Q / R dual-adaptive hybrid quantum filtering method for OTFS (On-The-The-File System) communication and inductance integrated system

Abstract

The invention provides a Q / R dual-adaptive hybrid quantum filtering method for an OTFS (Over the The Over the File System) communication and inductance integrated system, and the method comprises the following steps: constructing an OTFS communication and inductance integrated signal model, and obtaining a target measurement vector; establishing a state vector for describing a target motion state, and constructing a state transition equation and a measurement equation; the method comprises the following steps: constructing a Q / R mixed quantum adaptive adjustment module based on dual-channel features to construct a dual-channel feature input vector, generating a dual-path adjustment factor through a mixed quantum neural network, and constructing an adaptive Q matrix and an adaptive R matrix; and performing adaptive state prediction and updating at each time step by using the adaptive Q and R matrixes constructed in the step 3 to realize tracking of the motion state of the target. According to the method, the hybrid quantum neural network is introduced for driving, collaborative optimization of filter parameters is achieved, and therefore the precision, robustness and response speed of target tracking are remarkably improved in a complex dynamic noise environment.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of communication, and particularly relates to the field of the sixth generation mobile communication (6G), radar signal processing and target tracking, and particularly relates to a Q / R dual-adaptive hybrid quantum filtering method for an OTFS sensing integrated system. BACKGROUND

[0002] In the core technical field of automatic driving, radar target tracking, etc., the extended Kalman filter (EKF) is a cornerstone algorithm for state estimation of a nonlinear system. However, a key assumption of the traditional EKF is that the system model parameters, especially the process noise covariance matrix Q and the measurement noise covariance matrix R, are known and fixed. However, in the actual physical world, this assumption often does not hold. The target may make unexpected maneuvers, causing the process noise Q to change; especially in the OTFS wireless communication scenario, the signal will change dramatically and unpredictably due to factors such as building obstruction, multipath fading, weather changes, etc., resulting in dramatic and unpredictable dynamic changes in the signal-to-noise ratio (SNR) and the measurement noise R.

[0003] When using fixed, mismatched Q and R matrices, the traditional EKF often exposes serious defects such as a sharp decline in performance and slow convergence, and cannot achieve the desired high precision. Therefore, there is an urgent need in the prior art for an adaptive filtering method that can sense and compensate for the dynamic changes in the measurement noise R in real time, in order to improve the precision and robustness of the target tracking system in real complex environments.

[0004] I. According to the search, the Chinese invention patent with the publication number CN102299766A discloses a joint optimization method for communication signal dimension reduction and quantization of target state estimation. The specific steps include: 1) reducing the dimension of the system state through a linear dimension reduction method to meet the dimension limit of independent parallel channel data transmission; 2) obtaining the predicted value of the signal through a multi-level quantization innovation Kalman filter prediction, and then obtaining the innovation of the signal; 3) under the constraints of transmission power and bandwidth, the linear dimension reduction method and time-invariant symmetric quantization method are jointly designed to quantize the innovation, with the minimum mean square estimation as the criterion; 4) at the signal receiving end, a multi-level quantization information Kalman filter is used to filter the received innovation to estimate the state of the object.

[0005] The above-mentioned comparative document and the present application have the following differences:

[0006] 1、The comparison file belongs to decision and control optimization. The core is to design an optimal decision (where the agent goes, where the beam points), which is a physical layer control problem; the problem solved is the communication channel constraint problem, that is, high-dimensional state data cannot be effectively transmitted through a channel with limited bandwidth and power; the present application belongs to an intelligent filtering algorithm. The core is to design a more intelligent and adaptive filter algorithm itself; the problem solved is the model mismatch problem inside the EKF filter, that is, the Q (process noise) and R (measurement noise) matrices are fixed, which leads to performance degradation in a dynamic noise environment; 2、The comparison file adopts a DPCM (Differential Pulse Code Modulation) architecture, and transmits the innovation after dimensionality reduction and quantization ; and based on the signal preprocessing parameters, jointly optimize (design) the linear dimensionality reduction matrix and the time-invariant symmetric quantizer ; the present application adopts a standard EKF architecture, and the system (may) transmits the measurement value , the innovation is how to process this information at the receiving end; and based on the internal parameters of the algorithm, the process noise and the measurement noise matrix of the filter are adaptively adjusted; 3、The comparison file assumes that the Kalman filter (KF) itself is fixed, the focus is on compressing the signal to be transmitted, so that it can pass through a narrowband channel, solving the communication limitation problem, using a classical optimization method (such as the Lagrange multiplier method) to iteratively solve the optimal matrix and quantization level; the present application assumes that the measurement signal has been received, improves the EKF algorithm so that it can intelligently adapt to dynamic noise, solves the model uncertainty problem, and constructs a hybrid quantum neural network (QNN). The QNN network is used to analyze the filter state in real time and dynamically output the adjustment factor. II、After searching, the Chinese invention patent with publication number CN120201378A discloses a kind of full space intelligent metasurface assisted vehicle tracking method and system, including: roadside unit RSU, vehicle top IOS and in-vehicle communication receiver CR;The RSU includes MIMO multi-antenna system;IOS assists RSU and in-vehicle CR to communicate and track vehicle, by designing customized extended Kalman filter EKF method, utilize the position side information provided by IOS, realize high-precision vehicle tracking. The comparison file and the present application have the following differences:

