Three-dimensional imaging single-photon laser radar system based on multi-beam eye-like scanning

Abstract

The invention belongs to the field of laser radar systems, and discloses a three-dimensional imaging single-photon laser radar system based on multi-beam eye-like scanning, which is composed of a laser, a DOE, a perforated reflector, a Risley scanning prism, a telescope, a detector array, a time-to-digital converter and a two-dimensional holder. The laser generates a detection light beam, the detection light beam passes through the DOE to generate a two-dimensional light beam array, the light beam array passes through a small hole in the center of the perforated reflector, a view field range is scanned through the Risley prism, and a scanning path is an eye-like pattern; echo signals enter along the same optical axis through the Risley prism, are reflected to the telescope through the perforated reflector and are converged to the detector array through the telescope, and photosensitive surfaces of the detector array correspond to view fields of the detection light beam array one to one.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of laser radar systems, and particularly relates to a three-dimensional imaging single-photon laser radar system based on multi-beam eye scanning. BACKGROUND

[0002] In recent years, with the rapid development and commercialization of unmanned aerial vehicles, low, slow and small targets dominated by unmanned aerial vehicles have shown explosive growth in urban airspace due to their easy accessibility and wide range of applications, bringing numerous safety hazards. However, in the urban environment, the current microwave radar can only achieve target detection, but cannot image; two-dimensional photoelectric imaging technology is easily disturbed by light, rain and fog, and the detection accuracy and robustness are limited; passive radio detection technology is easily affected by electromagnetic interference and has low accuracy. Therefore, active three-dimensional imaging of low, slow and small targets dominated by unmanned aerial vehicles is of great significance for effective detection, control and countermeasures of unmanned aerial vehicles.

[0003] Laser radar is the most effective technology for realizing active three-dimensional imaging at present. However, three-dimensional imaging of low, slow and small targets based on laser radar in complex urban environments faces three main bottlenecks: 1) Short imaging distance: In the urban environment, under the laser power that meets personal safety, due to the small scattering cross-section of low, slow and small targets, as well as the influence of atmospheric absorption and scattering, the reflected laser echo of low, slow and small targets is submerged in a large amount of background noise, and the signal-to-noise ratio is extremely low. Therefore, it is difficult for traditional laser radar to effectively detect "low, slow and small" targets at a long distance, and the imaging distance is short.

[0004] 2) Slow imaging speed / low resolution: Traditional long-distance (>300m) imaging laser radars mostly use single-point uniform scanning to realize three-dimensional imaging, and the imaging resolution and speed are forced to be related. In order to meet the requirements of low, slow and small target detection and identification on imaging resolution, the scanning step is small and the scanning time is long. In addition, compared with image data, laser radar point cloud belongs to three-dimensional unordered data (lack of field information between pixels), and the data volume is large and the processing speed is slow. In summary, due to the limitations of scanning and data processing methods, the imaging speed of traditional laser radar is slow.

[0005] 3) Narrow imaging field of view: Due to the fact that the current laser radar mostly realizes three-dimensional imaging in a point scanning manner, in order to meet the requirements of low, slow and small target detection on imaging resolution (point cloud density) and imaging speed, the imaging field of view is narrow in long-distance imaging, and the target is easily lost in the imaging process of moving targets. SUMMARY

[0006] In order to meet the demand of three-dimensional active imaging of low, slow and small targets in complex urban environment, in view of the imaging distance, low speed / low resolution and narrow field of view of the laser radar, a three-dimensional imaging single-photon laser radar system based on multi-beam eye-like scanning is provided, which realizes fast active three-dimensional imaging of low, slow and small targets, improves the precision and robustness of low, slow and small target detection and identification in complex urban environment, and provides important technical support for unmanned aerial vehicle supervision and disposal.

