Passive positioning error prediction method and device based on radial basis function neural network
Patent Information
- Application Number
- CN202510933937.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-07
- Publication Date
- 2025-10-28
Smart Images
Figure CN120847718A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the fields of wireless positioning and machine learning, and in particular to a passive positioning error prediction method, device, computer equipment, and storage medium based on radial basis function neural networks. Background Technology
[0002] With the rapid development of wireless communication and intelligent sensing technologies, passive positioning technology has been widely applied in many fields such as vehicle positioning, target tracking, and indoor navigation. Passive positioning systems generally rely on the cooperation of multiple base stations, utilizing the signals emitted by the target itself, and combining parameters such as the time difference of arrival (TDOA) to achieve accurate estimation of the target's position.
[0003] In practical engineering applications, evaluating the performance of passive positioning systems, especially accurately predicting positioning errors, is a crucial step in system design and optimization. Currently, commonly used error prediction methods are mainly divided into two categories.
[0004] One type is theoretical analysis methods, such as the Cramér-Rao Lower Bound (CRLB). In the field of wireless positioning, CRLB is an important tool for performance analysis, used to evaluate the theoretical performance limits of location estimation methods. It gives the minimum lower bound of the variance of arbitrary parameter estimators under unbiased estimation conditions, reflecting the optimal positioning accuracy achievable by the system under ideal conditions, and can serve as a reference benchmark for measuring the performance limits of positioning algorithms or system structures. However, it should be noted that CRLB reflects the theoretical lower bound under ideal unbiased estimation, while real-world systems have many factors such as sampling rate, synchronization error, and non-Gaussian noise, which often makes the actual error higher than CRLB, and therefore it cannot fully represent the actual positioning accuracy.
[0005] Another type is the experimental / simulation method, such as Monte Carlo simulation. This method uses extensive random sampling and simulation to statistically analyze the error distribution of the actual positioning algorithm under different random noise levels. While the results are relatively reliable and the operation is relatively simple, it has significant drawbacks. It requires a sufficiently large number of simulations to ensure reliable and accurate results. In practice, when the number of simulations is small, the positioning error fluctuates significantly; only when the number of simulations reaches a high level does the result show a smooth curve. This leads to high computational cost and long processing time. Moreover, any change in parameters or conditions requires a re-simulation, further increasing the computational burden. Summary of the Invention
[0006] Therefore, it is necessary to provide a passive positioning error prediction method, apparatus, computer device, and storage medium based on radial basis function neural networks to address the above-mentioned technical problems and solve at least one of the problems in the prior art.
[0007] Firstly, a passive positioning error prediction method based on radial basis function neural networks is provided, including:
[0008] The key parameters of the passive radar system are obtained, and based on the key parameters, the radiation source signal and the received signal are simulated and generated.
[0009] Determine the time difference of arrival of the received signal at different receiving nodes;
[0010] Based on the time difference of arrival, the estimated location of the radiation source is determined;
[0011] Based on the estimated location of the radiation source and the actual location of the radiation source, a positioning error is generated, and the positioning error is used as a training label.
[0012] A training dataset is constructed based on the key parameters and the training labels, and the passive positioning error prediction model is iteratively updated based on the training dataset. The passive positioning error prediction model uses a Gaussian radial basis function neural network to perform nonlinear feature mapping on the input key parameters.
[0013] In one possible implementation, determining the time difference of arrival of the received signal to different receiving nodes includes:
[0014] Determine the cross-correlation function between the received signals from different receiving nodes;
[0015] The peak position of the cross-correlation function is detected, and the time offset corresponding to the peak position is used as the arrival time difference.
[0016] In one possible implementation, determining the estimated location of the radiation source based on the time difference of arrival includes:
[0017] Based on the arrival time difference, a constrained optimization objective function is constructed with the radiation source location as the unknown quantity.
[0018] Based on the location information of each receiving node, the constrained optimization objective function is solved to obtain the estimated location of the radiation source.
[0019] In one possible implementation, generating a positioning error based on the estimated location of the radiation source and the actual location of the radiation source includes:
[0020] Based on a predetermined number of Monte Carlo experiments, the estimated locations of multiple radiation sources were obtained;
[0021] Based on the estimated location of the radiation source and its actual location, the positioning error is calculated using the root mean square error function.
[0022] In one possible implementation, the passive positioning error prediction model includes an input layer, a hidden layer, and an output layer. The input layer is used to input input features into the hidden layer. The hidden layer uses a Gaussian radial basis function to perform nonlinear feature mapping on the input features to generate a nonlinear feature vector. The output layer is used to perform a weighted linear combination of the nonlinear feature vector to obtain the positioning error.
[0023] In one possible implementation, the iterative update of the passive positioning error prediction model based on the training dataset includes:
[0024] Initialize model parameters, including the center vector and width parameter of the hidden layer, wherein the center vector is initialized from the training dataset using a preset clustering algorithm;
[0025] Initial training data is randomly selected from the training dataset, preprocessed, and then input into the input layer.
[0026] The input data is fed into the hidden layer through the input layer, and the training data is nonlinearly mapped using the Gaussian radial basis function to obtain a nonlinear feature vector.
[0027] The output layer is used to perform a weighted linear combination of the nonlinear feature vectors to obtain the positioning error;
[0028] The loss value is calculated based on the positioning error, training labels, and a preset loss function;
[0029] The model parameters of the passive positioning error prediction model are updated based on the loss value, and the next iteration is performed based on the updated passive positioning error prediction model until the preset convergence condition is met.
