0015] The parameters in the neural network model to be trained are adjusted based on the first deviation filter value and the deviation prediction result to obtain the interference force prediction model.

[0016] In one exemplary embodiment of this disclosure, the second historical state estimate is input into a neural network model to be trained to obtain a bias prediction result, including:

[0017] Multiple different samples are randomly selected from the second historical state estimate as initial cluster centers, and training samples are randomly selected from the second historical state estimate as input samples.

[0018] Based on the input sample and the initial cluster centers, determine the sample category to which the input sample belongs, and update the initial cluster centers based on the sample category;

[0019] The updated cluster centers are updated again based on the neural network model to be trained, and it is determined whether the change in the updated cluster centers is less than or equal to a preset threshold.

[0020] If the change in the updated cluster centers is less than or equal to a preset threshold, then the deviation prediction result is obtained based on the updated cluster centers.

[0021] In one exemplary embodiment of this disclosure, adjusting the parameters in the neural network model to be trained based on the first deviation filter value and the deviation prediction result to obtain the interference force prediction model includes:

[0022] The standard deviation between the first bias filter value and the bias prediction result is calculated based on the Gaussian function in the neural network model to be trained, and the parameters in the neural network model to be trained are adjusted based on the standard deviation to obtain the interference force prediction model.

[0023] In one exemplary embodiment of this disclosure, determining the average observation value of the space non-cooperative target at the next time step corresponding to the current time step based on the current state estimate and the current covariance estimate includes:

[0024] A tasteless transformation is performed on the current state estimate and the current covariance estimate to obtain the current sampling point. Based on the current sampling point and the observation equation, the average observation value of the non-cooperative target at the next time step is determined.

[0025] In one exemplary embodiment of this disclosure, determining the predicted state estimate and predicted covariance estimate of the non-cooperative space target at the next time step based on the current predicted disturbance force value includes:

[0026] Based on the current predicted interference force value and the current sampling point, determine the predicted state estimate of the non-cooperative space target at the next moment;

[0027] Based on the current sampling point and the predicted state estimate, the covariance estimate of the non-cooperative spatial target at the next time step is determined.

[0028] In one exemplary embodiment of this disclosure, determining the target state estimate of the non-cooperative space target at the next time step based on the average observation value, the predicted state estimate value, and the predicted covariance estimate value includes:

[0029] The information covariance and cross covariance of the non-cooperative space target are determined based on the average observations, and the gain matrix of the non-cooperative space target is determined based on the information covariance and cross covariance.

[0030] Based on the predicted state estimate and the gain matrix, the target state estimate of the non-cooperative space target at the next time step is determined.

[0031] In one exemplary embodiment of this disclosure, determining the target state estimate of the non-cooperative spatial target at the next time step based on the predicted state estimate and the gain matrix includes:

[0032] Determine the target relative position between the non-cooperative space target and the service satellite at the next time step, and based on the predicted state estimate, gain matrix, and target relative position, determine the target state estimate of the non-cooperative space target at the next time step.

[0033] In one exemplary embodiment of this disclosure, determining the target relative position between the non-cooperative space target and the serving satellite at the next moment includes:

[0034] Determine the current satellite position of the service satellite in the orbital coordinate system at the current moment, and determine the current relative position of the non-cooperative space target with respect to the service satellite at the current moment based on the current state estimate;

[0035] Based on the current relative position and the current satellite position, determine the target relative position between the non-cooperative space target and the service satellite at the next moment.

[0036] In one exemplary embodiment of this disclosure, the state filter includes any one of an adaptive unscented Kalman filter, an adaptive extended Kalman filter, and an adaptive capacitive Kalman filter.

[0037] This disclosure provides a method for estimating the motion state of a non-cooperative space target. Firstly, it establishes a state-space equation for the non-cooperative space target and an observation equation from a serving satellite. A state filter is then created based on these equations. Next, the current state estimate and covariance estimate of the non-cooperative space target at the current moment are determined based on the state filter. This current state estimate is then input into an interference force prediction model to obtain the predicted interference force of the non-cooperative space target at the current moment. Finally, the average observation value of the non-cooperative space target at the next moment corresponding to the current moment is determined based on the current state estimate and covariance estimate, and the predicted interference force is then calculated based on the current interference force. The predicted values ​​determine the estimated state and predicted covariance of a non-cooperative target in space at the next time step. Finally, based on the average observed value, the estimated state, and the estimated covariance, the estimated state of the non-cooperative target in space at the next time step is determined, and the motion state of the non-cooperative target in space at the next time step is estimated based on the estimated state. Since the predicted value of the interference force can be determined based on the interference force cloud measurement model, and then the motion state is estimated based on the predicted value of the interference force, the accuracy of the estimated motion state is improved. On the other hand, since the interference force can be predicted using a trained interference force prediction model, there is no need to train the model in real time, which improves the efficiency of motion state estimation.

[0038] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description

[0039] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0040] Figure 1 The flowchart schematically illustrates a method for estimating the motion state of a non-cooperative target in space according to an exemplary embodiment of the present disclosure.

[0041] Figure 2 The diagram illustrates the implementation principle of a motion state estimation method for a non-cooperative target in space according to an exemplary embodiment of the present disclosure.

[0042] Figure 3 The diagram schematically illustrates an example structure of a radial basis function network according to an exemplary embodiment of the present disclosure.

[0043] Figure 4The flowchart schematically illustrates a training method for a radial basis function network according to an exemplary embodiment of the present disclosure.

[0044] Figure 5 An example diagram illustrating a training scenario for a radial basis function network according to an exemplary embodiment of the present disclosure is shown.

[0045] Figure 6 This diagram schematically illustrates an example of a location scenario for an observation satellite and a non-cooperative space target according to an exemplary embodiment of this disclosure.

[0046] Figure 7 The diagram schematically illustrates a motion state estimation apparatus for a non-cooperative target in space according to an exemplary embodiment of the present disclosure.

[0047] Figure 8 An electronic device is illustrated in accordance with an example embodiment of the present disclosure for a method of estimating the motion state of a non-cooperative target in space. Detailed Implementation

[0048] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided to make this disclosure more comprehensive and complete, and to fully convey the concept of the example embodiments to those skilled in the art. The described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a full understanding of embodiments of this disclosure. However, those skilled in the art will recognize that the technical solutions of this disclosure can be practiced with one or more of the specific details omitted, or other methods, components, apparatus, steps, etc., can be employed. In other instances, well-known technical solutions are not shown or described in detail to avoid obscuring various aspects of this disclosure.

