Global data fusion multi-broadband information source tracking method based on extended Kalman filtering

Abstract

The invention provides a global data fusion multi-broadband information source tracking method based on extended Kalman filtering. The method comprises the following steps: integrating time domain receiving signals of all sensors, and carrying out discrete Fourier transform to obtain frequency domain data; constructing a global fusion receiving data and discrete time motion model; estimating an unknown variable through a least square method; then, calculating a Jacobian matrix and calculating a Kalman gain; and finally, state updating is carried out according to the Kalman gain. According to the global data fusion multi-broadband information source tracking method based on extended Kalman filtering, a received signal is directly used as a measurement value, so that a strategy of firstly positioning and then tracking required by traditional tracking is avoided. Meanwhile, the method uses global data fusion and discrete time motion model fusion, and does not need a data association problem during multi-target tracking. In computer simulation, compared with other tracking methods, the method provided by the invention shows better tracking precision and better robustness.

Description

Technical Field

[0001] This invention belongs to the field of target tracking technology, and in particular relates to a multi-wideband source tracking method based on global data fusion and extended Kalman filtering. Background Technology

[0002] Over the past few decades, positioning technology has played a significant role in civilian and military fields such as radar, wireless communication, vehicle technology, and indoor navigation. Passive positioning, as an important component of this technology, has attracted increasing attention due to its advantages such as high accuracy and strong concealment. Although direct positioning technology performs excellently in the detection of static targets, radiation sources in real-world battlefields and security scenarios are often in a non-cooperative, highly dynamic state of motion. Relying solely on static position calculations from a single snapshot not only makes it difficult to grasp the target's velocity, acceleration, and other motion status in real time, but is also susceptible to transient interference that can cause abrupt changes in positioning results. Currently, a common tracking strategy is a two-step tracking method combining positioning and Kalman filtering (KF). This involves performing passive positioning at each tracking moment to obtain a sequence of target positions at all moments, and then using Kalman filtering to obtain a smoothed tracking curve. This method often yields relatively smooth tracking trajectories for single-target tracking, but when handling multi-target tracking, it requires data correlation of target positions, which poses a significant challenge to the final algorithm implementation. Summary of the Invention

[0003] Purpose of the invention: The technical problem to be solved by the present invention is to address the shortcomings of the prior art by providing a global data fusion-based multi-wideband source tracking method based on extended Kalman filtering, which achieves high-precision direct tracking without the need for data correlation.

[0004] This method includes the following steps:

[0005] Step 1: Integrate all time-domain received signals from the sensors and perform a discrete Fourier transform to obtain frequency-domain data;

[0006] Step 2: Construct a globally fused received data and discrete-time motion model;

[0007] Step 3: Estimate the unknown variables using the least squares method;

[0008] Step 4: Calculate the Jacobian matrix and the Kalman gain;

[0009] Step 5: Update the state based on the Kalman gain.

[0010] Step 1 includes: setting There are 1 sensing nodes, each configured with a sensor. The sensors are located in known fixed positions. Where T represents transpose. Indicates the first The x-coordinate of each sensor, Indicates the first The ordinate of each sensor;

[0011] All sensors use a time synchronization mechanism to ensure the temporal consistency of the observed data.

[0012] In step 1, the distributed single-sensor multi-target tracking system has An unknown far-field emission source, An unknown far-field emission source is confined to a fixed-height plane around the sensor and emits uncorrelated broadband signals. The first... An unknown source in the first The tracking time is located at ,in, Indicates the first An unknown source in the first The x-axis of each tracking time point, Indicates the first An unknown source in the first The vertical axis of each tracking moment.

[0013] In step 1, set the first The emitter moves according to a constant velocity model throughout the entire tracking interval, and the first emitter is defined as follows: Each emission source at time The state vector is ,in, and They represent time k at time k. Instantaneous velocity in direction and Instantaneous velocity in the direction; the state transition equation follows a discrete-time linear Gaussian model:

[0014] ,

[0015] Wherein, the transition matrix Represented as:

[0016] ,

[0017] in, For tracking time interval; process noise It is a zero-mean white Gaussian process. covariance matrix Represented as:

[0018] ,

[0019] in, and The process noise intensity along the x-axis velocity and the process noise intensity along the y-axis velocity are represented.

