An IMM-STEKF algorithm-based bearing-only underwater target tracking method

Abstract

The application particularly relates to a kind of bearing-only underwater target tracking methods based on IMM-STEKF algorithm, and belongs to the field of underwater target tracking.The method utilizes at least two passive sonars to measure the bearing-only of target, adopts centralized fusion architecture, combines interactive multiple model algorithm with strong tracking extended Kalman filter algorithm to process observation information.Interactive multiple model algorithm effectively tracks the complex maneuvering behavior of target by containing model set of multiple motion models and adaptive switching;Strong tracking extended Kalman filter algorithm enhances the robustness to system model uncertainty and state mutation by introducing dynamic adjustment fading factor.In addition, the application also adopts a waiting mechanism to solve the communication time delay problem in information fusion process.The application effectively improves the precision and stability of underwater maneuvering target tracking under bearing-only condition.

Description

Technical Field

[0001] This invention relates to the field of underwater target tracking technology, specifically to a pure azimuth underwater target tracking method based on interactive multi-model and strong tracking extended Kalman filter algorithm. Background Technology

[0002] Underwater target tracking technology is an important component of marine technology, playing a vital role in both military and civilian fields such as marine surveillance and defense, marine life tracking, and resource exploration. In recent years, with the development of sensor technology, data processing algorithms, and autonomous underwater systems, underwater target tracking technology has become a research hotspot in the field of marine science and technology.

[0003] Underwater target tracking technology refers to the technique of acquiring target range, azimuth, velocity, and other measurement information through active and passive sonar, and then using algorithms to estimate target position, velocity, acceleration, and other information. Based on the sensor's operating mode, it can be divided into active tracking and passive tracking. Active tracking works by sending sound waves through an active sonar and using the echo signals to obtain target motion parameters to estimate the target's state information. This method can directly obtain information such as the target's azimuth, range, and velocity, but its disadvantage is weak concealment, making it vulnerable to enemy countermeasures. Passive tracking, on the other hand, estimates the target's state information by using the azimuth information from the target's radiated signals received by a passive sonar. This method has the advantages of good concealment and low power consumption, but it also suffers from limitations in positioning accuracy and detection range.

[0004] For underwater target tracking based on passive sonar with pure azimuth detection, the low dimensionality of the target's azimuth information obtained using a single passive sonar leads to weak observability. Therefore, most researchers employ collaborative tracking using two or more passive sonars, fusing data from two or more sonars to obtain a more accurate estimate of the target's state information. The main fusion architectures include centralized, distributed, and hybrid architectures. To fuse data from two or more sonars, a corresponding fusion algorithm needs to be designed. The fusion algorithm mainly consists of two parts: a target motion model and a filtering algorithm. First, a target motion model needs to be constructed. Then, a filtering algorithm is used to accurately estimate the target's position, velocity, and heading angle. Common target motion models include uniform motion models, uniform acceleration motion models, uniform turning motion models, CS models, Singer models, and Jerk models. Commonly used filtering algorithms include Kalman filters, extended Kalman filters, unscented Kalman filters, and particle filters. Underwater target tracking based on pure azimuth detection is essentially a nonlinear filtering problem, therefore, nonlinear filtering algorithms are required for processing.

[0005] However, in reality, target motion behavior is often extremely complex, making it impossible to describe its dynamic characteristics with a single model. To address this issue, Bar-Shalom et al. proposed an Interacting Multiple Model (IMM) algorithm. This model designs a model set containing multiple target motion models and uses Markov transition probabilities to achieve adaptive model switching, thus enabling effective tracking of complex target maneuvers. However, most current IMM algorithms use Kalman filters or extended Kalman filters. While these filters can effectively handle linear and nonlinear filtering problems, they struggle to cope with uncertainties in the system model and sudden changes in target state. Furthermore, since information fusion requires sending data or tracks to a fusion center for processing, and the distance between passive sonars is not negligible, communication latency must also be considered.

[0006] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0007] This invention provides a pure orientation underwater target tracking method based on the IMM-STEKF algorithm, aiming to solve problems such as system model uncertainty and sudden changes in target state in underwater target tracking scenarios.

[0008] Other features and advantages of the invention will become apparent from the following detailed description, or may be learned in part by practice of the invention.

