Method for detecting and tracking low-observable object having boost-glide trajectory under slant range ambiguity condition

Abstract

The present invention relates to the field of near-space hypersonic object detection and tracking, and provides a method for detecting and tracking a low-observable object having a boost-glide trajectory under a slant range ambiguity condition. The method comprises: configuring an alternating pulse repetition frequency model used for radar ranging; defining an extended non-coherent accumulation model in a range-time plane used for object detection; configuring an S-type recursive energy tracking model used for object tracking; and designing a recursive energy filter, and performing updating by means of recursive energy, such that object tracking is always maintained under a high signal-to-noise ratio condition, and an object track is obtained by using a filtering algorithm. In the method of the present invention, the pulse repetition frequency in a same sampling period is designed to be a fixed value, so that sufficient energy is provided for coherent accumulation detection; and then the pulse repetition frequency between different sampling periods is designed to be an alternately convertible value, so that a condition for solving the problem of slant range ambiguity is provided. Additionally, conditions can be provided for solving the problem of slant range ambiguity.

Description

Low-observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions

[0001] Technical Field

[0002] The present invention belongs to the field of near-space hypersonic target detection and tracking; in particular, it relates to a low-observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions.

[0003] Background Art

[0004] Currently, near-space refers to airspace between 20km and 100km above sea level. Near-space hypersonic vehicles are atmospheric or suborbital vehicles capable of traveling at speeds exceeding Mach 5 in near-space. Unlike traditional aerodynamic and satellite orbital targets, near-space targets utilize a unique hypersonic boost-glide trajectory, enabling rapid attacks on any target worldwide within an hour. In particular, with the successful testing of hypersonic vehicles such as the AGM-183A and X-51A, near-space hypersonic weapons have become a preferred means of implementing a global strike strategy. However, existing radar early warning and defense systems are unable to effectively track and intercept these targets.

[0005] To achieve early warning of hypersonic targets, radars must detect them at long ranges. If these targets can be detected and tracked at long ranges, radar warning and defense systems will have ample time to respond to these hypersonic weapon threats. However, in long-range detection modes, radar ranging suffers from slant range ambiguity. With slant range ambiguity, it's difficult to distinguish which transmitted pulse signal a received radar echo originates from, making it impossible to determine the true distance between the target and the radar.

[0006] As a classic method for resolving slant range ambiguity, the multi-pulse repetition frequency (PRF) method is widely used in target detection and tracking. Its advantage is that it can resolve slant range ambiguity while simultaneously performing coherent integration detection of the target. However, its disadvantage is that because a single coherent integration cycle is divided among multiple PRFs, the echo energy after coherent integration rarely reaches the target detection threshold. In particular, in low signal-to-noise ratio conditions, slant range ambiguity cannot be resolved due to missed targets.

[0007] However, hypersonic targets inevitably exhibit certain stealth characteristics. When a target travels at hypersonic speeds, a large amount of shock plasma is generated around it. This shock plasma strongly absorbs, scatters, and reflects radar electromagnetic waves, thereby imparting a certain degree of stealth to the target. This also means that simply using coherent integration over a short period of time is difficult to achieve the energy required for target detection, and therefore cannot effectively resolve the problem of slant range ambiguity.

[0008] Summary of the Invention

[0009] The present invention provides a low-observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions, which is used to simultaneously solve the target detection and tracking problems under the combined influence of slant range ambiguity, low observability and boost-glide maneuvering derived from the target's hypersonic motion.

[0010] Methods include:

[0011] S1: Configures an alternating pulse repetition frequency model for radar ranging;

[0012] ①Measure the fuzzy slant distance of the target by alternating pulse repetition frequency;

[0013] ② Restore the target's true distance;

[0014] S2: Define an extended non-coherent accumulation model in the range-time plane for target detection;

[0015] ① Define the extended non-coherent accumulation model;

[0016] ② Select the distance-time plane;

[0017] ③ Expanding the non-coherent accumulation detection method based on distance-time Hough transform;

[0018] ④ Detection of low observable targets;

[0019] S3: Configure the S-type recursive energy tracking model for target tracking;

[0020] ①Configure S-type motion model;

[0021] ② Design a recursive energy filter and update it through recursive energy to keep the target tracking under high signal-to-noise ratio conditions, and use the filtering algorithm to obtain the target track.

[0022] It should be further explained that the method of measuring the fuzzy slant distance of the target by using the pulse repetition frequency alternating conversion method in step S1 also includes:

[0023] In the same sampling period, the pulse repetition frequency is constant. The fuzzy measurement of time is,

[0024] (1)

[0025] in, is the blurred slant distance, is the azimuth, is the pitch angle, is the amplitude of the echo pulse.

[0026] It should be further explained that, when the radar ranging model is designed using three alternating pulse repetition frequencies, the fuzzy slant distance of the target is expressed as

[0027] (2)

[0028] in,

[0029] (3)

[0030] Formula (3) calculates the The fuzzy slant distance of the pulse repetition frequency, The calculation is performed as follows:

[0031] (4)

[0032] is the actual delay of the echo pulse, represents the modular operation, is the pulse repetition period, It is Pulse repetition frequency, is the speed of light, .

