Loop optimization method based on mismatched filtering model under uncertain information

Abstract

The invention discloses a loop optimization method based on a mismatched filtering model under uncertain information. The loop optimization method comprises the following steps: step 1, determining a fuzzy function template based on an uncertain information mode; 2, constructing a zero-sum game model of a radar party and an interference party; 3, performing improvement based on a template model, and constructing and designing a model independent of a template; and step 4, iterating an optimized waveform through model derivation. Aiming at the problem that a traditional game solving algorithm is extremely difficult to solve in a large-scale network, the method can efficiently obtain the optimal transmitted waveform and the matched waveform, thereby improving the anti-interference capability of a radar system, and effectively solving the problem of calculation efficiency of attack and defense strategy selection in the large-scale network.

Description

Technical Field

[0001] The invention belongs to the technical field of radar waveform design, and in particular relates to a cyclic optimization method based on a mismatch filter model under uncertain information. Background Art

[0002] In modern radar systems, waveform design is one of the key technologies related to its performance and effectiveness. Radar systems detect and identify targets by emitting specific electromagnetic waveforms, while dealing with various complex electromagnetic environments and hostile interference. Traditional waveform design methods often rely on fixed waveform patterns or empirical designs. Although these designs meet basic detection needs to a certain extent, their performance and effectiveness are significantly limited when faced with changing electromagnetic environments and strong electronic warfare interference.

[0003] The development of modern radar technology has driven the continuous evolution and optimization of waveform design methods. Based on advanced signal processing technology and mathematical modeling, the new generation of radar waveform design aims to improve the performance of radar systems in target detection, tracking and anti-interference capabilities by optimizing the energy distribution, spectrum characteristics and spatiotemporal characteristics of the waveform.

[0004] The background technology of waveform design covers many aspects: first, a comprehensive understanding and analysis of the radar working environment and usage scenarios. Different mission requirements may pose different challenges to the waveform design of the radar system, such as high-resolution target recognition, low-probability interception, and effective signal transmission in complex electromagnetic environments. Secondly, waveform design also needs to take into account the actual characteristics and limitations of radar hardware, such as the frequency response, power output capability, and signal processing speed of the transmitter and receiver.

[0005] The steps of waveform design include: 1. Requirements analysis: clarify the performance requirements of the radar system, such as resolution, detection probability, anti-interference ability, etc. 2. Waveform selection: select the appropriate signal type and modulation method according to the requirements. 3. Parameter optimization: optimize the parameters of the signal, such as frequency, phase, amplitude, etc. through mathematical modeling and simulation. 4. Performance evaluation: evaluate the performance of the designed waveform through simulation and experiments to ensure that it meets the system requirements. 5. System integration: integrate the optimized waveform into the radar system for actual testing and verification.

[0006] In traditional waveform design, researchers usually rely on mathematical models and simulation tools to evaluate the performance of different waveform schemes. These models involve the propagation characteristics of radar signals, target feature extraction methods, and interference suppression techniques. With the improvement of computing power and algorithm optimization, modern waveform design increasingly adopts methods based on statistical learning and optimization theory, and maximizes the signal processing efficiency in dynamic scenarios through big data analysis and adaptive algorithms. Summary of the invention

[0007] In view of this, the present invention discloses a cyclic optimization method based on a mismatch filter model under uncertain information. Based on the existing target and interference signal models, a series of waveform templates or optimization parameters are designed, so that the radar system can extract target features to the greatest extent when receiving target signals, and can suppress interference to the greatest extent when facing interference signals, thereby ensuring the stability and performance of the system.

[0008] The object of the present invention is to achieve a loop optimization method based on a mismatch filter model under uncertain information through the following technical solution, the method comprising the following steps:

[0009] Step 1, determining a fuzzy function template based on an uncertain information pattern;

[0010] Step 2: Construct a zero-sum game model between the radar party and the jammer;

[0011] Step 3: Improve the template model to build and design a model that does not rely on the template;

[0012] Step 4: Iterate the optimized waveform through model derivation.

[0013] Furthermore, the uncertain information is randomly distributed based on the ideal model: the radar does not know the precise time delay t of the target. target , but has a certain probability distribution of the target delay; the radar does not know the precise Doppler frequency shift f of the target d,target , but has a certain probability distribution of the target Doppler; the radar knows the jammer's jamming pattern; the radar does not know the jammer's precise delay modulation based on the target delay t jammer , but knows its probability distribution; the radar does not know the precise Doppler frequency shift modulation f of the jammer based on the target Doppler frequency shift d,jammer , but knowing its probability distribution;

[0014] The uncertain information mode means that the radar does not have precise knowledge of the parameters in the target and interference signals, but only has knowledge in the form of probability distribution.

