A method for predicting a multifunction radar random waveform sequence

Abstract

The application discloses a prediction method of a multifunctional radar random waveform sequence, which regards a radar signal sequence as a multi-layer syntax structure of regularly connected mixed "radar word"-"radar phrase"-"radar sentence". The working modes of the radar are transformed into each other according to fixed transition probabilities, each working mode corresponds to a fixed phrase template library, and a phrase is selected from the phrase template library each time to complete the function of the working mode. The prediction method distinguishes the occurrence probability of the radar word under two different situations of mode and mode, and the radar word at the next moment can be predicted according to the historical sequence and the corresponding working mode. The method of the application trains a probability model in a statistical learning mode, has strong anti-noise capability, solves the problem of the reduction of the prediction accuracy rate caused by the random template in an adaptive output mode, and avoids multiple iterations and multiple loops through algorithm optimization and matrix design, so that the calculation efficiency and the anti-noise capability are improved.

Description

Technical Field

[0001] This application relates to the field of radar electronic warfare technology, and in particular to a method for predicting random waveform sequences of multifunctional radar. Background Technology

[0002] Pulse jamming is a type of jamming technique that uses high-frequency, short-duration pulses as the underlying signal. It possesses unique advantages such as strong coherence, high instantaneous interference-to-signal ratio, and avoidance of range sampling, effectively reducing the anti-jamming effects of techniques like sidelobe cancellation and space-time adaptive processing. However, modern multi-function radars (MFRs) based on active phased array technology typically employ various techniques such as carrier frequency agility, repetition rate variation / jitter / slip, and waveform phase coding to complicate their waveforms, making them difficult to analyze, identify, and recognize. This makes it difficult for jammers to accurately target and jam the signals. Jamming pulses with parameters significantly deviating from the true echo signal may fail to achieve the necessary suppression coefficient due to insufficient coherent processing gain, or they are likely to be identified as false points and filtered out during fine-tuning. Furthermore, some false points may be located outside the range gate or angle tracking loop, failing to disrupt the radar's target tracking and thus failing to achieve the desired jamming effect. Therefore, it is necessary to predict subsequent pulse parameters to improve the jamming effect.

[0003] Haykin and Visnevski, along with other researchers at McMaster University in Canada, proposed a syntactic structural model to describe MFR sequences, such as... Figure 1 As shown, several pulses are combined to form a "radar word," which serves as the smallest unit for analyzing and predicting the characteristics of the MFR signal. "Radar words" are sequentially combined to form "radar phrases," completing specific radar functions. Multiple "radar phrases" are combined in chronological order to form a "radar sentence," providing a complete description of the radar workflow and reflecting the process of MFR executing parallel tasks. The basic idea of ​​using Predictive State Representation (PSR) for signal sequence analysis and prediction is to statistically calculate the radar word transition probability based on a mathematical model, and then predict the most likely radar word to appear at the next moment based on the radar word strings from previous moments.

[0004] Ou Jian, Research on Multifunctional Radar Behavior Identification and Prediction Technology [D], 2017, National University of Defense Technology; Wolfe BD, Modeling Dynamical Systems with Structured Predictive State Representations [D], The University of Michigan, 2009; Kulesza A, Spectral Learning of Predictive State Representations with Insufficient Statistics [C]. Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015; This paper analyzes, studies, and experiments the basic theory, performance, and effects of PSR. Among them, Research on Multifunctional Radar Behavior Identification and Prediction Technology [D] attempts to apply PSR theory to radar sequence analysis and prediction. The author uses a preprocessing algorithm based on suffix arrays for modeling, iterative methods to search for core history and core events, and maximum likelihood estimation for behavior prediction. The entire process represents the basic idea of ​​mainstream PSR algorithms. However, it is insufficient in estimating the complexity and randomness of MFR signals, and the algorithm itself has some limitations, mainly in the following three aspects.