[0049] Furthermore, the accompanying drawings are merely illustrative of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0050] In the aerospace field, on-orbit servicing missions for non-cooperative targets in space ensures the safety of the space environment. Non-cooperative targets in space are uncontrollable and difficult to measure; therefore, accurately measuring their motion is fundamental to other types of on-orbit servicing. During flight, non-cooperative targets are subjected to various types of unmodeled, nonlinear external disturbances, including air drag, solar radiation pressure, and geomagnetic forces. This dynamics pose significant challenges to accurately calculating the motion of non-cooperative targets. Traditionally, the unmodeled portion of target dynamics is treated as generalized noise and filtered and eliminated using a low-pass filter. However, this method only applies to constant disturbance forces. In reality, in most cases, the disturbance force is related to the motion state of the non-cooperative target and is therefore time-varying. The estimated disturbance force obtained using a low-pass filter will have a phase difference from the actual disturbance force. Substituting the estimated disturbance force into the motion estimator will introduce significant errors, ultimately reducing the servicing satellite's estimation accuracy of the non-cooperative target's state.

[0051] Disturbance forces are typically related to the state of non-cooperative targets. If a motion state-disturbance force model can be constructed using a neural network, the motion state estimated by the motion state estimator can be input into the disturbance force model. The disturbance force currently experienced by the non-cooperative target, output by the disturbance force model, can then be input into the motion state estimator, making the dynamic integral part of the motion state estimator more accurate and ultimately significantly improving the motion estimation effect. From this perspective, existing offline training methods for calculating residuals of neural network estimators cannot be applied to the aerospace field for estimating the state of non-cooperative targets. Specifically, this is because: firstly, satellites cannot obtain data on external disturbances experienced by non-cooperative targets in space in advance, thus preventing offline training of the neural network; secondly, the residual data contains a large amount of noise and outliers, and direct use would severely pollute the training data. Therefore, designing new, accurate online algorithms for calculating environmental disturbances experienced by non-cooperative targets in space is extremely necessary.

[0052] Therefore, compared with previous patents, the innovation of this patent lies in: 1) proposing the idea of ​​"firstly using adaptive Kalman filtering to train a neural network online, and then using the neural network to improve the state estimation effect of the adaptive Kalman filter," which solves the problem of state-related interference forces in the motion state estimation of non-cooperative targets; 2) proposing a method for training a neural network online using adaptive Kalman filtering, wherein the state quantity output by the adaptive Kalman filter is used as the known quantity of the neural network, and the output residual quantity is used as the expected value of the neural network; 3) proposing to perform low-pass filtering on the residual obtained by adaptive Kalman filtering and time alignment on the obtained state, thereby obtaining a more accurate state-interference force data pair, providing high-quality data support for training a reliable interference force model. Meanwhile, in the example embodiments of this disclosure, the state estimator and the adaptive Kalman filtering method are essentially equivalent; the residual value of the state estimator is essentially the interference force, and the motion state quantity includes the position and velocity of the non-cooperative target. Furthermore, the state filter described in the example embodiments of this disclosure adopts an adaptive unscented Kalman filter, but other adaptive Kalman filter schemes such as adaptive extended Kalman filter or adaptive capacitive Kalman filter can also be adopted; similarly, the low-pass filter adopts a recursive averaging filter, but other low-pass digital filters such as averaging filter, recursive filter, etc. can also be adopted; similarly, the neural network adopts a radial basis function neural network, but other schemes such as multilayer perceptron neural network can also be adopted.

[0053] In one exemplary embodiment, the motion state estimation method for non-cooperative spatial targets described in this exemplary embodiment can run on a server, server cluster, or cloud server, etc.; of course, those skilled in the art can also run the method of this disclosure on other platforms as needed, and this exemplary embodiment does not impose any special limitations on this. Specifically, refer to Figure 1 As shown, the method for estimating the motion state of a non-cooperative target in space may include the following steps:

[0054] Step S110. Establish the state space equation of the non-cooperative space target and the observation equation of the serving satellite on the non-cooperative space target, and create a state filter based on the state space equation and the observation equation;

[0055] Step S120. Determine the current state estimate and current covariance estimate of the non-cooperative space target at the current moment based on the state filter, and input the current state estimate into the interference force prediction model to obtain the current interference force prediction value of the non-cooperative space target at the current moment;

[0056] Step S130. Determine the average observation value of the non-cooperative space target at the next time corresponding to the current time based on the current state estimate and the current covariance estimate, and determine the predicted state estimate and predicted covariance estimate of the non-cooperative space target at the next time based on the current disturbance force prediction value.

[0057] Step S140. Based on the average observation value, the predicted state estimate value, and the predicted covariance estimate value, determine the target state estimate value of the non-cooperative space target at the next time step, and estimate the motion state of the non-cooperative space target at the next time step based on the target state estimate value.

[0058] In the aforementioned method for estimating the motion state of a non-cooperative space target, on the one hand, a state-space equation for the non-cooperative space target and an observation equation for the non-cooperative space target from the serving satellite are established, and a state filter is created based on the state-space equation and the observation equation; then, based on the state filter, the current state estimate and the current covariance estimate of the non-cooperative space target at the current moment are determined, and the current state estimate is input into the interference force prediction model to obtain the current interference force prediction value of the non-cooperative space target at the current moment; furthermore, based on the current state estimate and the current covariance estimate, the average observation value of the non-cooperative space target at the next moment corresponding to the current moment is determined, and based on the current interference force prediction value, the average observation value of the non-cooperative space target at the next moment corresponding to the current moment is determined, and the average observation value of the non-cooperative space target at the next ... The method involves estimating the predicted state and predicted covariance of a non-cooperative target in space at the next time step. Based on the average observed value, the predicted state estimate, and the predicted covariance estimate, the target state estimate for the non-cooperative target at the next time step is determined. The motion state of the non-cooperative target at the next time step is then estimated based on this target state estimate. Since the predicted interference force can be determined based on the interference force cloud measurement model, and the motion state is then estimated based on the predicted interference force, the accuracy of the estimated motion state is improved. Furthermore, since the interference force can be predicted using a pre-trained interference force prediction model, real-time training of the model is unnecessary, thus improving the efficiency of motion state estimation.