[0020] No. The sensor at the first Signals received at each interception interval for:

[0021] ,

[0022] in, Indicates the first An unknown source in the first The tracking time to the 1st The unknown attenuation coefficient of each sensor, Indicates the first An unknown source in the first The transmitted signal at each tracking moment, Indicates the first An unknown source in the first The tracking time to the 1st The latency of each sensor, Indicates the first The sensor at the first Noise at each tracking moment, Indicates the first The sensor at the first The total number of sampling points at each tracking time point;

[0023] conduct The point discrete Fourier transform yields the transformed value. :

[0024] ,

[0025] Where e represents the natural constant. For imaginary numbers, Indicates the first One frequency, Represents the first in the frequency domain An unknown source in the first The tracking time corresponds to the first... Transmitted signals at various frequencies Represents the first in the frequency domain The sensor at the first The tracking time corresponds to the first... Noise at a certain frequency;

[0026] The start and cutoff frequencies of the effective spectrum are set as follows: and The length of the effective frequency band is denoted as ;comprehensive The received signal of the nth node, the nth Data at each effective frequency point It can be written in the following matrix form:

[0027] ,

[0028] in, , , These are intermediate parameters, expressed as:

[0029] ,

[0030] in, Represents the space of complex numbers. Indicates the first An unknown source in the first The signal flow at each tracking moment Indicates the first An unknown source in the first The tracking time to the 1st The latency of each sensor.

[0031] Step 2 includes: taking into account Each effective frequency point contains spectral information from the same signal source. The frequency domain signals of all selected frequency points are integrated to construct a comprehensive measurement equation, expressed as:

[0032] ,

[0033] in,

[0034] ,

[0035] ,

[0036]

[0037] ,

[0038] in, Indicates all Received data at each effective frequency point These are intermediate parameters. Indicates all Transmitted signal data at each effective frequency point Indicates all Noise data at each effective frequency point;

[0039] consider With multiple emission sources moving simultaneously, the discrete-time kinematic model is defined as follows:

[0040] ,

[0041] in,

[0042] ,

[0043] in, Represents the space of real numbers. Represents the global transition matrix. Indicates the first The global state vector at each tracking time step. Indicates the first Global process noise at each tracking moment, Let be the transition matrix. Indicates the first An unknown source in the first The state vector at each tracking time point express 3D identity matrix Represents the Kronecker product;

[0044] At this point, the state vector at time k covariance matrix Represented as:

[0045] ,

[0046] in, express The covariance matrix is ​​expressed as:

[0047] ;

[0048] in, express The covariance matrix; the complete state-space model of the tracking system is established as follows:

[0049] .

[0050] Step 3 includes: defining the deviation between the predicted signal and the actual signal. for:

[0051] ,

[0052] in, express Predicted values; define the loss function. for:

[0053] ,

[0054] The optimal solution is obtained using the following formula:

[0055] ,

[0056] in, Represents the loss function right Find the partial derivatives;

[0057] Use predicted state Replace the real state Rephrased as:

[0058] ,

[0059] Among them, the Submatrix corresponding to each frequency point Represented as:

[0060] ,

[0061] Where g takes values ​​from 1 to G, Indicates the first Predicting the tracking time step Each tracking moment , express The conjugate transpose of .

[0062] Step 4 includes:

[0063] The Jacobian matrix is ​​calculated using the following expression:

[0064] ;

[0065] in, Indicates the first Jacobian matrix at each tracking time step For intermediate parameters, Indicates the first Predicting the tracking time step The global state vector at each tracking time point. Indicates the first The one in the first Predicting the tracking time step The x-axis of each tracking time point, Indicates the first The one in the first Predicting the tracking time step The horizontal velocity at each tracking moment. Indicates the first The one in the first Predicting the tracking time step The vertical coordinate of each tracking moment Indicates the first The one in the first Predicting the tracking time step The vertical velocity at each tracking moment. express right Partial derivatives in predicted values The value, express right Partial derivatives in predicted values The value, express right Partial derivatives in predicted values The value, express right Partial derivatives in predicted values The value;

