Parallel interactive multi-model target tracking algorithm based on time sequence information

Abstract

Along with diversification and complexity of underwater target motion forms, an existing interactive multi-model algorithm has the problems of slow model switching and insufficient tracking precision when facing target state switching. Therefore, the invention provides a parallel interactive multi-model target tracking algorithm based on time sequence information by taking a classical IMM algorithm as a main body framework. According to the algorithm, model probability change trends at adjacent moments are compared, parameters of a state transition matrix are dynamically corrected, and self-adaptive updating of the state transition matrix is achieved through normalization processing. And meanwhile, the model probability is dynamically updated by utilizing a parallel IMM framework and information entropy, so that the tracking precision reduction caused by excessive correction of a state transition matrix is avoided. Simulation results show that compared with an existing algorithm, the algorithm provided by the invention has the advantage that the prediction precision of the target is improved by 3.52% to 7.87%. And meanwhile, the switching speed of the model is higher, and the underwater target tracking precision is effectively improved.

Description

Technical Field

[0001] The invention relates to a parallel interactive multi-model target tracking algorithm based on time series information, and belongs to the field of underwater target tracking. Background Art

[0002] Underwater target tracking is a highly challenging and crucial research area, widely used in fields such as military defense, ocean exploration, environmental monitoring, and resource exploration. Underwater target tracking can be viewed as a stochastic process. Its modeling process uses mathematical expressions to characterize the target's motion pattern and accurately estimates the target's current position, velocity, and other motion states. Common motion models include the uniform velocity model, uniform acceleration model, uniform turning motion model, Singer model, current statistical model, and Jerk model. However, the motion patterns of underwater targets (such as submarines, unmanned underwater vehicles, and autonomous underwater vehicles) change over time. A single model can only approximate a single motion pattern and cannot accurately describe the target's motion trend, which can easily lead to large tracking errors and even target loss. To address the shortcomings of single models, Bar-shalom et al. proposed an interactive multi-model algorithm. This algorithm uses the Markov transition probability matrix (TPM) to achieve dynamic switching and model fusion during the target state estimation process. Due to its excellent accuracy, robustness, and flexibility, it has been widely used in the field of underwater target tracking.

[0003] In the classic IMM algorithm, the TPM is typically a fixed value pre-set based on prior knowledge, which fails to fully reflect the actual complexity and diversity of target motion. In some complex or uncertain scenarios, this pre-set state can lead to inaccurate predictions of model switching, which in turn affects tracking accuracy. To overcome the limitations of the fixed state transition matrix in the classic IMM algorithm, researchers have proposed a series of improvements, primarily focusing on model selection, optimization of correction factors, parallel processing, and windowing correction. Initially, researchers selected a model ensemble based on turn rate to reduce competition between models, but this approach lacked generalizability. Building on this, a method was proposed that uses the maximum likelihood criterion to determine and correct each row in the TPM, but this incurs a high computational cost. Some researchers have also introduced a likelihood value to define the model compression ratio in the IMM algorithm to achieve adaptive updates. This approach can eliminate the dominant position of the main diagonal in the TPM, reducing the flexibility of model selection. Li Renhao et al. analyzed the sources of error in the model switching and non-switching phases and designed two correction functions. Xie Guo proposed a novel parallel IMM algorithm that combines the adaptive and standard IMM algorithms. This algorithm can ensure rapid TPM adjustments while controlling the lag in system response. Other researchers have also adopted the idea of windowing, using a sliding window to detect possible models and adjust specific rows of the TPM. However, these approaches suffer from high computational complexity, difficulty selecting window lengths, and limited adaptability to high noise and rapid changes, limiting their application in certain real-time and resource-constrained scenarios.

[0004] While existing adaptive IMM algorithms have improved target tracking accuracy to a certain extent, they still suffer from issues such as inaccurate TPM adjustment and delayed algorithm response. Building on previous research, this paper proposes a parallel interactive multi-model target tracking algorithm based on time series information. This algorithm dynamically adjusts the TPM by analyzing the time series information of the model's previous and subsequent probabilities. Furthermore, it corrects the model's probabilities by combining parallel processing with the information entropy of the model probabilities. This correction method effectively improves the flexibility and accuracy of model switching, thereby significantly enhancing the accuracy and robustness of underwater target tracking. Summary of the Invention

[0005] The technical problem solved by the present invention is to propose a parallel interactive multi-model target tracking algorithm based on time series information.