[0005] First, it is difficult to predict random signals. Within the same operating mode, signals are generated sequentially according to the constraints of "radar phrases," so the current PSR algorithm is relatively accurate in predicting signals within a mode. However, since the transition between modes is random, and the "radar phrase" actually used in each mode is also randomly selected, the probability distribution of these two random variables will affect the prediction accuracy. In other words, even if the algorithm accurately predicts the probability distribution of the next radar word, it cannot predict what the next radar word will actually be, so the algorithm cannot meet the functional requirements of interference guidance. In view of the above problems, the research on multi-functional radar behavior identification and prediction technology [D] is only applicable to predicting MFR signal sequences with fixed sequence templates. The characteristics of this type of sequence are: within the same mode, radar phrases are called sequentially according to a predetermined template. The actual signal sequence is a random template, that is, whenever a certain operating mode is in operation, one is randomly selected from a series of radar phrase libraries corresponding to that operating mode, and the phrase sequence is output. For the difference between the two, see [link to article]. Figure 2 .

[0006] Secondly, different training samples are needed for different operating modes. Traditional PSR cannot be directly trained using sequence signals with multiple mixed modes; instead, it must be trained separately for each mode. During training, the set of "radar phrases" corresponding to the operating mode must be concatenated in some way to form a periodic sample that is connected end-to-end and repeats continuously. Since radar signal sequences are multi-mode mixed, this method requires additional processing based on real sequences to generate training samples, increasing the total number of samples and training time, consuming excessive computational resources, and thus being inefficient and unable to achieve real-time or near-real-time prediction updates.

[0007] Third, it involves numerous computational steps and high complexity. Traditional PSR requires iterative methods to find core history and core events, and to solve the linear relationships between these core states and other states. This process involves inverting large matrices (probability transition matrices), and errors can easily accumulate if problems such as data sparsity or noise contamination occur, leading to inaccurate probability distribution estimation. Because the process of finding core events requires repeated iterations, the space and time complexity of the algorithm also increase. Moreover, many parts of the algorithm use multiple loops, resulting in low computational efficiency and poor accuracy. Summary of the Invention

[0008] This application provides a method for predicting multifunctional radar random waveform sequences. It trains a probability model through statistical learning, which has strong noise resistance. It solves the problem of reduced prediction accuracy caused by random templates by using adaptive output. Furthermore, it avoids multiple iterations and multiple loops and improves computational efficiency through algorithm optimization and matrix design.

[0009] This application provides a method for predicting multifunctional radar random waveform sequences. The radar signal sequence is viewed as a multi-layered syntactic structure consisting of regularly connected hybrid "radar words" – "radar phrases" – "radar sentences." Multiple radar operating modes transition between each other according to fixed transition probabilities. Each operating mode corresponds to a fixed phrase template library. Each time, a phrase is selected from the phrase template library to complete the function of that operating mode. The prediction method is used to predict the radar word for the next time step based on the historical sequence and the corresponding operating mode, including the following steps:

[0010] Calculate the mode transition probability p(φ) τ+1 |ψ τ ), in the same mode (i.e., I τ In (=0), the pattern remains unchanged between the two time steps, satisfying:

[0011]

[0012] Where, φ τ+1 and ψτ These represent the working mode at time τ+1 and the historical mode sequence at time τ, respectively.

[0013] If time τ and τ+1 are in different modes (i.e., I...) τ If = 1), then its mode transition probability can be obtained from frequency statistics, that is,

[0014]

[0015] Among them, #(ψ T φ T+1 ) represents the sequence ψ T φ T+1 Frequency of occurrence; T represents the Tth time block.

[0016] For non-time block event probability Predicting event E τ+1 Only with historical sequences within the current pattern Relevant, independent of historical sequences outside the pattern, and satisfying:

[0017]

[0018] in, p0 represents the historical sequence, and p0 represents I. τ In-mode radar word probability, φ when φ = 0 τ+1 The pattern at time τ+1;

[0019] For the probability of time block events The cross-modal event probability distribution is related to HLM, using time block T to measure the modal index and time block head sequence. The time block head probability is predicted as follows:

[0020]

[0021] Among them, l T The length of the historical time block used for prediction. The event at time T+1 is related to the pattern φ at the same time. T+1 Related to, and also related to, time block sequence Relevant. λ represents the weighting coefficient. Regarding φ T+1 If prior knowledge is available, use the first equation above for estimation; otherwise, use the second equation to directly obtain the result.