[0007] In order to achieve the above object, the present application provides the following scheme: A three-dimensional imaging single-photon laser radar system based on multi-beam eye-like scanning, the system comprises: a laser, a DOE, a perforated mirror, a Risley scanning prism, a telescope, a detector array, a time-to-digital converter and a two-dimensional holder; The laser is used for generating a laser beam as a detection beam, and transmitting an emission synchronization signal to the time-to-digital converter; The DOE is a two-dimensional laser beam splitting device, which is used for splitting a single incident laser beam into a two-dimensional planar array of beams; The perforated mirror is provided with a small hole in the middle, so that the two-dimensional planar array of beams can be emitted, and is used for reflecting the echo beam to the telescope objective, so as to realize the same optical axis of emission and reception; The Risley scanning prism is used to realize petal-shaped scanning of the two-dimensional planar array of beams and the echo beam along the same optical axis; The telescope is used for receiving the echo beam reflected by the perforated mirror and converging it on the light-sensitive surface of the detector array; The detector array is a multi-channel array detector, which is used for receiving the echo signal converged by the telescope, and transmitting an electric signal to the time-to-digital converter after detecting a photon event; The time-to-digital converter is used for receiving the synchronization signal emitted by the laser and the photon event signal of the detector array, measuring the time difference of arrival of the two signals as the photon flight time; The two-dimensional holder is used for positioning the position of the unmanned aerial vehicle according to the photon flight time signal, rotating the emission and reception system to align the optical axis with the unmanned aerial vehicle, and realizing the imaging detection and tracking of the unmanned aerial vehicle.

[0008] Preferably, the detection beam of the laser triggers the Pin light detection module to generate an emission synchronization signal through the stray light of the perforated mirror.

[0009] Preferably, the three-dimensional imaging of the unmanned aerial vehicle is obtained by using a photon point cloud fast three-dimensional imaging method fusing space-time information through the motor angle signal and the photon event signal. Wherein, the ABZ signal output by the photoelectric encoder is calculated by FPGA. The process of obtaining the three-dimensional image of the unmanned aerial vehicle using the photon point cloud fast three-dimensional imaging method fusing space-time information includes: constructing a background-tree for the background frame point cloud and a current-tree for the current frame point cloud; performing a difference set operation on the current frame point cloud and the background tree to obtain a preliminary foreground point cloud set ; calculating the distance between each point in the foreground point cloud set and the center of the nearest leaf node in the background-tree ; judging whether there is a motion misjudgment based on the distance , with the voxel edge length as the distance threshold; based on the result of the judgment, implementing three-dimensional reconstruction and imaging using the foreground point.

[0010] Preferably, the process of judging whether there is a motion misjudgment based on the distance , with the voxel edge length as the distance threshold, includes: if the distance , the point is a background point deviated to other nodes due to sensing error or edge disturbance, and is removed; if the distance , it is considered as an effective foreground point and is retained for target identification and tracking.

[0011] Preferably, the unmanned aerial vehicle target is detected using adaptive clustering and interactive multi-model, and the Kalman filter is used to predict the trajectory of the unmanned aerial vehicle target to control the two-dimensional holder to implement tracking on the unmanned aerial vehicle target.

[0012] Preferably, the process of detecting the unmanned aerial vehicle target using adaptive clustering and interactive multi-model includes: S1: for any unvisited point in the input point cloud , determine the parameters about the point, and set the minimum point number , defined as: ; wherein, is the average angular resolution of the laser radar; S2: calculate the number of all points with a distance less than or equal to from the point, if , the point is considered as a core point, and a point cloud cluster is established, and the point and all neighborhood points are contained. S3: In point cloud clusters Select another unvisited data point and repeat S1 and S2 until no new data points are added to the cluster. ; S4: Repeat S1, S2 and S3 until all points are classified.

[0013] Preferably, the process of predicting the UAV target trajectory using a Kalman filter and controlling the 2D gimbal to track the UAV target includes: S5: Calculate the value of each filter. Interactive input at any time will Time model The input is denoted as Then we have: ; ; ; in, Represents conditional probability. Representation Model To model Interaction probability, Indicates corresponding to The covariance matrix is ​​given by the model probability at the initial time step, which is derived from the Markov matrix, i.e.: , The total number of models to be interacted with. Indicates from Time's up The model flag being considered at any given time. Indicates the first The model is from Time's up The probability of occurrence at time 1. Representation Model To model The transition probability, , , Representation Model l To model The transition probability, , express Time of the first Estimation of the system state of a model filter, express Time of the first The error covariance matrix of each model filter, Represents conditional probability. express State estimation of the model at time ; S6: According to the single-step loop algorithm step of the Kalman filter method, the state estimation of the model at time is calculated by combining the interaction input of the system model at time and ; and the covariance matrix of the model at time , and the likelihood function of each model at time is further calculated: ; wherein denotes a probability density function, and are the measurement residual and its covariance, denotes a probability density function of a normally distributed random variable with a mean of 0 and a covariance matrix , denotes the observation data of the system at time k , denotes the set of data observed by the system at time k -1; S7: According to the probability of each model appearing , the result calculated and the prior Markov probability transition matrix have: ; wherein is a normalization constant, ; S8: The final state vector and covariance matrix estimation of the IMM algorithm at time are obtained by combining the estimation results of each filter and the probability of occurrence, i.e.: ; ; wherein denotes the estimation of the system state of the th model filter at time , and denotes the error covariance matrix of the th model filter at time , the final state vector of the IMM algorithm is , and the final covariance matrix estimation of the IMM algorithm is ; By continuously iterating S5, S6, S7 and S8, the IMM algorithm continuously predicts, updates and tracks the target.