[0066] Observation matrix Regardless of speed, we get:

[0067] ,

[0068] Next, the derivation The expression:

[0069] ,

[0070] in,

[0071] ,

[0072] in express right Partial derivatives in predicted values The value; then it was derived:

[0073] ,

[0074] in, express right Partial derivatives in predicted values The value, and For intermediate parameters, Represents the speed of light;

[0075] right The derivation of the partial derivatives is expressed as follows:

[0076] ,

[0077] in, express right Partial derivatives in predicted values The value, and These are intermediate parameters; the Kalman gain is expressed as:

[0078] ,

[0079] in, Indicates the first Kalman gain at each tracking time, Indicates the first Predicting the tracking time step The measurement error covariance matrix at each tracking time point; This represents the error covariance matrix of the measurement equation.

[0080] Step 5 includes: updating the state based on the Kalman gain, expressed as:

[0081] ,

[0082] in, Indicates the first The updated state vector at each tracking time step;

[0083] The state error covariance is updated as follows:

[0084] ,

[0085] in, It is an identity matrix.

[0086] The present invention also provides an electronic device, including a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method.

[0087] The present invention also provides a storage medium storing a computer program or instructions that, when the computer program or instructions are run on a computer, execute the steps of the method described.

[0088] Beneficial effects: The estimation accuracy of the algorithm proposed in this invention is superior to that of traditional two-step localization methods, direct localization methods, and traditional particle filtering methods. Furthermore, the complexity of the algorithm proposed in this invention is significantly improved compared to direct localization methods and traditional particle filtering methods, thanks to the fact that the algorithm can provide a closed-form solution throughout the entire tracking interval without requiring a search. Attached Figure Description

[0089] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, and the advantages of the present invention in the above and / or other aspects will become clearer.

[0090] Figure 1 This is a flowchart at any point in the present invention.

[0091] Figure 2 This is a schematic diagram of distributed single-sensor target tracking.

[0092] Figure 3 This is a trajectory diagram of the radiation source tracking in this invention.

[0093] Figure 4 This diagram illustrates a comparison of the complexity of the present invention with other methods.

[0094] Figure 5 This diagram illustrates the root mean square error performance of the present invention and other methods under different signal-to-noise ratios. Detailed Implementation

[0095] This invention provides a global data fusion method for tracking multiple broadband sources based on extended Kalman filtering, such as... Figure 1 As shown, in this embodiment, bold uppercase letters, bold lowercase letters, and italic letters are as follows: , and Representing matrices, vectors, and scalars respectively. Represents vector The One element, Representation matrix No. Line number Column elements, , and These represent the transpose, conjugate transpose, and inverse operations of a matrix, respectively. Expressing expectations, express Norm. This method specifically includes the following steps:

[0096] Step 1: Integrate all time-domain received signals from the sensors and perform a Discrete Fourier Transform to obtain frequency-domain data:

[0097] Consider tracking scenarios such as Figure 2 Assume there is There are 1 sensing nodes, each configured with a sensor. The sensors are located in known fixed positions. All sensors ensure the temporal consistency of observation data through a precise time synchronization mechanism. The system has... There are three unknown far-field emission sources, confined to a fixed-height plane around the sensor, emitting uncorrelated broadband signals. Assume the first... An unknown source in the first The tracking time is located at .

[0098] Assume the first The emitter moves according to a constant velocity model throughout the entire tracking interval, and the first emitter is defined as follows: Each emission source at time The state vector is ,in, and They represent in and Instantaneous velocity in the direction. The state transition equation follows a discrete-time linear Gaussian model:

[0099] ,

[0100] Wherein, the transition matrix Represented as:

[0101] ,

[0102] in, For tracking time intervals. And process noise. It is a zero-mean white Gaussian process, and its covariance matrix can be expressed as:

[0103] ,

[0104] in, and This represents the process noise intensity along the x-axis and y-axis.