[0059] The following will provide a detailed explanation and description of the motion state estimation method for non-cooperative targets in space as described in the exemplary embodiments of this disclosure, in conjunction with the accompanying drawings.

[0060] First, the technical implementation principle of the exemplary embodiments of this disclosure will be explained and described. Specifically, the motion state estimation method for non-cooperative targets in space described in the exemplary embodiments of this disclosure can accurately calculate online the impact of environmental disturbances such as solar perturbation and air resistance on the motion of non-cooperative targets; at the same time, it can also calculate the position of non-cooperative targets in space and conduct online training of neural networks that predict the state of non-cooperative targets from external disturbances, overcoming the inability of existing motion estimation algorithms for non-cooperative targets in space to handle state-related external disturbances.

[0061] Secondly, the motion state estimation method for a non-cooperative spatial target described in the exemplary embodiments of this disclosure can be divided into a training phase and an operation phase. The purpose of the training phase is to train the radial basis function neural network online and achieve relatively accurate motion estimation. The operation phase refers to the time period during which the neural network completes training, runs normally, and is used to correct the motion estimation algorithm. The specific implementation process can be found in [reference needed]. Figure 2 As shown; at the same time, in Figure 2 In the schematic diagram shown, the solid lines and dashed lines represent the training phase and the running phase, respectively.

[0062] In practical applications, the main idea of ​​the training phase is to use an adaptive Kalman filter framework to complete state-motion estimation. The residuals and state variables generated by the adaptive Kalman filter are low-pass filtered and time-aligned before being fed into the neural network for training. This ultimately yields a state-disturbance force model, which approximates the real disturbance force model. During the training phase, the disturbance force model does not participate in the motion estimation task. Therefore, the entire computation process in the training phase can be divided into two modules: a motion estimation module and a network training module. Specifically, the main process of motion estimation is as follows: a Kalman filter-based motion state estimator is used to estimate the position and velocity of a non-cooperative target in space. The residuals in the state equation are obtained and passed to a recursive averaging filter for noise reduction and outlier removal, thus obtaining the estimated disturbance force. This residual is then passed to the Kalman filter to correct the process equation, ultimately achieving a more accurate motion estimation. The main process of neural network training is as follows: considering the estimated disturbance force and motion estimate provided in the motion estimation, as mentioned above, the filtered values ​​generated by the recursive averaging filter have a definite phase difference. Therefore, the state estimate corresponding to the filtered residual value in time is searched. The state variables and residuals are then used as known variables and expected outputs of the neural network, respectively, and input into the radial basis function neural network for parameter training, and an interference model is generated.

[0063] Furthermore, the main idea of ​​the operational phase is to no longer train the neural network, but instead use a pre-trained neural network as the interference model. The current state is input, and the current interference force is output. The main process is as follows: the Kalman filter's estimate of the current motion state is fed into the interference model to calculate the interference force on the non-cooperative target. Then, in the next estimation loop, this estimate is substituted into the Kalman filter's dynamic recursive formula to complete the recursion of the motion state for the next moment. This significantly improves the accuracy of motion estimation for the interference force, while substantially reducing the computational load compared to the training phase, thus providing a more sufficient computational margin for other satellite payloads.

[0064] The following will combine Figure 3 The interference force prediction model involved in the exemplary embodiments of this disclosure will be explained and described. Specifically, refer to... Figure 3 As shown, the interference prediction model described here can be an RBFNN (Radial Basis Function Neural Network) model, which is a three-layer feedforward network that can include an input layer 301, a hidden layer 302, and an output layer 303. The neurons of the RBFNN are nonlinear functions, so even though it is a shallow network, it can achieve similar effects to a multilayer perceptron.

[0065] The following will combine Figure 4 This section explains and illustrates the specific training process of the interference force prediction model. For details, please refer to [link / reference]. Figure 4 As shown, the specific training process of the interference force prediction model may include the following steps:

[0066] Step S410: Determine the first historical state estimate, the first historical covariance estimate, and the first historical residual value of the spatial non-cooperative target at time k-1 based on the state filter.

[0067] Step S420: Perform amplitude limiting and recursive average filtering on the first historical residual value to obtain the first deviation filter value; wherein, the timestamp of the median value of the average filtering queue is denoted as M;

[0068] Step S430: Read the second historical state estimate corresponding to the timestamp M in the state filter, and input the second historical state estimate into the neural network model to be trained to obtain the deviation prediction result;

[0069] Step S440: Adjust the parameters in the neural network model to be trained according to the first deviation filter value and the deviation prediction result to obtain the interference force prediction model.

[0070] In one example embodiment, inputting a second historical state estimate into a neural network model to be trained to obtain a bias prediction result can be achieved as follows: randomly selecting multiple different samples from the second historical state estimate as initial cluster centers, and randomly selecting training samples from the second historical state estimate as input samples; determining the sample category to which the input sample belongs based on the input sample and the initial cluster centers, and updating the initial cluster centers based on the sample category; updating the updated cluster centers again based on the neural network model to be trained, and determining whether the change magnitude of the updated cluster centers is less than or equal to a preset threshold; if the change magnitude of the updated cluster centers is less than or equal to the preset threshold, then obtaining the bias prediction result based on the updated cluster centers.

[0071] In one exemplary embodiment, the interference force prediction model is obtained by adjusting the parameters in the neural network model to be trained based on the first deviation filter value and the deviation prediction result. This can be achieved by: calculating the standard deviation between the first deviation filter value and the deviation prediction result based on the Gaussian function in the neural network model to be trained, and adjusting the parameters in the neural network model to be trained based on the standard deviation to obtain the interference force prediction model.