[0022] Calculate the overall probability under the two possible conditions using the law of total probability:

[0023]

[0024] Where p(φ) τ+1 |ψτ ,I τ =0), p(ψ) τ+1 |ψ τ ,I τ =1) represents the mode transition probability, This represents the probability of events that are not time block headers. This represents the probability of the event at the beginning of the time block.

[0025] The probabilities mentioned above can be calculated from the event frequency through statistical methods and transformations. During prediction, the set of multiple results with the highest probabilities is output simultaneously, so that the sum of the probabilities of the corresponding radar characters exceeds a preset threshold.

[0026] Optionally, the following content can be predefined:

[0027] Block mode ω T+1 Satisfying the Markov property, the pattern ω at time T+1 T+1 Only with ω T It is related to, but not to, other factors;

[0028] Events within a pattern depend only on the pattern ψ τ and the historical state sequence starting from the current time block head Two factors, unrelated to other factors;

[0029] Time block events depend only on the pattern φ τ+1 Historical pattern block sequence Time block sequence Three factors.

[0030] Optionally, for the mode transition probability p(φ) τ+1 |ψ τ ), in the same mode (i.e., I τ In (=0), the pattern remains unchanged between the two time steps, satisfying:

[0031]

[0032] Where, φ τ+1 and ψ τ These represent the working mode at time τ+1 and the historical mode sequence at time τ, respectively.

[0033] If time τ and τ+1 are in different modes (i.e., I...) τ If = 1), then its mode transition probability can be obtained from frequency statistics, that is,

[0034]

[0035] Among them, #(φ T+1 ψ T ) represents the sequence φT+1 ψ T Frequency of occurrence; T represents the Tth time block.

[0036] Optionally, for non-time block event probabilities Predicting event E τ+1 Only with historical sequences within the current pattern It is relevant, but unrelated to historical sequences outside the pattern; therefore:

[0037]

[0038]

[0039] in, p0 represents a sequence of historical states, where p0 represents I. τ In-mode radar word probability when ψ = 0 τ+1 The pattern at time τ+1 is represented. This represents the pattern sequence within the current pattern. Clearly, all patterns within the time step [τ-k+1, τ+1] should be equal to φ. τ+1 ,Right now Substituting the result back into the above equation, we get...

[0040]

[0041] in, p0 represents the historical sequence, and p0 represents I. τ In-mode radar word probability, φ when φ = 0 τ+1 This represents the pattern at time τ+1.

[0042] Optionally, for the probability of time block events The cross-modal event probability distribution is related to HLM, using time block T to measure the modal index and time block head sequence. The time block head probability is predicted as follows:

[0043]

[0044] Among them, l T The length of the historical time block used for prediction. The event at time T+1 is related to the pattern φ at the same time. T+1 Related to, and also related to, time block sequence Relevant. λ represents the weighting coefficient. Regarding φ T+1 If prior knowledge is available, use the first equation above for estimation; otherwise, use the second equation to directly obtain the result.

[0045] Optionally, the events to be predicted are divided into time block head events and non-time block events according to their position in the pattern, and the overall probability under the above two possible conditions is calculated using the law of total probability:

[0046]

[0047] Where p(ψ) τ+1 |ψ τ ,I τ =0), p(φ) τ+1 |ψ τ ,I τ =1) represents the mode transition probability, Indicates the probability of events within the pattern. This represents the probability of the event at the beginning of the time block.

[0048] Optionally, output the set of multiple results with the highest probabilities simultaneously, satisfying the following:

[0049]

[0050]

[0051] in, Let M represent the set of states for the predicted output, M be the largest integer that makes the above inequality true, and E represent the set of states formed by arranging the probabilities of each state in descending order, i.e.,

[0052] p(E(1))≥…p(E(M))≥…p(E(N)),M≤N

[0053] Where E(m) represents the m-th state in E, N represents the size of the state set, and p TH It is a probability threshold that is set in advance according to the required prediction accuracy.

[0054] This application also proposes a prediction device for a multifunctional radar random waveform sequence. The prediction device includes a processor and a memory. The memory stores a computer program, which, when executed by the processor, implements the steps of the prediction method described above.

[0055] This application also proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the prediction method described above.