[0007] 1. The prior art utilizes a fully-in-space intelligent metasurface (IOS) as physical hardware to actively reconstruct the channel, addressing signal weakness and link interruption issues caused by urban environment occlusion (NLOS). This application enhances the intelligence and robustness of the EKF algorithm itself through AI and quantum computing, primarily innovating at the algorithmic level to address filter model mismatch caused by target maneuvering (Q changes) or channel interference (R changes). 2. The prior art uses a fixed noise parameter for EKF, but its measurement model (Jacobi matrix) is different. The model is highly customized based on the physical location of IOS; the EKF model (Jacobi matrix) in this application is standard, but its noise parameters are different. and is customized by QNN in real time; 3, the contrast file uses advanced IOS hardware (reflection / refraction) and complex ZO optimization algorithm, actively reconfigures the wireless channel environment, creates a more information-rich measurement condition for EKF, and performs high-dimensional joint optimization, which needs to solve a complex non-convex optimization problem (joint beam and IOS configuration) online, and relies on the complex iterative algorithm ZO-IPDD; the present application upgrades the EKF algorithm fundamentally by introducing the QNN agent, so that it can intelligently adjust the internal parameters to cope with uncertain environment; use AI model training, train QNN offline, so that it learns a strategy. Online operation is an efficient forward propagation process. The above-mentioned contrast file and the present application have the following differences: 1, the contrast file is applicable to vehicle management, intelligent power grid inspection and other scenarios where multiple vehicles communicate and perceive at the same time, mainly solving the joint problem of communication resource conflict and perception performance guarantee of multiple users (multiple inspection vehicles) in NLOS environment; the present application is applicable to automatic driving, radar tracking and other scenarios with extremely high precision requirements for a single target, mainly solving the model mismatch problem of EKF filter inside. That is, the Q / R matrix is fixed; 2, the contrast file is based on maximizing communication rate, and its optimization target is to "maximize the communication rate of multiple inspection vehicles"; the present application is based on minimizing tracking error for optimization, aiming to significantly improve the precision, robustness and response speed of target tracking; 3, the contrast file regards EKF tracking precision as a constraint that must be met, and under this premise, optimizes the resource (power) allocation of multi-user communication to realize more efficient resource scheduling, and solves a convex optimization problem using CVX toolbox. At each time, the system will solve a convex optimization problem based on the latest state of EKF (as a constraint) to find the current optimal power allocation scheme ; the present application upgrades the EKF algorithm fundamentally by introducing the QNN agent, so that it can intelligently adjust the internal parameters to cope with uncertain environment, and dynamically adjusts the Q / R matrix according to the real-time "internal state" and "external new information" characteristics by training a QNN offline. This is a self-adaptation based on quantum machine learning.

[0008] In summary, this application significantly surpasses the traditional adaptive filtering methods represented by the prior art in multiple dimensions, including technical architecture, intelligence level, implementation path, and application prospects, demonstrating outstanding technical innovation and progress. Summary of the Invention

[0009] To address the aforementioned problems, this invention provides a Q / R dual adaptive hybrid quantum filtering method for an OTFS integrated sensing system.

[0010] The specific plan is as follows:

[0011] A Q / R dual adaptive hybrid quantum filtering method for an OTFS inductive integrated system includes the following steps:

[0012] Step 1: Construct the OTFS integrated sensing signal model and obtain the target measurement vector;

[0013] Step 2: Establish a state vector describing the target's motion state, and construct the state transition equation and measurement equation;

[0014] Step 3: Construct a Q / R hybrid quantum adaptive adjustment module based on dual-channel features to construct dual-channel feature input vectors, generate dual-path adjustment factors through a hybrid quantum neural network, and construct adaptive Q and R matrices;

[0015] Step 4: Execute a Q / R dual adaptive extended Kalman filter loop, using the adaptive Q and R matrices constructed in Step 3 at each time step to perform adaptive state prediction and update, thereby achieving target motion state tracking. Further, the specific process of Step 1 includes:

[0016] Step 1-1: Generate and send a sensor-integrated transmission signal for OTFS. :

[0017] An M×N transmit resource grid is constructed in the delay-Doppler (DD) domain. The communication data and sensing pilots are mixed and mapped onto the discrete index (l,k) of this grid, denoted as the integrated sensing transmit symbol. Symbol mapping is performed on (l=0,...,M-1;k=0,...,N-1), where l is the discrete index of the time delay domain, k is the discrete index of the Doppler domain, M is the number of subcarriers (set to 8), and N is the number of time slots (set to 8);

[0018] By using the inverse symplectic Fourier transform, the transmitted symbols in the time-delay-Doppler domain are... Transmitted signal converted to the time domain And send it:

[0019] ;

[0020] in, It is the subcarrier spacing. It is the pulse shaping function at the transmitting end, T sym It is the OFDM symbol period (equal to) );

[0021] Step 1-2: Send signal Based on the target reflection, model its channel response and calculate the channel gain. Based on channel gain Calculate the received signal :

[0022] Send signal The channel response of the moving target in the DD domain is modeled based on its reflection.

[0023] ;

[0024] in, and These are the target's actual time delay and Doppler frequency shift, respectively, where τ is the time delay variable and ν is the Doppler frequency shift variable; This is the channel gain, the magnitude of which is affected by the two-way path loss and is determined by the radar range equation:

[0025] ;

[0026] in, It's the transmission power. It's the antenna gain. It is the radar cross-section of the target. It is the carrier wavelength. It is the distance between the base station and the target;

[0027] Based on channel gain Calculate the received signal :

[0028] ;

[0029] in, It is sending a signal. It is additive white Gaussian noise;

[0030] Steps 1-3: Receive the signal Process to obtain the receiving grid Estimate the target's time delay and Doppler shift to obtain the target measurement vector at time k. :

[0031] The received signal is transformed using the symptotic Fourier transform. Convert back to delay-Doppler domain resources to obtain the receiving grid. :

[0032] ;

[0033] Where l and k are the discrete indices corresponding to the time delay domain and the Doppler domain, respectively. It is a phase rotation. It is noise in the DD domain, l true It is the discrete index corresponding to the actual time delay of the target, k true It is the discrete index corresponding to the target's true Doppler frequency shift;

[0034] Using known two-dimensional pilot patterns With receiving grid The corresponding area Perform two-dimensional cross-correlation operation to obtain the cross-correlation function. To estimate the target's time delay and Doppler shift:

[0035] ;

[0036] By finding the cross-correlation function peak position The estimated indices corresponding to the time delay and Doppler frequency shift are obtained:

[0037] ;

[0038] The discrete index is converted into a physical quantity to obtain the target measurement vector at time k. :

[0039] Furthermore, the specific process of step 2 includes:

[0040] Establish a description of the target's motion in a two-dimensional plane. The state vector at time 1 The state vector includes at least position, velocity, and acceleration.