[0033] It should be further explained that the steps of restoring the target's true distance also include:

[0034] Based on radar ranging The pulse repetition frequency is ,but The corresponding maximum unambiguous slant distance is,

[0035] (5)

[0036] If the interval Blurred slant distance If the expansion is performed, the extended slope distance is expressed as,

[0037] , (6)

[0038] in, It is Extended tilt distance, is the amount of extended slant distance;

[0039] If the true range is less than the radar range, the amount of extended slant range is given by:

[0040] (7)

[0041] in, is the radar’s ranging range, Indicates rounding operation;

[0042] The extended measure of the target is given by:

[0043] , (8)

[0044] in, For the The first PRF An extended measurement.

[0045] It should be further explained that the definition of the extended non-coherent accumulation model in step S2 also includes:

[0046] First, multi-hypothesis processing is performed on the alternating multi-pulse repetition frequency measurement; second, non-coherent accumulation detection is performed simultaneously with the coherent accumulation detection of the target, so that the accumulated energy of the low-observable target reaches the target detection threshold; finally, the detection of the low-observable target is completed.

[0047] It should be further explained that the selection of the distance-time plane in step S2 also includes:

[0048] Assume that the slant distance of the target is , the radar angle measurement error is , then the target position measurement deviation is,

[0049] (9)

[0050] Based on 3 The judgment criterion is that the maximum value of the target position measurement deviation is , the target position measurement deviation is much larger than the radar distance measurement error of hundreds of meters.

[0051] It should be further explained that the non-coherent accumulation detection method based on distance-time Hough transform in step S2 also includes: setting is a point in the distance-time plane, where is the pulse repetition frequency No. Extended tilt distance, yes The time stamp, The way to obtain the unique curve corresponding to the point in the plane is as follows,

[0052] (10)

[0053] in, yes The distance from the point to the origin, yes Axis and The angle between the axes;

[0054] If multiple curves are If they intersect at one point in the plane, there is a straight line corresponding to the multiple curves in the distance-time plane, and the straight line is expressed as

[0055] (11)

[0056] in, is the intersection of multiple curves. and are the distance variable and time variable corresponding to the straight line respectively.

[0057] It should be further explained that the method of detecting low observable targets in step S2 also includes: The plane is divided into Several cells, so that the target energy is accumulated in one of the cells;

[0058] Cell The center of is represented as,

[0059] (12)

[0060] (13)

[0061] in,

[0062] (14)

[0063] (15)

[0064] yes the number of units, yes the number of units, is the radar’s range;

[0065] In the pair Based on the plane discretization, The curve in the plane is represented by a pair of The mapping is replaced by,

[0066] (16)

[0067] in, is a point in the distance-time plane, yes In the plane A collection of points, ;

[0068] In the pair 1 pair of curves in a plane After mapping, click The energy in will be stored in the cells that the curve passes through, and the cells The energy in is expressed as,

[0069] (17)

[0070] in, It is a cell The existing energy in yes Energy of a point;

[0071] If multiple points in the distance-time plane are approximately connected into a straight line, the energy of the multiple points will be concentrated In a cell in the plane, low-observable object detection is formulated as the following hypothesis test:

[0072] : , in the cell The target is detected in

[0073] : , in the cell No target was detected in the

[0074] in, is the energy threshold;

[0075] In the assumption Under the condition that , the target trajectory is obtained by the following Hough inverse mapping,

[0076] (18)

[0077] Low observable targets are then detected from extended slant ranges.

[0078] It should be further explained that the configuration of the S-type motion model in step S3 also includes:

[0079] The autocorrelation function of the target acceleration is designed as,

[0080] (19)

[0081] in, for The target acceleration at the moment, for The instantaneous covariance of Angular rate for a boost-glide trajectory to the target;

[0082] Perform Fourier transform on the autocorrelation function of the target acceleration, and the power spectrum of the target acceleration is expressed as,

[0083] (20)

[0084] Configure the approximate whitening filter as,

[0085] (twenty one)

[0086] Assumptions yes The expression in the time domain is The Laplace transform of

[0087] (twenty four)

[0088] and then The differential equation is expressed as

[0089] (25)

[0090] in, has zero mean and constant variance Input white noise;

[0091] Assumptions

[0092] (26)

[0093] yes The target state vector in the X direction at time t, , , and are the target's position, velocity, acceleration, and jerk, respectively, and there is

[0094] (27)

[0095] The state phasor Substitution The continuous motion equation of the target is expressed as

[0096] (28)

[0097] in,

[0098] (29)

[0099] (30)

[0100] Integrate both sides of the target continuous motion equation to obtain the target discrete motion equation

[0101] (31)

[0102] The discrete motion equation of the target is rewritten as

[0103] (32)

[0104] in

[0105] (33)

[0106] is the state transition matrix, is the time interval,

[0107] (34)

[0108] is a constant variance

[0109] (35)

[0110] Zero-mean Gaussian white noise.