[0030] In one possible implementation, the step of simulating and generating the radiation source signal and the received signal based on the key parameters includes:
[0031] Construct a multi-node signal receiving model;
[0032] Based on the multi-node receiving signal model, the low-frequency baseband signal is modulated to generate an analog signal that is easy to transmit in the analog channel and has a frequency range greater than the preset frequency range.
[0033] The analog signal is transmitted through the channel to the receiving end for demodulation to obtain the received signal.
[0034] Secondly, a passive positioning error prediction device based on a radial basis function neural network is provided, comprising:
[0035] The signal simulation unit is used to acquire key parameters of the passive radar system and, based on the key parameters, simulate and generate radiation source signals and received signals.
[0036] The arrival time difference determination unit is used to determine the arrival time difference of the received signal to different receiving nodes;
[0037] A radiation source estimation location determination unit is used to determine the estimated location of the radiation source based on the arrival time difference;
[0038] The training label generation unit is used to generate a positioning error based on the estimated location of the radiation source and the actual location of the radiation source, and to use the positioning error as a training label.
[0039] The model training unit is used to construct a training dataset based on the key parameters and the training labels, and to iteratively update the passive positioning error prediction model based on the training dataset. The passive positioning error prediction model uses a Gaussian radial basis function neural network to perform nonlinear feature mapping on the input key parameters.
[0040] Thirdly, a computer device is provided, including a memory, a processor, and computer-readable instructions stored in the memory and executable on the processor, wherein the processor, when executing the computer-readable instructions, implements the steps of the passive positioning error prediction method based on radial basis function neural network as described above.
[0041] Fourthly, a readable storage medium is provided, which stores computer-readable instructions that, when executed by a processor, implement the steps of the passive positioning error prediction method based on radial basis function neural networks as described above.
[0042] The aforementioned passive positioning error prediction method, apparatus, computer device, and storage medium based on radial basis function neural networks are implemented as follows: The method includes: acquiring key parameters of a passive radar system, and simulating and generating a radiation source signal and a received signal based on the key parameters; determining the arrival time difference of the received signal at different receiving nodes; determining the estimated location of the radiation source based on the arrival time difference; generating a positioning error based on the estimated location of the radiation source and the actual location of the radiation source, and using the positioning error as a training label; constructing a training dataset based on the key parameters and the training label, and iteratively updating the passive positioning error prediction model based on the training dataset. The passive positioning error prediction model employs a Gaussian radial basis function neural network to perform nonlinear feature mapping on the input key parameters. In this embodiment, by comparing the TDOA calculation with the actual position, the error is accurately fed back and the source of the scene error is clearly traced. The Gaussian radial basis function (RBF) is introduced to adapt to the nonlinear coupling of multiple factors and break through the bottleneck of traditional linear modeling. The iterative update mechanism allows the model to evolve dynamically with the data, which not only accurately describes the error law of complex scenes, but also reduces the high computational cost and long time consumption of Monte Carlo simulation. It also makes up for the difference between the Cramer-Rao lower bound (CRLB) theory and the actual error, and provides high-precision and high-efficiency error prediction support for the design and optimization of passive positioning systems. Attached Figure Description
[0043] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments of the present application. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.
[0044] Figure 1 This is a flowchart illustrating a passive positioning error prediction method based on a radial basis function neural network in one embodiment of this application;
[0045] Figure 2 This is a schematic diagram of a digital communication system model in one embodiment of this application;
[0046] Figure 3 This is a schematic diagram of an experimental result in one embodiment of this application;
[0047] Figure 4 This is a schematic diagram of a passive positioning error prediction device based on a radial basis function neural network in one embodiment of this application;
[0048] Figure 5 This is a schematic diagram of a computer device according to one embodiment of this application. Detailed Implementation
[0049] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.
[0050] In one embodiment, such as Figure 1 As shown, a passive positioning error prediction method based on radial basis function neural network is provided, including the following steps:
[0051] In step S110, key parameters of the passive radar system are obtained, and based on the key parameters, radiation source signals and received signals are simulated and generated.
[0052] Passive radar systems are widely used in scenarios such as autonomous driving, drone navigation, target tracking, and indoor positioning. Their core task is to accurately calculate the spatial position of the target by receiving signals radiated by the target itself (such as communication equipment, radar transmitters, etc.) and combining the cooperation of multiple base stations.
[0053] Specifically, key parameters of the passive radar system are dynamically initialized based on target type and application scenario. These key parameters may include power, observation time, baud rate, and target position coordinates. Dynamic parameter initialization ensures the diversity and realism of the simulated data, providing high-quality input features and error training labels for subsequent model training.
[0054] Optionally, the simulation of the radiation source signal includes baseband signal generation, shaping filtering, and the implementation of various modulation methods (such as binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), 8PSK, 16 quadrature amplitude modulation (16QAM), etc.). The baseband signal is optimized for spectral characteristics through specific filters and then modulated to form a high-frequency signal, thereby simulating the real communication signal environment. The introduction of different modulation methods can reflect the complex and varied signal characteristics in the actual scenario, enabling the model to learn a wider range of signal characteristics during training, thereby improving generalization ability and adaptability. Channel modeling adopts a far-field, fast-fading wireless channel model. Gaussian white noise following a complex Gaussian distribution is superimposed, and then the amplitude fading (Rayleigh distribution) and phase fluctuations of the signal are simulated through a far-field fast-fading channel model to generate the received signal.
[0055] In step S120, the arrival time difference of the received signal to different receiving nodes is determined;
[0056] Among them, the time difference of arrival (TDOA) is the core parameter of passive radar positioning. Its physical meaning is the time difference between the arrival of a signal from the target to different receiving nodes. The corresponding distance difference is the speed of light × TDOA, which refers to the time difference between the arrival of the same signal from the target to different receiving nodes after radiation or reflection.