[0015] Furthermore, Q target and Q jammer Represents the characteristic set of the target and the interference source respectively, according to Q target ,Q jammer Probability distribution on :

[0016]

[0017] α k,p is the probability that the kth element in the target feature set is selected under the pth condition, β k,pis the probability that the kth element in the interference source feature set is selected under the pth condition; k is the identifier of different targets or interference sources, and p is the condition associated with each target or interference source;

[0018] To determine the fuzzy function template g k,p ,(k,p)∈T×F corresponding weight

[0019]

[0020] α k′,p′ is the probability that the kth element in the target feature set under the fuzzy function template is selected under the pth condition, β k′,p′ is the probability that the kth element in the interference source feature set under the fuzzy function template is selected under the pth condition, k′ is the identifier of the target or interference source under the fuzzy function template, p′ is the condition associated with each target or interference source under the fuzzy function template, Q zero is a feature set in which the weights of the elements contained in it are uniformly set to 1.

[0021] Furthermore, according to the zero-sum game model of uncertain information pattern + mismatch filtering + mutual fuzzy function:

[0022] Radar side:

[0023]

[0024] Interfering Party:

[0025]

[0026] Among them, χ cross,S,W (τ, f) is the mutual ambiguity function, which is a function of time delay τ and frequency offset f, where τ represents the time delay parameter and f represents the frequency offset parameter. and They represent the local signal-to-noise ratio and interference-to-noise ratio respectively, and their dynamic changes are determined by the internal state of the system and the external control input u radar (t) and v jammer (t) determined by and It is a function that describes the dynamic evolution and is used to calculate the rate of change of the local signal-to-noise ratio and interference-to-noise ratio;

[0027] Building a zero-sum game model:

[0028]

[0029] Among them, min X,Y It indicates that the variables X and Y are minimized. represents the sum of the index set T×F of time delay and frequency offset, gkp Represents the discrete template of the mutual ambiguity function, describing the characteristics of the signal under time delay k and frequency offset p, represents the modulus of the expected value of the mutual fuzzy function template, X H represents the conjugate transpose of X, J kp represents the complex number representation of the mutual ambiguity function template, Y represents the received signal processing vector in the optimization model;

[0030] Equivalent to

[0031]

[0032] in, Represents the variables X, Y and phase angle φ k,p To minimize the operation, Represents a complex exponential function, introducing a phase angle φ kp The phase shift, φ k,p Represents the phase angle, which is used to describe the phase shift of the signal;

[0033] Its standard model form is

[0034]

[0035] Among them, min means minimizing the objective function, represents the sum of the index set T×F of time delay and frequency offset, |X k | represents the modulus of the kth element in X, Indicates that all indexes k that meet the conditions are constrained, and st indicates the constraints. represents the square root of MN, φ kp ∈[0,2π) represents the phase angle φ kp The value range constraints.

[0036] Furthermore, a simplified model is established as follows:

[0037] Determine the symbol vector of the first pulse

[0038] The following M-1 pulse symbol vectors are derived from the symbol vector of the first pulse:

[0039]

[0040] at this time

[0041]

[0042] Get the simplified model:

[0043]

[0044] Among them, min means that the goal is to minimize the subsequent expression, g kp Represents the discrete template of the mutual ambiguity function, describing the characteristics of the signal under time delay k and frequency offset p, Represents a complex exponential function, introducing a phase angle φ kp The phase shift, φ kp Represents the phase angle, which is used to describe the phase shift of the signal. H represents the conjugate transpose of X, J kp represents the complex representation of the mutual ambiguity function template, Y represents the received signal processing vector in the optimization model, st represents the constraint condition, |X 1,n |=1 indicates a constraint condition, ensuring that the first element X in X 1,n The modulus is 1, and for all n, |ρ m |=1 indicates a constraint condition, ensuring ρ m The modulus is 1, for all m, X m,n =ρ m X 1,n Represents constraints, describing how the subsequent parts of X are constructed, where X m,n By m Multiply by X 1,n Get, X m,N+l =0 indicates a constraint condition, ensuring that some elements in X are zero. Represents a constraint condition, ensuring that the modulus of Y is φ kp ∈[0,2π) represents the constraint condition, limiting the phase angle φ kp The value range of .