[0111] It should be further explained that the design of the recursive energy filter in step S3 also includes:

[0112] Assumptions The recursive energy at the moment is:

[0113] (36)

[0114] in, It is The energy of each trajectory point, ;

[0115] The recursive energy The filtering algorithm is introduced to provide a high signal-to-noise ratio condition for low-observable target tracking; the target track update is then expressed by the following hypothesis test:

[0116] : ,The update of target track is achieved by recursive energy update;

[0117] : , the target track is terminated;

[0118] in, is the energy threshold, which is the same as the energy threshold for target detection;

[0119] In the assumption Under the condition of low signal-to-noise ratio, the target track is updated by measuring the maximum energy in the tracking gate, so that the target is tracked in real time.

[0120] Assumptions

[0121] (37)

[0122] is the maximum measurement point energy in the tracking gate, where It is the first The energy of the candidate measurement, is the number of candidate measurements;

[0123] Will By introducing the filtering algorithm, the target track is updated by tracking the measurement point with the maximum energy in the gate, and the energy is updated recursively as follows:

[0124] (38)

[0125] in, is the trajectory point energy at the last moment in the recursive energy;

[0126] By recursively updating the energy, target tracking is always maintained under the condition of high signal-to-noise ratio, and then the target track is obtained using the filtering algorithm.

[0127]

[0128] It can be seen from the above technical solutions that the present invention has the following advantages:

[0129] 1) The low-observable boost-glide trajectory target detection and tracking method under slant range ambiguity provided by the present invention, on the one hand, designs the pulse repetition frequency within the same sampling period to be a constant value, so that it has sufficient energy for coherent accumulation detection; on the other hand, designs the pulse repetition frequency between different sampling periods to be an alternating value, so that it has the conditions to resolve the slant range ambiguity problem, so that the conditions for resolving the slant range ambiguity problem can be provided during target detection and tracking.

[0130] 2) The method of the present invention combines extended measurement after multi-hypothesis processing with anti-stealth technology, which can detect low-observable targets while resolving slant range ambiguity. The method of the present invention no longer converts the target measurement into traditional position measurement, but instead detects low-observable targets directly in the range-time plane, which can effectively avoid the position measurement bias introduced by long-range detection.

[0131] 3) This invention also addresses the low observability of targets. Rather than limiting the target trajectory to linear motion, it utilizes a periodic glide method to predict the target's boost-glide trajectory. This ensures a high probability of detection while also taking into account the target's maneuverability. Furthermore, this method addresses the target's boost-glide trajectory characteristics. Instead of using traditional nearest neighbor filtering for real-time tracking of target measurements, this method utilizes a maximum recursive energy decision method for recursive tracking of target measurements. This allows for real-time tracking of the target's boost-glide trajectory while maintaining a high probability of detection.

[0132] 4) The present invention can simultaneously solve the detection and tracking problems under the combined influence of slant range ambiguity, low observability and boost-glide maneuvers derived from the target's hypersonic motion.

[0133] BRIEF DESCRIPTION OF THE DRAWINGS

[0134] In order to more clearly illustrate the technical solution of the present invention, the following is a brief introduction to the drawings required for the description. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0135] FIG1 is a flow chart of a method for detecting and tracking a low-observable boost-glide trajectory target under slant range ambiguity conditions;

[0136] Figure 2 is a diagram of an alternating pulse repetition frequency ranging model;

[0137] Figure 3 is an extended measurement diagram at a single pulse repetition frequency;

[0138] Figure 4 is an extended measurement diagram when alternating pulse repetition frequencies;

[0139] Accompanying drawing 5 is the design scheme diagram of the extended non-coherent accumulation model;

[0140] Figure 6 is a non-coherent accumulation detection diagram based on distance-time Hough transform;

[0141] Figure 7 is a design diagram of the acceleration autocorrelation function of the S-type motion model;

[0142] Figure 8 is a diagram showing the construction of recursive energy;

[0143] Figure 9 is an update diagram of recursive energy;

[0144] FIG10 is a diagram of maximum energy filtering.

[0145] DETAILED DESCRIPTION

[0146] The low-observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions provided by the present invention aims to break through the constraints of traditional target detection and tracking methods, while solving the target detection and tracking problems under the combined influence of slant range ambiguity, low observability and boost-glide maneuvers, thereby improving the ability of existing radars to detect and track hypersonic targets.

[0147] The low-observable boost-glide trajectory target detection and tracking method provided by this invention can acquire and process associated data based on artificial intelligence technology. Specifically, the low-observable boost-glide trajectory target detection and tracking method under slant range ambiguity utilizes digital computers or machines controlled by digital computers to simulate, extend, and expand human intelligence, to perceive the environment, acquire knowledge, and use that knowledge to achieve optimal results. The theory, method, technology, and application device.

[0148] The low-observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions incorporates both hardware and software technologies. The underlying technologies of this invention generally include sensors, dedicated artificial intelligence chips, cloud computing, distributed storage, big data processing, operating / interaction systems, and mechatronics. The software technologies for intelligent diagnostic methods for CNC machine tools primarily include machine learning / deep learning and programming languages. Programming languages ​​include, but are not limited to, object-oriented programming languages ​​such as Java, Smalltalk, and C++, as well as conventional procedural programming languages ​​such as C or similar languages.