[0057] Optionally, the cross-correlation function between the received signals of different receiving nodes can be calculated when the received signal arrives at different receiving nodes. Then, the peak value of the cross-correlation function is detected. For example, when the received signal of receiving node A is shifted along the time axis to be completely aligned with the target waveform in the received signal of receiving node B, the cross-correlation function will have a peak value. The time offset corresponding to the peak value is used as the delay.
[0058] In step S130, the estimated location of the radiation source is determined based on the time difference of arrival;
[0059] Optionally, determining the estimated location of the radiation source based on the time difference of arrival utilizes the time difference in signal arrival at different receiving nodes during spatial propagation. This time difference is converted into a distance difference by combining the speed of light. In a two-dimensional scene, according to the hyperbolic positioning principle, the radiation source location lies on a hyperbola with the two receiving nodes as foci. In a three-dimensional scene, the radiation source location is constrained to a cluster of hyperbolas with each receiving node as a foci and the distance difference as a parameter. The Chan algorithm is used to solve this by constructing a system of hyperbolic equations containing multiple receiving nodes. It should be noted that the Chan algorithm can use a double-weighted least squares method to solve for the target location. The first weighted least squares (WLS) linearizes the nonlinear TDOA equations to obtain an initial estimate of the location. The second weighted least squares constructs a weighting matrix using the initial estimate and solves for the optimal unbiased estimate. This method can provide a non-recursive analytical solution while linearizing the nonlinear equations. Compared to iterative algorithms such as the Newton-Raphson algorithm, the Chan algorithm does not require initial value assumptions and is suitable for scenarios without prior location information.
[0060] In step S140, a positioning error is generated based on the estimated location of the radiation source and the actual location of the radiation source, and the positioning error is used as a training label.
[0061] Optionally, 500 sets of estimated radiation source locations can be obtained through 500 Monte Carlo experiments (each time the target location, noise parameters and channel conditions are randomly generated). Then, the location error (RMSE) is used to calculate the location error between the estimated location and the true location, and it is used as a training label in the subsequent training process of the passive location error prediction model.
[0062] In step S150, a training dataset is constructed based on the key parameters and the training labels, and the passive positioning error prediction model is iteratively updated based on the training dataset. The passive positioning error prediction model uses a Gaussian radial basis function neural network to perform nonlinear feature mapping on the input key parameters.
[0063] Optionally, the passive positioning error prediction model employs an RBF neural network, whose topology includes an input layer, a hidden layer, and an output layer. The input layer is used to input input features into the hidden layer, and the hidden layer uses a Gaussian radial basis function to perform nonlinear feature mapping on the input features to generate a nonlinear feature vector. The output layer is used to perform a weighted linear combination of the nonlinear feature vector to obtain the positioning error.
[0064] Specifically, training data can be randomly selected from the training dataset. This training data is a multi-dimensional feature vector, which may include power, observation time, baud rate, and target position coordinates. This vector is input to the input layer, which receives the input vector but does not perform weighting or nonlinear processing. Its main function is to pass the feature data to the hidden layer. This hidden layer uses a Gaussian Radial Basis Function (RBF) to achieve nonlinear feature mapping, mapping the low-dimensional input to a high-dimensional latent space. This allows the output layer to output results through linear combination, simplifying training. The output layer then performs a weighted linear combination of the nonlinear feature vectors output by the hidden layer to obtain the localization error. Based on this localization error, training labels and a preset loss function are used to calculate the loss value for this iteration. The model parameters are updated based on this loss value, and the next iteration is performed based on the updated passive localization error prediction model until a preset convergence condition is met, resulting in a trained passive error prediction model for subsequent predictions.
[0065] To enhance the training stability and generalization ability of the model, the input features can be normalized using MinMaxScaler to scale them to a uniform numerical range [0,1] before being input into the input layer.
[0066] It should be noted that in each iteration, a batch from the training dataset can be input into the model. The model output is calculated through forward propagation, and the current prediction error is then calculated based on the loss function. Subsequently, the gradient is calculated through backpropagation, and the model parameters are updated using the Adam optimizer. The training loss for each round is recorded during training to facilitate subsequent analysis of the model's convergence and performance.
[0067] The validation process is performed after each training round to evaluate the model's performance on the validation set. The validation set is input into the model, and the validation error is calculated to determine the model's generalization ability. To ensure optimal model performance, a grid search is used to optimize hyperparameters (such as the number of RBF centers, learning rate, and number of training rounds). Specifically, all possible parameter combinations are traversed, the model is trained for each combination, and the error on the validation set is recorded. The parameter combination with the smallest validation error is selected as the final model's hyperparameters.
[0068] After hyperparameter tuning, the model is jointly trained on both the training and validation sets with optimal hyperparameters, and then subjected to a final test. The test set independently evaluates the model's true performance after training. Model parameters and loss curves are saved after training to provide a basis for subsequent deployment and performance analysis.
[0069] Furthermore, after training, the model can be input with any combination of parameters in real time and output the corresponding predicted positioning error value. Compared with traditional CRLB or Monte Carlo simulation methods, the real-time prediction capability of the RBF neural network reduces computational costs and accurately captures the relationship between key features and errors through nonlinear modeling. This efficient and accurate error prediction method not only improves the performance evaluation efficiency of passive radar systems but also provides important support for system optimization.
