Robust tracking filter method for group-oriented target

Abstract

The application discloses a robust tracking filtering method for group targets, and belongs to the field of radars and signal processing.The implementation method of the application is as follows: a dynamic model of group targets and a three-coordinate ground-based radar detection probability and measurement model are established; a Poisson random finite set is used to realize the Bayesian recursion of a multi-target state random finite set; and a Gaussian mixture form is used to describe the intensity function of the Poisson random finite set.The maximum movement distance of the targets between two adjacent filtering steps is estimated based on the dynamic characteristics of the group targets, so that the targets are detected; a Bernoulli distribution is used to describe the detection probability; in the case that the clutter intensity is not more than the real target intensity, the prior clutter intensity is used as a threshold, the detection probability is adaptively adjusted in the filtering iteration process, the weights of the measurement-independent part and the measurement-dependent part are updated, and the strong robustness multi-target tracking under the condition of sensor missed detection is realized.The application also has the advantages of strong robustness, high tracking precision and small calculation amount.

Description

Technical Field

[0001] This invention relates to a robust tracking filtering method for group targets, and more particularly to a multi-target tracking method in scenarios where sensors randomly miss detections, belonging to the field of radar and signal processing. Background Technology

[0002] Target tracking is the process of estimating the position, velocity, and other states of a target, as well as the number of targets, using detection sensors such as radar, lasers, and visible light cameras. Based on the number of targets, target tracking technology can be divided into single-target tracking and multi-target tracking. However, in real-world tracking scenarios, the number of targets to be tracked is often more than one, and single-target tracking can no longer meet the increasingly complex tracking tasks. Compared to single-target tracking, multi-target tracking not only tracks more targets but also tracks multiple targets whose numbers vary over time, and it is capable of handling false alarms and missed detections caused by various factors such as sensor misses, false targets, and clutter. Multi-target tracking algorithms mainly include two technical paths, based on data association and random finite set theory, respectively. Data association-based multi-target tracking algorithms aim to establish a mapping relationship between targets and measurement values, transforming the multi-target tracking problem into a parallel single-target tracking problem. Data association algorithms, represented by joint probabilistic data association algorithms and multi-hypothesis tracking algorithms, require correlation analysis of all measurement values ​​and target states to determine the measurement value corresponding to each target, which leads to a high computational cost for data association-based multi-target tracking algorithms. Multi-target tracking methods based on stochastic finite set theory have attracted widespread attention due to their significant advantages of small computational scale and strong real-time performance. Gaussian mixture probability hypothesis density (GM-PHD) filters, as a core component of multi-target tracking algorithms based on stochastic finite set theory, are easy to implement and have low computational cost, leading to their widespread application in multi-target tracking scenarios. However, the tracking and interception of groups of targets faces complex challenges related to observation correlation and trajectory correlation. Furthermore, in real-world scenarios, sensors cannot achieve complete observation of targets, resulting in potential missed detections. When observation data is missing, the GM-PHD filter will lose target tracking, ultimately leading to missed alarms and erroneous termination of the trajectory. Therefore, research on robust multi-target filtering tracking algorithms for sensor-missed detection scenarios has significant practical value and engineering implications.

[0003] Robust tracking filtering methods for swarm targets first require the kinematic and dynamic equations of the swarm targets, as well as the measurement equations of the sensors, as their foundation, based on the theory of random finite sets. During flight, targets are affected by Earth's gravity and aerodynamics, making it difficult for linear equations of motion to accurately describe their motion. Therefore, this invention uses a model of Earth's central gravitational field and a Gaussian noise model, fitting the non-central gravitational field and aerodynamics with Gaussian noise, allowing the algorithm to approximate the actual forces acting on the target during iteration. Target detection by sensors, such as radar, is affected by factors such as the target's radar cross-section, attitude, and distance. To accurately describe the radar's measurement relationship with the target, this invention obtains the radar's target detection probability based on the Albersheim formula and radar power model, establishing a radar measurement model. To address the problem that sensor misses lead to GM-PHD filters misestimating the number of targets, resulting in lost stable tracking and erroneous track termination, this invention innovatively reconstructs the detection probability based on Gaussian mean correlation. By calculating the sum of the values ​​of the intensity function mapped to the single-target measurement space at the measurement set, the detection probability of the target in the filter is adjusted, and the weights of the measurement-independent and measurement-dependent parts during the iteration process are redistributed. This effectively solves the sensor miss problem and ensures continuous tracking of missed targets in multi-target tracking tasks. Summary of the Invention

[0004] To address the problem of multi-target tracking loss caused by missed detections in scenarios similar to radar, this invention aims to provide a robust tracking filtering method for group targets. This method distinguishes between real targets and background noise by utilizing the kinematic and dynamic characteristics of the targets, enabling the detection of emerging targets and avoiding false alarms. Based on the distribution of multi-target states in the state space, a state-dependent variable detection probability is established, thereby achieving accurate estimation of the number of multiple targets and stable trajectory tracking even in cases of random sensor misses, avoiding missed alarms caused by sensor malfunctions. This invention has the advantages of strong robustness, high tracking accuracy, and low computational cost.