[0149] A low-observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions is applied to one or more detection terminals. The detection terminal is a device that can automatically perform numerical calculations and / or information processing according to pre-set or stored instructions. Its hardware includes but is not limited to microprocessors, application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), digital signal processors (DSPs), embedded devices, etc.

[0150] The detection terminal may be any electronic product capable of performing human-computer interaction with a user, such as a personal computer, a tablet computer, a smart phone, a personal digital assistant (PDA), an interactive network television (IPTV), etc.

[0151] The detection terminal may also include network equipment and / or user equipment. The network equipment includes, but is not limited to, a single network server, a server group consisting of multiple network servers, or a cloud based on cloud computing consisting of a large number of hosts or network servers.

[0152] The network where the detection terminal is located includes but is not limited to the Internet, wide area network, metropolitan area network, local area network, virtual private network (VPN), etc.

[0153] The low-observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions provided by the present invention aims to solve the following problems:

[0154] 1) Joint detection and tracking challenges arising from the target’s hypersonic motion, including slant range ambiguity, low observability, and boost-glide maneuvers.

[0155] 2) Under the condition of slant range ambiguity, the existing single-pulse repetition frequency ranging method has sufficient energy for coherent accumulation, but cannot solve the problem of slant range ambiguity; while the existing multi-pulse repetition frequency ranging method can solve the problem of slant range ambiguity, it cannot provide sufficient energy for coherent accumulation detection of the target.

[0156] 3) Under the dual effects of slant-range ambiguity and low observability, there are significant incompatibilities between existing slant-range ambiguity solutions and low observable target detection methods. On the one hand, existing low observable target detection methods mostly focus on the stealth characteristics of targets, but fail to fully consider the problem of low observable target detection under slant-range ambiguity. On the other hand, existing slant-range ambiguity solutions mostly assume a high signal-to-noise ratio. Under low signal-to-noise ratio conditions, the slant-range ambiguity problem cannot be solved due to missed targets.

[0157] 4) Under the dual influence of low observability and irregular maneuvers, existing low observable target tracking methods and maneuvering target tracking methods are no longer applicable, making it difficult to effectively track low observable targets with boost-glide trajectories. On the one hand, existing maneuvering target tracking methods are mostly based on the assumption of a high signal-to-noise ratio and are not capable of handling stealth targets under low signal-to-noise ratio conditions. On the other hand, existing low observable target tracking methods mostly limit the target's motion to a straight line, while the target's true trajectory is not limited to a single straight line and is not suitable for the target's boost-glide trajectory.

[0158] Based on the above problems, the present invention provides a low-observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions, which includes the following technical measures:

[0159] Step 1: Improve the existing radar ranging method and design a radar ranging model using pulses with alternating pulse repetition frequencies. In this case, the radar pulse repetition frequency is constant within the same sampling period but changes alternately between different sampling periods. Consequently, the radar echo has sufficient energy for coherent accumulation within the same sampling period, and the conditions for resolving slant range ambiguity between different sampling periods are met. This also means that this method can provide conditions for resolving slant range ambiguity during target detection and tracking.

[0160] Step 2: Improve existing target detection methods by directly combining extended measurements after multi-hypothesis processing with anti-stealth technology in the range-time plane. Through extended non-coherent accumulation detection in the range-time plane, the problem of low-observable target detection under slant range ambiguity can be effectively solved.

[0161] Step 3: Improve the existing target tracking method by designing a boost-glide trajectory matching motion model and developing a maximum recursive energy filtering algorithm to achieve the dual advantages of real-time processing and anti-stealth, thereby effectively solving the target tracking problem under the dual influence of low observability and boost-glide maneuvers.

[0162] 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 creative efforts are within the scope of protection of the present invention.

[0163] FIG1 is a flowchart of a method for detecting and tracking a low-observable boost-glide trajectory target under slant range ambiguity conditions according to a specific embodiment. The method includes the following steps:

[0164] S1: Configures an alternating pulse repetition frequency model for radar ranging;

[0165] In one exemplary embodiment, the radar's ranging model is improved to a new model with alternating pulse repetition frequencies (PRFs). This model maintains a constant PRF within the same sampling period, ensuring sufficient radar echo energy for coherent integration detection. The PRFs vary between sampling periods, and after multi-hypothesis processing, this allows for target detection and tracking while resolving slant range ambiguity.

[0166] ①Measure the fuzzy slant distance of the target by alternating pulse repetition frequency;

[0167] The pulse repetition frequency is constant within the same sampling period, but changes alternately between different sampling periods, as shown in FIG2 .

[0168] Assume the target is The fuzzy measurement of time is,

[0169] (1)

[0170] in, is the blurred slant distance, is the azimuth, is the pitch angle, is the amplitude of the echo pulse.