[0070] This application provides a passive positioning error prediction method based on a radial basis function neural network, comprising: acquiring key parameters of a passive radar system, and simulating and generating a radiation source signal and a received signal based on the key parameters; determining the arrival time difference of the received signal to different receiving nodes; determining the estimated position of the radiation source based on the arrival time difference; generating a positioning error based on the estimated position of the radiation source and the actual position of the radiation source, and using the positioning error as a training label; constructing a training dataset based on the key parameters and the training label, and iteratively updating the passive positioning error prediction model based on the training dataset, wherein the passive positioning error prediction model employs a Gaussian radial basis function neural network to perform nonlinear feature mapping on the input key parameters. In this embodiment, by comparing the TDOA calculation with the actual position, the error is accurately fed back and the source of the scene error is clearly traced. The Gaussian radial basis function (RBF) is introduced to adapt to the nonlinear coupling of multiple factors and break through the bottleneck of traditional linear modeling. The iterative update mechanism allows the model to evolve dynamically with the data, which not only accurately describes the error law of complex scenes, but also reduces the high computational cost and long time consumption of Monte Carlo simulation. It also makes up for the difference between the Cramer-Rao lower bound (CRLB) theory and the actual error, and provides high-precision and high-efficiency error prediction support for the design and optimization of passive positioning systems.
[0071] In one embodiment of this application, the step of simulating and generating radiation source signals and received signals based on the key parameters includes:
[0072] Construct a multi-node signal receiving model;
[0073] Based on the multi-node receiving signal model, the low-frequency baseband signal is modulated to generate an analog signal that is easy to transmit in the analog channel and has a frequency range greater than the preset frequency range.
[0074] The analog signal is transmitted through the channel to the receiving end for demodulation to obtain the received signal.
[0075] Optionally, the simulation of the radiation source signal includes baseband signal generation, shaping filtering, and the implementation of various modulation methods (such as BPSK, QPSK, 8PSK, 16QAM, etc.). The baseband signal is optimized for spectral characteristics through specific filters and then modulated to form a high-frequency signal, thereby simulating the real communication signal environment. The introduction of different modulation methods can reflect the complex and varied signal characteristics in real-world scenarios, enabling the model to learn a wider range of signal characteristics during training, thus improving its generalization ability and adaptability. Specifically:
[0076] Digital communication system model such as Figure 2 As shown, the low-frequency baseband signal is first modulated to generate an analog signal (called a frequency band signal) that is easy to transmit in an analog channel, and then this frequency band signal is transmitted in the analog channel.
[0077] The baseband signal is modulated at the transmitter, shifted to a higher frequency, and transmitted through a channel to the receiver for demodulation. Let the baseband signal under ideal channel conditions be x(t). The difference between the baseband signal before modulation and after demodulation lies in the influence of the channel on the signal. After up-conversion, the baseband signal becomes:
[0078]
[0079] Where x(t) represents the complex baseband signal, f c Indicates the carrier frequency. Re represents the initial phase of the carrier wave, and Re represents the real part extraction operation. This represents a radio frequency carrier in complex exponential form. This represents the complex phase factor.
[0080] Therefore, it is ordered It can also be represented as x LP (t)=x I (t)+jx Q (t), decomposes the complex baseband signal into in-phase (I) and quadrature (Q) components, where
[0081]
[0082] Where, x LP To represent a complete complex baseband signal, x I (t) represents the in-phase (I) component of the complex baseband signal, x Q (t) represents the quadrature (Q) component of the complex baseband signal. The complex baseband signal up-converted to an RF signal via quadrature modulation (IQ modulation) can be expressed as:
[0083]
[0084] Where j represents the phase relationship of the signal, x LP Representing a complete complex baseband signal, x I (t) represents the in-phase (I) component of the complex baseband signal, x Q (t) represents the quadrature (Q) component of the complex baseband signal, x(t) represents the complex baseband signal, and f c Indicates the carrier frequency. This represents a radio frequency carrier in complex exponential form.
[0085] The receiving end demodulates the I and Q signals of the baseband signal through the I and Q channels respectively. When transmitting the baseband signal in a non-ideal channel, μ(t) describes the multiplicative noise of the channel, and n(t) describes the additive noise. The received equivalent complex signal (i.e., the baseband equivalent signal) y LP It can be represented as:
[0086] y LP (t)=μ(t)x LP (t)+n(t);
[0087] The received signal is superimposed with Gaussian white noise, which follows a complex Gaussian distribution. A far-field, fast-fading channel model is used to reproduce the real wireless signal propagation environment. Channel modeling employs a far-field, fast-fading wireless channel model. In a simplified scenario, assuming that the transmitter and receiver are each equipped with only one antenna and are relatively stationary, the channel model from the transmitter to the i-th receiver can be represented as a. i =b i e jφ The received signals of each sensing node are as follows:
[0088] y i (·t )·=a i g(·t-τ i )·+n i (·t·)·,i=1,…·,N,
[0089] Among them, a i Let g(t) represent the complex channel gain from the signal source to the i-th receiving station, g(t) represent the transmitted signal from the radiating source at time t, D represent the signal delay from the radiating source to the i-th receiving station, and τ represent the signal delay.i n represents the signal delay from the radiation source to the i-th receiving station. i (t) represents the noise of the i-th receiving station, which follows a zero-mean complex Gaussian distribution.
[0090] In one embodiment of this application, determining the arrival time difference of the received signal to different receiving nodes includes:
[0091] Determine the cross-correlation function between the received signals from different receiving nodes;
[0092] The peak position of the cross-correlation function is detected, and the time offset corresponding to the peak position is used as the arrival time difference.