[0005] The objective of this invention is achieved through the following technical solutions.

[0006] This invention discloses a robust tracking filtering method for group targets, establishing a dynamic model of the group targets and a detection probability and measurement model for a three-coordinate ground-based radar. A Bayesian recursion is implemented using a Poisson random finite set to realize the state random finite set of multiple targets, and the intensity function of the Poisson random finite set is described by a Gaussian mixture form. Based on the dynamic characteristics of the group targets, the maximum target movement distance between two adjacent filtering steps is estimated to achieve target detection. A Bernoulli distribution is used to describe the detection probability. Under the condition that the clutter intensity does not exceed the true target intensity, the prior clutter intensity is used as a threshold to adaptively adjust the detection probability during the filtering iteration process, updating the weights of the measurement-independent and measurement-related parts, thus achieving robust multi-target tracking under sensor miss conditions. Numerical calculation methods are used to simulate the ground-based radar's measurement of the group targets and the tracking trajectory of the group targets, providing indicators such as target number error.

[0007] The robust tracking filtering method for group targets disclosed in this invention includes the following steps:

[0008] Step 1: Considering Earth's gravity and aerodynamics, establish the target's motion equations; establish a radar measurement model based on the Albersheim formula and radar power model;

[0009] Step 2: Use a Poisson random finite set to describe the state of multiple targets, measurements, and sensor misses. Use an intensity function to fully characterize the Poisson random finite set and achieve a filter. Then, use a Gaussian mixture form to specifically describe the intensity function and construct a GM-PHD filter.

[0010] Step 3: Based on the motion characteristics described by the target motion equation in Step 1, achieve effective detection of new targets and avoid false alarms; based on the detection characteristics of missed detections in the radar measurement model in Step 1, map the prediction intensity function of the GM-PHD filter in Step 2 to the measurement space, and achieve continuous tracking of the target by adjusting the weights of trajectory prediction and measurement update.

[0011] The method also includes the following application: a method to improve the continuous tracking of multiple targets and the formation of coherent trajectories by sensors such as radar that have the problem of missed detection. The filter is used to process data and track targets of the sensor to achieve continuous tracking of multiple targets and formation of coherent trajectories.

[0012] Furthermore, the target motion equation described in step one is:

[0013]

[0014] In the formula, For the first One goal is The state at any given moment; For the first The process noise of each objective follows a mean of . covariance is Gaussian distribution; For a single-objective state space; For discrete nonlinear state transition functions, we have

[0015]

[0016] In the formula, The gravitational constant of Earth; distance , For discrete time intervals.

[0017] Furthermore, the radar measurement model described in step one is as follows:

[0018]

[0019] In the formula, for Time for the first Measurement of the quantity of each target; To measure noise, it follows the mean value. covariance is Gaussian distribution; For single-target measurement space; For discrete nonlinear measurement equations, when the sensor is radar, we have:

[0020]

[0021] In the formula, , , These are the azimuth, elevation, and range of the target obtained after radar measurement. , , These represent the target's position in the radar's northeast-sky coordinate system.

[0022] Furthermore, the method described in step two for using Poisson random finite sets to describe the state of multiple targets, measurements, and sensor missed detections is as follows:

[0023] In the scene Always For each objective, the set of states of the group can be derived from a random finite set. To describe:

[0024]

[0025] Without considering target visibility constraints, define the measurement set of group targets.

[0026]

[0027] In the formula, and They represent The first moment Target status and measurement; and They are a multi-objective state space and a multi-objective measurement space, respectively, which are composed of a single-objective state space. and single-target measurement space The set consisting of all finite subsets of ; and The mapping between them is as follows:

[0028]

[0029] In the formula Depend on Sure;

[0030] Further consider the geometric visibility constraints in the target observation process and define the mapping. have:

[0031]

[0032] Consider the missed detections of the target and define the mapping. When a sensor misses a detection, the target does not generate any valid measurement values; to describe the target measurement sequence after a missed detection, the following will be used: Let the pulse modulation result of the measurement sequence satisfy the visibility constraint be given, therefore:

[0033]

[0034] In the formula This represents the measurement sequence after a missed detection, where For a unit pulse, it is represented as:

[0035]

[0036] and Represents a unit pulse, and has

[0037]

[0038] Obviously This indicates that a certain target in the group experienced [something] during the tracking process. The missed detection occurred at the time of ; final combination -Mode We can conclude that Measurement set after target miss occurs at any time For measurement set A subset of, i.e.