[0014] Compared with the prior art, the present application has the following advantages: The present application provides a multi-beam eye-like scanning three-dimensional imaging single-photon laser radar system, which adopts single-photon detection technology to improve the detection sensitivity to the order of photons, solves the problem of low signal-to-noise ratio of the echo signal at a long distance, and greatly improves the detection distance; adopts multi-beam, eye-like scanning technology and photon point cloud fast three-dimensional imaging method of fusing space-time information, breaks through the bottleneck of mutual restriction of imaging speed and imaging resolution, and improves the imaging speed and imaging resolution; adopts a target detection and tracking algorithm based on distance adaptive clustering and interactive multi-model, overcomes the difficulty of narrow imaging field of view, and ensures that the target is always in the center of the imaging field of view. The present application not only provides important theoretical reference and technical exploration for the development of laser radar imaging technology, but also has important theoretical significance and practical application value for constructing a complex urban environment low, slow and small target perception system. BRIEF DESCRIPTION OF DRAWINGS

[0015] In order to more clearly illustrate the technical solutions of the present application, the following briefly introduces the drawings needed to be used in the embodiments. Obviously, the drawings described in the following embodiments are only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor.

[0016] Figure 1 The present application provides a multi-beam eye-like scanning three-dimensional imaging single-photon laser radar system structure schematic diagram. Figure 2 The present application provides a signal transmission link schematic diagram. DETAILED DESCRIPTION

[0017] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0018] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0019] Embodiment one This invention provides a three-dimensional imaging single-photon lidar system based on multi-beam eye-like scanning, comprising a laser, a DOE (Distributed Optical Array), a perforated mirror, a Risley scanning prism, a telescope, a detector array, a time-to-digital converter (TD-SCDMA), and a two-dimensional gimbal. The laser generates a 532nm laser beam as the detection beam and transmits a transmission synchronization signal to the TD-SCDMA. The DOE is a two-dimensional laser beam splitter that divides a single incident laser beam into a two-dimensional planar array beam. The perforated mirror has a small hole in the center to allow the detection beam to exit; one side is blackened to reduce detection beam reflection, and the other side is coated to increase echo beam reflection, reflecting the echo beam to the telescope objective lens to achieve coaxial transmission and reception. The Risley scanning prism consists of two wedge-shaped prisms and... Its driving components consist of two parallel wedge-shaped prisms arranged perpendicular to the optical axis, rotating in a given manner to achieve petal-shaped scanning of the detection beam; the telescope receives the echo beam reflected by the perforated mirror and focuses it onto the photosensitive surface of the detector array; the detector array is a multi-channel array detector that receives the echo signal focused by the telescope, and after detecting a photon event, transmits an electrical signal to a time-to-digital converter; the time-to-digital converter receives the emission synchronization signal of the laser and the photon event signal of the detector array, measures the arrival time difference of the two signals as the photon flight time; the two-dimensional gimbal locates the UAV position based on the above photon flight time signal, rotates the two-dimensional gimbal to align the optical axis with the UAV, and realizes UAV imaging detection and tracking.

[0020] The specific implementation process is as follows: The present invention provides a three-dimensional imaging single-photon lidar based on multi-beam eye-like scanning, such as... Figure 1 As shown, it consists of a laser, a DOE, a perforated mirror, a Risley scanning prism, a telescope, a detector array, a time-to-digital converter, and a two-dimensional gimbal.

[0021] like Figure 1 The laser generates a probe beam, which is then used by the DOE to generate a two-dimensional beam array. This beam array passes through a small hole in the center of a perforated mirror and is scanned by a Risley prism. The scanning path is an eye-like pattern. The echo signal is incident along the same optical axis through the Risley prism and reflected by the perforated mirror to the telescope. The signal is then converged by the telescope onto the detector array. The photosensitive surface of the detector array corresponds one-to-one with the field of view of the probe beam array.