[0093] Optionally, the received signal can be processed by a cross-correlation algorithm to calculate the time difference of arrival (TDOA) of the signal at different receiving nodes. By calculating the cross-correlation function between the received signals at different receiving nodes when the received signal arrives at different receiving nodes, and then detecting the peak value of the cross-correlation function, the time offset corresponding to the peak value is used as the delay.
[0094] For example, assuming the signals received by the two receivers are y1(t) and y2(t), the signal models of the two receivers can be obtained, simplified as follows:
[0095] y1(t) = g(t) + n1(t);
[0096] y2(t) = Ag(tD) + n2(t);
[0097] Where g(t) represents the original signal waveform emitted by the radiation source, D represents the delay corresponding to the time difference between the arrival of the signal at the two receivers, A represents the signal amplitude attenuation factor, n1(t) and n2(t) represent the noise signals of the two receivers, and t represents the time variable.
[0098] Discretizing the above equation, let t = kT, where T is the sampling period of the signal, satisfying the Nyquist sampling theorem. Then the cross-correlation function of signals y1(k) and y2(k) is:
[0099]
[0100] Where R(τ) represents the cross-correlation function, k represents the discrete-time index, E represents the expectation operation, τ represents the discrete-time offset, and g * (k) represents the original signal of the radiation source after discretization, R gg (τ-D) represents the target signal g * (k) its own autocorrelation function, Let yi represent the discrete observation signal of receiver 1, n1(k) represent the additive noise of receiver 1, y2(k+τ) represent the discrete observation signal of receiver 2, and n2(k+τ) represent the additive noise of receiver 2. Let Ri be the discrete observation signal of receiver 1, n1(k) represent the additive noise of receiver 2, gg Represents the target signal g * The autocorrelation function of (k), Represents the target signal g * (k) Cross-correlation with receiver 2 noise, This represents the cross-correlation between the noise of receiver 1 and the noise of receiver 2.
[0101] Since the noise is a random sequence with a mean of 0 and is independent of the signal, the above equation can be simplified to:
[0102] R(τ)=AR gg (τ-D);
[0103] When τ = D, R(τ) reaches its maximum value. Therefore, the estimated value of the time delay D can be obtained by detecting the point corresponding to the peak value. Specifically, it is expressed as follows:
[0104]
[0105] in, This represents the estimated value of the time delay D. Let rgmax represent the cross-correlation function of the received signals y1 and y2, and rgmax represent taking the maximum value. The efficiency and accuracy of this cross-correlation algorithm in this stage directly determine the quality of TDOA data and lay the foundation for subsequent calculation of positioning errors and model training.
[0106] In one embodiment of this application, determining the estimated location of the radiation source based on the time difference of arrival includes:
[0107] Based on the arrival time difference, a constrained optimization objective function is constructed with the radiation source location as the unknown quantity.
[0108] Based on the location information of each receiving node, the constrained optimization objective function is solved to obtain the estimated location of the radiation source.
[0109] Optionally, determining the estimated location of the radiation source based on the time difference of arrival utilizes the time difference in arrival times of the signal at different receiving nodes during its propagation in space. This time difference is converted into a distance difference by incorporating the speed of light. Based on the hyperbolic positioning principle, the location of the radiation source is constrained onto a family of hyperbolas with each receiving node as its focus and the distance difference as its parameter. This is achieved by constructing a system of hyperbolic equations containing multiple receiving nodes, i.e., a constrained optimization objective function, as detailed below:
[0110]
[0111] Where, ps =[x s ,y s ] T This is the actual location of the radiation source. This is the location of the receiving station. i Let c represent the distance from the radiation source to the i-th receiving station, and r represent the speed of light. i1 τ represents the distance difference between the radiation source and the reference receiving station relative to other receiving stations. i1 This represents the delay difference between the radiation source and the reference receiving station relative to other receiving stations.
[0112] To solve the above equations (which have high computational complexity due to their nonlinear characteristics), the Chan algorithm can be used. The Chan algorithm uses a double-weighted least squares method to solve for the target position, which can provide a non-recursive analytical solution while linearizing the nonlinear equations, thus avoiding dependence on the initial estimate.
[0113] In one embodiment of this application, generating a positioning error based on the estimated location of the radiation source and the actual location of the radiation source includes:
[0114] Based on a predetermined number of Monte Carlo experiments, the estimated locations of multiple radiation sources were obtained;
[0115] Based on the estimated location of the radiation source and its actual location, the positioning error is calculated using the root mean square error function.
[0116] Optionally, a Monte Carlo simulation can be introduced. By randomly sampling key parameters multiple times (e.g., assuming the radiation source location follows a uniform distribution within a certain area and the noise follows a Gaussian distribution), N different real-world scenarios (a preset number of simulations) can be simulated. In each random simulation, the estimated location of the radiation source can be calculated using the TDOA localization algorithm. For example, performing 500 Monte Carlo simulations will yield 500 estimated radiation source locations. Then, the root mean square error (RMSE) is used to calculate the root mean square localization error between the estimated and actual locations, as detailed below:
[0117]
[0118] Where, p s =[x s ,y s ] T This is the actual location of the radiation source. M represents the estimated location of the radiation source, and M is the Monte Carlo number.
[0119] In one embodiment of this application, the iterative update of the passive positioning error prediction model based on the training dataset includes:
[0120] Initialize model parameters, including the center vector and width parameter of the hidden layer, wherein the center vector is initialized from the training dataset using a preset clustering algorithm;
[0121] Initial training data is randomly selected from the training dataset, preprocessed, and then input into the input layer.