[0039]

[0040] Based on the group's state set After mapping, the set of measurements that indicate a missed target detection is obtained. Its mapping is:

[0041]

[0042] Furthermore, the method described in step two for completely characterizing the Poisson random finite set using an intensity function and achieving the filter implementation is as follows:

[0043] by Let the intensity function be defined as a random finite set at any time.

[0044]

[0045] The integral in the formula is a set integral, defined as follows:

[0046]

[0047] Intensity function of random finite sets Characterized The density of the number of targets at a given location, therefore the intensity function in the set The integral in the set represents the integral in the set. The number of expected targets included; For random finite sets The number of elements in;

[0048] The Poisson random finite set is the most basic random finite set and is uniquely described by the intensity function:

[0049]

[0050] In the formula, Let be the intensity function of a Poisson random finite set; For the entire multi-objective state space The expected target number, It describes the distribution of the target in the single-target state space;

[0051] The optimal multi-objective Bayesian filter is expressed as the following prediction and update steps.

[0052]

[0053]

[0054] In the formula, for A random finite set of multi-objective states at time t. for A random finite set of multi-objective states at time t. for A random finite set of multi-target measurements at time points. From the start time until A random finite set of multi-target measurements at time points. From the start time until A random finite set of multi-target measurements at time points; For measurement set to state set Predict probability density function, for arrive The multi-objective state transition probability density function, For measurement set to state set Posterior probability density function; For measurement set to state set Posterior probability density function, For multi-target measurement probability density function, For measurement set to state set Posterior probability density function;

[0055] Since the probability density function of a Poisson random finite set is given by equation A unique description, therefore based on the theory of random finite sets, equation Japanese style The optimal multi-objective Bayesian filter described can be used to derive the PHD filter, and the prediction and update intensity functions are as follows:

[0056]

[0057]

[0058] In the formula, This refers to the state at the previous moment. The current state; , and These represent the intensities of new generation, derived generation, and clutter, respectively. for The posterior intensity function at time t. for Time's up The predicted intensity function at time t. for The posterior intensity function at time t; This represents the probability density function of the target state transition between two consecutive steps; Given the current state hour, The probability density function of measurement at time t; and They are respectively from the state and state The probability of survival and the probability of detection are determined.

[0059] Furthermore, the method described in step two, which uses a Gaussian mixture form to specifically describe the intensity function and ultimately realize the GM-PHD filter, is as follows:

[0060] The state transition probability density function and the measurement probability density function are expressed as follows:

[0061]

[0062]

[0063] In the formula, Characterization Follow the mean Covariance The expression follows a Gaussian distribution, and different variables will appear in their respective positions and play their respective roles. and These are the discrete nonlinear state transition function and the measurement function, respectively, which are expressed as equation [equation missing]. Japanese style The described state transition function and measurement function;

[0064] The posterior intensity function at time t is in the following Gaussian mixture form.

[0065]

[0066] In the formula, for The number of posterior Gaussian components at time step; for Time of the first The weights of the posterior Gaussian components; and They are respectively Time of the first Given the mean and covariance of each posterior Gaussian component, then... Time's up Prior strength function at time t Also in Gaussian mixture form, there is

[0067]

[0068] In the formula, , and These are the intensity functions for surviving targets, derived targets, and newly emerging targets, respectively; the prior intensity function for surviving targets. have

[0069]

[0070] In the formula, and These are the mean and covariance of the Gaussian components of the surviving target, respectively.

[0071] Mode The prior intensity function represented is in Gaussian mixture form, then The posterior intensity function at time t is

[0072]

[0073] Mode Japanese style The prediction and update steps described are the Gaussian mixture filter.

[0074] Furthermore, based on the motion characteristics described by the target motion equation in step one, the method for effectively detecting new targets and avoiding false alarms is as follows:

[0075] At any given time, the distance between any two targets in the group is not less than the sensor's discrimination limit, meaning the targets do not intersect; without considering derived targets in the group, all newly generated targets consist only of newly generated targets, as shown in the equation. Derived target intensity function Always equal to 0; formula Intensity function of newborn targets Also in Gaussian mixture form, there is

[0076]

[0077] In the formula, The number of Gaussian components of the intensity function of the new target; the weight of the Gaussian components of the new target. have

[0078]

[0079] In the formula, The minimum distance to a newly formed target depends on the target's speed and the sensor's observation accuracy. for For the goal With measurement The distance between them; The Gaussian component weights for a given new target;

[0080] when When the number of targets obtained after filtering at a given time is not 0, the number of targets obtained after filtering is... The multi-objective state of n objectives, where the nth objective is... The speed of each target is ,So have

[0081]

[0082] In the formula, Sampling time, for Time of the first The L2 norm of the target velocity, This is a correction factor;