[0009] According to a first aspect of the present invention, a pure azimuth underwater target tracking method based on the IMM-STEKF algorithm is provided, the method comprising: Use at least two passive sonars to measure the azimuth of the target and obtain the target's azimuth angle observation information; A centralized fusion architecture is adopted, in which azimuth observation information is input into a fusion algorithm based on interactive multi-model and strong tracking extended Kalman filter for processing to estimate the target's state information; the centralized fusion architecture adopts a parallel filtering method.

[0010] In some exemplary embodiments, the interactive multi-model model set contains at least two different target motion models, each target motion model corresponding to a filter.

[0011] In some exemplary embodiments, the target motion model includes a uniform motion model, a uniformly accelerated motion model, and a uniform turning motion model.

[0012] In some exemplary embodiments, the step of inputting the azimuth observation information into a fusion algorithm based on interactive multi-model and strong tracking extended Kalman filter for processing to estimate the target's state information includes: Input the state estimates and covariance matrices of each filter at the previous time step, and perform weighted fusion of the state estimates and covariance matrices of all sub-models in the model set to obtain the fused state estimates and covariance matrices; Each filter performs strong tracking extended Kalman filter prediction and update based on the interactively fused state and covariance to obtain the state estimate and covariance of each model; The likelihood function is calculated based on the filtered observation residuals of each model, and the occurrence probability of each model at the current time is updated. Based on the updated probabilities of each model, the state estimates of each filter are weighted and fused to output the final target state estimate and covariance.

[0013] In some exemplary embodiments, the weighted fusion of the state estimates and covariance matrices of all sub-models in the model set to obtain the fused state estimates and covariance matrices specifically involves: Time filter The state estimate is The covariance matrix is We perform a weighted fusion of the state estimates and covariance matrices of all sub-models in the model set to obtain the fused state estimates and covariance matrices as follows:

[0014]

[0015] in, for Time model With model The correlation is calculated as follows:

[0016] in, for Time model The probability of occurrence For the model To model The probability of interaction.

[0017] In some exemplary embodiments, each filter performs strong tracking extended Kalman filtering prediction and update based on the interactively fused state and covariance to obtain the state estimate and covariance corresponding to each model, specifically: Substituting the values ​​obtained from the interaction into the filter yields the following result: Time-filtered estimate and covariance matrix The specific process is as follows: First, calculate the predicted state value:

[0018] Calculate the predicted value of the state covariance:

[0019] in, The fading factor is dynamically adjusted, and the specific calculation steps are as follows: Define observation residuals:

[0020] Calculate the theoretical residual covariance:

[0021] Calculate the normalized square of the innovation:

[0022] Construct a sliding window and process the normalized squared innovation over the most recent 10 time steps to obtain the average of the normalized squared innovation. and standard deviation ; but The possible values ​​are as follows:

[0023] Calculate the filter gain, state estimate, and covariance:

[0024]

[0025] .

[0026] In some exemplary embodiments, the method further includes employing a waiting mechanism to address the communication latency issue between the passive sonars within the centralized fusion architecture.

[0027] In some exemplary embodiments, the waiting mechanism is specifically as follows: Let the communication delay be... ,exist Data is collected by both master and slave nodes at all times; among them... T Indicates the observation period; The master node acts as the data fusion center, waiting to receive data from the slave nodes. At that moment, the master node receives data from the slave node and sets the master node in... The data collected in real time is fused with the data arriving from the node with a delay.

[0028] According to a second aspect of the present invention, a storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the pure azimuth underwater target tracking method based on the IMM-STEKF algorithm described in the first aspect.

[0029] According to a third aspect of the present invention, a computer program product is provided, on which a computer program is stored, wherein when the computer program is executed by a processor, the pure azimuth underwater target tracking method based on the IMM-STEKF algorithm described in the first aspect is implemented.

[0030] According to a fourth aspect of the present invention, an electronic device is provided, comprising: Processor; and Memory for storing the executable instructions of the processor; The processor is configured to implement the pure azimuth underwater target tracking method based on the IMM-STEKF algorithm described in the first aspect above by executing the executable instructions.