[0122] The input data is fed into the hidden layer through the input layer, and the training data is nonlinearly mapped using the Gaussian radial basis function to obtain a nonlinear feature vector.
[0123] The output layer is used to perform a weighted linear combination of the nonlinear feature vectors to obtain the positioning error;
[0124] The loss value is calculated based on the positioning error, training labels, and a preset loss function;
[0125] The model parameters of the passive positioning error prediction model are updated based on the loss value, and the next iteration is performed based on the updated passive positioning error prediction model until the preset convergence condition is met.
[0126] Optionally, the model parameters of the passive localization prediction model can be initialized first, including the center vector and width parameter of the hidden layers. The center vector is initialized from the training data using the KMeans clustering algorithm to ensure that its distribution in the input feature space is representative, and the width parameter is initially set to 1.0. Subsequently, the model begins training with the goal of minimizing the prediction error.
[0127] The training process is as follows: Training data is randomly selected from the training dataset, which may include power, observation time, baud rate, and target location coordinates. This data is then input as an input vector to the input layer. The input layer receives the input vector but does not perform weighting or nonlinear processing. Its main function is to pass the feature data to the hidden layer. This hidden layer uses a Gaussian Radial Basis Function (RBF) to achieve nonlinear feature mapping, mapping the low-dimensional input to a high-dimensional latent space. This allows the output layer to output the results through linear combination, simplifying the training process. See below for details:
[0128] For the input vector The response of the j-th hidden neuron is defined as:
[0129]
[0130] Among them, c j σ represents the center vector of the neuron; jThis corresponds to the width parameter (kernel function expansion radius). The center vector is initialized from the training data using the KMeans clustering algorithm to ensure its distribution in the feature space is representative; the width parameter is initially set to 1.0 and is optimized and adjusted during training to enhance the model's responsiveness to local changes in the input space.
[0131] The output layer can then perform a weighted linear combination of the nonlinear feature vectors output by the hidden layer to obtain the localization error, as shown below:
[0132]
[0133] Among them, w j These are the output layer weights, where b is the bias term, and the final output value is... This represents the model's prediction of the target variable (such as localization error). Through end-to-end training, this structure can effectively capture the complex nonlinear relationships between input features, improving the accuracy and robustness of error prediction.
[0134] Based on the positioning error, training labels, and a preset loss function, the loss value of this iteration is calculated. If the loss value is greater than the preset loss threshold, the above process is repeated for the next iteration until the preset convergence condition is met, such as the number of iterations reaching the preset number or the loss value being less than or equal to the preset loss threshold. The trained passive error prediction model is then obtained and used for subsequent predictions.
[0135] The preset loss function can be the absolute error loss function L1. The L1 loss function is more robust to outliers and can more accurately reflect the distribution characteristics of positioning errors.
[0136] To enhance the training stability and generalization ability of the model, the input features can be normalized using MinMaxScaler to scale them to a uniform numerical range [0,1] before being input into the input layer.
[0137] To further verify the technical effectiveness of this application, the following experiment was designed.
[0138] An experimental dataset was constructed, whose feature vector α includes the emitted power (W), observation duration (s), symbol rate (Baud), and the two-dimensional coordinates (x, y) of the radiation source. The data training labels were obtained from 500 Monte Carlo experiments, and their logarithm (log) was used to compress the error range and stabilize the training. The radiation source signals were modulated using binary phase-shift keying (BPSK). These modulated signals were generated using the MATLAB Communication Toolbox.
[0139] The passive positioning error prediction model consists of an input layer, hidden layers, and an output layer, aiming to nonlinearly model and predict positioning errors. The input layer receives feature vectors (including parameters such as power, observation time, baud rate, and target position). The hidden layer performs nonlinear mapping of features using a radial basis function (RBF) kernel function (such as a Gaussian kernel). The output layer is a linear layer used to generate predicted values for the positioning error. The center points of the hidden layers are extracted by clustering the input features of the training data using the K-Means algorithm. This method effectively avoids the instability of random initialization and utilizes the distribution information of the data, making the activation of the RBF kernel function more reflective of the actual distribution of the input features, thereby improving the model's stability and prediction accuracy. The width parameter is initialized to a constant to control the expansion range of the RBF kernel function, adapting it to different distributions of input features.
[0140] The model training uses the L1 loss function (mean absolute error) as the performance evaluation metric. L1 loss is more robust to outliers and more accurately reflects the distribution characteristics of localization errors. During optimization, the Adam optimizer is used to adaptively adjust the learning rate, ensuring rapid convergence of model parameters. To ensure optimal model performance, grid search is used to optimize hyperparameters (RBF centers of 100, learning rate of 0.005, training epochs of 2000, etc.). By traversing different parameter combinations and comparing model performance on the validation set, the parameter combination with the smallest validation error is selected for final training.
[0141] from Figure 3 As can be seen, with other parameters constant, changing the baud rate yields results similar to Monte Carlo simulations using the RBF network, with a mean absolute error of 0.014. Through this network architecture and optimization process, the model can accurately capture the nonlinear relationship between input features and positioning error, achieving efficient and accurate error prediction in various scenarios, while significantly reducing computational costs and improving the performance evaluation efficiency of passive radar systems.
[0142] In this embodiment, by comparing the TDOA calculation with the actual position, the error is accurately fed back and the source of the scene error is clearly traced. The Gaussian radial basis function (RBF) is introduced to adapt to the nonlinear coupling of multiple factors and break through the bottleneck of traditional linear modeling. The iterative update mechanism allows the model to evolve dynamically with the data, which not only accurately describes the error law of complex scenes, but also reduces the high computational cost and long time consumption of Monte Carlo simulation. It also makes up for the difference between the Cramer-Rao lower bound (CRLB) theory and the actual error, and provides high-precision and high-efficiency error prediction support for the design and optimization of passive positioning systems.