[0083] when When the number of targets obtained after filtering at time step 0 is 0. Let be the maximum speed that the target can achieve throughout its entire motion; then Represented as:

[0084]

[0085] Furthermore, based on the detection characteristics of the radar measurement model in step one, the predicted intensity function of the GM-PHD filter in step two is mapped to the measurement space. The method for achieving continuous target tracking by adjusting the weights of trajectory prediction and measurement updates is as follows:

[0086] In engineering applications, the detection probability can be a time variable, then the equation... Represented as

[0087]

[0088] In the formula, For being Time measurement set Measurement in The strength function of dominance;

[0089] Then constitute Gaussian component weights Given by the following formula

[0090]

[0091] In the formula, express Time belongs to the goal Likelihood measurement Correspondingly, express Time belongs to the goal Likelihood measurement , for The intensity function of clutter at any given time;

[0092] When the prior strength function For the form of When the Gaussian mixture form is used, the equation is... The described posterior intensity function Specifically there are

[0093]

[0094] In the formula, for the prior intensity function The Middle Gaussian components It describes the measurement-independent portion of the posterior intensity function. It describes the measurement-related part of the posterior intensity function;

[0095] for Time of the first One Gaussian component, detection probability have

[0096]

[0097] In the formula, To determine the first Does each Gaussian component have a threshold for a relevant detection item? Due to the detection probability... If it follows a Bernoulli distribution, then we have

[0098]

[0099] During the filter's operation, to ensure effective differentiation between the target and clutter, when the target... When detected by the sensor, there exists , making

[0100]

[0101] When the prior intensity function is in Gaussian mixture form, when the th When a target represented by a Gaussian component is detected by a sensor, there exists , making

[0102]

[0103] Clutter is uniformly distributed within the sensor's observation area.

[0104]

[0105] because Then when the first When a target represented by a Gaussian component is detected by a sensor, there must be

[0106]

[0107] Therefore, when clutter is uniformly distributed within the sensor's observation area, equation The middle judgment of the first Does each Gaussian component have a threshold for relevant detection items? Desirable ;when Time of the first When the target described by each Gaussian component has a relevant detection term, it satisfies the equation... Otherwise, the condition is not met, meaning the target may be lost or missed; in this case, it is the first... A prior Gaussian component assigns a sensor detection probability. Increase its posterior strength function The proportion of the irrelevant part in the middle measurement is thus achieved, which realizes the measurement of the first... The target represented by the prior Gaussian component is maintained for a longer time, thus effectively solving the problem of sensor missed detection.

[0108] Beneficial effects:

[0109] 1. The robust tracking and filtering method for group targets disclosed in this invention establishes a target motion equation, establishes a radar measurement model based on the Albersheim formula and radar power model, and establishes a multi-target tracking algorithm based on random finite set theory. By describing the number and state of group targets simultaneously through random finite set theory, it is helpful for the implementation of multi-target tracking algorithms and filtering.

[0110] 2. The robust tracking filtering method for group targets disclosed in this invention maps the prediction intensity function from the target state space to the sensor measurement space, and calculates the sum of the values ​​of the measurements at the mapping function, which is used as a threshold to describe the Bernoulli distribution of the detection probability. The detection probability of the filter is dynamically adjusted to achieve accurate estimation of the number of targets and stable tracking of the target trajectory in the case of sensor missed detection. It has the advantages of strong robustness, high tracking accuracy and low computational cost.

[0111] 3. The robust tracking filtering method for group targets disclosed in this invention, based on achieving the beneficial effects 1 and 2, maps the predicted intensity function in the state space to the measurement space, calculates the sum of the intensity functions of the sensor measurements in the measurement space, establishes the state-dependent dynamic detection probability, adjusts the weights of trajectory prediction and measurement update, realizes accurate estimation of the number of targets and stable tracking of the trajectory under the condition of missed detection, and maintains the advantage of low computational cost of random finite set filters. Attached Figure Description

[0112] Figure 1 is a flowchart of the robust tracking and filtering method for group targets according to the present invention;

[0113] Figure 2 shows the trajectory of the group target movement;

[0114] Figure 3 shows the horizontal polar coordinates of the group of targets in the radar's northeast-sky coordinate system;

[0115] Figure 4 shows the azimuth and elevation angles of the group of targets in the radar's northeast-sky coordinate system.

[0116] Figure 5 shows the radar cross-section of the target;

[0117] Figure 6 shows the probability of radar detecting a target;

[0118] Figure 7 shows the latitude, longitude, and altitude of the tracking trajectory for the group target.

[0119] Figure 8 shows the three-axis position of the tracking trajectory of the group target;

[0120] Figure 9 shows the number of targets observed, observed by sensors, and estimated by filters.