[0041] ;

[0042] in, These represent the target's position on the X-axis and Y-axis, respectively. They represent their speeds respectively; They represent their accelerations respectively;

[0043] State transition equations are constructed to describe the evolution of the system state:

[0044] ;

[0045] in, It is a state transition matrix, constructed based on a constant acceleration model. It is process noise;

[0046] In the The actual measurement value of the base station at that moment Including the time delay of the target relative to the base station and Doppler shift Based on a nonlinear measurement function Constructing nonlinear measurement equations:

[0047] ;

[0048] in, It measures noise. It is a nonlinear function that maps the state vector to the theoretical measurement value:

[0049] ;

[0050] in, It's the speed of light, p BSx p is the horizontal coordinate of the base station. BSy It is the vertical coordinate of the base station. This is the signal carrier frequency (in an integrated sensing system, this frequency is used for both radar detection and communication transmission). Further, in step 3, the specific process of constructing the dual-channel feature input vector includes:

[0051] Build Q-adaptation channel :

[0052] Extract the state estimation vector of the filter at the current time. And error covariance matrix The diagonal elements are used as features, with the tanh activation values ​​of the state vector and the tanh activation values ​​of the ratio of the diagonal elements of the error covariance to the state vector.

[0053] ;

[0054] Among them, f state It is the state feature vector, f p It is the covariance eigenvector, P k|k-1 It is the prior error covariance matrix, X k|k-1 It is the prior state estimation vector. It is a small constant to prevent the denominator from being zero;

[0055] Constructing R adaptation channels :

[0056] Information calculation and caching:

[0057] At each time step, the system acquires the actual measurement values ​​from the base station. At that time, calculate and obtain the filter information at the current moment. :

[0058] ;

[0059] Then the new information Stored in a new information buffer of fixed length;

[0060] Statistical estimation of the covariance of new information:

[0061] Once the news buffer is full, at each new time step, the news sample data stored in the buffer is used. Online calculation of the actual covariance matrix of the new information :

[0062] ;

[0063] in, Indicates that recently The distribution of the true deviation between the filter prediction and the actual measurement within a given time period; It is the innovation vector at time i. It is the transpose of the vector;

[0064] Simultaneously, based on the current prediction state of the filter, the theoretically required covariance matrix of the innovation is calculated, denoted as... :

[0065] ;

[0066] in, It is a measurement function Prior state estimation Jacobian matrix at the location, It is a preset benchmark measurement noise covariance;

[0067] Construction of features:

[0068] The actual new information covariance obtained Covariance with theoretical information Compare the two and extract a feature vector representing the degree of mismatch. As input to a hybrid quantum neural network:

[0069] ;

[0070] Where, diag(⋅) represents taking the diagonal elements of the matrix. It is a small constant to prevent the denominator from being zero. Each element reflects the logarithmic difference between the real noise and the nominal noise in the corresponding measurement dimension;

[0071] Finally, the external innovation features of the above three feature vectors are... Internal state characteristics and internal covariance characteristics Vertically concatenated, they form a hybrid quantum neural network input feature vector. :

[0072] ;

[0073] Among them, S k This is the theoretically expected covariance matrix of the new information. Further, in step 3, the specific process of generating the dual-path adjustment factor through the hybrid quantum neural network includes:

[0074] Input feature vector The input is fed into a classical fully connected layer and subjected to a linear transformation to extract preliminary features and match the input dimension of the quantum circuit.

[0075] ;

[0076] in, , These are the trainable weights and biases of the classic layer;

[0077] Classic features Encoding to a In parameterized quantum circuits for qubits:

[0078] ;

[0079] in, It is the initial quantum state. It is the unitary operator of the entire quantum circuit, which depends on the characteristic input vector. and trainable quantum gate parameters ;

[0080] The 4-dimensional measurement result vector is separated into two groups, each with 2 dimensions. The last two elements are used for Q, and the first two elements are used for R.

[0081] One set of 2D vectors is processed through a Sigmoid activation function and linear scaling to generate scaling factors for adjusting the diagonal elements of the Q matrix. :

[0082] ;

[0083] in, These are the scaling and translation parameters hard-coded in the code. These are the last two elements of the measurement vector. These are the scaling and translation parameters hard-coded in the code;

[0084] Another set of 2D vectors is similarly processed using the Sigmoid activation function and linear scaling to generate scaling factors for adjusting the diagonal elements of the R matrix. :

[0085] ;

[0086] in, These are the first two elements of the measurement vector. It is the scaling factor adjusted by the R matrix (set to 4.0 in this embodiment). This is the translation coefficient adjusted by the R matrix (set to 0.5 in this embodiment). Further, in step 3, the specific process of constructing the adaptive Q and R matrices includes:

[0087] Use scaling factor , To adjust the reference noise covariance Q separately base and reference noise covariance The adaptive process noise covariance Q used at the current moment is obtained. k and adaptive measurement noise covariance :

[0088] ;

[0089] ;

[0090] Among them, diag( ) and diag( ) is a diagonal matrix.

[0091] Furthermore, the specific process of step 4 includes:

[0092] At each time step k, perform the following adaptive state prediction and update steps:

[0093] Adaptive state prediction steps:

[0094] ;

[0095] ;

[0096] Adaptive state update steps:

[0097] (1) Calculate the Kalman gain :

[0098] ;

[0099] (2) Update state estimation :

[0100] ;

[0101] (3) Update error covariance:

[0102] .

[0103] Furthermore, the hybrid quantum neural network obtains its parameters through offline training, the training process of which includes:

[0104] a. Construct a training dataset: Generate a large number of simulated trajectories, maintaining a fixed signal-to-noise ratio throughout the entire trajectory;

[0105] b. Define the loss function: The loss function is based on the error between the filter-estimated location and the true location;

[0106] c. Perform backpropagation: Using a framework that supports automatic differentiation, calculate the gradient of the loss function with respect to all trainable parameters of the hybrid quantum neural network;

[0107] d. Optimize parameters: Use an optimizer to update the network parameters based on the gradient until the loss function converges.

[0108] Compared with the prior art, the present invention has the following beneficial effects:

[0109] 1. Significantly Improved Accuracy and Robustness: This invention achieves simultaneous and collaborative adaptive adjustment of process noise Q and measurement noise R through a unified intelligent hub. This enables the filter to simultaneously cope with both abnormal target maneuvers and deteriorating measurement environments, greatly enhancing its robustness in complex real-world environments. Simulation experiments show that, in scenarios where simulated signal obstruction leads to drastic changes in measurement noise, its performance is significantly improved compared to traditional EKFs using fixed parameters and the more advanced UKFs, especially in harsh environments with low signal-to-noise ratios, where its performance advantage is substantial.