[0105] No. The sensor at the first The signals received during each interception interval are:

[0106] ,

[0107] To conduct Point discrete Fourier transform yields:

[0108] ,

[0109] It should be noted that frequency domain data It does not possess effective energy across the entire frequency band. Assume the start and cutoff frequencies of the effective spectrum are respectively... and The length of the effective frequency band is denoted as .comprehensive The received signal of the nth node, the nth The data at each effective frequency point can be written in the following matrix form:

[0110] ,

[0111] in,

[0112] ;

[0113] Step 2: Construct a globally fused received data and discrete-time motion model:

[0114] Considering Each effective frequency point contains spectral information from the same signal source. The frequency domain signals of all selected frequencies are integrated to construct a comprehensive measurement equation. This method aims to improve the robustness and estimation accuracy of the measurement model by fusing multi-frequency information. The comprehensive measurement model is expressed as:

[0115] ,

[0116] in,

[0117] ,

[0118] ,

[0119] ,

[0120] In multi-source scenarios, the motions of each source are independent. Therefore, the discrete-time kinematic model describing single-target motion is extended to the multi-target case. Under this generalized model, the system simultaneously incorporates multiple emission sources and their individual dynamics, thus enabling a comprehensive characterization of the parallel motions and potential interactions between emission sources. Consider... With multiple emission sources moving simultaneously, the discrete-time kinematic model is defined as follows:

[0121] ,

[0122] in,

[0123] ,

[0124] At this time, the state vector The covariance matrix is ​​expressed as:

[0125] ,

[0126] in, express The covariance matrix is ​​expressed as:

[0127] ;

[0128] At this point, the complete state-space model of the tracking system is established as follows:

[0129] ;

[0130] Step 3: Estimate the unknown variables using the least squares method:

[0131] There is an unknown variable in the above spatial state model. Therefore, the received data is used to estimate the emitted data vector of the radiation source. The deviation between the predicted signal and the actual signal is defined as:

[0132] ,

[0133] in, Represents the residual. express The predicted value. The loss function is defined as:

[0134] ,

[0135] To find the optimal estimate We need to minimize the loss function. By setting the gradient of the loss function to zero and solving the equation, we obtain the optimal solution:

[0136] ,

[0137] However, due to the actual state Unknown, using predicted state Instead, it should be restated as follows:

[0138] ,

[0139] Among them, the Submatrix corresponding to each frequency point Represented as:

[0140] ;

[0141] Step 4: Calculate the Jacobian matrix and the Kalman gain:

[0142] After obtaining the estimate of the transmitted signal using the above method, the next step in EKF is to calculate the Jacobian matrix, expressed as:

[0143] ;

[0144] Considering the observation matrix Regardless of speed, we get:

[0145] ,

[0146] Next, the derivation The expression:

[0147] ,

[0148] in,

[0149] ,

[0150] Finally, it was deduced that:

[0151] ,

[0152] right The derivation of the partial derivatives is similar, and can be expressed as:

[0153] ,

[0154] Therefore, the Kalman gain is expressed as:

[0155] ,

[0156] in, This represents the error covariance matrix of the measurement equation.

[0157] Step 5: Update the state based on the Kalman gain:

[0158] Then, the state is updated based on the Kalman gain described above, as follows:

[0159] ,

[0160] The state error covariance can be updated to

[0161] ,

[0162] in, It is an identity matrix.

[0163] The effectiveness of the algorithm of this invention will be further described below with reference to simulation examples.

[0164] Simulations were performed on a single-channel, multi-base station positioning scenario, considering two far-field moving broadband radiation sources, each emitting a bandwidth... The trajectory of a 16QAM modulated signal can be represented as:

[0165] ,

[0166] in, For discrete-time indexing, sampling interval .

[0167] The number of sensing nodes is , respectively located , , , The sensor sampling rate on each node is set to Regarding the algorithm simulation parameters, the number of sensor sampling points is... The number of effective frequency points selected is ,initialization The algorithm uses the measurement noise variance assumption as follows. . Figure 3 It is a tracking trajectory diagram of the method described in the invention.