[0121] Figure 10 shows a magnified view of the target's actual trajectory and sensor measurements.

[0122] Figure 11 is a magnified view of the target tracking trajectory and sensor measurements. Detailed Implementation

[0123] To better illustrate the purpose and advantages of this invention, the specific embodiments of the invention will be further described in detail below with reference to the accompanying drawings. Figure 1 shows a flowchart of a robust tracking filtering method for swarm targets. The method described in this invention will be applied to a specific target and radar, and verified using numerical simulation. Throughout the simulation, the swarm targets complete their ascent trajectory based on their own propulsion, and then fly autonomously under the influence of Earth's gravity and aerodynamics. Under possible missed detection conditions, the radar automatically estimates the number of targets and generates a tracking trajectory based on the algorithm. The simulation is conducted in the MATLAB environment.

[0124] Example 1:

[0125] During their motion, targets are affected by Earth's gravity and aerodynamics, requiring full consideration of the influence of non-central Earth's gravity and aerodynamic forces. Furthermore, radar measurements of targets are influenced by various factors, such as the target's radar cross-section, necessitating the establishment of accurate radar measurement equations using the Albersheim formula and radar power model. Subsequently, the distribution of multiple target states in the state space is described using Gaussian mixture theory to achieve multi-target tracking under ideal conditions. This embodiment establishes a state-dependent dynamic detection probability by mapping the predicted intensity function in the state space to the measurement space and calculating the cumulative sum of the intensity functions of sensor measurements in the measurement space. This adjusts the weights of trajectory prediction and measurement updates, effectively achieving accurate estimation of the number of targets and stable trajectory tracking under conditions of missed detection, while maintaining the advantage of low computational cost of random finite set filters.

[0126] This embodiment discloses a robust filtering and tracking method for group targets, using radar as the sensor to measure the group targets. The radar parameters are set as follows: peak transmit power of 500kW, antenna gain of 36dB, and effective antenna receiving area of ​​150... The radar receiver bandwidth is 100kHz, the radar system noise is 4dB, and considering a false alarm probability of 0.0001, the radar always provides at least 80 pulse signals to any target at any given time. The radar is located at east longitude... ,north latitude ,altitude Place.

[0127] Step 1: Generate trajectories based on the resultant external forces acting on the group of targets and the radar's target detection probability curves.

[0128] Step 1.1: Generate the motion trajectory based on the target's net external force and the target's equation of motion.

[0129] The target trajectories are shown in Figure 2. A total of 7 targets are set in the scenario, forming 3 groups of flying together, and multiple targets forming different groups of flying together. In the radar's local geographic coordinate system, the horizontal polar coordinates of the 7 targets are shown in Figure 3. The targets take off from the southeast of the radar and fly northwest. The azimuth and elevation angles are shown in Figure 4, indicating the targets are at an altitude of... Takeoff location. Due to the Earth's curvature, during the initial period, the target is below the local radar horizon and cannot be effectively observed by the radar. This results in each target appearing at an arbitrary location within the radar's observation area at a different speed for the first time. Figures 3 and 4 together fully characterize the three-dimensional motion trajectory of the target in the radar coordinate system.

[0130] Step 1.2: Calculate the radar's target detection probability curve based on the Albersheim formula and radar power model.

[0131] Based on given radar performance parameters, target trajectory, target attitude relative to radar station, and atmospheric parameters at the target's location, calculate the target's radar cross section and target range.

[0132] The Albertsheim empirical formulas for radar detection probability, false alarm probability, and signal-to-noise ratio are as follows:

[0133]

[0134] In the formula, This represents the signal-to-noise ratio after pulse accumulation. The number of pulses accumulated. , have

[0135]

[0136]

[0137] In the formula, This represents the radar false alarm probability. This represents the radar detection probability.

[0138] Radar accumulation The signal-to-noise ratio at each pulse is:

[0139]

[0140] In the formula, This represents the radar's peak transmit power. For antenna gain, The effective receiving area of ​​the antenna. The radar cross section of the target. Boltzmann's constant, The effective noise temperature is generally taken as... , For radar receiver bandwidth, The system noise figure is... The target distance.

[0141] Therefore, once the radar model and performance are determined, the relationship between the radar's detection probability of a target, false alarm probability, and distance to the target is as follows:

[0142]

[0143] In the formula, when When the minimum signal-to-noise ratio at which the radar can distinguish the target from the noise is obtained, the current detection probability can be determined. and false alarm probability Theoretical maximum detection range for the target .

[0144] The radar emits electromagnetic waves at the seven targets mentioned above, and the obtained radar cross-section is shown in Figure 5. Substituting the radar parameters of this embodiment and the radar cross-section shown in Figure 5 into the above formula, the signal-to-noise ratio of the radar for that target can be obtained. Furthermore, the detection probability of the radar for each of the seven targets can be obtained, as shown in Figure 6. As can be seen from Figure 6, the detection probability of the radar for each target is not 1, which means that the radar may miss some targets at any time during target detection, thus causing the target tracking trajectory to be interrupted.