[0056] This application's embodiments address the issue of reduced prediction accuracy caused by random templates through adaptive output. By optimizing the algorithm and using matrix design, multiple iterations and multiple loops are avoided, thereby improving computational efficiency and noise resistance.

[0057] This application's embodiments address the issue of reduced prediction accuracy caused by random templates through adaptive output. By optimizing the algorithm and using matrix design, multiple iterations and multiple loops are avoided, thereby improving computational efficiency and noise resistance.

[0058] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0059] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this application. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0060] Figure 1 This refers to the existing MFR syntactic structure model.

[0061] Figure 2 This illustrates fixed sequence templates and random sequence templates in the prior art.

[0062] Figure 3 Symbols for the terms used in this application are for illustrative purposes only.

[0063] Figure 4 A schematic diagram of the radar lettering for the "Mercury" multi-functional radar;

[0064] Figure 5 This is a schematic diagram of the basic prediction process for this application.

[0065] Figure 6 This is a schematic diagram of the algorithm implementation process for example in this application;

[0066] Figure 7 This is a schematic diagram illustrating the predicted transition probability of the "Mercury" radar operating mode in this application example;

[0067] Figure 8 This is a table illustrating the "Mercury" radar operating mode to be predicted and the corresponding radar phrase in the example of this application.

[0068] Figure 9 This is an example of the pattern transition probability prediction results in this application;

[0069] Figure 10 This is an example of the algorithm prediction effect in this application;

[0070] Figure 11 This is a schematic diagram illustrating the noise resistance of the algorithm used in this application. Detailed Implementation

[0071] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0072] This application provides a method for predicting multifunctional radar random waveform sequences, treating the radar signal sequence as a multi-layered syntactic structure of regularly connected hybrid "radar words" – "radar phrases" – "radar sentences" (e.g., Figure 1 As shown, the radar's various operating modes transition between each other according to a fixed transition probability. Each operating mode corresponds to a fixed phrase template library, and a phrase is selected from the phrase template library each time to complete the function of that operating mode. If the phrase selection is performed in a fixed order, it is called a fixed sequence template; if the phrase selection is random, it is called a random sequence template. The difference between the two is as follows: Figure 2 As shown. The embodiments of this application are effective for both sequence modes.

[0073] like Figure 3 As shown, for ease of expression, the following terms are used consistently in this embodiment:

[0074] Time step τ: Each basic unit of time is called a time step. The time to complete one radar word is called one time step.

[0075] Time block T: The minimum time required to complete one mode is called a time block. It consists of several time steps; for example, in the Mercury multi-function radar, T = 4τ.

[0076] Time steps and time blocks are two different levels of time measurement scales. The former is a time measurement for low-level models (LLM), while the latter is a time measurement for high-level models (HLM).

[0077] The state S at time step τ τ At a certain time step, the observable and measurable parameters emitted by the radar can also be referred to as observations. In the embodiments of this application, a radar term represents a state. Related concepts include:

[0078] The state at the moment to be predicted can be called an event, denoted as E. τ+1 =S τ+1 .

[0079] State set S = {S(m) | m = 1, ..., M}: The set of all states. The elements in the set can be ordered according to a certain rule, where the m-th state is denoted by the label of S(m). The state sets studied in this project are all finite, enumerable closed sets.

[0080] State sequence: A sequence of states arranged in order of time steps, where the subscripts and superscripts indicate the end and start time steps of the sequence, respectively. For example...

[0081] Historical state sequence at time τ: The sequence of states that have occurred up to time τ. Denoteed as...

[0082] l H - Metamodel: In this model, future observations depend on previous observations of length l H History; H This is called the model element number or the history state length.

[0083] Time block header: The first state of each time block. For example, if the T-th time block starts at time step τ0, then the header of the T-th time block should be the state of that time step, i.e.

[0084] Time block header sequence: A sequence of time block headers arranged in the order of the time blocks. For example...

[0085] The pattern of the τth time step ω τ Each operating mode corresponds to a radar phrase, which is randomly selected from the set of phrases corresponding to that mode. It also forms a set of related concepts, namely:

[0086] The pattern for the time to be predicted can be denoted as φ τ+1 It is obviously equal to ω τ+1 .