[0031] The pure azimuth underwater target tracking method based on interactive multi-model and strong tracking extended Kalman filter algorithm provided in the embodiments of the present invention has the following advantages compared with the prior art: 1. Improved tracking accuracy and robustness: By combining an interactive multi-model algorithm, this method can adaptively match the complex maneuvering patterns of the target (such as constant speed, turning, and acceleration), overcoming the limitations of a single motion model. Simultaneously, the dynamic fading factor introduced in the strong tracking extended Kalman filter algorithm effectively suppresses estimation errors caused by system model mismatch and sudden state changes, enhancing the robustness of the filter and thus obtaining more accurate and stable state estimates under target maneuvering conditions.

[0032] 2. Effectively solves the communication latency problem: In view of the inherent latency characteristics of underwater acoustic communication, the waiting mechanism proposed in this invention ensures the spatiotemporal alignment of data from different nodes within the same fusion cycle by actively waiting for the delayed observation data from slave nodes at the fusion center (master node). This avoids the performance degradation caused by asynchronous data fusion and ensures the effective operation of the centralized fusion architecture.

[0033] 3. Enhanced system adaptability and practicality: This invention employs a pure azimuth observation mode using dual (or multiple) passive sonars, maintaining the system's stealth advantage. The proposed algorithm framework comprehensively addresses target maneuverability, model uncertainty, and communication delays, making it more suitable for complex and ever-changing underwater tracking scenarios and enhancing the method's engineering practical value.

[0034] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0035] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0036] Figure 1 Flowchart of the interactive multi-model and strong tracking extended Kalman filter algorithm; Figure 2 Error plots for position estimation using interactive multi-model and strong tracking extended Kalman filter algorithms; Figure 3 Error plots for velocity estimation in interactive multi-model and strong tracking extended Kalman filter algorithms; Figure 4 Error plot of heading estimation for interactive multi-model and strong tracking extended Kalman filter algorithms; Figure 5 A trajectory estimation diagram for underwater maneuvering targets using interactive multi-model and strong tracking extended Kalman filter algorithms; Figure 6 This is a graph showing the change of probability over time in an interactive multi-model approach. Detailed Implementation

[0037] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the invention will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0038] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0039] To address the shortcomings and deficiencies of existing technologies, this example implementation provides a pure azimuth underwater target tracking method based on interactive multi-model and strong tracking extended Kalman filter algorithm. This method uses two passive sonars, adopts a centralized fusion architecture, and combines interactive multi-model and strong tracking extended Kalman filter algorithm to accurately estimate the target's state information. At the same time, a waiting mechanism is adopted to solve the communication delay problem in the information fusion process.

[0040] refer to Figure 1 As shown, the specific steps may include: Step 1: Use at least two passive sonars to measure the azimuth of the target and obtain the target's azimuth angle observation information; Step 2: A centralized fusion architecture is adopted, in which the azimuth observation information is input into a fusion algorithm based on interactive multi-model and strong tracking extended Kalman filter for processing to estimate the target's state information; wherein, the centralized fusion architecture adopts a parallel filtering method.

[0041] The steps in this exemplary embodiment will now be described in more detail with reference to the accompanying drawings and examples.

[0042] Step 1: Use two passive sonars to measure the azimuth angle. The observation period of the passive sonar is 0.5s. Let the coordinates of passive sonar 1 be... The coordinates of passive sonar 2 are The target's location is In practical applications, filtering algorithms are used to process noise, so noise is ignored here.

[0043] exist At that moment, the azimuth angle observation value of passive sonar 1 was:

[0044] The azimuth observations of passive sonar 2 are:

[0045] Step 2: A centralized fusion architecture is adopted, combining interactive multi-model and strong tracking extended Kalman filter algorithms to process the measured azimuth information. The centralized fusion architecture employs parallel filtering. Based on this, underwater target system modeling can be performed.

[0046] The observation equation can be specifically expressed as:

[0047] in: For the target state variable observation vector State transition matrix noise input matrix For process noise For system noise for Position of passive sonar 1 for Position of passive sonar 2 for Position of underwater target at all times Then, linearization is performed on the area near the current estimated point:

[0048] The target's state information can be obtained by running an interactive multi-model and strong tracking extended Kalman filter. The steps are as follows: Step a: Construct an interactive multi-model model set. In this invention, the interactive multi-model model set includes three target motion models: uniform motion model, uniform acceleration motion model, and uniform turning motion model.