[0145] Step 2: Implement the Gaussian mixture probability hypothesis density filter

[0146] Step 2.1: Establish a multi-target state and measurement description and a sensor missed detection description based on a Poisson random finite set.

[0147] Step 2.2: Completely characterize the Poisson random finite set with an intensity function and implement the filter.

[0148] Step 2.3: Describe the intensity function in Gaussian mixture form and implement the GM-PHD filter.

[0149] Furthermore, The described prediction intensity function The description in and have

[0150]

[0151]

[0152] In the formula, State transition equation The Jacobian matrix has

[0153]

[0154] Mode The described posterior intensity function is subject to Time measurement set Measurement in Dominance strength function have

[0155]

[0156] Target survival probability The probability of the sensor detecting the target The target state is irrelevant, that is, it is the formula. , In and ;but and have

[0157]

[0158]

[0159] Under the assumption that the target survival probability and the target detection probability are both constant, a GM-PHD filter can be established.

[0160] Step 3: Detect newly emerging targets based on dynamic features; reconstruct detection probability based on mapping function.

[0161] Step 3.1: Based on the motion characteristics described by the target motion equation established in Step 1.1, achieve effective detection of new targets and avoid false alarms.

[0162] Setting The maximum speed that the prior neonatal goal can achieve is A coefficient used to measure the accuracy of radar observation of a target and the target's possible acceleration motion. When the measured quantity meets the threshold, a Gaussian distribution describing the nascent target is established, and the formula is set. The weights of the goals for middle school students are: .

[0163] Step 3.2: Based on the detection characteristics of the radar measurement model in Step 1.2, the prediction intensity function of the GM-PHD filter is mapped to the measurement space, and the target is continuously tracked by adjusting the weights of trajectory prediction and measurement update.

[0164] Setting middle , , respectively used as weights for trajectory prediction and measurement updates of the detected target and the missed target; set up The clutter intensity is Clutter intensity characterizes the density of clutter in the radar observation area.

[0165] Through the above steps, the tracking trajectory of the target group, as well as various metrics and parameter curves, can be obtained.

[0166] Figures 7 and 8 illustrate the target tracking trajectory. Figure 7 shows the radar tracking trajectory of the target using latitude and longitude, while Figure 8 shows the radar tracking trajectory of the target using a fixed Earth coordinate system. Due to the obstruction of radar waves by the horizon, the target can only be detected by the radar with a certain probability after flying for a certain period of time and reaching a certain altitude. Therefore, the starting point of the tracking trajectory is later than the starting point of the actual trajectory and earlier than the ending point of the actual trajectory.

[0167] Figure 9 shows, in three sub-figures, the number of targets that may be detected by radar within the radar's field of view, the number of targets actually detected by the sensor, and the number of targets estimated by this invention. (See Figure 9 sub-figures) Figure 1 As shown, the three target groups entered the radar detection range at approximately 185 seconds, 300 seconds, and 350 seconds, respectively, and left the radar detection range after 670 seconds. While a target is within the radar detection range, the radar continuously detects it. Since the probability of radar detection of a target is not 1, missed detections may occur during the detection process, resulting in numerous discontinuities between the obtained measurements and the actual trajectories. The final number of targets detected by the radar is shown in Figure 9. Figure 2 As shown. Using the new target identification parameters described in step 3.1 of this invention and the target continuous tracking parameters described in step 3.2 of this invention, the estimation result of the number of targets is as follows. Figure 9 son Figure 3 As shown in Figure 9. Figure 3 When radar detects a target for the first time, this invention can effectively identify it as a new target within an existing target cluster. Furthermore, even when radar misses a target, this invention can still correctly estimate the number of targets. Moreover, during the entire observable time period for the radar, the proportion of times the radar incorrectly estimates the number of targets is 0.0792%, while the proportion of times this invention incorrectly estimates the number of targets is 0.0425%. This invention significantly reduces the adverse impact of radar misses on target number estimation and effectively improves the robustness of tracking group targets.

[0168] Figures 10 and 11 illustrate the actual trajectory of the target, the tracking trajectory of the target by the present invention, and the radar measurement of the target. When the present invention achieves stable tracking of multiple target groups, and the sensor misses a target, the present invention can still predictively track the missed target based on dynamic characteristics. Furthermore, when the sensor detects the target again, it can re-match the target with the existing trajectory to form a coherent trajectory. Moreover, the tracking trajectory formed for the missed target is close to the actual target trajectory, avoiding trajectory matching errors caused by missed detection.