[0045] Furthermore, the codeword vectors of the first and second pulses are optimized, and other pulse codeword vectors are based on the codewords of the first and second pulses through overall initial phase modulation to establish multiple sub-models.

[0046] Furthermore, a special model that is computationally feasible is constructed. That is, when N+L=1, the code element degenerates into a pulse, and a pulse repetition period is a code element. At this time, the phase coding degenerates into the initial phase modulation of the pulse X=(X1,X2,…,X m ,…,X M ) T , which is the initial phase modulation of M pulses, the model becomes:

[0047]

[0048] At this time, the index set is T = [-M, ..., 0, ..., M],

[0049] Furthermore, the model that does not rely on templates is:

[0050]

[0051] Here is the indicator set Is a proper subset of the original index

[0052] Model

[0053]

[0054] Written in standard model form, we get

[0055]

[0056] Going a step further, create a simplified model for models that do not rely on templates:

[0057] Determine the symbol vector of the first pulse

[0058] The following M-1 pulse symbol vectors are derived from the symbol vector of the first pulse.

[0059]

[0060] at this time

[0061]

[0062] Get the simplified model

[0063]

[0064] Furthermore, a special model that is computationally feasible is constructed. That is, when N+L=1, the code element degenerates into a pulse, and a pulse repetition period is a code element. At this time, the phase coding degenerates into the initial phase modulation of the pulse X=(X1,X2,…,X m ,…,X M ) T is the initial phase modulation of M pulses, and the model becomes

[0065]

[0066] At this time, the indicator set is

[0067]

[0068] Compared with the existing methods, the advantage of the method of the present invention is that network game is a research hotspot in recent years. However, traditional game solving algorithms are extremely difficult to solve in large-scale networks. The present invention can efficiently obtain the optimal transmission waveform and matching waveform, thereby improving the anti-interference ability of the radar system and effectively solving the computational efficiency problem of attack and defense strategy selection in large-scale networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 A schematic diagram of a process flow of an embodiment of the present invention is shown;

[0070] Figure 2 The range Doppler diagram of the target echo and the interference before optimization in the embodiment of the present invention is shown;

[0071] Figure 3 A 2D mutual ambiguity function diagram of a transmission waveform before optimization according to an embodiment of the present invention is shown;

[0072] Figure 4 The optimized range Doppler diagram of the target echo and interference according to the embodiment of the present invention is shown. DETAILED DESCRIPTION

[0073] The present invention is further described below in conjunction with the accompanying drawings, but the present invention is not limited in any way. Any changes or substitutions made based on the teachings of the present invention belong to the protection scope of the present invention.

[0074] In this embodiment, linear frequency modulation is adopted to add noise and interference to the waveform, and the effectiveness of the method is verified by comparing the signal-to-interference-noise ratio before and after optimization.

[0075] like Figure 1 As shown, a loop optimization method based on a mismatch filter model under uncertain information comprises the steps of:

[0076] Step 1, determine the radar and jamming targets based on prior information;

[0077] Step 2, designing a self-fuzzy function template under prior information;

[0078] Step 3: Construct a zero-sum game model between the radar party and the jammer;

[0079] Step 4: Generate optimized waveforms based on the model derivation iterative method.

[0080] Specifically, the uncertain information is:

[0081] The uncertain information model is a random distribution based on the ideal model: the radar does not know the precise time delay t of the target target , but has a certain probability distribution of the target delay; the radar does not know the precise Doppler frequency shift f of the targetd,target , but has a certain probability distribution of the target Doppler; the radar knows the jammer's jamming pattern (assuming it is forwarding deception jamming); the radar does not know the jammer's precise delay modulation t based on the target delay jammer , but knows its approximate probability distribution; the radar does not know the precise Doppler frequency shift modulation f of the jammer based on the target Doppler frequency shift d,jammer , but we know its approximate probability distribution.

[0082] The so-called uncertain information mode means that the radar does not have precise knowledge of the parameters in the target and interference signals, but rather has knowledge in the form of probability distribution.

[0083]

[0084] in They are discrete probability distributions. The uncertain model should be set differently according to different problems, and it is a priori and uncertain a priori.