[0110] 2. Innovative Integration of Quantum Computing: This invention is the first to apply a hybrid quantum neural network (QNN) to the Q / R dual adaptive adjustment of an EKF. It leverages the powerful feature extraction and function fitting capabilities of quantum computing in high-dimensional Hilbert spaces to model the complex, nonlinear mapping relationship between the filter's internal state and the statistical characteristics of external innovations, providing a novel and more promising technical path for solving the adaptive filtering problem in intelligent signal processing.

[0111] 3. Clear Physical Meaning and Fast Response: The adaptive mechanism of this invention has clear physical and statistical significance. The adjustment of R is directly based on the statistical mismatch of the inherent "innovation" concept of Kalman filtering, allowing the system to react immediately when measurement quality deteriorates. The adjustment of Q is based on the filter's judgment of its own state and uncertainty. This adjustment mechanism based on the model's intrinsic information is more reliable and efficient than traditional heuristic rule-based methods.

[0112] 4. Foresight for 6G Sensing Integration: This invention is designed and verified directly on the signal-level simulation platform of OTFS-ISAC, a key 6G candidate technology. It is not only a theoretical algorithm, but also a complete solution tightly integrated with the sensing integration physical layer, providing a solid technical foundation for high-precision and high-robust target perception applications in next-generation mobile communication systems. Attached Figure Description

[0113] Figure 1 This is a schematic diagram illustrating the application scenario of the present invention in the OTFS integrated communication and sensing system;

[0114] Figure 2 This is a schematic flowchart of the method of the present invention;

[0115] Figure 3 This is a schematic diagram of the internal structure of the decision center of the hybrid quantum neural network (QNN) of the present invention. Detailed Implementation

[0116] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. The specific implementation methods of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0117] like Figure 1 As shown, in the Orthogonal Time-Frequency-Spacetime (OTFS) communication-sensing integration (ISAC) scenario, this invention proposes a Q / R dual adaptive hybrid quantum filtering method for OTFS integrated communication-sensing systems. Its core lies in designing a unified hybrid quantum neural network (QNN) driven by dual-channel features of internal state and external innovation, serving as an intelligent decision-making center. This QNN outputs adjustment factors in real time and uses these factors to dynamically adjust the process noise covariance matrix Q and measurement noise covariance matrix R of the extended Kalman filter (EKF), thereby achieving high-precision and robust target tracking in dynamic noise environments.

[0118] like Figure 2 As shown, the method of the present invention specifically includes the following steps:

[0119] Step 1: Construct the OTFS integrated sensing signal model and obtain the target measurement vector;

[0120] Specifically, this invention first constructs an OTFS-ISAC physical layer signal model that fits the real-world scenario. This is crucial for obtaining non-ideal measurement values ​​in subsequent filtering steps. The foundation.

[0121] Step 1-1: Generate and send a sensor-integrated transmission signal for OTFS. :

[0122] An M×N transmit resource grid is constructed in the core of the OTFS system—the Delay-Doppler (DD) domain. Communication data and sensing pilot signals are mixed and mapped onto the discrete index (l,,k) of this network, denoted as the transmit symbol. (l=0,...,M-1; k=0,...,N-1), where l is the discrete index of the time delay domain, k is the discrete index of the Doppler, M is the number of subcarriers (set to 8), and N is the number of time slots (set to 8). This symbol... Simultaneously carrying communication data and sensing pilots: most of the communication symbol grid is filled with random QAM modulation symbols for data transmission. The sensing pilots embed a known two-dimensional pilot pattern with good autocorrelation properties in the central region of the grid. This is used for subsequent target parameter estimation.

[0123] The DD domain grid is transformed using the inverse symplectic Fourier transform (ISFFT). Convert to time domain signal Send:

[0124] ;

[0125] in, It is the subcarrier spacing. It is the pulse shaping function at the transmitting end, T sym It is the OFDM symbol period (equal to) ).

[0126] Step 1-2: Send signal Based on the target reflection, model its channel response and calculate the channel gain. Based on channel gain Calculate the received signal :

[0127] Specifically, sending signals The propagation process of a target is affected by the channel after being reflected from a moving target. For a point target, its channel response in the DD domain can be modeled as follows:

[0128] ;

[0129] in, and These are the target's actual time delay and Doppler frequency shift, respectively, where τ is the time delay variable and ν is the Doppler frequency shift variable. This is the channel gain, the magnitude of which is affected by the two-way path loss and can be determined by the radar range equation:

[0130] ;

[0131] in, It's the transmission power. It's the antenna gain. It is the radar cross-section of the target. It is the carrier wavelength. This is the distance between the base station and the target. Since the filter's state variables (position) are directly related, the channel gain and received signal-to-noise ratio (SNR) will change dynamically as the target moves.

[0132] Received time-domain signal It can be represented as:

[0133] ;

[0134] in, It is transmitting a signal. It is additive white Gaussian noise.

[0135] Steps 1-3: Receive the signal Process to obtain the receiving grid Estimate the target's time delay and Doppler shift to obtain the target measurement vector at time k. :

[0136] The receiving end uses the Synchronous Fourier Transform (SFFT) to convert the received signal. Convert back to DD domain to obtain the receiving grid. :

[0137] ;

[0138] in, l and k are the discrete indices corresponding to the time delay domain and the Doppler domain, respectively. It is a phase rotation. It is noise in the DD domain, l true It is the discrete index corresponding to the actual time delay of the target, k true It is the discrete index corresponding to the true Doppler frequency shift of the target.

[0139] To estimate the target's time delay and Doppler effect, this invention utilizes known pilot patterns. The corresponding area in the receiving grid Perform two-dimensional cross-correlation calculations:

[0140] ;

[0141] By finding the cross-correlation function peak position This allows us to obtain the estimated indices for time delay and Doppler:

[0142] ;

[0143] Finally, the discrete index is converted into physical quantities to obtain the measurement vector at time k. :

[0144] ;

[0145] Due to channel gain With the presence of noise n(t), the estimated , It must contain error, and the statistical properties of this error (i.e., measurement noise covariance) It will vary depending on the distance to the target. And the channel conditions change dynamically.