[0072] The following section will further explain and illustrate the specific training process of the interference force prediction model. Specifically, the training process of the interference force prediction model first requires designing a radial basis function neural network-assisted adaptive unscented Kalman filter algorithm for the training phase. The main steps of the training phase are: using the adaptive Kalman filter framework to complete state motion estimation and obtain the first historical state estimate at step k-1. and the first historical residual Positive superscripts for the two variables indicate estimated or predicted values, distinct from true values ​​without positive superscripts; the superscript of the plus sign indicates an estimated value, distinct from predicted values ​​in the filter; the first historical residual generated by the adaptive Kalman filter. And the first historical state to estimate the state quantity After performing low-pass filtering and time alignment, k-1 steps are obtained. and The superscript indicates the expected value and input quantity used in the RBFNN neural network, to distinguish it from the output quantity of the adaptive Kalman filter. and The data is fed into a neural network for training, which eventually yields a state-disturbance force model. This model approximates the real disturbance force model. During the training phase, the disturbance force model does not participate in the motion estimation task. Besides being used to train neural networks, it is also used in the extrapolation process of the state estimator. The state estimator uses the corrected predicted values ​​to complete the estimation, ultimately achieving a more accurate motion estimation. Therefore, the specific implementation process of the tasteless Kalman filter method for estimating the target motion state during the training phase is as follows:

[0073] (1) Randomly initialize the BRFNN to generate μ0, σ0, and W0, which are all parameters of the RBFNN. These three parameters will be described in detail below. Then, initialize the AUKF (i.e., state filter) to generate... (First historical residual value) (First historical state estimate) (First historical covariance estimate); further, let k = 1, and start the loop;

[0074] (2) Amplitude limiting is performed, followed by recursive averaging filtering. The timestamp of the median value in the averaging filtering queue is denoted as M. The filtering process generates a new bias filter value. (That is, the first deviation filter value);

[0075] (3) Retrieve historical filter values ​​of AUKF (That is, the second historical state estimate), as mentioned above, can be denoted as... Will Stored in memory for later retrieval;

[0076] (4) Use and Train RBFNN and update μ k-1 σ k-1 W k-1 The structure and training expression of RBFNN are listed below;

[0077] Furthermore, to enable iterative training of the RBFNN, it is necessary to cyclically generate historical residual values, historical state estimates, and historical covariance estimates. This can be achieved using the suffixless transformation and state filters. Specifically, the implementation process of the suffixless transformation is as follows:

[0078] (1) When the state estimate is known Covariance estimate Sampling points are generated based on the tasteless transformation: The sampling point is represented by the odorless transformation, which is a common method in state estimation techniques and will not be elaborated here.

[0079] (2) The sampling state Substituting these values ​​into the process equation allows us to extrapolate all sampling points, i.e.:

[0080] Here, the right subscript of k|k-1 indicates the value at time k predicted based on the process equation or observation equation and using the state at time k-1.

[0081] (3) The predicted state and the predicted covariance are:

[0082]

[0083] Among them, Q k Let be the covariance matrix of the process noise. These are the weights of the unscented transform, and their calculation method is also a common method for unscented Kalman filtering, which will not be elaborated here.

[0084] (4) Substituting the predicted sample values ​​into the observation equation, we have:

[0085] The average observed value is:

[0086] (5) The methods for solving the innovation covariance, cross covariance, and gain matrix are as follows:

[0087]

[0088] Among them, S k The covariance matrix of the observed noise is usually easy to calculate in engineering and is a known quantity. The update methods for the state vector, process disturbance, state covariance matrix, and deviation values ​​are as follows:

[0089]

[0090] Where α is the forgetting factor, and its value ranges from 0 to 1.

[0091] Finally, determine whether the RBFNN has converged. If it has not converged, let k = k + 1 and recursively repeat the filtering steps; if the convergence condition is met, stop training.

[0092] Furthermore, after obtaining the second historical state estimate, the RBFNN can be trained. For details, refer to... Figure 5 As shown, the neurons in RBFNN are non-linear functions, therefore even though it is a shallow network, it can achieve similar effects to a multilayer perceptron. Figure 5 In the example scene diagram shown, the input layer of the neuron is denoted as... Hidden layers are represented as The output layer is denoted as The RBFNN can be written as a function of d(x). The radial basis functions (RBFNNs) in the hidden layer can map low-dimensional linearly inseparable input values ​​to a high-dimensional linearly separable space. The activation functions of the hidden layer neurons respond locally to the input information. When the input value is located in the central region of the basis function, the output of the hidden layer neuron is large; conversely, the output decays exponentially as the input value moves away from the center point. The RBFNN ensures that the function value is radially symmetric about the center point, and that the function value is a non-negative real number, depending only on the distance from the input to the center point. Euclidean distance or a Gaussian function can be used, denoted as Φ. i (x)=L(||x-μ i || 2 ); where μ i Let L be the center point of the i-th hidden layer neuron, and L(·) represent a configurable scalar function; in this project, a nonlinear Gaussian function is selected. Where σ i σ is the width parameter of the i-th hidden layer neuron. i The smaller the value, the more concentrated the distribution is towards the center point, and the narrower the central region of the curve; the larger the value, the flatter the curve. On the one hand, a narrow Gaussian function increases the responsiveness of the RBFNN; on the other hand, if the overlap of neuron functions is limited due to the narrow Gaussian central region, the network will struggle to obtain non-zero outputs. (RBFNN output value) The value of the l-th element is Based on this equation, the hidden layer-output layer can be written as d(x) = W. T Φ(x); where W is the weight coefficient matrix, and W = [w il ], i=1,...,m, l=1,...,j. Φ(x)=[Φ1(x) Φ2(x) ...Φ m (x)] T .

[0093] As mentioned above, RBFNN has three types of unknown parameters, namely the center point matrix of the hidden layer. and weight coefficient matrix Meanwhile, RBFNN can use a self-organizing algorithm to train all network parameters online. The specific training process is as follows:

[0094] (1) The K-means algorithm is used to select a reasonable center location, dividing the input into several major categories. The same category has similar characteristics and properties, thus ensuring that the selected center point is representative; specifically, assume that the i-th cluster center in the k-th iteration is μ. i,k Then you can perform the following steps:

[0095] First, initialization is performed by randomly selecting I distinct samples from the input sample data (i.e., the second historical state estimate) as the initial cluster centers μ.i,k Secondly, input samples; that is, randomly selecting training samples x from the training data. k As input; then, matching; that is, calculating which cluster center the input sample is closest to, and then classifying it into the same cluster as that center, i.e., calculating i(x) k )=argmin||x k -μ i,k ||; Find the corresponding i, and assign xk to the i-th class; Further, update the cluster centers; that is, since x k The addition of [a new cluster] will change the cluster center of the i-th cluster. The new cluster centers are updated as follows:

[0096] Where η is the learning step size, satisfying 0 < η < 1; only one cluster center is updated each time, and the others are not updated; finally, a judgment is made; that is, it is necessary to judge whether the algorithm has converged; for example, a small threshold can be set, if the change of cluster centers is less than the threshold, the algorithm is considered to have converged; otherwise, the iteration continues.