[0169] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A robust tracking filtering method for group targets, characterized by: Includes the following steps, Step 1: Considering Earth's gravity and aerodynamics, establish the target's motion equations; establish a radar measurement model based on the Albersheim formula and radar power model; Step 2: Use a Poisson random finite set to describe the state of multiple targets, measurements, and sensor misses. Use an intensity function to fully characterize the Poisson random finite set and achieve a filter. Then, use a Gaussian mixture form to specifically describe the intensity function and construct a GM-PHD filter. Step 3: Based on the motion characteristics described by the target motion equation in Step 1, achieve effective detection of new targets and avoid false alarms; based on the detection characteristics of missed detections in the radar measurement model in Step 1, map the prediction intensity function of the GM-PHD filter in Step 2 to the measurement space, and achieve continuous tracking of the target by adjusting the weights of trajectory prediction and measurement update.

2. The method as described in claim 1, characterized in that: The method also includes the application of the GM-PHD filter to perform data processing and target tracking on the sensor, thereby achieving continuous tracking of multiple targets and forming a coherent trajectory.

3. The method as described in claim 1, characterized in that: The target motion equation described in step one is: In the formula, For the first One goal is The state at any given moment; For the first The process noise of each objective follows a mean of . covariance is Gaussian distribution; For a single-objective state space; For discrete nonlinear state transition functions, we have In the formula, The gravitational constant of Earth; distance , For discrete time intervals.

4. The method as described in claim 1, characterized in that: The radar measurement model described in step one is as follows: In the formula, for Time for the first Measurement of the quantity of each target; To measure noise, it follows the mean value. covariance is Gaussian distribution; For single-target measurement space; For discrete nonlinear measurement equations, when the sensor is radar, we have: In the formula, , , These are the azimuth, elevation, and range of the target obtained after radar measurement. , , These represent the target's position in the radar's northeast-sky coordinate system.

5. The method as described in claim 1, characterized in that: The method described in step two, which uses Poisson random finite sets to describe the state of multiple targets, measurements, and sensor missed detections, is as follows: In the scene Always The goal is a group whose state set is composed of a random finite set. describe: Without considering target visibility constraints, define the measurement set of group targets. In the formula, and They represent The first moment Target status and measurement; and They are a multi-objective state space and a multi-objective measurement space, respectively, which are composed of a single-objective state space. and single-target measurement space The set consisting of all finite subsets of ; and The mapping between them is as follows: In the formula Depend on Sure; Consider the geometric visibility constraints in the target observation process and define the mapping. have: Consider the missed detections of the target and define the mapping. When a sensor misses a detection, the target does not generate any valid measurement values; to describe the target measurement sequence after a missed detection, the following will be used: The pulse modulation result of the measurement sequence satisfying the visibility constraint is expressed as follows: In the formula This represents the measurement sequence after a missed detection, where For a unit pulse, it is represented as: and Represents a unit pulse, and has Obviously This indicates that a certain target in the group experienced [something] during the tracking process. The missed detection occurred at the time of Combined -Mode It is concluded that Measurement set after target miss occurs at any time For measurement set A subset of, i.e. Based on the group's state set After mapping, the set of measurements that indicate a missed target detection is obtained. Its mapping is: 。 6. The method as described in claim 1, characterized in that: Step two describes the method for fully characterizing a Poisson random finite set using an intensity function and implementing the filter. by Let the intensity function be defined as a random finite set at any time. The integral in the formula is a set integral, defined as follows: Intensity function of random finite sets Characterized The density of the number of targets at a location, and the intensity function in the set. The integral in the set represents the integral in the set. The number of expected targets included; For random finite sets The number of elements in; The Poisson random finite set is the most basic random finite set and is uniquely described by the intensity function: In the formula, Let be the intensity function of a Poisson random finite set; For the entire multi-objective state space The expected target number, Describes the distribution of the target in the state space of a single target; The optimal multi-objective Bayesian filter is expressed as the following prediction and update steps. , In the formula, for A random finite set of multi-objective states at time t. for A random finite set of multi-objective states at time t. for A random finite set of multi-target measurements at time points. From the start time until A random finite set of multi-target measurements at time points. From the start time until A random finite set of multi-target measurements at time points; For measurement set to state set Predict probability density function, for arrive The multi-objective state transition probability density function, For measurement set to state set Posterior probability density function; For measurement set to state set Posterior probability density function, For multi-target measurement probability density function, For measurement set to state set Posterior probability density function; Since the probability density function of a Poisson random finite set is given by equation Unique description, based on the theory of random finite sets, equation Japanese style The optimal multi-objective Bayesian filter derivation described above yields the PHD filter, and the prediction and update intensity functions are as follows: , In the formula, This refers to the state at the previous moment. The current state; , and These represent the intensities of new generation, derived generation, and clutter, respectively. for The posterior intensity function at time t. for Time's up The predicted intensity function at time t. for The posterior intensity function at time t; This represents the probability density function of the target state transition between two consecutive steps; Given the current state hour, The probability density function of measurement at time t; and They are respectively from the state and state The probability of survival and the probability of detection are determined.