[0085] Furthermore, the fuzzy function template is:

[0086] The so-called uncertain information mode refers to the radar's response to Q target ,Q jammer is uncertain, so the discrete template g of the designed mutual fuzzy function k,p It is not accurate enough and needs to be adjusted according to Q target ,Q jammer The probability distribution above

[0087]

[0088] To determine the fuzzy function template g k,p ,(k,p)∈T×F corresponding weight

[0089]

[0090] Furthermore, the zero-sum game model is:

[0091] The probability distribution is essentially converted into weights, so the weight distribution can be given directly without giving the probability distribution, which also reflects the uncertainty. Then we can use the zero-sum game model of uncertain information pattern + mismatch filter + mutual fuzzy function:

[0092] Radar side:

[0093]

[0094] Interfering Party:

[0095]

[0096] Can build models

[0097]

[0098] Equivalent to

[0099]

[0100] Written in standard model form, we get

[0101]

[0102] Many simplified models can be established. For example, we determine the code element vector of the first pulse

[0103]

[0104] The following M-1 pulse symbol vectors are derived from the symbol vector of the first pulse.

[0105]

[0106] Then at this time

[0107]

[0108] A simplified model can be obtained

[0109]

[0110] In one embodiment, the symbol vectors of the first and second pulses are further optimized, and other pulse symbol vectors are obtained based on the symbols of the first and second pulses through overall initial phase modulation. Based on this idea, a large number of sub-models are established.

[0111] In one embodiment, a computationally feasible special model is constructed, that is, when

[0112] When $N+L=1$, the code element degenerates into a pulse, and one pulse repetition period is one code element. At this time, the phase coding degenerates into the initial phase modulation of the pulse.

[0113] X=(X1,X2,…,X m ,…,X M ) T

[0114] is the initial phase modulation of M pulses, and the model becomes

[0115]

[0116] At this time, the index set is T = [-M, ..., 0, ..., M],

[0117] The design of the template requires considerable accuracy to achieve good results, which requires the help of intelligent technology. We can improve the above model based on the template model and build and design a model that does not rely on the template.

[0118]

[0119] It must be noted that the indicator set here

[0120]

[0121] Generally speaking, it is a proper subset of the original index. That is because, if a proper subset is not selected, when w kp =C, then according to the law of conservation of energy, we have

[0122]

[0123] Then the optimization is meaningless.

[0124] Model

[0125]

[0126] Written in standard model form, we get

[0127]

[0128] In one embodiment, multiple simplified models are further established. For example, the symbol vector of the first pulse is determined.

[0129]

[0130] The subsequent $M-1$ pulse codeword vectors are derived from the codeword vector of the first pulse.

[0131]

[0132] Then at this time

[0133]

[0134] A simplified model can be obtained

[0135]

[0136] In one embodiment, the symbol vectors of the first and second pulses are further optimized, and other pulse symbol vectors are based on the symbols of the first and second pulses through overall initial phase modulation. With this idea, a large number of sub-models can be established.

[0137] In one embodiment, a computationally feasible special model is constructed, that is, when

[0138] When $N+L=1$, the code element degenerates into a pulse, and one pulse repetition period is one code element. At this time, the phase coding degenerates into the initial phase modulation of the pulse:

[0139] X=(X1,X2,…,X m ,…,X M ) T

[0140] is the initial phase modulation of M pulses, and the model becomes

[0141]

[0142] At this time, the indicator set is

[0143] T=[-M,…,1,…,M],

[0144] According to the above content, the range Doppler image before optimization in this embodiment is as follows: Figure 2 As shown, the mutual fuzzy function diagram before optimization is as follows Figure 3 As shown. To optimize the waveform, first, the radar initial waveform, filter and other necessary parameters are given. The two-dimensional color map and three-dimensional function map of the fuzzy function of the initial waveform and filter are calculated. According to the model of the target and interference, a range Doppler image is formed, and the local signal-to-interference-noise ratio of the target unit is calculated. The initial waveform and filter of the radar are modulated using the fuzzy function-based model and algorithm in the previous article, and the waveform and filter are output. The two-dimensional color map and three-dimensional function map of the fuzzy function of the modulated waveform and filter are calculated. Again, according to the signal model of the target and interference, a range Doppler image is formed, and the local signal-to-interference-noise ratio of the target unit is calculated. Compare the shapes of the fuzzy functions before and after, and compare the clarity and local signal-to-interference-noise ratio of the target units before and after. The optimized range Doppler map is shown as follows. Figure 4 shown.

[0145] Compared with the traditional waveform design method, the loop optimization method based on the mismatch filter model under uncertain information proposed in this invention can significantly improve the performance of the radar system in a complex electromagnetic environment. By optimizing the waveform design, not only can the detection and recognition capabilities of the target be improved, but also various forms of interference signals can be effectively suppressed, thereby improving the anti-interference ability and survivability of the radar system.