[0171] If three alternating pulse repetition frequencies are used to design the radar ranging model, the fuzzy slant range of the target is expressed as

[0172] (2)

[0173] in,

[0174] (3)

[0175] Formula (3) calculates the The fuzzy slant distance of the pulse repetition frequency,

[0176] (4)

[0177] Formula (4) is the fuzzy delay of the echo pulse, is the actual delay of the echo pulse, represents the modular operation, is the pulse repetition period, It is Pulse repetition frequency, is the speed of light, .

[0178] ②Restore the target's true distance;

[0179] Since the fuzzy slant distance is not the true distance of the target, the sampling multi-hypothesis processing method expands the fuzzy slant distance to several uncertainty intervals. At this time, the true position of the target can be obtained from one of the uncertainty intervals.

[0180] Since radar ranging The pulse repetition frequency is , then the corresponding maximum unambiguous slant distance is,

[0181] (5)

[0182] If the interval Blurred slant distance If the expansion is carried out, the extended slope distance can be expressed as,

[0183] , (6)

[0184] in, It is Extended tilt distance, is the amount of extended slope distance.

[0185] At the same time, the true range is less than the radar range, then the amount of extended slant range is given by:

[0186] (7)

[0187] in, is the radar’s ranging range, Indicates a rounding operation.

[0188] The extended measurement of the target can then be given by:

[0189] , (8)

[0190] in, For the The first PRF An extended measurement.

[0191] Through multi-hypothesis processing, the ambiguous slant range is expanded to several uncertainty intervals. For a single pulse repetition frequency, the target's true range can be recovered from one of these uncertainty intervals, but it is difficult to distinguish which is the target's true range, as shown in Figure 3. For alternating pulse repetition frequencies, an uninterrupted track is formed at the target's true position, as shown in Figure 4. This means that the target's true range can be distinguished during both target detection and tracking.

[0192] S2: Define an extended non-coherent accumulation model in the range-time plane for target detection;

[0193] In the detection phase, the target detection model is improved to a new extended non-coherent accumulation mode in the range-time plane. This method not only resolves slant range ambiguity while detecting low-observable targets, but also effectively avoids position measurement bias introduced by long-range radar detection.

[0194] ①Define the extended non-coherent accumulation model;

[0195] In this embodiment, multi-hypothesis processing can resolve the slant range ambiguity problem while simultaneously detecting and coherently accumulating the target. However, under low signal-to-noise ratio conditions, the target may be missed because the energy of the coherent accumulation does not reach the detection threshold. In this case, the slant range ambiguity problem cannot be resolved due to missed target detection.

[0196] To this end, this embodiment extends the non-coherent accumulation model as shown in FIG5 to achieve detection of low observable targets while solving the slant range ambiguity problem.

[0197] First, multi-hypothesis processing is performed on alternating multi-pulse repetition frequency measurements to create conditions for detecting low-observable targets while resolving the problem of slant range ambiguity.

[0198] Secondly, while performing coherent accumulation detection on the target, non-coherent accumulation detection is performed to make the accumulated energy of the low-observable target reach the target detection threshold;

[0199] Finally, the two are combined to achieve the detection of low-observable targets while solving the slant range ambiguity problem.

[0200] ②Select the distance-time plane;

[0201] According to the embodiments of the present application, unlike the classic non-coherent accumulation detection method, the extended slant range measurement is no longer converted into traditional position measurement, but non-coherent accumulation detection is performed directly on the range-time plane. In this case, the method of the present invention can not only complete the detection of low-observable targets while resolving slant range ambiguity, but also effectively avoid the position measurement deviation introduced by radar long-range detection.

[0202] Since the radar position deviation is mainly caused by the radar's angle measurement error and is proportional to the target's slant distance, assume that the target's slant distance is , the radar angle measurement error is , then the target position measurement deviation is,

[0203] (9)

[0204] According to 3 The judgment criteria are as follows: the maximum deviation of the target position measurement can reach , this deviation is much larger than the radar distance measurement error of hundreds of meters.

[0205] In this case, if distance-time measurement is used to replace traditional position measurement during non-coherent target accumulation detection, the position measurement bias introduced by radar long-range detection can be effectively avoided. To this end, the range-time plane is selected to perform extended non-coherent target accumulation detection.

[0206] ③ Expand the non-coherent accumulation detection method based on distance-time Hough transform;

[0207] According to the embodiments of the present application, considering that the target trajectory over a short period of time can be approximately viewed as a straight line, the Hough transform method is used to design an extended range-time non-coherent accumulation detection method. This is because, by applying the Hough transform to the target measurement, the linear detection problem over a short period of time can be transformed into an energy accumulation problem, thereby enabling detection of low-observable targets while improving the signal-to-noise ratio.

[0208] Assumptions is a point in the distance-time plane, where is the pulse repetition frequency No. Extended tilt distance, yes The time stamp, and then, A unique curve corresponding to the point can be obtained in the plane,

[0209] (10)

[0210] in, yes The distance from the point to the origin, yes Axis and The angle between the axes.

[0211] If multiple such curves are If the two curves intersect at one point in the distance-time plane, there is a straight line corresponding to the multiple curves in the distance-time plane. This straight line can be expressed as

[0212] (11)

[0213] in, is the intersection of multiple curves. and are the distance variable and time variable corresponding to the straight line respectively.