[0049] Step b: Input interaction Time filter The state estimate is The covariance matrix is We perform a weighted fusion of the state estimates and covariance matrices of all sub-models in the model set to obtain the fused state estimates and covariance matrices as follows:

[0050]

[0051] in, for Time model With model The correlation is calculated as follows:

[0052] in, for Time model The probability of occurrence For the model To model The probability of interaction.

[0053] Step c: Model matching target state estimation Substituting the values ​​obtained from the interaction into the filter yields the following result: Time-filtered estimate and covariance matrix The specific process is as follows: First, calculate the predicted state value:

[0054] Calculate the predicted value of the state covariance:

[0055] in, The gradually decreasing factor is dynamically adjusted. The specific calculation steps for the process noise covariance are as follows: Define observation residuals:

[0056] Calculate the theoretical residual covariance:

[0057] in, To observe noise covariance Calculate the normalized square of the innovation:

[0058] Construct a sliding window and process the normalized squared innovation over the most recent 10 time steps to obtain the average of the normalized squared innovation. and standard deviation .

[0059] but The possible values ​​are as follows:

[0060] Calculate the filter gain, state estimate, and covariance:

[0061]

[0062]

[0063] Step d: Model probability update Hypothesis Model Observation residuals If it follows a Gaussian distribution, then the likelihood function is... and the probability of occurrence of the model The formula is:

[0064]

[0065] Step e: State synthesis output The weighted average of the model estimates outputs the final state and covariance as follows:

[0066]

[0067] Furthermore, since underwater information transmission is achieved through underwater acoustic signals, transmission delay is indispensable. The passive sonar involved in this invention has an observation period of 0.5 seconds, and in actual target tracking scenarios, the tracking platform will not be too far away. Therefore, it is assumed that the transmission delay will not exceed the observation period. Based on this, this invention employs a waiting mechanism, which assumes a communication delay of... ,exist At any given time, both the master and slave nodes collect data. The master node acts as the data fusion center, waiting to receive data from the slave nodes. At any given moment, the master node receives data from the slave node and performs data fusion using the parallel filtering method mentioned above.

[0068] The method of the present invention is further illustrated below through simulation: (1) Passive sonar parameter settings: Let the coordinates of passive sonar 1 be... The passive sonar 2 coordinates are .

[0069] (2) Target motion parameter settings: The initial position of the underwater maneuvering target is... The initial velocity is The total simulation duration is 150 seconds. The target motion is divided into three segments: the first segment is uniform motion, the second segment is uniform turning motion, and the third segment is uniformly accelerated motion, each segment lasting 50 seconds. The turning angular velocity of the uniform turning motion is 0.05 rad / s, and the eastward acceleration of the uniformly accelerated linear motion is 0.1 rad / s. The northward acceleration is 0.05. .

[0070] (3) Interactive multi-model parameter settings: The initial probabilities of the three target motion models (CV model, CT model, and CA model) in the interactive multi-model are set to... And the probability matrix of the model transition is:

[0071] (4) Strong tracking extended Kalman filter parameter settings: When the motion model is CV and CT model, the initial value is The estimated error covariance matrix is When the motion model is a CA model, the initial value is The estimated error covariance matrix is , The initial value is 1, which can be dynamically adjusted according to different scenarios.

[0072] (5) Noise parameter settings: The basic standard deviation of process noise is 0.05, and it is adjusted according to different motion models. The standard deviation of passive sonar observation noise is... .

[0073] The simulation output statistics include piecewise error statistics for the three motion models (CV, CT, and CA), overall error statistics, and probability changes for the interactive multi-model approach, allowing for more intuitive data analysis. Simulation results based on these parameters are as follows: Figures 2 to 6 As shown: like Figure 2 As shown, the initial position estimation error of the IMM-STEKF algorithm is 25m, the overall average position estimation error is 2.05m, and the RMSE of the position estimation error is 2.92m.

[0074] like Figure 3 As shown, the initial velocity estimation error of the IMM-STEKF algorithm is... The overall average velocity estimation error is 0.82 m / s, and the RMSE of the velocity estimation error is 1.21 m / s.

[0075] like Figure 4 As shown, the initial heading estimation error of the IMM-STEKF algorithm is The overall average heading estimation error is The RMSE of the heading estimation error is .

[0076] like Figure 5 The image shows a visualization of the tracking performance of the IMM-STEKF algorithm.