[0006] The present invention proposes a parallel interactive multi-model target tracking method based on entropy adjustment and window correction, the method comprising:

[0007] S1. To address the problem of fixed state transfer matrix in traditional interactive multi-model algorithms, we use windowing to determine the probability change of the model and dynamically modify the state transfer matrix according to certain rules.

[0008] S2. To address the problem that the state transfer matrix may diverge during correction, a parallel interactive multi-model algorithm is used to smooth the state transfer matrix.

[0009] S3. Use information entropy to smooth the probability changes of the model to prevent the model from being over-corrected or incorrectly corrected due to some noise interference.

[0010] Preferably, in S1, the core idea of the IMM algorithm is to dynamically estimate the state of the target by running multiple motion models in parallel and interacting with each other, and to achieve efficient tracking when switching between different motion modes. The core of accurate tracking is how to quickly switch between models. Therefore, the present invention implements dynamic correction of the dynamic transfer matrix according to the following rules:

[0011] (1) Find the model with the highest probability at time t and time t-1 respectively and And record:

[0012]

[0013] (2) If Then no update or correction is performed on TPM. On the contrary, assuming that model i at time t is the model with the highest probability, the following correction principle is obtained:

[0014] π' ij =απ ij i=j

[0015]

[0016] Where α is the growth adjustment coefficient and β is the shrinkage adjustment coefficient.

[0017] (3) If the sum of the elements in any row of the state transition matrix is 1, the modified TPM needs to be normalized, and the normalized matrix obtained is:

[0018]

[0019] Preferably, in S2, the model's probability distribution is stabilized by introducing an uncorrected state transition matrix to address the impact of traditional TPM corrections due to measurement noise or state deviation. The uncorrected TPM retains the system's theoretical transition information and can be considered a form of "a priori" knowledge, while the correction process introduces the influence of measurement information. By combining these two factors to calculate model probabilities, a good balance can be achieved between model a priori knowledge and real-time adjustments, improving the algorithm's adaptability and accuracy.

[0020] Preferably, in S3, the model probability of the IMM algorithm of the modified state transfer matrix is combined with the standard IMM algorithm, and the information entropy is used to smooth the probability of the model to prevent the model from being excessively corrected or incorrectly corrected due to interference from some noise. The specific correction method is as follows:

[0021]

[0022] Where H is the information entropy function.

[0023] Beneficial effects of the present invention. The present invention proposes a parallel interactive multi-model target tracking algorithm based on time series information. The algorithm draws on the ideas of windowing and parallel IMM, and dynamically adjusts TPM through changes in model probability to achieve its correction. In addition, the parallel IMM method is used to correct the model probability, which effectively avoids excessive fluctuations in TPM. Simulation results show that compared with existing algorithms, the algorithm proposed in the present invention has significant advantages in tracking accuracy and stability, and can quickly identify model switching and accurately track targets. Therefore, the algorithm has high practical application value in the field of underwater target tracking. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 Overall framework of the implementation method

[0025] Figure 2 Information entropy of ternary probability distribution

[0026] Figure 3 Observation model diagram

[0027] Figure 4 Tracking comparison chart

[0028] Figure 5 Model probability curve change diagram

[0029] Figure 6 Position error curve

[0030] Figure 7 Comparison of position errors in the X and Y directions DETAILED DESCRIPTION

[0031] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0032] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0033] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0034] This embodiment provides a parallel interactive multi-model target tracking method based on entropy adjustment and window correction. The algorithm combines the previous and next model probabilities and corrects the state transfer matrix according to certain rules. At the same time, it uses the parallel IMM framework and information entropy method to dynamically update the model probability, thereby effectively avoiding the loss of tracking accuracy caused by over-correction of the state transfer matrix. The root mean square error and average error are selected as evaluation indicators for simulation experiments. The overall block diagram of this embodiment is shown below. Figure 1 As shown, the method of this embodiment includes:

[0035] The core idea of the S1 and IMM algorithms is to dynamically estimate the state of the target through the parallel operation and interactive cooperation of multiple motion models, and to achieve efficient tracking when switching between different motion modes. The key to accurate tracking is how to quickly switch between models. Therefore, in order to increase the speed of model switching, the idea of adding windows is adopted. The size of the window is shortened to only consider the probability of the previous and next two models. According to the corresponding rules, π ij The specific amendment rules are as follows:

[0036] (1) Find the model with the highest probability at time t and time t-1 respectively and And record:

[0037]

[0038] (2) If Then no update or correction is performed on TPM. On the contrary, assuming that model i at time t is the model with the highest probability, the following correction principle is obtained:

[0039] When i=j, model i is the main model and the switching probability from model i to model i should be increased:

[0040] π' ij =απ ij

[0041] Where α is the growth adjustment coefficient.

[0042] When i≠j, adjustments should be made based on the changes in the probability of the two models before and after. i (t)-u i When (t-1)≥0, in order to determine the switching probability from model i to model j and from model j to model i, the probability change trend of model j is considered. j (t)-u j (t-1)>u i (t)-ui When (t-1), the switching probability from model i to model j should be increased and the switching probability from model j to model i should be reduced to obtain formula (1).

[0043] π' ij =απ ij ,π' ji =βπ ji

[0044] Conversely, formula (2):

[0045] π' ij =βπ ij ,π' ji =απ ji

[0046] Where β is the reduction adjustment coefficient. i (t)-u i (t-1)<0 and u j (t)-u j (t-1)<u i (t)-u i When (t-1), it indicates that the decay rate of model j is greater, which means that π should be reduced at the next moment. ij and increase π ji Then use formula (1) to adjust it, and vice versa, use formula (2) to adjust it. In this way, the transition probability of the model can be dynamically adjusted by the probabilities of the two previous and subsequent models, not only considering the switch from model i to model j, but also considering the switch from model j to model i. At the same time, to ensure that the sum of the elements in any row of the state transition matrix is 1, the modified TPM needs to be normalized, and the normalized matrix obtained is:

[0047]

[0048] Through the above processing, TPM can make adaptive adjustments according to the actual motion state of the target, dynamically reflect the motion characteristics of the target and quickly respond to the switching requirements of the model, reduce the impact of model conflicts on the final fusion state, and improve estimation accuracy.

[0049] S2. Traditional TPM corrections, often affected by measurement noise or state deviation, are subject to certain influences. This approach stabilizes the model's probability distribution by introducing an uncorrected state transition matrix. The uncorrected TPM retains the system's theoretical transition information, which can be considered a form of "a priori" knowledge, while the correction process introduces the influence of measurement information. By combining these two factors to calculate model probabilities, a good balance is achieved between model a priori knowledge and real-time adjustments, improving the algorithm's adaptability and accuracy.

[0050] S3. In the IMM algorithm, when the probability distribution of the models tends to be average, it means that the state of the target is uncertain. When the probability of one or a few models is significantly higher than that of other models, it means that the algorithm has a strong confidence in the motion state of the target and believes that the current motion state of the target conforms to a certain model. Figure 1 Module A in S1 modifies the state transfer matrix and uses a parallel standard IMM algorithm to process the data. The information entropy of the different model probabilities obtained by modules A and B is used to calculate the new model probability. According to the characteristics of entropy, the larger the entropy value is when the probability distribution is relatively even, assuming that there are three models in total, the entropy values of different probability distributions are shown in the figure. Figure 2 As shown. Therefore, the parallel IMM algorithm designed by combining the above two situations uses the modified IMM to achieve fast jumps between models, and combines it with the standard IMM to prevent the model from excessive or incorrect correction due to some noise interference. Therefore, information entropy is used to smooth the model probability. The specific calculation method is as follows:

[0051]

[0052] Where H is the information entropy function.