[0146] As used herein, the word "preferred" is intended to be used as an example, instance, or illustration. Any aspect or design described herein as "preferred" is not necessarily to be construed as being more advantageous than other aspects or designs. On the contrary, the use of the word "preferred" is intended to present concepts in a specific way. The term "or" as used in this application is intended to mean an inclusive "or" rather than an exclusive "or". That is, unless otherwise specified or clear from the context, "X uses A or B" means any one of the naturally included permutations. That is, if X uses A; X uses B; or X uses both A and B, then "X uses A or B" is satisfied in any of the foregoing examples.

[0147] Moreover, although the present disclosure has been shown and described with respect to one or implementations, those skilled in the art will think of equivalent variations and modifications based on the reading and understanding of this specification and the accompanying drawings. The present disclosure includes all such modifications and variations, and is limited only by the scope of the appended claims. In particular, with respect to the various functions performed by the above-mentioned components (such as elements, etc.), the terms used to describe such components are intended to correspond to any component (unless otherwise indicated) that performs the specified function of the component (such as it is functionally equivalent), even if the structure is not equivalent to the disclosed structure of the function in the exemplary implementation of the present disclosure shown herein. In addition, although the specific features of the present disclosure have been disclosed with respect to only one of several implementations, such features can be combined with one or other features of other implementations that may be desired and advantageous for a given or specific application. Moreover, insofar as the terms "including", "having", "containing" or their variations are used in specific embodiments or claims, such terms are intended to be included in a manner similar to the term "comprising".

[0148] The functional units in the embodiments of the present invention may be integrated into a processing module, or each unit may exist physically separately, or multiple or more units may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium. The above-mentioned storage medium may be a read-only memory, a disk or an optical disk, etc. The above-mentioned devices or systems may execute the storage method in the corresponding method embodiment.

[0149] To sum up, the above embodiment is an implementation mode of the present invention, but the implementation mode of the present invention is not limited by the embodiment. Any other changes, modifications, substitutions, combinations, and simplifications that deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A loop optimization method based on a mismatch filter model under uncertain information, characterized in that: The following steps are involved: Step 1, determining a fuzzy function template based on an uncertain information pattern; Step 2: Construct a zero-sum game model between the radar party and the jammer; Step 3: Improve the template model to build and design a model that does not rely on the template; Step 4: Iterate the optimized waveform through model derivation.

2. The loop optimization method based on the mismatch filter model under uncertain information according to claim 1, characterized in that: The uncertain information is randomly distributed based on the ideal model: the radar does not know the precise time delay t of the target. target , but there is a certain probability distribution of the target delay; The radar does not know the exact Doppler shift f of the target. d,target , but has a certain probability distribution of the target Doppler; the radar knows the jammer's jamming pattern; the radar does not know the jammer's precise delay modulation based on the target delay t jammer , but knows its probability distribution; the radar does not know the precise Doppler frequency shift modulation f of the jammer based on the target Doppler frequency shift d,jammer , but knowing its probability distribution; The uncertain information mode means that the radar does not have precise knowledge of the parameters in the target and interference signals, but only has knowledge in the form of probability distribution.

3. The loop optimization method based on the mismatch filter model under uncertain information according to claim 2 is characterized in that: Q target and Q jammer Represents the characteristic set of the target and the interference source respectively, according to Q target ,Q jammer Probability distribution on : α k,p is the probability that the kth element in the target feature set is selected under the pth condition, β k,p is the probability that the kth element in the interference source feature set is selected under the pth condition; k is the identifier of different targets or interference sources, and p is the condition associated with each target or interference source; T and F are the index sets of time delay and frequency offset, which determine the fuzzy function template g k,p ,(k,p)∈T×F corresponding weight α k′,p′ is the probability that the kth element in the target feature set under the fuzzy function template is selected under the pth condition, β k′,p′ is the probability that the kth element in the interference source feature set under the fuzzy function template is selected under the pth condition, k′ is the identifier of the target or interference source under the fuzzy function template, p′ is the condition associated with each target or interference source under the fuzzy function template, Q zero is a feature set in which the weights of the elements contained in it are uniformly set to 1.