[0087] Pattern sequence: A sequence of patterns organized in units of time steps. The subscripts and superscripts indicate the end and start time steps of the sequence, respectively. Pattern block sequence: A pattern sequence composed of time blocks. The superscripts and subscripts represent the end and start time blocks of the sequence, respectively.

[0088] Historical pattern sequence:

[0089] Block mode: ω T This represents the pattern corresponding to the T-th time block. If the time step τ corresponding to this time block is between τ1 and τ2, then ω τ =ω T ,ifτ∈[τ1,τ2].

[0090] Pattern completion indicator: I τ Used to represent the state S at time τ τ Is this the last state of the current pattern?

[0091]

[0092] Suppose if ω τ =ω T ,I τ =I T Then there must be ω τ+1 =ω T+1 ,φ τ+1 =φ T+1 .

[0093] In practical applications, a single radar word contains a series of pulse trains. Therefore, the algorithm only needs to focus on the design of single-step prediction to guide pulse train interference. For example, in a typical Mercury multi-function radar, each radar word has a total duration of 7.14 ms, consisting of a Doppler pulse sequence and 12 fixed-interval synchronization pulse sequences. Figure 4 As shown. Once a radar word is accurately predicted, the precise parameters of all its pulses can be determined, achieving the goal of precise guidance.

[0094] Traditional PSR algorithms require core event extraction, matrix inversion, and model updates in multi-step prediction, which increases computational load and leads to model instability. This application implements single-step prediction without these steps, reducing resource consumption and improving prediction speed. The prediction method proposed in this application predicts the radar word for the next time step based on historical sequences and corresponding operating modes. The embodiments of this application first calculate the mode transition probability, which determines the likelihood of transitioning from the current mode to other modes. Then, the events to be predicted are divided into time block head events and non-time block head events according to their position in the mode, and the calculation methods for the probabilities of the two types in each mode are determined as follows. Finally, the results obtained from the above steps are combined using the law of total probability to calculate the overall probability of a certain state occurring under various conditions.

[0095] like Figure 5 Specifically, the process includes the following steps:

[0096] The first state of each pattern is called the time block header, and the other states are called non-time block headers or in-pattern states. In this embodiment, the following is predefined (prerequisite):

[0097] Prerequisite 1: Block mode ω T+1 Satisfying the Markov property, the pattern ω at time T+1 T+1 Only with ω T It is related to, but not to, other factors;

[0098] Premise 2: Non-time block events, only dependent on pattern ψ τ and the historical state sequence starting from the beginning of the time block Two factors, unrelated to other factors;

[0099] Premise 3: Time block events depend only on pattern φ τ+1 Historical pattern block sequence ψ τ Time block sequence Three factors.

[0100] Since the events at the beginning of a time block and those not at the beginning of a time block are classified based on whether the pattern has changed, step S501 requires determining the probability of a pattern change. If the pattern has not changed at time τ+1, then the pattern remains unchanged for the two time steps before and after it, i.e.,

[0101]

[0102] Mode transition probability p(φ) τ+1 |ψ τ ,I τ =1) can be obtained from frequency statistics, that is:

[0103]

[0104] Among them, #(ψ T φ T+1 ) represents the sequence ψ T φ T+1 Frequency of occurrence.

[0105] In step S502, for the probability of events within the pattern Predicting event E τ+1 It only relates to the history within the current pattern, and is independent of the history outside the pattern. Assuming the time step interval between time τ and the nearest time block head is i, and the longest history length used by the LLM model is l... H Therefore, the actual historical sequence length k used for prediction should be the smaller of the two, i.e., k = min(i, l H To avoid ambiguity, the embodiments of this application use... Representing historical sequences and using Instead of ψ τ .