7. The method as described in claim 1, characterized in that: The method described in step two, which further describes the intensity function using Gaussian mixture form to ultimately realize the GM-PHD filter, is as follows: The state transition probability density function and the measurement probability density function are expressed as follows: In the formula, Characterization Follow the mean Covariance The expression follows a Gaussian distribution, and different variables will appear in their respective positions and play their respective roles. and These are the discrete nonlinear state transition function and the measurement function, respectively, which are expressed as equation [equation missing]. Japanese style The described state transition function and measurement function; The posterior intensity function at time t is in the following Gaussian mixture form. In the formula, for The number of posterior Gaussian components at time step; for Time of the first The weights of the posterior Gaussian components; and They are respectively Time of the first The mean and covariance of the posterior Gaussian components, then Time's up Prior strength function at time t Also in Gaussian mixture form, there is In the formula, , and These are the intensity functions for surviving targets, derived targets, and newly emerging targets, respectively; the prior intensity function for surviving targets. have In the formula, and These are the mean and covariance of the Gaussian components of the surviving target, respectively. Mode The prior intensity function represented is in Gaussian mixture form, then The posterior intensity function at time t is Mode Japanese style The prediction and update steps described are the Gaussian mixture filter.

8. The method as described in claim 1, characterized in that: Based on the motion characteristics described by the target motion equation in step one, the method for effectively detecting new targets and avoiding false alarms is as follows: At any given time, the distance between any two targets in the group is not less than the sensor's discrimination limit, meaning the targets do not intersect; without considering derived targets in the group, all newly generated targets consist only of newly generated targets, as shown in the equation. Derived target intensity function Always equal to 0; formula Intensity function of newborn targets Also in Gaussian mixture form, there is In the formula, The number of Gaussian components of the intensity function of the new target; the weight of the Gaussian components of the new target. have In the formula, The minimum distance to a newly formed target depends on the target's speed and the sensor's observation accuracy. for For the goal With measurement The distance between them; The Gaussian component weights for a given new target; when When the number of targets obtained after filtering at a given time is not 0, the number of targets obtained after filtering is... The multi-objective state of n objectives, where the nth objective is... The speed of each target is ,but have In the formula, Sampling time, for Time of the first The L2 norm of the target velocity, This is a correction factor; when When the number of targets obtained after filtering at time step 0 is 0. Let be the maximum speed that the target can achieve during its entire motion; then Represented as: 。 9. The method as described in claim 1, characterized in that: Based on the detection characteristics of the radar measurement model in step one, the predicted intensity function of the GM-PHD filter in step two is mapped to the measurement space. The method for achieving continuous target tracking by adjusting the weights of trajectory prediction and measurement updates is as follows: When the detection probability is a variable, then the equation is... Represented as In the formula, For being Time measurement set Measurement in The strength function of dominance; constitute Gaussian component weights Given by the following formula In the formula, express Time belongs to the goal Likelihood measurement Correspondingly, express Time belongs to the goal Likelihood measurement , for The intensity function of clutter at any given time; When the prior strength function For the form of When the Gaussian mixture form is used, the equation is... The described posterior intensity function Specifically there are In the formula, for the prior intensity function The Middle Gaussian components Describe the measurement-independent part of the posterior intensity function. Describe the measurement-related part of the posterior intensity function; for Time of the first One Gaussian component, detection probability have In the formula, To determine the first Does each Gaussian component have a threshold for a relevant detection item? Due to the detection probability... It follows a Bernoulli distribution and has During the filter's operation, to ensure effective differentiation between the target and clutter, when the target... When detected by the sensor, there exists , making When the prior intensity function is in Gaussian mixture form, when the th When a target represented by a Gaussian component is detected by a sensor, there exists , making Clutter is uniformly distributed within the sensor's observation area. because Then when the first When a target represented by a Gaussian component is detected by a sensor, there must be When clutter is uniformly distributed within the sensor's observation area, the equation... The middle judgment of the first Does each Gaussian component have a threshold for relevant detection items? Desirable ;when Time of the first When the target described by each Gaussian component has a relevant detection term, it satisfies the equation... Otherwise, the condition is not met, meaning the target may be lost or missed; in this case, it is the first... A prior Gaussian component assigns a sensor detection probability. Increase its posterior strength function The proportion of the irrelevant part in the middle measurement is used to achieve the measurement of the first... The target represented by the prior Gaussian component is maintained for a longer time, thus avoiding sensor misses.

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