[0097] (2) Calculate the standard deviation; that is, even if the algorithm converges, it is still necessary to calculate the standard deviation to determine whether the model has been trained successfully. Specifically, in the example embodiment of this disclosure, a Gaussian function is used as the basis function, and the standard deviation can be selected as:

[0098] Where, max||μ i,k -μ j,k || represents the maximum distance between cluster centers. This method can prevent radial basis functions from being too concentrated or too dispersed.

[0099] (3) Learning weights; specifically, the Least Mean Square (LMS) algorithm can be used directly. The input of LMS is the output generated by the hidden layer, i.e., W = Φ + d; Φ + =(Φ T Φ) -1 Φ T .

[0100] Based on the above methods, the Kalman filter algorithm continuously... The data pairs are input into the training algorithm to generate network parameters μ, W, and σ, thereby completing the construction of the radial basis function neural network.

[0101] The following will combine Figures 2-5 right Figure 1 The method for estimating the motion state of non-cooperative targets in space, as shown in the illustration, will be further explained and illustrated. Specifically:

[0102] In step S110, the state space equation of the non-cooperative space target and the observation equation of the serving satellite on the non-cooperative space target are established, and a state filter is created based on the state space equation and the observation equation.

[0103] Specifically, firstly, refer to Figure 6 As shown, assuming an orbital coordinate system can be established near the orbit of the non-cooperative target 601, with the x-direction representing the velocity and the y-direction pointing towards the Earth's center, and the z-axis direction determined according to the right-hand coordinate system; then, according to the CW equations, as the non-cooperative target 601 gradually moves away from the origin of the orbital coordinate system, and considering that environmental disturbances can be decomposed into non-zero components and zero-mean Gaussian noise, the differential equations of motion for the position r and velocity v of the non-cooperative target 601 can be as follows:

[0104]

[0105] Where d represents the non-zero environmental disturbance term (i.e., the disturbance value), which is difficult to remove by the filter and is usually state-dependent. ξ represents the zero-mean Gaussian noise term, which will be treated as process noise in the following text. The forms of matrices A and B are as follows:

[0106]

[0107] Where w represents the orbital angular velocity of the non-cooperative target, which is a known constant.

[0108] Furthermore, the differential motion formulas for position and velocity can be transformed into discrete motion formulas, namely:

[0109]

[0110] Where Δt is the discrete-time step size, which can be selected according to actual needs in practical applications. The subscript of the variable indicates the number of discrete-time steps. Furthermore, writing the above equation in matrix form, we have:

[0111]

[0112] Where I represents a 3x3 identity matrix. For convenience, the state variable can be simplified to a matrix form, i.e., the state variable itself. Furthermore, the first term on the right-hand side of the above equation can be simplified to [formula missing], and the coefficients of the second and third terms on the right-hand side can be written as C. Therefore, the above formula can be simplified to:

[0113] x k =f k-1 +Cd k-1 +Cξ k-1 ;

[0114] Furthermore, due to f k-1 d k-1 With x k-1 Therefore, the above formula can also be written as:

[0115] x k =f(x) k-1 )+Cd(x k-1 )+Cξ k-1 In this formula, the parentheses represent a functional relationship, not an operator. As mentioned above, the function f(x) in this formula... k-1 The form of ξ is known, the coefficient matrix C is known, and the process noise ξ is known. k-1 The statistical properties of d(x) are known. k-1 The function form of ) is unknown.

[0116] Finally, continue to refer to Figure 6 As shown, based on geometric relationships and taking into account observation noise, the value for the position of the non-cooperative target measured by the serving satellite is:

[0117] z k =r k-1 -r s,k-1 +θ k-1 ;where z k r represents the relative position of the non-cooperative target measured by the serving satellite at time k. s θ represents the known position of the serving satellite in the orbital coordinate system. k The observation noise is zero-mean and its statistical properties are known. Similarly, the above equation can be written as z k =z(x k-1 ,r s,k-1 )+θ k-1 In the form of z(·), the parentheses in z(·) represent a function, not an operator. This equation is the observation equation.

[0118] Finally, after obtaining the observation equation and the state space equation, the state filter, namely AUKF (Adaptive Unscented Kalman Filter), can be obtained based on the observation equation and the state space equation. Furthermore, the motion state estimation method for non-cooperative targets described in the exemplary embodiments of this disclosure can ultimately be applied to d(x) k-1 To achieve the determination of x under the conditions of unknown form, process noise, and observation noise interference. k The goal is to achieve accurate estimation of the motion state of non-cooperative targets, thereby improving the accuracy of such estimations.

[0119] In step S120, the current state estimate and current covariance estimate of the non-cooperative space target at the current moment are determined based on the state filter, and the current state estimate is input into the interference force prediction model to obtain the current interference force prediction value of the non-cooperative space target at the current moment.

[0120] In step S130, the average observation value of the non-cooperative space target at the next time corresponding to the current time is determined based on the current state estimate and the current covariance estimate, and the predicted state estimate and predicted covariance estimate of the non-cooperative space target at the next time are determined based on the current disturbance force prediction value.

[0121] In one exemplary embodiment, determining the average observation value of the non-cooperative spatial target at the next time step corresponding to the current time step based on the current state estimate and the current covariance estimate can be achieved by performing a tasteless transformation on the current state estimate and the current covariance estimate to obtain the current sampling point, and determining the average observation value of the non-cooperative target at the next time step based on the current sampling point and the observation equation.

[0122] In one exemplary embodiment, determining the predicted state estimate and predicted covariance estimate of the non-cooperative space target at the next time step based on the current predicted interference force value can be achieved as follows: determining the predicted state estimate of the non-cooperative space target at the next time step based on the current predicted interference force value and the current sampling point; and determining the covariance estimate of the non-cooperative space target at the next time step based on the current sampling point and the predicted state estimate.

[0123] In step S140, based on the average observation value, the predicted state estimate value, and the predicted covariance estimate value, the target state estimate value of the non-cooperative space target at the next time moment is determined, and the motion state of the non-cooperative space target at the next time moment is estimated based on the target state estimate value.