[0106] That is, in some embodiments, the probability of events within a pattern is... satisfy:

[0107]

[0108] Where p0 represents I τIn-mode radar word probability when φ = 0. The first equation is derived by considering the mode factor φ. τ+1 The role of this is to improve the accuracy of modeling and prediction. The second equation is derived from premises 1 and 2. Based on the aforementioned analysis, all modes are consistent within the time step [τ-k+1,τ+1], that is... The probability of events within a pattern can be simplified as follows:

[0109]

[0110] In step S503, the probability of the time block head event is... The cross-modal event probability distribution is related to HLM, and the sequence on which the prediction is based is measured using time block T, and its calculation formula becomes:

[0111]

[0112] In the formula, p1 represents I τ The probability of the time block radar word when =1, l T The length of the historical time block used for prediction. Since the block pattern distribution satisfies the Markov property, the pattern transition probability is only related to the most recent pattern; therefore, the second item in this embodiment... It can be simplified to p(φ) T+1 |ω T ), and use the mode transition probability method for training estimation.

[0113] The first term in the formula This indicates that the event at time T+1 is related to both the current temporal pattern and several historical state sequences. In practical applications, it has been found that due to the sparsity of the sample data, this probability is usually difficult to estimate accurately. In this embodiment, interpolation deletion is used to introduce prior probabilities for smoothing, and this term is written as a weighted sum of two probabilities, that is, the probability of the time block head event is calculated as:

[0114]

[0115] Among them, l T The length of the historical time block used for prediction. The expression represents an event at time T+1 that is related to both the current temporal pattern and several historical observations, with λ representing a weighting coefficient. This formula has a clear physical meaning. φ T+1 For E T+1 The probability distribution has two effects. First, the current model φ T+1 This determines which time blocks "should" be observed, and their probability distribution p(E) T+1 |φ T+1 The value is a theoretical value defined by radar designers, and it should correspond to the historical state sequence. Irrelevant. Secondly, it was actually observed that the time block header in this mode is E. T+1 What is the probability of this? Theoretically, the two should be consistent, but due to the pseudo-randomness of engineering implementation, the probability of certain events occurring in a time block will drift relative to its theoretical distribution. These patterns are represented by the second term. The statistical characterization. λ reflects the relative magnitude of the two factors; a larger value indicates that E... T+1 The closer it conforms to the ideal distribution, the better; conversely, the less it conforms to the ideal distribution, the worse it is

[0116] Based on the foregoing embodiments, such as Figure 6 As shown, the probability of the time block head is predicted in the following way:

[0117]

[0118] In relation to φ T+1 If prior knowledge is available, use the first equation above for estimation; otherwise, use the second equation to directly obtain the result.

[0119] In step S504, based on the above results, the conditional probabilities in the two cases are weighted and summed to obtain the total probability of each state occurring:

[0120]

[0121] Where p(φ) τ+1 |ψ τ ,I τ =0), p(φ) τ+1 |ψ τ ,I τ =1) represents the mode transition probability (calculated in step S501), This represents the probability of events within the pattern (calculated in step S502). This represents the probability of the time block head event (calculated in step S503).

[0122] In step S505, the set of multiple results with the highest probability is output simultaneously to make the prediction accuracy higher than a preset threshold.

[0123] This application's embodiments address the prediction accuracy reduction issue caused by random templates through adaptive output. Since the probability distribution of time block headers depends on the radar phrase set corresponding to the pattern, its sample space is typically large, and the probability of each time block header taking a value is relatively small. If only the radar word with the highest probability is output, the prediction accuracy will not exceed the probability of that radar word itself appearing. In this embodiment, the set of the M results with the highest probabilities is output simultaneously, i.e.:

[0124]

[0125]

[0126] in, Let E represent the set of states for the predicted output, where E is the set of states whose probabilities of occurrence are arranged in descending order.

[0127] p(E(1))≥…p(E(M))≥…p(E(N)),M≤N

[0128] Where E(m) represents the m-th state in E, N represents the size of the state set, M is the largest integer that makes the inequality true, and M is the total number of states output in one iteration of the adaptive prediction algorithm, and p TH Positively correlated with the information entropy H(E) of the probability distribution of E, and negatively correlated with it. TH This is a pre-set probability threshold; the higher the value, the higher the prediction accuracy. The size M of the output set is adaptively adjusted according to the probability distribution. If the values ​​of p(E(m)) are generally large, then... TH Assuming the value of M remains constant, it will inevitably decrease.

[0129] As a convenient calculation method, the probability models involved in steps S502 and S503 can be trained using the following approach.