[0168] In the simulation, the performance estimation standard of this invention is the root mean square error (RMSE), which is defined as follows:

[0169] ,

[0170] in, Indicates the first During the Monte Carlo experiment, the first Each radiation source at time The estimated value. Set the total number of Monte Carlo runs to 800.

[0171] Figure 4 This is a bar chart showing the complexity of the method of this invention compared to traditional particle filtering and direct localization methods as the number of sensing nodes changes. From Figure 4 It can be seen that the algorithm proposed in this invention is not much different in complexity from the traditional particle filtering method. However, this difference increases with the number of sensing nodes. Since the direct localization method requires a two-dimensional search, its complexity is significantly higher than the other two methods. Because the traditional particle filtering method uses particles to represent the grid position information to be "searched," it is equivalent to performing only a one-dimensional search each time it is used. Since the method proposed in this invention does not require a search process and has a closed-form solution throughout, its algorithm complexity is the lowest.

[0172] Figure 5 This is a performance curve showing the root mean square error of the tracking results of the method of this invention, compared with the two-step method, the direct positioning method, and the traditional particle filtering method, as a function of the signal-to-noise ratio. Its simulation conditions and... Figure 3 Same. From Figure 5 As can be seen, this invention still maintains the highest positioning accuracy.

[0173] In summary, the analysis of the simulation results shows that the global data fusion-based multi-wideband source tracking method based on extended Kalman filtering proposed in this invention can avoid data correlation and can meet the direct tracking of multiple targets by distributed single-channel multi-base stations. At the same time, the algorithm can significantly improve tracking accuracy and has better performance in harsh environments and when the signal-to-noise ratio is low.

[0174] This invention provides a global data fusion method for tracking multiple broadband sources based on extended Kalman filtering. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A global data fusion method for tracking multiple wideband sources based on extended Kalman filtering, characterized in that, Includes the following steps: Step 1: Integrate all time-domain received signals from the sensors and perform a discrete Fourier transform to obtain frequency-domain data; Step 2: Construct a globally fused received data and discrete-time motion model; Step 3: Estimate the unknown variables using the least squares method; Step 4: Calculate the Jacobian matrix and the Kalman gain; Step 5: Update the state based on the Kalman gain.

2. The method as described in claim 1, characterized in that, Step 1 includes: setting There are 1 sensing nodes, each configured with a sensor. The sensors are located in known fixed positions. Where T represents transpose. Indicates the first The x-coordinate of each sensor, Indicates the first The ordinate of each sensor; All sensors use a time synchronization mechanism to ensure the temporal consistency of the observed data.

3. The method as described in claim 2, characterized in that, In step 1, the distributed single-sensor multi-target tracking system has An unknown far-field emission source, An unknown far-field emission source is confined to a fixed-height plane around the sensor and emits uncorrelated broadband signals. The first... An unknown source in the first The tracking time is located at ,in, Indicates the first An unknown source in the first The x-axis of each tracking time point, Indicates the first An unknown source in the first The vertical axis of each tracking moment.

4. The method as described in claim 3, characterized in that, In step 1, set the first The emitter moves according to a constant velocity model throughout the entire tracking interval, and the first emitter is defined as follows: Each emission source at time The state vector is ,in, and They represent time k at time k. Instantaneous velocity in direction and Instantaneous velocity in the direction; the state transition equation follows a discrete-time linear Gaussian model: ， Wherein, the transition matrix Represented as: ， in, For tracking time interval; process noise It is a zero-mean white Gaussian process. covariance matrix Represented as: ， in, and The process noise intensity along the x-axis velocity and the process noise intensity along the y-axis velocity are represented. No. The sensor at the first Signals received at each interception interval for: ， in, Indicates the first An unknown source in the first The tracking time to the 1st The unknown attenuation coefficient of each sensor, Indicates the first An unknown source in the first The transmitted signal at each tracking moment, Indicates the first An unknown source in the first The tracking time to the 1st The latency of each sensor, Indicates the first The sensor at the first Noise at each tracking moment, Indicates the first The sensor at the first The total number of sampling points at each tracking time point; conduct The point discrete Fourier transform yields the transformed value. : ， Where e represents the natural constant. For imaginary numbers, Indicates the first One frequency, Represents the first in the frequency domain An unknown source in the first The tracking time corresponds to the first... Transmitted signals at various frequencies Represents the first in the frequency domain The sensor at the first The tracking time corresponds to the first... Noise at a certain frequency; The start and cutoff frequencies of the effective spectrum are set as follows: and The length of the effective frequency band is denoted as ;comprehensive The received signal of the nth node, the nth Data at each effective frequency point It can be written in the following matrix form: ， in, , , These are intermediate parameters, expressed as: ， in, Represents the space of complex numbers. Indicates the first An unknown source in the first The signal flow at each tracking moment Indicates the first An unknown source in the first The tracking time to the 1st The latency of each sensor.