[0146] Step 2: Establish a state vector describing the target's motion state, and construct the state transition equation and measurement equation;

[0147] This invention considers a target moving in a two-dimensional plane, whose dynamic process is represented by a 6-dimensional state vector containing position, velocity, and acceleration. In the Describe each moment in time:

[0148] ;

[0149] in, These represent the target's position on the X-axis and Y-axis, respectively. They represent their speeds respectively; These represent their accelerations.

[0150] The state of the system evolves through a linear state transition equation:

[0151] ;

[0152] in, It is a state transition matrix, constructed based on a constant acceleration model. It is process noise, assumed to be zero-mean Gaussian white noise, and its covariance matrix is... .

[0153] In the The actual measurement value of the base station at that moment Including the time delay of the target relative to the base station and Doppler shift This measurement process is performed by a nonlinear measurement function. The system's measurement equations are described as follows:

[0154] ;

[0155] in, From step 1, It is measurement noise, and its covariance is . It is a nonlinear function that maps the state vector to the theoretical measurement value:

[0156] ;

[0157] in, It's the speed of light, p BSx p is the x-coordinate of the base station. BSy It is the vertical coordinate of the base station. It is the signal carrier frequency (in this system, this frequency is used for both radar detection and communication transmission).

[0158] Step 3: Construct a Q / R hybrid quantum adaptive adjustment module based on dual-channel features to construct dual-channel feature input vectors, generate dual-path adjustment factors through a hybrid quantum neural network, and construct adaptive Q and R matrices;

[0159] The internal structure of the hybrid quantum neural network (QNN) decision center described in this invention can be as follows: Figure 3 As shown, the classical preprocessing, parameterized quantum circuit, and classical postprocessing modules are illustrated.

[0160] (1) Constructing a dual-channel feature input vector :

[0161] Constructing Q-adaptive channels (internal state features) :

[0162] Extract the state estimation vector of the filter at the current time. And error covariance matrix The diagonal elements are used. Specifically, the tanh activation values ​​of the state vector and the tanh activation values ​​of the ratio of the diagonal elements of the error covariance to the state are used as features. These features mainly reflect the target's own motion and the degree of uncertainty of the filter's state estimation.

[0163] ;

[0164] Among them, fstate It is the state feature vector, f p It is the covariance eigenvector, P k|k-1 It is the prior error covariance matrix, X k|k-1 It is the prior state estimation vector. It is a small constant to prevent the denominator from being zero;

[0165] Constructing an R-adaptive channel (external information feature) :

[0166] Innovation calculation and caching:

[0167] At each time step, the system acquires the actual measurement values ​​from the base station. At that time, first calculate the new information. Calculate and obtain the filter information at the current time. (That is, the difference between the actual measured value and the predicted measured value):

[0168] ;

[0169] The new information is then stored in a first-in, first-out (FIFO) buffer of a fixed length (e.g., 8 time steps). This method uses a buffer of length... A sliding time window is used to cache the most recent data. The new information sequence at each moment .

[0170] ii. Statistical estimation of the covariance of the new information:

[0171] Once the news buffer is full, at each new time step, the news sample data stored in the buffer is used. Online calculation of the actual covariance matrix of the new information :

[0172] ;

[0173] Indicates that recently The distribution of the true deviation between the filter prediction and the actual measurement within a given time period.

[0174] Simultaneously, based on the current prediction state of the filter, the theoretically required covariance matrix of the innovation is calculated, denoted as... :

[0175] ;

[0176] in, It is a measurement function Prior state estimation The Jacobian matrix at that location. It is a preset benchmark measurement noise covariance.

[0177] Characteristic Structure:

[0178] The actual new information covariance obtained Covariance with theoretical information Compare the two and extract a feature vector representing the degree of mismatch. As input to a hybrid quantum neural network:

[0179] ;

[0180] Where, diag(⋅) represents taking the diagonal elements of the matrix. It is a small constant that prevents the denominator from being zero. Each element reflects the logarithmic difference between the real noise and the nominal noise in the corresponding measurement dimension.

[0181] Finally, the above three feature vectors—external innovation features—are combined. Internal state characteristics and internal covariance characteristics — Perform vertical concatenation to construct a complete 14-dimensional hybrid quantum neural network (QNN) input feature vector. Its structure is as follows:

[0182] ;

[0183] Among them, S k It is the theoretical new information covariance matrix.

[0184] (2) Generate dual-path adjustment factors through a hybrid quantum neural network (QNN):

[0185] Hybrid quantum neural networks consist of the following components:

[0186] Classic preprocessing module: Employs a fully connected layer (torch.nn.Linear) responsible for inputting the concatenated 14-dimensional feature vector. Linearly map to n_qubits dimensions (8 dimensions in this embodiment) to generate feature vectors suitable for quantum circuit encoding, so as to match the encoding requirements of quantum circuits.

[0187] Input feature vector The input is fed into a classical fully connected layer and subjected to a linear transformation to extract preliminary features and match the input dimension of the quantum circuit.

[0188] ;

[0189] in , These are the trainable weights and biases of the classic layers.

[0190] The parameterized quantum circuit module employs a variable quantum circuit containing n_qubits (8 qubits). First, classical features are loaded as the rotation angles of the qubits through angle encoding (qml.AngleEmbedding). Then, the quantum state is deeply evolved through multiple basic entanglement layers (qml.BasicEntanglerLayers) containing trainable parameters (quantum_weights). Finally, Pauli Z operator measurements are performed on the first 4 qubits of the output quantum state to obtain its expected value, outputting a 4-dimensional adjustment vector.

[0191] Classic features Encoding to a In parameterized quantum circuits (PQC) of qubits, this process can be formally represented as:

[0192] ;

[0193] in, It is the initial quantum state. It is the unitary operator of the entire quantum circuit, which depends on the input characteristics. (Through angle encoding AngleEmbedding) and trainable quantum gate parameters (In entanglerLayers).

[0194] Classic post-processing modules:

[0195] The 4-dimensional measurement result vector is separated into two groups (2-dimensional each). The last two elements are used for Q, and the first two elements are used for R.

[0196] Q-adjustment factor: A scaling factor is generated by passing one set of 2D vectors through a Sigmoid activation function and linear scaling to adjust the diagonal elements of the Q matrix. :

[0197] ;

[0198] R scaling factor: Another set of 2D vectors is also processed through the Sigmoid activation function and linear scaling to generate a scaling factor used to adjust the diagonal elements of the R matrix. .