[0143] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.
[0144] In one embodiment, a passive positioning error prediction device based on a radial basis function neural network is provided, which corresponds one-to-one with the passive positioning error prediction method based on a radial basis function neural network in the above embodiments. For example... Figure 4 As shown, the passive positioning error prediction device based on radial basis function neural network includes a signal simulation unit 10, a time difference of arrival determination unit 20, a radiation source estimation and location determination unit 30, a training label generation unit 40, and a model training unit 50. Detailed descriptions of each functional module are as follows:
[0145] The signal simulation unit 10 is used to acquire key parameters of the passive radar system and, based on the key parameters, simulate and generate radiation source signals and received signals.
[0146] The arrival time difference determination unit 20 is used to determine the arrival time difference of the received signal to different receiving nodes;
[0147] Radiation source estimation location determination unit 30 is used to determine the estimated location of the radiation source based on the arrival time difference;
[0148] The training label generation unit 40 is used to generate a positioning error based on the estimated position of the radiation source and the actual position of the radiation source, and to use the positioning error as a training label.
[0149] The model training unit 50 is used to construct a training dataset based on the key parameters and the training labels, and to iteratively update the passive positioning error prediction model based on the training dataset. The passive positioning error prediction model uses a Gaussian radial basis function neural network to perform nonlinear feature mapping on the input key parameters.
[0150] In one embodiment of this application, the arrival time difference determination unit 20 is further configured to:
[0151] Determine the cross-correlation function between the received signals from different receiving nodes;
[0152] The peak position of the cross-correlation function is detected, and the time offset corresponding to the peak position is used as the arrival time difference.
[0153] In one embodiment of this application, the radiation source estimation location determination unit 30 is further configured to:
[0154] Based on the arrival time difference, a constrained optimization objective function is constructed with the radiation source location as the unknown quantity.
[0155] Based on the location information of each receiving node, the constrained optimization objective function is solved to obtain the estimated location of the radiation source.
[0156] In one embodiment of this application, the training label generation unit 40 is further configured to:
[0157] Based on a predetermined number of Monte Carlo experiments, the estimated locations of multiple radiation sources were obtained;
[0158] Based on the estimated location of the radiation source and its actual location, the positioning error is calculated using the root mean square error function.
[0159] In one embodiment of this application, the passive positioning error prediction model includes an input layer, a hidden layer, and an output layer. The input layer is used to input input features into the hidden layer. The hidden layer uses a Gaussian radial basis function to perform nonlinear feature mapping on the input features to generate a nonlinear feature vector. The output layer is used to perform a weighted linear combination of the nonlinear feature vector to obtain the positioning error.
[0160] In one embodiment of this application, the model training unit 50 is further configured to:
[0161] Initialize model parameters, including the center vector and width parameter of the hidden layer, wherein the center vector is initialized from the training dataset using a preset clustering algorithm;
[0162] Initial training data is randomly selected from the training dataset, preprocessed, and then input into the input layer.
[0163] The input data is fed into the hidden layer through the input layer, and the training data is nonlinearly mapped using the Gaussian radial basis function to obtain a nonlinear feature vector.
[0164] The output layer is used to perform a weighted linear combination of the nonlinear feature vectors to obtain the positioning error;
[0165] The loss value is calculated based on the positioning error, training labels, and a preset loss function;
[0166] The model parameters of the passive positioning error prediction model are updated based on the loss value, and the next iteration is performed based on the updated passive positioning error prediction model until the preset convergence condition is met.
[0167] In one embodiment of this application, the signal simulation unit 10 is further configured to:
[0168] Construct a multi-node signal receiving model;
[0169] Based on the multi-node receiving signal model, the low-frequency baseband signal is modulated to generate an analog signal that is easy to transmit in the analog channel and has a frequency range greater than the preset frequency range.
[0170] The analog signal is transmitted through the channel to the receiving end for demodulation to obtain the received signal.
[0171] In this embodiment, by comparing the TDOA calculation with the actual position, the error is accurately fed back and the source of the scene error is clearly traced. The Gaussian radial basis function (RBF) is introduced to adapt to the nonlinear coupling of multiple factors and break through the bottleneck of traditional linear modeling. The iterative update mechanism allows the model to evolve dynamically with the data, which not only accurately describes the error law of complex scenes, but also reduces the high computational cost and long time consumption of Monte Carlo simulation. It also makes up for the difference between the Cramer-Rao lower bound (CRLB) theory and the actual error, and provides high-precision and high-efficiency error prediction support for the design and optimization of passive positioning systems.
[0172] Specific limitations regarding the passive positioning error prediction device based on radial basis function neural networks can be found in the limitations of the passive positioning error prediction method based on radial basis function neural networks mentioned above, and will not be repeated here. Each module in the aforementioned passive positioning error prediction device based on radial basis function neural networks can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the corresponding operations of each module.
[0173] In one embodiment, a computer device is provided, which may be a terminal device, and its internal structure diagram may be as follows: Figure 5 As shown, the computer device includes a processor, memory, and network interface connected via a system bus. The processor provides computational and control capabilities. The memory includes a readable storage medium storing computer-readable instructions. The network interface communicates with external terminals via a network connection. When executed by the processor, the computer-readable instructions implement a passive positioning error prediction method based on a radial basis function neural network. The readable storage medium provided in this embodiment includes both non-volatile and volatile readable storage media.