5. The method as described in claim 4, characterized in that, Step 2 includes: taking into account Each effective frequency point contains spectral information from the same signal source. The frequency domain signals of all selected frequency points are integrated to construct a comprehensive measurement equation, expressed as: ， in, ， ， ， in, Indicates all Received data at each effective frequency point These are intermediate parameters. Indicates all Transmitted signal data at each effective frequency point Indicates all Noise data at each effective frequency point; consider With multiple emission sources moving simultaneously, the discrete-time kinematic model is defined as follows: ， in, ， in, Represents the space of real numbers. Represents the global transition matrix. Indicates the first The global state vector at each tracking time step. Indicates the first Global process noise at each tracking moment, Let be the transition matrix. Indicates the first An unknown source in the first The state vector at each tracking time point express 3D identity matrix Represents the Kronecker product; At this point, the state vector at time k covariance matrix Represented as: ， in, express The covariance matrix is ​​expressed as: ； in, express The covariance matrix; the complete state-space model of the tracking system is established as follows: 。 6. The method as described in claim 5, characterized in that, Step 3 includes: defining the deviation between the predicted signal and the actual signal. for: ， in, express Predicted values; define the loss function. for: ， The optimal solution is obtained using the following formula: ， in, Represents the loss function right Find the partial derivatives; Use predicted state Replace the real state Rephrased as: ， Among them, the Submatrix corresponding to each frequency point Represented as: ， Where g takes values ​​from 1 to G, Indicates the first Predicting the tracking time step Each tracking moment , express The conjugate transpose of .

7. The method as described in claim 6, characterized in that, Step 4 includes: The Jacobian matrix is ​​calculated using the following expression: ； in, Indicates the first Jacobian matrix at each tracking time step For intermediate parameters, Indicates the first Predicting the tracking time step The global state vector at each tracking time point. Indicates the first The one in the first Predicting the tracking time step The x-axis of each tracking time point, Indicates the first The one in the first Predicting the tracking time step The horizontal velocity at each tracking moment. Indicates the first The one in the first Predicting the tracking time step The vertical coordinate of each tracking moment Indicates the first The one in the first Predicting the tracking time step The vertical velocity at each tracking moment. express right Partial derivatives in predicted values The value, express right Partial derivatives in predicted values The value, express right Partial derivatives in predicted values The value, express right Partial derivatives in predicted values The value; Observation matrix Regardless of speed, we get: ， Next, the derivation The expression: ， in, ， in express right Partial derivatives in predicted values The value; then it was derived: ， in, express right Partial derivatives in predicted values The value, and For intermediate parameters, Represents the speed of light; right The derivation of the partial derivatives is expressed as follows: ， in, express right Partial derivatives in predicted values The value, and These are intermediate parameters; the Kalman gain is expressed as: ， in, Indicates the first Kalman gain at each tracking time, Indicates the first Predicting the tracking time step The measurement error covariance matrix at each tracking time point; This represents the error covariance matrix of the measurement equation.

8. The method as described in claim 7, characterized in that, Step 5 includes: updating the state based on the Kalman gain, expressed as: ， in, Indicates the first The updated state vector at each tracking time step; The state error covariance is updated as follows: ， in, It is an identity matrix.

9. An electronic device, characterized in that, It includes a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method as described in any one of claims 1 to 8.

10. A storage medium, characterized in that, It stores a computer program or instructions that, when run on a computer, perform the steps of the method as described in any one of claims 1 to 8.

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