[0199] ;

[0200] in These are the last two elements of the measurement vector. It refers to the first two elements. It is the scaling factor adjusted by the R matrix (set to 4.0 in this embodiment). It is the translation coefficient adjusted by the R matrix (set to 0.5 in this embodiment).

[0201] (3) Construct the adaptive Q and R matrices:

[0202] Use the output scaling factor , To adjust the reference noise covariance separately and reference noise covariance The adaptive process noise covariance Q used at the current moment is obtained. k and adaptive measurement noise covariance :

[0203] ;

[0204] ;

[0205] Among them, diag( ) and diag( ) is a diagonal matrix, this operation is equivalent to... and Multiply the diagonal elements by the corresponding scaling factor.

[0206] Step 4: Execute the Q / R dual adaptive extended Kalman filter loop. At each time step, use the adaptive Q and R matrices constructed in Step 3 to perform adaptive state prediction and update, thereby tracking the target motion state.

[0207] At each time step k, perform the following adaptive prediction and update steps:

[0208] Adaptive prediction phase:

[0209] ;

[0210] ;

[0211] Adaptive update phase:

[0212] (1) Calculate the Kalman gain :

[0213] ;

[0214] (2) Update state estimation :

[0215] ;

[0216] (3) Update error covariance

[0217] ;

[0218] Through the above steps, this invention seamlessly integrates a high-fidelity OTFS-ISAC signal physical layer model with an advanced quantum-classical hybrid intelligent filtering algorithm, creating a complete end-to-end solution. This solution can sense environmental changes at the signal level and intelligently adjust the core parameters of the filter, thereby achieving superior target tracking performance in complex and dynamic real-world application scenarios.

[0219] In embodiments of the present invention, the hybrid quantum neural network obtains its parameters through offline training. To ensure the robustness of the adaptive network of the present invention in the worst environments, its training process is performed at a fixed, extremely low signal-to-noise ratio (-15dB), rather than at a dynamically changing signal-to-noise ratio.

[0220] The training process includes:

[0221] a. Construct a training dataset: Generate a large number of simulated trajectories, with the signal-to-noise ratio maintained at a fixed low value (e.g., -15dB) throughout the entire trajectory.

[0222] b. Define the loss function: The loss function is defined as the root mean square error (RMSE) between the filter-estimated position and the true position over the entire trajectory.

[0223] c. Perform backpropagation: Utilize frameworks that support automatic differentiation, such as PyTorch and PennyLane, to calculate the gradient of the loss function with respect to all parameters of QCHN.

[0224] d. Optimize parameters: Use optimizers such as AdamW to update the parameters of QCHN according to the gradient until the loss function converges.

[0225] By training in this extreme environment, the network can learn a universal adaptive strategy that is highly sensitive to noise changes, enabling it to make effective judgments and adjustments when faced with dynamic noise environments across the entire spectrum, ranging from good to bad.

[0226] To enable those skilled in the art to better understand and reproduce the present invention, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings and key implementations in the Python code.

[0227] This invention is implemented in a two-dimensional scenario containing a moving target and four fixed ground base stations (BS). The core task of the system is to use the OTFS-ISAC signal received by the base stations to perform high-precision real-time tracking of the target's position, velocity, and acceleration.

[0228] System initialization and parameter settings:

[0229] Scenario parameters: Total simulation duration T_sim=4.0, dt=0.2, M=8, N=8, buffer_size=8, training_epochs=60, optimizer is Adam. Four base stations (BSs) are deployed at the location [[50, 50], [50, -50], [-50, 50], [-50, -50]].

[0230] OTFS parameters: Carrier frequency CARRIER_FREQ=60GHz, number of subcarriers SUBCARRIERS_M=32, number of time slots TIME_SLOTS_N=32.

[0231] Filter initialization: Define a basic process noise standard deviation `process_noise_std` and a basic measurement noise covariance `r_matrix_nominal` calculated based on the nominal SNR. The DualAdaptive_QEKF class of this invention is initialized, which internally contains an innovation_buffer of length 10.

[0232] Implementation details of the core adaptive filtering module DualAdaptive_QEKF:

[0233] Reference Figure 2 The core QNN decision center is implemented through the `_get_scaling_factors` method:

[0234] Feature construction:

[0235] Internal features: Extract the current state self.state and covariance self.P, and calculate state_feature and p_diag_feature.

[0236] External features: Check if the innovation_buffer is full. If not, R-adaptation will not start yet; if full, retrieve the 10 most recent innovation samples from the buffer and calculate their actual covariance S_hat. Simultaneously, calculate the theoretical covariance S_temp based on the current P and H. The final innovation_feature is the logarithm of the ratio of the diagonal elements of the two.

[0237] Concatenation: The three sets of features [innovation_feature, state_feature, p_diag_feature] are concatenated into a 14-dimensional input tensor nn_input.

[0238] QNN forward propagation:

[0239] nn_input is first transformed into 8 dimensions through a classic nn.Linear layer, self.classical_preprocessor.

[0240] The 8-dimensional feature vector is fed into dual_quantum_circuit and evolved through angular encoding and an entangled layer containing trainable weights self.quantum_weights.

[0241] The Pauli Z expectation value of the first 4 qubits is measured to obtain a 4-dimensional output q_outputs.

[0242] Factor generation and matrix update:

[0243] The first two elements r_outputs and the last two elements q_outputs are separated.

[0244] Apply the torch.sigmoid function to them respectively and perform linear scaling (e.g., multiply the R factor by 4.0 and add 0.5) to obtain the final q_scaling_factors and r_scaling_factors.

[0245] In the `predict` method, `q_scaling_factors` is used to scale `Q_base` to obtain `adaptive_Q`.

[0246] In the update method, r_scaling_factors is used to scale R_base to obtain adaptive_R.

[0247] Training and Assessment:

[0248] Data generation: Twenty training trajectories are generated using the `generate_realistic_data` function. Each trajectory has a random initial state and maneuverability. Crucially, the `dynamic_snr_func` function abruptly drops the SNR from 10dB to -5dB in the middle (1 / 3 to 2 / 3) of each trajectory to simulate a harsh measurement environment where the signal is blocked.