4. The loop optimization method based on the mismatch filter model under uncertain information according to claim 3 is characterized in that: Based on the zero-sum game model of uncertain information pattern + mismatch filtering + mutual fuzzy function: Radar side: Interfering Party: Among them, χ cross,S,W (τ, f) is the mutual ambiguity function, which is a function of time delay τ and frequency offset f, where τ represents the time delay parameter and f represents the frequency offset parameter. and They represent the local signal-to-noise ratio and interference-to-noise ratio respectively, and their dynamic changes are determined by the internal state of the system and the external control input u radar (t) and v jammer (t) determined by and It is a function that describes the dynamic evolution and is used to calculate the rate of change of the local signal-to-noise ratio and interference-to-noise ratio; Building a zero-sum game model: Among them, min X,Y It indicates that the variables X and Y are minimized. represents the sum of the index set T×F of time delay and frequency offset, g kp Represents the discrete template of the mutual ambiguity function, describing the characteristics of the signal under time delay k and frequency offset p, represents the modulus of the expected value of the mutual fuzzy function template, X H represents the conjugate transpose of X, J kp represents the complex number representation of the mutual ambiguity function template, Y represents the received signal processing vector in the optimization model; Equivalent to in, Represents the variables X, Y and phase angle φ k,p To minimize the operation, Represents a complex exponential function, introducing a phase angle φ kp The phase shift, φ k,p Represents the phase angle, which is used to describe the phase shift of the signal; Its standard model form is Among them, min means minimizing the objective function, represents the sum of the index set T×F of time delay and frequency offset, |X k | represents the modulus of the kth element in X, Indicates that all indexes k that meet the conditions are constrained, and st indicates the constraints. represents the square root of MN, φ kp ∈[0,2π) represents the phase angle φ kp The value range constraints.

5. The loop optimization method based on mismatch filter model under uncertain information according to claim 4 is characterized in that: The simplified model is established as follows: Determine the symbol vector of the first pulse The following M-1 pulse symbol vectors are derived from the symbol vector of the first pulse: at this time Get the simplified model: Among them, min means that the goal is to minimize the subsequent expression, g kp Represents the discrete template of the mutual ambiguity function, describing the characteristics of the signal under time delay k and frequency offset p, Represents a complex exponential function, introducing a phase angle φ kp The phase shift, φ kp Represents the phase angle, which is used to describe the phase shift of the signal. H represents the conjugate transpose of X, J kp represents the complex representation of the mutual ambiguity function template, Y represents the received signal processing vector in the optimization model, st represents the constraint condition, |X 1,n |=1 indicates a constraint condition, ensuring that the first element X in X 1,n The modulus is 1, and for all n, |ρ m |=1 indicates a constraint condition, ensuring ρ m The modulus is 1, for all m, X m,n =ρ m X 1,n Represents constraints, describing how the subsequent parts of X are constructed, where X m,n By m Multiply by X 1,n Get, X m,N+l =0 indicates a constraint condition, ensuring that some elements in X are zero. Represents a constraint condition, ensuring that the modulus of Y is φ kp ∈[0,2π) represents the constraint condition, limiting the phase angle φ kp The value range of .

6. The loop optimization method based on mismatch filter model under uncertain information according to claim 5 is characterized in that: The code element vectors of the first and second pulses are optimized, and other pulse code element vectors are based on the code elements of the first and second pulses through overall initial phase modulation to establish multiple sub-models.

7. The loop optimization method based on mismatch filter model under uncertain information according to claim 6 is characterized in that: Construct a special model that is computationally feasible, that is, when N+L=1, the code element degenerates into a pulse, and a pulse repetition period is a code element. At this time, the phase coding degenerates into the initial phase modulation of the pulse X=(X1,X2,…,X m ,…,X M ) T , which is the initial phase modulation of M pulses, the model becomes: At this time, the index set is T = [-M, ..., 0, ..., M], 8. The loop optimization method based on mismatch filter model under uncertain information according to claim 7, characterized in that: The models that do not rely on templates are: Here is the indicator set Is a proper subset of the original index Model Written in standard model form, we get 9. The loop optimization method based on mismatch filter model under uncertain information according to claim 8, characterized in that: Create a simplified model for a model that does not rely on templates: Determine the symbol vector of the first pulse The following M-1 pulse symbol vectors are derived from the symbol vector of the first pulse. at this time Get the simplified model 10. The loop optimization method based on mismatch filter model under uncertain information according to claim 9, characterized in that: Construct a special model that is computationally feasible, that is, when N+L=1, the code element degenerates into a pulse, and a pulse repetition period is a code element. At this time, the phase coding degenerates into the initial phase modulation of the pulse X=(X1,X2,…,X m ,…,X M ) T is the initial phase modulation of M pulses, and the model becomes At this time, the indicator set is

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