[0214] The present invention uses the method of energy accumulation in By finding the intersection of multiple curves in the plane, low observable targets can be detected in the range-time plane, as shown in Figure 6.

[0215] ④Detection of low observable targets;

[0216] In a short time, the target trajectory can be approximated as a straight line, but it is not a true straight line after all. In actual situations, the target is Curves in a plane do not intersect at a point, but are concentrated in a certain area.

[0217] Therefore, here we will The plane is divided into Several cells, so that the target energy is accumulated in one of the cells;

[0218] Cell The center of is represented as,

[0219] (12)

[0220] (13)

[0221] in,

[0222] (14)

[0223] (15)

[0224] yes the number of units, yes the number of units, is the radar’s range;

[0225] In the pair Based on the plane discretization, The curve in the plane is represented by a pair of The mapping is replaced by,

[0226] (16)

[0227] in, is a point in the distance-time plane, yes In the plane A collection of points, ;

[0228] In the pair 1 pair of curves in a plane After mapping, click The energy in will be stored in the cells that the curve passes through, and the cells The energy in is expressed as,

[0229] (17)

[0230] in, It is a cell The existing energy in yes Point of energy.

[0231] If some points in the distance-time plane are approximately connected by a straight line, the energy of the points will be concentrated In a unit in the plane. Then the problem of low-observable target detection can be formulated as the following hypothesis test:

[0232] : , in the cell The target is detected in

[0233] : , in the cell No target was detected in the

[0234] in, is the energy threshold;

[0235] In the assumption Under the condition that , the target trajectory is obtained by the following Hough inverse mapping,

[0236] (18)

[0237] This in turn enables detection of low-observable targets from extended slant ranges.

[0238] S3: Configure the S-type recursive energy tracking model for target tracking;

[0239] In the tracking phase, the target tracking model is improved to a new S-shaped recursive energy tracking mode. In this case, the target's boost-glide trajectory can be predicted using the S-shaped motion model, and the target track under low signal-to-noise ratio conditions can be updated using a recursive energy filtering algorithm.

[0240] ①Configure S-type motion model;

[0241] In one exemplary embodiment, an S-shaped motion model is designed to match the boost-glide trajectory characteristic of hypersonic targets. Unlike the classic Singer motion model, this model no longer designs the target acceleration as a zero-mean Markov random process with exponential autocorrelation. Instead, it designs the target acceleration as a zero-mean Markov process with cosine autocorrelation, taking into account the target's periodic motion characteristics, as shown in Figure 7.

[0242] The autocorrelation function of the target acceleration is designed as,

[0243] (19)

[0244] in, for The target acceleration at the moment, for The instantaneous covariance of Angular rate for a boost-glide trajectory to the target;

[0245] Performing Fourier transform on the autocorrelation function of the target acceleration, the power spectrum of the target acceleration can be expressed as:

[0246] (20)

[0247] This embodiment can be designed as follows:

[0248] (twenty one)

[0249] Formula (21) is an approximate whitening filter, is the power spectrum of the input white noise, then The output can be expressed as,

[0250] (twenty two)

[0251] contrast and Can obtain,

[0252] (twenty three)

[0253] That is to say, It is reasonable to design it as an approximate whitening filter.

[0254] If this example assumes yes The expression in the time domain is The Laplace transform of can be expressed as

[0255] (twenty four)

[0256] and then The differential equation is expressed as

[0257] (25)

[0258] in, has zero mean and constant variance Input white noise;

[0259] Assumptions

[0260] (26)

[0261] Formula (26) is The target state vector in the X direction at time t, , , and are the target's position, velocity, acceleration, and jerk, respectively, and there is

[0262] (27)

[0263] The state phasor Substitution The target's continuous motion equation can be expressed as

[0264] (28)

[0265] in,

[0266] (29)

[0267] (30)

[0268] By integrating both sides of the target continuous motion equation, the discrete motion equation of the target can be obtained.

[0269] (31)

[0270] Rewriting this formula, we can obtain

[0271] (32)

[0272] in

[0273] (33)

[0274] Formula (33) is the state transfer matrix, is the time interval,

[0275] (34)

[0276] Formula (34) is the zero-mean Gaussian white noise with constant variance in Formula (35).

[0277] (35)

[0278] ② This embodiment also designs a recursive energy filter;

[0279] Since the boost-glide trajectory of the target can be predicted by the designed S-type motion model, the remaining work is to design a filter algorithm to update the target track under low observability conditions.

[0280] It should be noted that recursive energy is introduced in target tracking to transform the problem of low-observable target tracking into the problem of high-observable target tracking.

[0281] On the one hand, the recursive energy is composed of the energies of m tracking points, so that low-observable targets can be tracked under high signal-to-noise ratio conditions, as shown in Figure 8.

[0282] On the other hand, the update of the recursive energy is achieved by replacing the tracking point energy at the last moment with the measurement point energy, so that the real-time tracking processing of low-observable targets can be completed, as shown in Figure 9.