[0249] Offline training: A fixed SNR of -15dB is set. The `generate_realistic_data` function is called to generate 15 training trajectories, with the SNR remaining constant at -15dB throughout the entire trajectory. The `DualAdaptive_QEKF` is initialized, and the Adam optimizer is used to train its trainable parameters for 200 epochs. The loss function is the mean squared error between the estimated and true locations.

[0250] Performance evaluation:

[0251] Monte Carlo simulations were performed with dynamic signal-to-noise ratio. A range of "severe region signal-to-noise ratio" was set (e.g., from 10dB to -15dB). Two benchmarks were set: (1) the classic EKF with fixed Q / R; (2) the classic UKF imported from the filterpy library, which was given "prophetic" capabilities (i.e., it knows the true SNR at every moment and uses the optimal R matrix).

[0252] Performance metrics: The root mean square error (RMSE) of the three filters was recorded and compared under different “severe signal-to-noise ratio” conditions. The final performance charts (such as RMSE vs. SNR curves) clearly show that the method of this invention significantly outperforms the classic EKF and the robust UKF benchmarks across the entire signal-to-noise ratio range, especially under severe signal-to-noise ratio conditions, demonstrating a significant performance advantage and verifying the robustness and superiority of this invention.

[0253] Through the above embodiments, this invention fully demonstrates how to embed a hybrid quantum model into the classical Kalman filter framework, and through end-to-end training, enable it to intelligently adjust the Q and R matrices in dynamic noise environments, thereby effectively solving the target tracking problem in complex scenarios. The process is clear and can be understood and implemented by those skilled in the art.

[0254] This invention proposes a novel filtering framework capable of simultaneously adaptively adjusting the process noise covariance Q and the measurement noise covariance R. The originality of this framework lies in using a unified decision center to process two different types of feature inputs (state / covariance features reflecting internal model uncertainty are used for Q adjustment, and innovative statistical features reflecting external environmental changes are used for R adjustment), achieving for the first time the coordinated, online estimation and compensation of the two core sources of uncertainty in the filter. Simultaneously, this invention innovatively designs a unified, multi-output hybrid quantum neural network as the core for realizing the aforementioned dual adaptive mechanism. Its innovations are: (1) using a classical neural network as a preprocessor to achieve the fusion and dimension matching of heterogeneous features; (2) utilizing the strong expressive power of parameterized quantum circuits to extract deep, nonlinear correlations from the fused features; (3) designing multiple measurement outputs and post-processing, enabling a single QNN to generate independent adjustment factors for Q and R simultaneously in a single forward propagation, achieving efficient coordinated control. This invention is not only a theoretical algorithm, but its key innovation also lies in applying the aforementioned quantum dual adaptive filtering method to a high-fidelity OTFS-ISAC signal-level simulation platform. This platform integrates integrated waveform design, radar equation-based physical channels, dynamic SNR variations, and pilot-based parameter estimation algorithms. This allows the performance verification of this invention to be built on a solid, 6G-oriented physical model, providing a complete and practical novel solution for high-precision, high-robust target tracking in next-generation mobile communication systems.

[0255] The above embodiments are for illustrative purposes only and are not intended to limit the scope of this invention. Although this invention has been described in detail with reference to the embodiments, those skilled in the art should understand that various combinations, modifications, or equivalent substitutions of the technical solutions of this invention do not depart from the spirit and scope of the technical solutions of this invention and should be covered within the scope of the claims of this invention.

Claims

1. A Q / R dual-adaptive hybrid quantum filtering method for an OTFS communication-sensing integrated system, characterized in that, The method comprises the following steps: Step 1: constructing an OTFS all-source integrated signal model to obtain a target measurement vector; Step 2: establishing a state vector describing the motion state of the target, and constructing a state transition equation and a measurement equation; Step 3: constructing a Q / R hybrid quantum adaptive adjustment module based on double-channel features, for constructing a double-channel feature input vector, generating a double-channel adjustment factor through a hybrid quantum neural network, and constructing adaptive Q and R matrices; Step 4: performing a Q / R double-adaptive extended Kalman filtering cycle, and at each time step, performing adaptive state prediction and update using the adaptive Q and R matrices constructed in step 3 to realize tracking of the motion state of the target.

2. The Q / R dual-adaptive hybrid quantum filtering method for OTFS sensor fusion integrated system according to claim 1, wherein, The specific process of step 1 comprises: Step 1-1: Generating and transmitting a sensor-fusion integrated transmission signal for OTFS : A MxN transmit resource grid is constructed in the delay-Doppler domain. The communication data and sensing pilots are mixed and mapped to the discrete indices (l, k) of the grid, denoted as the integrated sensing and communication (ISAC) transmit symbol (l = 0,..., M-1; k = 0,..., N-1); where l is the discrete index in the delay domain, k is the discrete index in the Doppler domain, M is the number of subcarriers, and N is the number of time slots. The transmitted symbols in the delay-Doppler domain are converted into time domain transmitted signals by inverse symplectic Fourier transform and transmitted ​ ； wherein is a subcarrier spacing, is a pulse shaping function at the transmitting end, T sym is an OFDM symbol period, equal to ; Step 1-2: Transmit signal From the target reflection, model its channel response, compute channel gain , based on channel gain Compute received signal : Transmitting a signal Modeling the channel response of the target in the DD domain via motion-induced target reflections: ； where, and are the target's true delay and Doppler shift, respectively, τ is the delay variable, and v is the Doppler shift variable; is the channel gain, whose magnitude is affected by the two-way path loss, determined by the radar range equation: ； wherein, is the transmit power, is the antenna gain, is the radar cross section of the target, is the carrier wavelength, is the distance between the base station and the target; Based on channel gain Computing received signal : ； where s(t) is the transmitted signal, is an additive white Gaussian noise; Steps 1-3: Processing the received signal to obtain a received grid , estimating the time delay and Doppler shift of the target, to obtain a target measurement vector at the kth time instant : By means of a sine Fourier transform, the received signal is converted back into the delay-Doppler domain, resulting in a received signal : ； wherein l, k are the discrete indices corresponding to the delay and Doppler domains, respectively, is the phase rotation, is the noise in the DD domain, l true is the discrete index corresponding to the target real delay, k true is the discrete index corresponding to the target real Doppler shift; Using a known two-dimensional pilot pattern with the received signal corresponding region in the two-dimensional cross-correlation operation to obtain a cross-correlation function to estimate the time delay and Doppler shift of the target: ； By finding the peak position of the cross-correlation function the corresponding estimation index of time delay and Doppler shift is obtained:​ ； convert the discrete index into a physical quantity to obtain a target measurement vector at the kth time instant : 。 3. The Q / R dual-adaptive hybrid quantum filtering method for OTFS sensor fusion integrated system according to claim 2, characterized in that, The specific process of step 2 comprises: establishing a state vector at a first time instant describing the motion of the object in a two-dimensional plane wherein the state vector comprises at least position, velocity and acceleration​ ； wherein, respectively represent the position of the target in the X-axis and Y-axis; respectively represent the velocity thereof; respectively represent the acceleration thereof; The state transition equation is constructed to describe the evolution of the system state: ； wherein is the state transition matrix, constructed based on a constant acceleration model, is the process noise; At a first moment, the actual measurements of the base station include the time delay and the Doppler shift of the target relative to the base station and a non-linear measurement function is constructed from the non-linear measurement equation: ； where is the measurement noise, is a nonlinear function mapping the state vector to the theoretical measurement value: ； wherein is the speed of light, p BSx is the abscissa of the base station, p BSy is the ordinate of the base station, is the signal carrier frequency, which is used in the system both for radar detection and for communication transmission.