[0130] S1. The state sequence from the training samples and the corresponding pattern sequence spliced ​​into a sequence Following a similar approach to S501, the model is trained using frequency statistics. (Use square brackets to represent matrix models, the same below), then adjust the matrix row and column coordinates accordingly to form the [LLM] model.

[0131] S2. From and Extracting time block sequences The [LLMK] model is obtained based on the training method of S1.

[0132] S3. In the [LLMK] model, make the x-coordinate ω. T+1 The rows are added together to form the [E|phy] model [p(S T+1 |ω T+1 )).

[0133] S4. Sequence of pattern blocks With pattern completion identifier I τ The sequences are concatenated into a single sequence, and the [Close] model is trained using the S1 method.

[0134] After model training is complete, state prediction can be performed according to steps S501 to S505. The detailed implementation process is as follows: Figure 6 As shown.

[0135] This application example further uses the "Mercury" MFR to test the performance of the prediction algorithm, and the radar's mode transition probability is as follows: Figure 7 As shown, the radar phrases corresponding to the operating modes are as follows: Figure 8 As shown. 1500 randomly generated radar phrase sequences were used to train the model, and then predictions were performed on subsequent 4000 radar character sequences. The results are shown below. Figures 9-11 As shown.

[0136] Figure 9 The algorithm's prediction results for the operating mode transition matrix are shown. Labels 1-5 represent five operating modes: search, interception, non-adaptive tracking, range-resolved, and track-and-hold, respectively, while p(E1|H) to p(E5|H) represent the transition probabilities from the current mode to modes 1-5. This is compared with... Figure 7 As can be seen from the theoretical probability comparison shown, the HLM model can accurately reflect the probability of state transition, demonstrating the correctness and reliability of the PSR basic algorithm.

[0137] Figure 10 The prediction results of 100 randomly selected radar word sequences were analyzed. The gray background in the figure highlights the accurately predicted samples, indicating an accuracy of approximately 90%. Further analysis reveals that prediction errors often occur at the beginning of the time block. For signal sequences with random templates, the space of possible random samples at the beginning of the time block is large, and even the most probable predicted states (represented by boxes) are likely to be inconsistent with the actual states. Therefore, this algorithm uses an adaptive output method to increase the number of predicted states each time and employs interpolation smoothing, which effectively improves prediction accuracy.

[0138] Figure 11 This demonstrates the algorithm's robustness to noise. We added a certain percentage of noise to the training data and retested the prediction accuracy; the results are as follows. Figure 11 As shown, when the noise rate exceeds 0.4, the prediction accuracy drops sharply, with the intra-model prediction accuracy (represented by squares) and overall accuracy (represented by circles) showing the most significant decline. The time block prediction accuracy (represented by triangles), due to the use of adaptive output, generally maintains a relatively high level above 0.8; however, the KL divergence between the predicted state's probability distribution and the true distribution increases rapidly by 8-10 times from 0.4, indicating that the algorithm's prediction accuracy for the probability distribution has decreased. It is also noted that when the noise rate is below 0.4, the algorithm maintains good prediction accuracy, demonstrating that, under normal circumstances, the proposed prediction method possesses good noise resistance.

[0139] Compared with mainstream PSR radar sequence prediction techniques, the prediction method in this application has the following advantages:

[0140] (1) It can make predictions for random sequence templates, not just sequential templates. The algorithm is backward compatible and can automatically adapt to MFRs that use sequential templates.

[0141] (2) It has strong predictive ability. The prediction accuracy for radar characters without a fixed output order can reach over 90%.

[0142] (3) The training method is convenient and quick. The actual sequences of various modes appearing in a mixed manner are used for training directly. There is no need to develop a special cycle training template for each mode or reset the training sequence.

[0143] (4) High prediction accuracy. By adopting an adaptive output algorithm, the prediction accuracy of time blocks with low original probability is significantly improved by increasing the number of outputs at one time, based on the accurate estimation of the radar word probability distribution.

[0144] (5) It has strong resistance to noise interference. The model used in the algorithm is trained using statistical methods, and it can achieve high prediction accuracy for training samples with a noise ratio of less than 0.4.

[0145] (6) Strong robustness. The interpolation smoothing method is used to solve the data sparsity problem that is common in time block prediction.