[0283] This example assumes The recursive energy at the moment is,

[0284] (36)

[0285] in, It is The energy of each trajectory point, ;

[0286] The recursive energy The introduction of filtering algorithm provides high signal-to-noise ratio conditions for low observable target tracking. The target track update can be expressed by the following hypothesis test:

[0287] : ,The update of target track is achieved by recursive energy update.

[0288] : , the target track is terminated.

[0289] in, is the energy threshold, which is the same as the energy threshold for target detection.

[0290] In the assumption Under the condition of low signal-to-noise ratio, the target track is updated by measuring the maximum energy in the tracking gate, so that the target can be tracked in real time under the condition of low signal-to-noise ratio, as shown in Figure 10.

[0291] This embodiment is the same as the traditional filtering algorithm, and the target track is updated online through the measurements in the tracking gate, so that the boost-glide trajectory of the target can be tracked in real time.

[0292] Different from traditional filtering algorithms, the target track is updated by the measurement point with the maximum energy instead of the measurement point with the minimum statistical distance, which can transform the problem of low-observable target tracking into the problem of high-observable target tracking.

[0293] This embodiment assumes that formula (37) is the maximum measurement point energy in the tracking gate, where It is the first The energy of the candidate measurement, is the number of candidate measurements.

[0294] Assumptions

[0295] (37)

[0296] Will By introducing the filtering algorithm, the target track is updated by tracking the measurement point with the maximum energy in the gate, and the energy is updated recursively as follows:

[0297] (38)

[0298] in, is the trajectory point energy at the last moment in the recursive energy.

[0299] By recursively updating the energy, target tracking can always be maintained under the condition of high signal-to-noise ratio, and the target track can be obtained using the existing filtering algorithm.

[0300] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0301] Thus, the present invention addresses the challenges of target detection and tracking under the combined effects of slant range ambiguity, low observability, and boost-glide maneuvers, arising from target hypersonic motion. This invention improves upon conventional radar ranging methods by adapting the existing radar ranging model to a new model with alternating pulse repetition frequencies (PRFs), thereby enabling simultaneous target detection and tracking with slant range ambiguity. Furthermore, the existing target detection method is improved by combining extended measurement after multi-hypothesis processing with anti-stealth technology in the range-time plane. This not only enables detection of low-observable targets while resolving slant range ambiguity, but also effectively avoids position measurement bias introduced by long-range radar detection. Finally, the existing target tracking method is improved by designing a boost-glide trajectory matching motion model and developing a maximum recursive energy filtering algorithm, achieving the dual advantages of real-time processing and anti-stealth, thereby effectively addressing the challenges of target tracking under the combined effects of low observability and boost-glide maneuvers.

[0302] The units and algorithm steps of each example described in the embodiments disclosed in the low-observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions of the present invention can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the above description has generally described the components and steps of each example according to their functions. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0303] The features, structures, or characteristics described in the present invention for the low-observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions can be combined in any suitable manner in one or more embodiments. In the following description, many specific details are provided to provide a full understanding of the embodiments of the present invention. However, those skilled in the art will appreciate that the technical solutions of the present invention can be practiced without one or more of the specific details, or that other methods, components, devices, steps, etc. can be employed. In other cases, well-known methods, devices, implementations, or operations are not shown or described in detail to avoid obscuring aspects of the present invention.

[0304] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A low observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions, characterized in that: Methods include, S1: Configure the alternating pulse repetition frequency model for radar ranging; ①Measure the fuzzy slant distance of the target by alternating the pulse repetition frequency; ② Restore the real distance of the target; S2: Define an extended non-coherent accumulation model in the range-time plane for target detection; ① Define the extended non-coherent accumulation model; ② Select the distance-time plane; ③ Expand the non-coherent accumulation detection method based on distance-time Hough transform; ④ Detection of low observable targets; S3: Configure the S-type recursive energy tracking model for target tracking; ①Configure S-type motion model; ② Design a recursive energy filter and update it through recursive energy so that target tracking is always maintained under high signal-to-noise ratio conditions, and use the filtering algorithm to obtain the target track.

2. The low observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions according to claim 1 is characterized in that: The method of measuring the fuzzy slant distance of the target by using the pulse repetition frequency alternating conversion method in step S1 also includes: In the same sampling period, the pulse repetition frequency is constant. The fuzzy measurement at the moment is, (1) in, is the blurred slant distance, is the azimuth, is the pitch angle, is the amplitude of the echo pulse.

3. The low observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions according to claim 2 is characterized in that: Using three alternating pulse repetition frequencies to design the radar ranging model, the fuzzy slant distance of the target is expressed as (2) in, (3) Formula (3) calculates the The fuzzy slant distance of the pulse repetition frequency, The calculation is performed as follows: (4) is the actual delay of the echo pulse, represents the modulo operation, is the pulse repetition period, It is The pulse repetition frequency, is the speed of light, 。 4. The low observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions according to claim 1 or 2, characterized in that: The steps of restoring the real distance of the target also include: the first step based on radar ranging The pulse repetition frequency is ,but The corresponding maximum unambiguous slant distance is, (5) If the interval Blurred slant distance If the expansion is carried out, the extended slope distance is expressed as, , (6) in, It is Extended tilt distance, is the amount of extended slant distance; If the true range is less than the radar range, then the amount of extended slant range is given by: (7) in, is the radar’s ranging range, Indicates rounding operation; The extended measure of the target is given by: , (8) in, For the The first PRF An extended measurement.