4. The Q / R dual-adaptive hybrid quantum filtering method for OTFS sensor fusion integrated system according to claim 3, characterized in that, In step 3, the specific process of constructing the double-channel feature input vector comprises: Constructing a Q-adaptive channel : extracting a state estimation vector of the filter at the current time and diagonal elements of the error covariance matrix using tanh activations of the state vector and tanh activations of the ratio of the error covariance diagonal elements to the state as features: ； where f state is the state feature vector, f p is the covariance feature vector, P k|k-1 is the prior error covariance matrix, X k|k-1 is the prior state estimate vector, is a small constant to prevent the denominator from being zero. Constructing an R adaptation channel : Calculation and caching of innovations: The system obtains actual measurement values from the base station at each time step At this time, the filter innovation at the current time is calculated and obtained : ； The new information is then stored in a new information buffer having a fixed length. ; ii. Statistical estimation of innovation covariance: When the innovation buffer is filled, at each new time step, the innovation sample data stored in the buffer is used to compute the actual covariance matrix of the innovations online : ； wherein, represents the true bias distribution between the filter prediction and the actual measurement over the last moments; v i is the innovation vector at the i-th moment, v i T is the transpose of this vector; At the same time, according to the current prediction state of the filter, the covariance matrix of the theoretically new information is calculated, denoted as : ； wherein is a measurement function at the prior state estimate is the Jacobian matrix at the prior state estimate, is a predetermined reference measurement noise covariance; , the configuration of the features: The resulting actual innovation covariance is compared to the theoretical innovation covariance and a feature vector representing the degree of mismatch between the two is extracted as input to the hybrid quantum neural network: ； where diag(·) denotes taking the diagonal elements of a matrix, is a small constant preventing the denominator from being zero, each element of the matrix reflects the log difference between the true noise and the nominal noise in the corresponding measurement dimension. Finally, the above three feature vectors of external innovation feature , internal state feature and internal covariance feature are vertically spliced to form a hybrid quantum neural network input feature vector : ； where S k is the theoretical innovation covariance matrix.

5. The Q / R dual-adaptive hybrid quantum filtering method for OTFS sensor fusion integrated system according to claim 4, characterized in that, In step 3, the specific process of generating a double-channel adjustment factor through a hybrid quantum neural network comprises: The feature input vector is fed into a classical fully connected layer for linear transformation to extract preliminary features and match the input dimension of the quantum circuit: ； wherein, , are trainable weights and biases of the classical layer; classical features encoding into a quantum bit in a parameterized quantum circuit: ； wherein, is an initial quantum state, is a unitary operator of the entire quantum circuit, which depends on a characteristic input vector and trainable quantum gate parameters ; Separate the 4-dimensional measurement result vector, and the measurement results are divided into two groups, each group has 2 dimensions, the last 2 elements are used for Q, and the first 2 elements are used for R; One of the sets of 2D vectors is passed through a sigmoid activation function and linear scaling to generate scaling factors for adjusting the diagonal elements of the Q matrix : ； wherein, is a hard-coded scaling and translation parameter in the code, is the last 2 elements of the measurement vector, is a hard-coded scaling and translation parameter in the code; Another set of 2-dimensional vectors are also passed through a Sigmoid activation function and linear scaling to generate scaling factors for adjusting the diagonal elements of the R matrix : ； wherein, is the first 2 elements of the measurement vector, is a scaling coefficient for the R matrix adjustment, is a translation coefficient for the R matrix adjustment.

6. The Q / R dual-adaptive hybrid quantum filtering method for OTFS sensor fusion integrated system according to claim 5, wherein, In step 3, the specific process of constructing adaptive Q and R matrices comprises: using a scaling factor , to adjust the reference noise covariance and the reference noise covariance , respectively, to obtain the finally used adaptive process noise covariance and the adaptive measurement noise covariance at the current time instant: ； ； where diag( ) and diag( ) are diagonal matrices.

7. The Q / R dual-adaptive hybrid quantum filtering method for OTFS sensor fusion integrated system according to claim 6, characterized in that, The specific process of step 4 comprises: At each time step k, the following adaptive state prediction and update steps are performed: Adaptive state prediction step: ； ； Adaptive state update step: (1) Calculate Kalman gain : ； (2) updating the state estimate : ； (3) Update error covariance: 。 8. The Q / R dual adaptive hybrid quantum filtering method for OTFS sensor fusion integrated system of claim 1, wherein, The hybrid quantum neural network obtains its parameters through offline training, and the training process comprises: a. Construct a training data set: generate a large number of simulated trajectories, and maintain a fixed signal-to-noise ratio during the entire trajectory; b. Define a loss function: the loss function is based on the error between the estimated position of the filter and the true position; c. Perform backpropagation: use a framework that supports automatic differentiation to calculate the gradient of the loss function with respect to all trainable parameters of the hybrid quantum neural network; d. Optimize parameters: use an optimizer to update network parameters according to the gradient until the loss function converges.

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