[0077] like Figure 5 As shown, the probability of the IMM model changes over time. The initial probabilities of the three models are 0.33, 0.33 and 0.34. Ideally, when a certain movement is performed, the probability of that movement model will gradually increase.

[0078] exist Figure 2 , Figure 3 , Figure 4 and Figure 6 The motion patterns at the corresponding time steps are marked with gray vertical lines and text such as CV segment, CT segment and CA segment.

[0079] This invention also performed piecewise error statistics for three motion models, and the error statistics are shown in Table 1. Table 1. Segmentation error statistics for the three motion models

[0080] As can be seen from the table, the CV model has the simplest motion and therefore the best tracking effect, followed by CT tracking, and CA tracking has the worst effect.

[0081] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention, and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0082] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the claims.

[0083] It should be understood that the present invention is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is defined only by the appended claims.

Claims

1. A pure azimuth underwater target tracking method based on the IMM-STEKF algorithm, characterized in that, The method includes: Use at least two passive sonars to measure the azimuth of the target and obtain the target's azimuth angle observation information; A centralized fusion architecture is adopted, in which azimuth observation information is input into a fusion algorithm based on interactive multi-model and strong tracking extended Kalman filter for processing to estimate the target's state information; the centralized fusion architecture adopts a parallel filtering method.

2. The method according to claim 1, characterized in that, The interactive multi-model model set contains at least two different target motion models, each target motion model corresponding to a filter.

3. The method according to claim 2, characterized in that, The target motion model includes a uniform motion model, a uniform acceleration motion model, and a uniform turning motion model.

4. The method according to claim 3, characterized in that, The process of inputting azimuth observation information into a fusion algorithm based on interactive multi-model and strong tracking extended Kalman filter for processing to estimate the target's state information includes: Input the state estimates and covariance matrices of each filter at the previous time step, and perform weighted fusion of the state estimates and covariance matrices of all sub-models in the model set to obtain the fused state estimates and covariance matrices; Each filter performs strong tracking extended Kalman filter prediction and update based on the interactively fused state and covariance to obtain the state estimate and covariance of each model; The likelihood function is calculated based on the filtered observation residuals of each model, and the occurrence probability of each model at the current time is updated. Based on the updated probabilities of each model, the state estimates of each filter are weighted and fused to output the final target state estimate and covariance.

5. The method according to claim 4, characterized in that, The weighted fusion of the state estimates and covariance matrices of all sub-models in the model set to obtain the fused state estimates and covariance matrices is specifically as follows: Time filter The state estimate is The covariance matrix is We perform a weighted fusion of the state estimates and covariance matrices of all sub-models in the model set to obtain the fused state estimates and covariance matrices as follows: in, for Time model With model The correlation is calculated as follows: in, for Time model The probability of occurrence For the model To model The probability of interaction.

6. The method according to claim 5, characterized in that, Each filter performs strong tracking extended Kalman filter prediction and update based on the interactively fused state and covariance, obtaining the state estimate and covariance corresponding to each model, specifically: Substituting the values ​​obtained from the interaction into the filter yields the following result: Time-filtered estimate and covariance matrix The specific process is as follows: First, calculate the predicted state value: Calculate the predicted value of the state covariance: in, The fading factor is dynamically adjusted, and the specific calculation steps are as follows: Define observation residuals: Calculate the theoretical residual covariance: Calculate the normalized square of the innovation: Construct a sliding window and process the normalized squared innovation over the most recent 10 time steps to obtain the average of the normalized squared innovation. and standard deviation ; but The possible values ​​are as follows: Calculate the filter gain, state estimate, and covariance: 。 7. The method according to claim 1, characterized in that, The method also includes employing a waiting mechanism in the centralized fusion architecture to handle the communication latency issue between the passive sonars.

8. The method according to claim 7, characterized in that, The waiting mechanism is specifically as follows: Let the communication delay be... ,exist Data is collected by both master and slave nodes at all times; among them... T Indicates the observation period; The master node acts as the data fusion center, waiting to receive data from the slave nodes. At that moment, the master node receives data from the slave node and sets the master node in... The data collected in real time is fused with the data arriving from the node with a delay.

9. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the pure azimuth underwater target tracking method based on the IMM-STEKF algorithm as described in any one of claims 1 to 8.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the pure azimuth underwater target tracking method based on the IMM-STEKF algorithm as described in any one of claims 1 to 8.

Images