[0146] (7) High computational efficiency. Calculations are performed using a matrix approach, involving operations such as row and column shifting, merging, repeating, and searching, thus improving training and prediction speed. There is no need to extract core history and core events, nor to calculate and update the matrix.

[0147] This application also proposes a prediction device for a multifunctional radar random waveform sequence. The prediction device includes a processor and a memory. The memory stores a computer program, which, when executed by the processor, implements the steps of the prediction method described above.

[0148] This application also proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the prediction method described above.

[0149] It should be noted that, in the embodiments of this application, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0150] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0151] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of this application.

[0152] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims. All of these forms are within the protection scope of this application.

Claims

1. A method for predicting a sequence of multifunction radar random waveforms, characterized in that, The radar signal sequence is regarded as a multi-layer syntax structure of regularly connected mixed "radar word"-"radar phrase"-"radar sentence", and various working modes of the radar are transformed into each other according to fixed transition probabilities, each working mode corresponds to a fixed phrase template library, and each time a phrase is selected from the phrase template library to complete the function of the working mode; the prediction method is used for predicting the radar word at the next time step according to the historical sequence and the corresponding working mode, and comprises the following steps: Computing mode transition probabilities In the same mode, i.e. The mode remains the same for two consecutive time steps, satisfying: wherein, and respectively represent the working mode at the time instant and the history mode sequence at the time instant If With Two moments in different modes, namely Its mode transition probability is derived from frequency statistics, namely: wherein, denotes a sequence occurs; denotes the time block, denotes the state at time whether it is the last state of the current mode; The event to be predicted is divided into time block header events and non-time block header events according to its position in the mode, and the calculation method of the probabilities of the two types in each mode is determined in the following manner: For non-time-block head event probabilities , the predicted event is only related to the history sequence within the current pattern , and is not related to the history sequence outside the pattern, satisfying: wherein, denotes a history sequence, denotes the intra-modal radar word probability in case of, denotes the mode at time instant For time block head event probability The cross-mode event probability distribution is related to the HLM with time block T The time block head probability is predicted in the following way: in, The length of the historical time block used for prediction. express The event at a given moment is both related to the time-to-time pattern. Related to, and also related to, time block sequence related; Indicates the weighting coefficient; in the If there is prior knowledge, use the first equation above to estimate; otherwise, use the second equation to get the result directly. The total probability under the above two possible conditions is calculated by using the total probability formula: wherein, , denotes the mode transition probability, denotes the non-time block head event probability, denotes the time block head event probability; The total probability of the occurrence of a certain state under various conditions is calculated by using the total probability formula to integrate the results obtained in the above steps; During prediction, a set composed of multiple results with the largest probabilities is output simultaneously, so that the sum of the probabilities of the corresponding radar words is higher than a preset threshold.

2. The prediction method of claim 1, wherein, The following contents are defined in advance: Block mode satisfies the Markov property, Mode at time only with regard to, independent of other factors; Intra-mode events, depending only on the mode and the history state sequence from the current time block head 2 factors, independent of other factors; Time block header event, depends only on mode , history mode block sequence , time block header sequence 3 factors.

3. The prediction method of claim 1, wherein, For non-time block header event probabilities satisfies: where, All modes within a time step should be equal to i.e. Thus: 。 4. The prediction method of claim 1, wherein, The set composed of multiple results with the largest probabilities is output simultaneously, and the following conditions are satisfied: wherein, denotes a set of states of the prediction output, is the largest integer that makes the above inequality true, denotes a set of states formed by arranging the probabilities of the occurrence of each state from large to small, that is, wherein, denotes the i-th state, denotes the size of the state set, is a probability threshold which is set in advance according to the prediction accuracy requirement.

5. A device for predicting a sequence of multifunction radar random waveforms, characterized in that, The prediction device comprises a processor and a memory, the memory stores a computer program, and the computer program is executed by the processor to realize the steps of the prediction method in any one of claims 1 to 4.

6. A computer-readable storage medium, characterized in that, The computer readable storage medium stores a computer program, and the computer program is executed by the processor to realize the steps of the prediction method in any one of claims 1 to 4.

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