[0124] In one exemplary embodiment, determining the target state estimate of the non-cooperative space target at the next time step based on the average observation, the predicted state estimate, and the predicted covariance estimate can be achieved as follows: determining the information covariance and cross covariance of the non-cooperative space target based on the average observation, and determining the gain matrix of the non-cooperative space target based on the information covariance and cross covariance; and determining the target state estimate of the non-cooperative space target at the next time step based on the predicted state estimate and the gain matrix.

[0125] In one exemplary embodiment, determining the target state estimate of the non-cooperative space target at the next moment based on the predicted state estimate and the gain matrix can be achieved by: determining the target relative position between the non-cooperative space target and the service satellite at the next moment, and determining the target state estimate of the non-cooperative space target at the next moment based on the predicted state estimate, the gain matrix, and the target relative position.

[0126] In an exemplary embodiment of this disclosure, determining the target relative position between the non-cooperative space target and the service satellite at the next moment can be achieved by: determining the current satellite position of the service satellite in the orbital coordinate system at the current moment, and determining the current relative position between the non-cooperative space target and the service satellite at the current moment based on the current state estimate; and determining the target relative position between the non-cooperative space target and the service satellite at the next moment based on the current relative position and the current satellite position.

[0127] The following will provide further explanation and description of steps S120-S140. Specifically, in practical applications, the estimated value of the Mann filter can be... (That is, the current state estimate) is fed into the disturbance model, and the disturbance amount can be directly calculated. (That is, the current interference force prediction value of the non-cooperative space target at the current moment), and then substituted into the dynamic recursive formula of the filter in the next estimation loop, which greatly improves the accuracy of motion estimation, while significantly reducing the amount of computation compared to the training phase, thus providing more sufficient computational margin for other satellite payloads.

[0128] The specific calculation process of the RBFNN-AUKF for estimating the target state of a non-cooperative target in space at the next time step can be achieved as follows:

[0129] (1) Initialize AUKF, let These are equal to the last time point of the training phase.

[0130] (2) Set k = 1 and start the loop;

[0131] (3) Imported into RBFNN, it generates prediction perturbation, i.e. (That is, the predicted value of the current disturbance force of the non-cooperative space target at the current moment);

[0132] (4) Known state estimate Covariance estimate Sampling points are generated based on the tasteless transformation:

[0133] (5) The sampling state Substituting these values ​​into the process equation, we can extrapolate all the sampling points to obtain:

[0134] (6) The predicted state and the predicted covariance are:

[0135]

[0136] (7) Substituting the predicted sample values ​​into the observation equation, we have:

[0137]

[0138] (8) The average observed value is:

[0139]

[0140] (9) The methods for solving the innovation covariance, cross covariance, and gain matrix are as follows:

[0141]

[0142] (10) The update methods for the state vector (i.e., the target state estimate of the non-cooperative target in space at the next moment), process disturbances, state covariance matrix, and deviation values ​​are as follows:

[0143]

[0144]

[0145] Determine if the task has ended; if not, let k = k + 1, return to the third step and repeat the calculation to calculate the target state estimate of the non-cooperative target in space at multiple different times.

[0146] Thus, the motion state estimation method for non-cooperative targets in space described in the exemplary embodiments of this disclosure has been fully implemented. Based on the foregoing description, it can be understood that the motion state estimation method for non-cooperative targets in space described in the exemplary embodiments of this disclosure, on the one hand, can achieve high-precision state estimation of non-cooperative targets subject to state-related disturbances; on the other hand, it does not require offline training of the neural network, achieving online training while ensuring the normal operation of motion estimation.

[0147] The following are embodiments of the apparatus disclosed herein, which can be used to execute embodiments of the method disclosed herein. For details not disclosed in the apparatus embodiments of this disclosure, please refer to the embodiments of the method disclosed herein.

[0148] This disclosure also provides an example embodiment of a motion state estimation device for a non-cooperative target in space. Specifically, refer to... Figure 7As shown, the motion state estimation device for a non-cooperative space target may include a state filter creation module 710, a current disturbance force prediction value determination module 720, an average observation value determination module 730, and a state estimation module 740. Wherein:

[0149] The state filter creation module 710 can be used to establish the state space equation of a non-cooperative space target and the observation equation of the serving satellite on the non-cooperative space target, and create a state filter based on the state space equation and the observation equation.

[0150] The current interference force prediction value determination module 720 can be used to determine the current state estimate and the current covariance estimate of the non-cooperative space target at the current moment based on the state filter, and input the current state estimate into the interference force prediction model to obtain the current interference force prediction value of the non-cooperative space target at the current moment.

[0151] The average observation determination module 730 can be used to determine the average observation of the non-cooperative space target at the next moment corresponding to the current moment based on the current state estimate and the current covariance estimate, and to determine the predicted state estimate and predicted covariance estimate of the non-cooperative space target at the next moment based on the current disturbance force prediction value.

[0152] The state estimation module 740 can be used to determine the target state estimate of the non-cooperative space target at the next moment based on the average observation value, the predicted state estimate value, and the predicted covariance estimate value, and to estimate the motion state of the non-cooperative space target at the next moment based on the target state estimate value.

[0153] In an exemplary embodiment of this disclosure, the interference force prediction model is obtained as follows: a first historical state estimate, a first historical covariance estimate, and a first historical residual value of a non-cooperative spatial target at time k-1 are determined based on the state filter; the first historical residual value is subjected to amplitude limiting and recursive averaging filtering to obtain a first deviation filter value; wherein the timestamp of the intermediate value of the averaging filter queue is denoted as M; a second historical state estimate corresponding to timestamp M is read from the state filter, and the second historical state estimate is input into the neural network model to be trained to obtain a deviation prediction result; the parameters in the neural network model to be trained are adjusted based on the first deviation filter value and the deviation prediction result to obtain the interference force prediction model.

[0154] In one exemplary embodiment of this disclosure, inputting the second historical state estimate into a neural network model to be trained to obtain a bias prediction result includes: randomly selecting multiple different samples from the second historical state estimate as initial cluster centers, and randomly selecting training samples from the second historical state estimate as input samples; determining the sample category to which the input sample belongs based on the input sample and the initial cluster centers, and updating the initial cluster centers based on the sample category; updating the updated cluster centers again based on the neural network model to be trained, and determining whether the change magnitude of the updated cluster centers is less than or equal to a preset threshold; if the change magnitude of the updated cluster centers is less than or equal to the preset threshold, then obtaining a bias prediction result based on the updated cluster centers.