[0053] Experimental data processing and analysis

[0054] 1. Experimental environment

[0055] This example proposes a parallel interactive multi-model target tracking method based on temporal information, implemented using Matlab programming. The experimental equipment uses an Intel(R) Core(TM) i7-9700 CPU @ 3.00GHz, 32GB of installed memory, a 64-bit Windows 10 operating system, and a GeForce RTX 2080Ti GPU.

[0056] 2. Evaluation indicators

[0057] To verify the performance of the algorithm, root mean square error (RMS) and mean error (AWE) are used as evaluation metrics. The advantages of RMS error lie in its intuitiveness, sensitivity to large errors, and wide applicability. For tasks such as target tracking, RMS error can both quantify the global error level and reflect the algorithm's performance in dealing with drastic changes or outliers, making it a highly comprehensive evaluation metric. AWE serves as a supplementary metric to comprehensively evaluate model performance.

[0058]

[0059] Where N is the number of Monte Carlo iterations, and T is the experimental parameter for tracking time series length.

[0060] 3. Experimental parameters

[0061] To verify the performance of the proposed algorithm, a two-dimensional rectangular coordinate system was established, assuming the target was moving on a horizontal plane. The sonar position was the origin, with the y-axis being due north and the x-axis being due east. The target's initial position was assumed to be (3000 m, 4500 m), and its initial velocity was (20 m / s, 15 m / s). The total tracking duration was 150 s, and the target's specific motion conditions are shown in Table 1.

[0062] Table 1 Target motion

[0063]

[0064] During the simulation, three motion sub-models, CV, left CT, and right CT, are used to track the target’s motion. The initial model probability is set to u = [1 / 3, 1 / 3, 1 / 3]. Assuming that both the process noise and the observation noise conform to the normal distribution, the process noise Q is set to cv =diag([0.1,0.1,0.1 2 ,0.1 2 ]), observation noise where σ r The distance variance is 50m, σ θ The angular variance is 0.05 rad / s.

[0065] 4. Simulation and result analysis

[0066] (1) In order to verify the performance of the algorithm of the present invention, the standard IMM algorithm, Algorithm 1 and Algorithm 2 proposed by Wang Pingbo and Wang Xiaomin are used as comparative experiments. A total of 100 Monte Carlo simulations are performed, and the tracking trajectory of the target tracking is randomly selected, such as Figure 4 shown.

[0067] according to Figure 3 The analysis shows that all four algorithms can successfully track the maneuvering object throughout the entire tracking process, and their tracking performance is superior to that obtained from the observation data. However, by analyzing the local tracking performance near turning points A (4130m, 5220m) and turning points B (5345m, 5310m), it can be found that the algorithm proposed in this paper is closer to the true value during the turning process than the other three algorithms, and its tracking performance in the turning phase is significantly better than that of the other algorithms.

[0068] (2) The probability of the model in the IMM algorithm plays a decisive role in the performance of the algorithm. The probability change curves of the four algorithm models obtained during the tracking process are shown in Figure 4. Figure (a) is the algorithm of the present invention, Figure (b) is the standard IMM algorithm, Figure (c) is the algorithm 1 proposed by Wang Pingbo, and Figure (d) is the algorithm 2 proposed by Wang Xiaomin.

[0069] according to Figure 5 The observation results show that the algorithm proposed in this paper can quickly identify the main model in the initial tracking process, while the algorithm proposed in the literature

[17] is more difficult to accurately distinguish the main model. In the third tracking process, the algorithm of this paper is more effective in distinguishing different motion models and can quickly remove the interference of model three. For the two uniform speed turning processes, the algorithm of this paper begins to jump to the model at about 44 seconds, showing certain advantages compared with other algorithms.

[0070] (3) In order to evaluate the algorithm performance more intuitively, the present invention uses the root mean square error and the average error as evaluation indicators, and draws the position error curve under the same conditions as (1). Figure 5 As shown, the error curves in the X and Y directions are as follows Figure 6 In addition, the present invention also measures the overall performance of the algorithm by calculating the average error, and the relevant data are listed in Table 2.