5. The low observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions according to claim 1, characterized in that: The definition of the extended non-coherent accumulation model in step S2 further includes: Firstly, multi-hypothesis processing is performed on the alternating multi-pulse repetition frequency measurement; secondly, non-coherent accumulation detection is performed while the target is coherently accumulated, so that the accumulated energy of the low-observable target reaches the threshold of target detection; finally, the detection of the low-observable target is completed.

6. The low observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions according to claim 5, characterized in that: The step S2 of selecting the distance-time plane further includes: Assume that the slant distance of the target is , the radar angle measurement error is , then the target position measurement deviation is, (9) Based on 3 The judgment criterion is that the maximum value of the target position measurement deviation is , the target position measurement deviation is much larger than the radar distance measurement error of hundreds of meters.

7. The low observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions according to claim 5, characterized in that: The non-coherent accumulation detection method based on distance-time Hough transform in step S2 also includes: set up is a point in the distance-time plane, where is the pulse repetition frequency No. Extended tilt distance, yes The time stamp, The way to obtain the unique curve corresponding to the point in the plane is as follows, (10) in, yes The distance from the point to the origin, yes Axis and The angle between the axes; If multiple curves are If they intersect at one point in the plane, then there is a straight line corresponding to the multiple curves in the distance-time plane, and the straight line is expressed as (11) in, is the intersection of multiple curves. and They are the distance variable and time variable corresponding to the straight line.

8. The low observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions according to claim 7, characterized in that: The method of detecting low observable targets in step S2 also includes: Will The plane is divided into Several cells are formed so that the target energy is accumulated in one of the cells; Cell The center of is represented as, (12) (13) in, (14) (15) yes The number of units, yes The number of units, is the radar’s range; In the right Based on the plane discretization, The curves in the plane are represented by a pair of The mapping is replaced by, (16) in, is a point in the distance-time plane, yes In the plane A collection of points, ； In the right The curves in the plane are 1 pair After mapping, click The energy in will be stored in the cells through which the curve passes, and the cells The energy in is expressed as, (17) in, It is a cell The existing energy in yes The energy of a point; If multiple points in the distance-time plane are approximately connected into a straight line, the energy of the multiple points will be concentrated In a cell in the plane, low-observable object detection is formulated as the following hypothesis test: ： , in the cell The target is detected in ： , in the cell No target was detected in the in, is the energy threshold; In the assumption Under the condition that , the target trajectory is obtained through the following Hough inverse mapping, (18) Low observable targets are then detected from extended slant ranges.

9. The low observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions according to claim 1, characterized in that: The method of configuring the S-type motion model in step S3 also includes: The autocorrelation function of the target acceleration is designed as, (19) in, for The target acceleration at the moment, for The instantaneous covariance of Angular rate for a boost-glide trajectory for the target; The autocorrelation function of the target acceleration is Fourier transformed, and the power spectrum of the target acceleration is expressed as: (20) Configure the approximate whitening filter as, (21) Assumptions yes The expression in the time domain is The Laplace transform of (24) and then The differential equation is expressed as (25) in, has zero mean and constant variance Input white noise; Assumptions (26) yes The target state vector in the X direction at time, , , and are the position, velocity, acceleration and jerk of the target respectively, and there is (27) The state phasor Substitution The continuous motion equation of the target is expressed as (28) in, (29) (30) Integrate both sides of the target continuous motion equation to obtain the target discrete motion equation (31) The discrete motion equation of the target is rewritten as (32) in (33) is the state transition matrix, is the time interval, (34) is a constant variance (35) Zero-mean Gaussian white noise.

10. The low observable boost-glide trajectory target detection and tracking method under slant range ambiguity conditions according to claim 9, characterized in that: Designing the recursive energy filter in step S3 also includes: Assumptions The recursive energy at the moment is: (36) in, It is The energy of each trajectory point, ； The recursive energy The filtering algorithm is introduced to provide a high signal-to-noise ratio condition for low observable target tracking; the target track update is then expressed by the following hypothesis test: ： ,The update of target track is realized by recursive energy update; : , the target track is terminated; in, is the energy threshold, which is the same as the energy threshold for target detection; In the assumption Under the condition of low signal-to-noise ratio, the target track is updated by measuring the maximum energy in the tracking gate, so that the target is tracked in real time under the condition of low signal-to-noise ratio. Assumptions (37) is the maximum measurement point energy in the tracking gate, where It is the first The energy of the candidate measurements, is the number of candidate measurements; Will The filtering algorithm is introduced, and the target track is updated by tracking the measurement point with the largest energy in the gate, and the energy is recursively updated as follows: (38) in, is the trajectory point energy at the last moment in the recursive energy; By recursively updating the energy, the target tracking is always maintained under the condition of high signal-to-noise ratio, and then the target track is obtained using the filtering algorithm.

Images