[0155] In one exemplary embodiment of this disclosure, adjusting the parameters in the neural network model to be trained based on the first deviation filter value and the deviation prediction result to obtain the interference force prediction model includes: calculating the standard deviation between the first deviation filter value and the deviation prediction result based on the Gaussian function in the neural network model to be trained, and adjusting the parameters in the neural network model to be trained based on the standard deviation to obtain the interference force prediction model.

[0156] In one exemplary embodiment of this disclosure, determining the average observation value of the non-cooperative spatial target at the next time corresponding to the current time based on the current state estimate and the current covariance estimate includes: performing a tasteless transformation on the current state estimate and the current covariance estimate to obtain the current sampling point, and determining the average observation value of the non-cooperative target at the next time based on the current sampling point and the observation equation.

[0157] In one exemplary embodiment of this disclosure, determining the predicted state estimate and predicted covariance estimate of the non-cooperative space target at the next time step based on the current predicted interference force value includes: determining the predicted state estimate of the non-cooperative space target at the next time step based on the current predicted interference force value and the current sampling point; and determining the covariance estimate of the non-cooperative space target at the next time step based on the current sampling point and the predicted state estimate.

[0158] In one exemplary embodiment of this disclosure, determining the target state estimate of the non-cooperative space target at the next time step based on the average observation, the predicted state estimate, and the predicted covariance estimate includes: determining the information covariance and cross covariance of the non-cooperative space target based on the average observation, and determining the gain matrix of the non-cooperative space target based on the information covariance and cross covariance; and determining the target state estimate of the non-cooperative space target at the next time step based on the predicted state estimate and the gain matrix.

[0159] In one exemplary embodiment of this disclosure, determining the target state estimate of the non-cooperative space target at the next moment based on the predicted state estimate and the gain matrix includes: determining the target relative position between the non-cooperative space target and the service satellite at the next moment, and determining the target state estimate of the non-cooperative space target at the next moment based on the predicted state estimate, the gain matrix, and the target relative position.

[0160] In one exemplary embodiment of this disclosure, determining the target relative position between the non-cooperative space target and the service satellite at the next moment includes: determining the current satellite position of the service satellite in the orbital coordinate system at the current moment, and determining the current relative position between the non-cooperative space target and the service satellite at the current moment based on the current state estimate; and determining the target relative position between the non-cooperative space target and the service satellite at the next moment based on the current relative position and the current satellite position.

[0161] In one exemplary embodiment of this disclosure, the state filter includes any one of an adaptive unscented Kalman filter, an adaptive extended Kalman filter, and an adaptive capacitive Kalman filter.

[0162] The specific details of each module in the aforementioned state estimation device for non-cooperative space targets have been described in detail in the corresponding state estimation method for non-cooperative space targets, so they will not be repeated here.

[0163] It should be noted that although several modules or units for the device used to perform actions have been mentioned in the detailed description above, this division is not mandatory. In fact, according to embodiments of this disclosure, the features and functions of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units.

[0164] Furthermore, although the steps of the method in this disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result. Additional or alternative steps may be omitted, multiple steps may be combined into one step, and / or a step may be broken down into multiple steps.

[0165] In an exemplary embodiment of this disclosure, an electronic device capable of implementing the above-described method is also provided.

[0166] Those skilled in the art will understand that various aspects of this disclosure can be implemented as a system, method, or program product. Therefore, various aspects of this disclosure can be specifically implemented in the following forms: a completely hardware implementation, a completely software implementation (including firmware, microcode, etc.), or a combination of hardware and software aspects, collectively referred to herein as a "circuit," "module," or "system."

[0167] The following reference Figure 8 To describe an electronic device 800 according to such an embodiment of the present disclosure. Figure 8 The electronic device 800 shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments disclosed herein.

[0168] like Figure 8 As shown, the electronic device 800 is manifested in the form of a general-purpose computing device. The components of the electronic device 800 may include, but are not limited to: at least one processing unit 810, at least one storage unit 820, a bus 830 connecting different system components (including storage unit 820 and processing unit 810), and a display unit 840.

[0169] The storage unit stores program code that can be executed by the processing unit 810, causing the processing unit 810 to perform the steps described in the "Exemplary Methods" section of this specification according to various exemplary embodiments of this disclosure. For example, the processing unit 810 can perform actions such as... Figure 1Step S110: Establish the state space equation of the non-cooperative space target and the observation equation of the serving satellite for the non-cooperative space target, and create a state filter based on the state space equation and the observation equation; Step S120: Determine the current state estimate and the current covariance estimate of the non-cooperative space target at the current moment based on the state filter, and input the current state estimate into the interference force prediction model to obtain the current interference force prediction value of the non-cooperative space target at the current moment; Step S130: Determine the average observation value of the non-cooperative space target at the next moment corresponding to the current moment based on the current state estimate and the current covariance estimate, and determine the predicted state estimate and the predicted covariance estimate of the non-cooperative space target at the next moment based on the current interference force prediction value; Step S140: Determine the target state estimate of the non-cooperative space target at the next moment based on the average observation value, the predicted state estimate, and the predicted covariance estimate, and estimate the motion state of the non-cooperative space target at the next moment based on the target state estimate.

[0170] Storage unit 820 may include a readable medium in the form of a volatile storage unit, such as random access memory (RAM) 8201 and / or cache memory 8202, and may further include a read-only memory (ROM) 8203.

[0171] The storage unit 820 may also include a program / utility 8204 having a set (at least one) of program modules 8205, including but not limited to: an operating system, one or more application programs, other program modules, and program data, each or some combination of these examples may include an implementation of a network environment.

[0172] Bus 830 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the various bus structures.

[0173] Electronic device 800 can also communicate with one or more external devices 900 (e.g., keyboard, pointing device, Bluetooth device, etc.), and with one or more devices that enable a user to interact with electronic device 800, and / or with any device that enables electronic device 800 to communicate with one or more other computing devices (e.g., router, modem, etc.). This communication can be performed via input / output (I / O) interface 850. Furthermore, electronic device 800 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 860. As shown, network adapter 860 communicates with other modules of electronic device 800 via bus 830. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 800, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0174] From the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, terminal device, or network device, etc.) to execute the methods according to the embodiments of this disclosure.