[0071] Table 2 Error comparison of four algorithms

[0072]

[0073]

[0074] By comparison Figure 6 、 Figure 7 From Table 2, it can be concluded that the algorithm proposed in this invention is superior to the other three algorithms in terms of overall tracking accuracy. Figure 6 From the position error curve, although the tracking accuracy is slightly lower than other algorithms in some periods, combined with Figure 7 The error trends and average error data show that the proposed algorithm improves tracking accuracy by 7.87% compared to the standard IMM algorithm, and by 3.6% and 3.52% respectively compared to Wang Pingbo's Algorithm 1 and Wang Xiaomin's Algorithm 2. Furthermore, the proposed algorithm also demonstrates significant superiority in terms of average error in the X and Y directions, further validating its effectiveness in complex scenarios.

[0075] (4) In order to evaluate the application effect of the algorithm in engineering, the total running time of 100 Monte Carlo simulations of the four algorithms was calculated respectively, and the average running time of each algorithm in the entire tracking time was calculated. The experimental data are summarized in Table 3.

[0076] Table 3 Running time of four algorithms

[0077]

[0078] Although the TIP-IMM algorithm's runtime is slightly longer than comparable algorithms, it achieves breakthrough improvements in tracking accuracy and stability by introducing an improved model interaction mechanism and dynamic adaptation strategy. This balance of computational efficiency and performance is of great practical value in scenarios requiring stringent accuracy. Furthermore, the algorithm's runtime remains within the millisecond-level real-time range, outperforming existing methods overall.

Claims

1. A parallel interactive multi-model target tracking method based on entropy adjustment and window correction, characterized in that: include: S1. To address the problem of fixed state transfer matrix in traditional interactive multi-model algorithms, we use windowing to determine the probability change of the model and dynamically modify the state transfer matrix according to certain rules. S2. To address the problem that the state transfer matrix may diverge during correction, a parallel interactive multi-model algorithm is used to smooth the state transfer matrix. S3. Use information entropy to smooth the probability changes of the model to prevent the model from being over-corrected or incorrectly corrected due to some noise interference.

2. The method for parallel interactive multi-model target tracking based on entropy adjustment and window correction according to claim 1, characterized in that: In S1: The core idea of the IMM algorithm is to dynamically estimate the target's state by running multiple motion models in parallel and interacting with each other, and to achieve efficient tracking when switching between different motion modes. The key to accurate tracking is how to quickly switch between models. Therefore, the present invention implements dynamic correction of the dynamic transfer matrix according to the following rules: (1) Find the model with the highest probability at time t and time t-1 respectively and And record: (2) If Then no update or correction is performed on TPM. On the contrary, assuming that model i at time t is the model with the highest probability, the following correction principle is obtained: p′ ij =from ij i=j Where α is the growth adjustment coefficient, β is the reduction adjustment coefficient, and π is the state transition moment. (3) If the sum of the elements in any row of the state transition matrix is 1, the modified TPM needs to be normalized, and the normalized matrix obtained is:

3. The method for parallel interactive multi-model target tracking based on entropy adjustment and window correction according to claim 1, characterized in that: In S2: The IMM algorithm uses a likelihood function to reflect the degree of match between the model and the true motion model. However, measurement noise or state deviations can affect TPM corrections. Therefore, an uncorrected state transition matrix is introduced to stabilize the model's probability distribution. The uncorrected TPM retains the system's theoretical transition information and can be considered a form of "prior" knowledge, while the correction process introduces the influence of measurement information. By combining these two factors to calculate model probabilities, a good balance is achieved between model priors and real-time adjustments, improving the algorithm's adaptability and accuracy.

4. The method for parallel interactive multi-model target tracking based on entropy adjustment and window correction according to claim 1, characterized in that: In the S3: Combining the model probability of the IMM algorithm with the modified state transfer matrix and the standard IMM algorithm, the information entropy is used to smooth the model probability to prevent the model from being over-corrected or incorrectly corrected due to some noise interference. The specific correction method is as follows: Where H is the information entropy function.

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