[0174] In this application embodiment, a computer device is provided, including a memory, a processor, and computer-readable instructions stored in the memory and executable on the processor. When the processor executes the computer-readable instructions, it implements the steps of the passive positioning error prediction method based on radial basis function neural network described above.
[0175] In one embodiment of the application, a readable storage medium is provided, which stores computer-readable instructions. When the computer-readable instructions are executed by a processor, they implement the steps of the passive positioning error prediction method based on radial basis function neural network described above.
[0176] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by instructing related hardware with computer-readable instructions. These computer-readable instructions can be stored in a non-volatile readable storage medium or a volatile readable storage medium. When executed, these computer-readable instructions can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), Synchronous Link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.
[0177] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is used as an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above.
[0178] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.
Claims
1. A passive positioning error prediction method based on radial basis function neural networks, characterized in that, The method includes: The key parameters of the passive radar system are obtained, and based on the key parameters, the radiation source signal and the received signal are simulated and generated. Determine the time difference of arrival of the received signal at different receiving nodes; Based on the time difference of arrival, the estimated location of the radiation source is determined; Based on the estimated location of the radiation source and the actual location of the radiation source, a positioning error is generated, and the positioning error is used as a training label. A training dataset is constructed based on the key parameters and the training labels, and the passive positioning error prediction model is iteratively updated based on the training dataset. The passive positioning error prediction model uses a Gaussian radial basis function neural network to perform nonlinear feature mapping on the input key parameters.
2. The passive positioning error prediction method based on radial basis function neural network as described in claim 1, characterized in that, Determining the arrival time difference of the received signal to different receiving nodes includes: Determine the cross-correlation function between the received signals from different receiving nodes; The peak position of the cross-correlation function is detected, and the time offset corresponding to the peak position is used as the arrival time difference.
3. The passive positioning error prediction method based on radial basis function neural network as described in claim 1, characterized in that, Determining the estimated location of the radiation source based on the time difference of arrival includes: Based on the arrival time difference, a constrained optimization objective function is constructed with the radiation source location as the unknown quantity. Based on the location information of each receiving node, the constrained optimization objective function is solved to obtain the estimated location of the radiation source.
4. The passive positioning error prediction method based on radial basis function neural network as described in claim 1, characterized in that, The step of generating a positioning error based on the estimated location of the radiation source and the actual location of the radiation source includes: Based on a predetermined number of Monte Carlo experiments, the estimated locations of multiple radiation sources were obtained; Based on the estimated location of the radiation source and its actual location, the positioning error is calculated using the root mean square error function.
5. The passive positioning error prediction method based on radial basis function neural network as described in claim 1, characterized in that, The passive positioning error prediction model includes an input layer, a hidden layer, and an output layer. The input layer is used to input input features into the hidden layer. The hidden layer uses a Gaussian radial basis function to perform nonlinear feature mapping on the input features to generate a nonlinear feature vector. The output layer is used to perform a weighted linear combination of the nonlinear feature vector to obtain the positioning error.
6. The passive positioning error prediction method based on radial basis function neural network as described in claim 5, characterized in that, The iterative update of the passive positioning error prediction model based on the training dataset includes: Initialize model parameters, including the center vector and width parameter of the hidden layer, wherein the center vector is initialized from the training dataset using a preset clustering algorithm; Initial training data is randomly selected from the training dataset, preprocessed, and then input into the input layer. The input data is fed into the hidden layer through the input layer, and the training data is nonlinearly mapped using the Gaussian radial basis function to obtain a nonlinear feature vector. The output layer is used to perform a weighted linear combination of the nonlinear feature vectors to obtain the positioning error; The loss value is calculated based on the positioning error, training labels, and a preset loss function; The model parameters of the passive positioning error prediction model are updated based on the loss value, and the next iteration is performed based on the updated passive positioning error prediction model until the preset convergence condition is met.
7. The passive positioning error prediction method based on radial basis function neural network as described in any one of claims 1-6, characterized in that, The process of simulating and generating radiation source signals and received signals based on the aforementioned key parameters includes: Construct a multi-node signal receiving model; Based on the multi-node receiving signal model, the low-frequency baseband signal is modulated to generate an analog signal that is easy to transmit in the analog channel and has a frequency range greater than the preset frequency range. The analog signal is transmitted through the channel to the receiving end for demodulation to obtain the received signal.
8. A passive positioning error prediction device based on a radial basis function neural network, characterized in that, The device includes: The signal simulation unit is used to acquire key parameters of the passive radar system and, based on the key parameters, simulate and generate radiation source signals and received signals. The arrival time difference determination unit is used to determine the arrival time difference of the received signal to different receiving nodes; A radiation source estimation location determination unit is used to determine the estimated location of the radiation source based on the arrival time difference; The training label generation unit is used to generate a positioning error based on the estimated location of the radiation source and the actual location of the radiation source, and to use the positioning error as a training label. The model training unit is used to construct a training dataset based on the key parameters and the training labels, and to iteratively update the passive positioning error prediction model based on the training dataset. The passive positioning error prediction model uses a Gaussian radial basis function neural network to perform nonlinear feature mapping on the input key parameters.
9. A computer device comprising a memory, a processor, and computer-readable instructions stored in the memory and executable on the processor, characterized in that, When the processor executes the computer-readable instructions, it implements the steps of the passive positioning error prediction method based on radial basis function neural network as described in any one of claims 1 to 7.
10. A readable storage medium storing computer-readable instructions, characterized in that, When the computer-readable instructions are executed by the processor, they implement the steps of the passive positioning error prediction method based on radial basis function neural networks as described in any one of claims 1 to 7.