[0175] In exemplary embodiments of this disclosure, a computer-readable storage medium is also provided, on which a program product capable of implementing the methods described above is stored. In some possible implementations, various aspects of this disclosure may also be implemented as a program product including program code that, when the program product is run on a terminal device, causes the terminal device to perform the steps of the various exemplary embodiments of this disclosure described in the "Exemplary Methods" section above.

[0176] The program product for implementing the above-described method according to embodiments of the present disclosure may employ a portable compact disc read-only memory (CD-ROM) and include program code, and may run on a terminal device, such as a personal computer. However, the program product of the present disclosure is not limited thereto. In this document, the readable storage medium may be any tangible medium containing or storing a program that may be used by or in conjunction with an instruction execution system, apparatus, or device.

[0177] The program product may employ any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0178] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable signal medium may also be any readable medium other than a readable storage medium, capable of sending, propagating, or transmitting programs for use by or in conjunction with an instruction execution system, apparatus, or device.

[0179] The program code contained on the readable medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0180] Program code for performing the operations of this disclosure can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0181] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of this disclosure and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0182] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention described herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not invented by this disclosure. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the claims.

Claims

1. A method for estimating the motion state of a non-cooperative target in space, characterized in that, include: Establish the state space equations for the non-cooperative space target and the observation equations for the non-cooperative space target by the serving satellite, and create a state filter based on the state space equations and the observation equations; The current state estimate and current covariance estimate of the non-cooperative space target at the current moment are determined based on the state filter, and the current state estimate is input into the interference force prediction model to obtain the current interference force prediction value of the non-cooperative space target at the current moment. Based on the current state estimate and the current covariance estimate, the average observation value of the non-cooperative space target at the next time corresponding to the current time is determined, and based on the current disturbance force prediction value, the predicted state estimate and the predicted covariance estimate of the non-cooperative space target at the next time are determined. Based on the average observed value, the predicted state estimate, and the predicted covariance estimate, the target state estimate of the non-cooperative space target at the next time step is determined, and the motion state of the non-cooperative space target at the next time step is estimated based on the target state estimate.

2. The method for estimating the motion state of a non-cooperative target in space according to claim 1, characterized in that, The interference force prediction model was obtained in the following way: The first historical state estimate, the first historical covariance estimate, and the first historical residual value of the non-cooperative spatial target at time k-1 are determined based on the state filter. The first historical residual value is subjected to amplitude limiting and recursive averaging filtering to obtain the first deviation filter value; wherein, the timestamp of the median value of the average filtering queue is denoted as M; Read the second historical state estimate corresponding to the timestamp M from the state filter, and input the second historical state estimate into the neural network model to be trained to obtain the deviation prediction result; The parameters in the neural network model to be trained are adjusted based on the first deviation filter value and the deviation prediction result to obtain the interference force prediction model.

3. The method for estimating the motion state of a non-cooperative target in space according to claim 2, characterized in that, The second historical state estimate is input into the neural network model to be trained to obtain the bias prediction result, including: Multiple different samples are randomly selected from the second historical state estimate as initial cluster centers, and training samples are randomly selected from the second historical state estimate as input samples. Based on the input sample and the initial cluster centers, determine the sample category to which the input sample belongs, and update the initial cluster centers based on the sample category; The updated cluster centers are updated again based on the neural network model to be trained, and it is determined whether the change in the updated cluster centers is less than or equal to a preset threshold. If the change in the updated cluster centers is less than or equal to a preset threshold, then the deviation prediction result is obtained based on the updated cluster centers.

4. The method for estimating the motion state of a non-cooperative target in space according to claim 2, characterized in that, The parameters in the neural network model to be trained are adjusted based on the first deviation filter value and the deviation prediction result to obtain the interference force prediction model, including: The standard deviation between the first bias filter value and the bias prediction result is calculated based on the Gaussian function in the neural network model to be trained, and the parameters in the neural network model to be trained are adjusted based on the standard deviation to obtain the interference force prediction model.

5. The method for estimating the motion state of a non-cooperative target in space according to claim 1, characterized in that, Based on the current state estimate and the current covariance estimate, determine the average observation value of the non-cooperative space target at the next time step corresponding to the current time step, including: A tasteless transformation is performed on the current state estimate and the current covariance estimate to obtain the current sampling point. Based on the current sampling point and the observation equation, the average observation value of the non-cooperative target at the next time step is determined.

6. The method for estimating the motion state of a non-cooperative target in space according to claim 5, characterized in that, Based on the current predicted disturbance force value, determine the predicted state estimate and predicted covariance estimate of the non-cooperative space target at the next time step, including: Based on the current predicted interference force value and the current sampling point, determine the predicted state estimate of the non-cooperative space target at the next moment; Based on the current sampling point and the predicted state estimate, the covariance estimate of the non-cooperative spatial target at the next time step is determined.

7. The method for estimating the motion state of a non-cooperative target in space according to claim 1, characterized in that, Based on the average observed value, the predicted state estimate, and the predicted covariance estimate, the target state estimate of the non-cooperative space target at the next time step is determined, including: The information covariance and cross covariance of the non-cooperative space target are determined based on the average observations, and the gain matrix of the non-cooperative space target is determined based on the information covariance and cross covariance. Based on the predicted state estimate and the gain matrix, the target state estimate of the non-cooperative space target at the next time step is determined.

8. The method for estimating the motion state of a non-cooperative target in space according to claim 7, characterized in that, Based on the predicted state estimate and the gain matrix, the target state estimate of the non-cooperative target in space is determined at the next time step, including: Determine the target relative position between the non-cooperative space target and the service satellite at the next time step, and based on the predicted state estimate, gain matrix, and target relative position, determine the target state estimate of the non-cooperative space target at the next time step.

9. The method for estimating the motion state of a non-cooperative target in space according to claim 8, characterized in that, Determining the relative position of the non-cooperative space target with the serving satellite at the next moment includes: Determine the current satellite position of the service satellite in the orbital coordinate system at the current moment, and determine the current relative position of the non-cooperative space target with respect to the service satellite at the current moment based on the current state estimate; Based on the current relative position and the current satellite position, determine the target relative position between the non-cooperative space target and the service satellite at the next moment.

10. The method for estimating the motion state of a non-cooperative target in space according to claim 1, characterized in that, The state filter includes any one of the following: an adaptive unscented Kalman filter, an adaptive extended Kalman filter, and an adaptive capacitive Kalman filter.

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