[0022] In this embodiment, the detector array is a Hamamatsu 4×4 PMT, and the DOE is a Holoor 4×4 beam splitter.

[0023] Figure 2The signal transmission link of the system is shown, wherein the laser emission synchronization signal does not need to split the emission beam additionally, and the Pin light detection module is used to detect the stray light generated by the emission beam passing through the perforated mirror. This method can ensure the power of the emission and detection beams as much as possible to achieve the purpose of long-distance detection. In the embodiment, the Pin light detection module uses a KY-PDM high-speed light detection module.

[0024] The motor driver controls the motor to continuously operate at a fixed rotating speed, and a photoelectric encoder outputs a motor angle signal in real time. In the embodiment, an FPGA is used to calculate the motor angle by accumulating the ABZ signals output by the photoelectric encoder, and the process is as follows: 1) Signal synchronization: two D flip-flops are used to synchronize each input signal (A, B, Z); 2) State saving: save the current clock and the AB state of the last clock cycle; 3) Four times frequency direction detection: by comparing the current and last states, the state transition table is used to judge the rotating direction, and the delta ∈ {-1, 0, +1} is outputted; 4) Position accumulation: the register pos is used to accumulate the delta value to realize position tracking. The Z phase is used as the "origin" signal, which is cleared under certain conditions. The final output register pos value is used as the rotating angle position value.

[0025] The emission synchronization signal and the motor angle signal are received by the FPGA, and then sent to the host computer after being time-stamped.

[0026] The time-to-digital converter outputs the photon flight time by the emission synchronization signal and the photon event signal of the detector array (the function of the detector array is to output a pulse as a photon event signal when a photon is detected), and sends it to the host computer in combination with the time stamp.

[0027] The host computer uses the photon point cloud fast three-dimensional imaging method based on spatio-temporal information fusion to obtain the three-dimensional imaging of the unmanned aerial vehicle by the motor angle signal and the photon flight time, uses the adaptive clustering and interactive multi-model based detection unmanned aerial vehicle target, and uses the Kalman filter to predict the trajectory of the unmanned aerial vehicle target to control the two-dimensional holder to track the unmanned aerial vehicle target. The three-dimensional imaging method is based on the octree model of structured space search and the KNN algorithm based on local feature judgment, and the process is as follows: 1) Constructing an octree structure: construct a background-tree for the background frame point cloud and a current-tree for the current frame point cloud. Specifically, each frame of point cloud is constructed as an octree, which can divide the space into subdivisions, and finally divide the size into The three-dimensional spatial structure of the octree, and each small cube can be regarded as a node of the tree. Through the spatial division of the octree, the point cloud of the entire space can be divided and managed, and divided into each corresponding node; 2) Difference set extraction: difference set operation is performed on the current frame point cloud and the background tree to obtain a preliminary suspected foreground point cloud set ； wherein, is the current frame point cloud set, difference set operation is performed in the background tree with a threshold of ; 3) KNN space correction: for each point in the set , the distance between the point and the center of the nearest leaf node in the background tree is calculated wherein, is the set of background tree leaf nodes, is the geometric center of the i-th leaf node; 4) Error elimination threshold judgment: with the voxel edge length as the distance threshold, it is judged whether there is a motion error: if , the point is likely to be a background point deviated to other nodes due to sensing error or edge disturbance and should be eliminated; if , it is considered to be an effective foreground point and is retained for target recognition and tracking.

[0028] 5) Three-dimensional imaging: using the foreground points to implement three-dimensional reconstruction and imaging (directly displaying the point cloud).

[0029] The detection target uses an improved DBSCAN clustering method, and the specific process is as follows: 1) For any unvisited point in the input point cloud, determine the parameters about the point, and set the minimum point number , defined as follows: ; wherein, is the average angular resolution of the laser radar.

[0030] 2) Calculate the number of points whose distance from the point is less than or equal to , if , the point is considered to be a core point , and a point cloud cluster is established, and the point and all neighborhood points are included.

[0031] 3) Select another unvisited data point in the point cloud cluster Repeat step 1 and step 2 until no new data point is added to the cluster ; 4) Repeat process 1, 2, 3 until all points are classified.

[0032] Where the trajectory prediction process is as follows: 1) The interaction input of the model: This step needs to calculate the interaction input of each filter at time , and the input of the model at time is denoted as , then: ; ; ; Where, represents the conditional probability, represents the interaction probability of the model to the model , represents the covariance matrix corresponding to . The initial model probability at time can be obtained by Markov matrix, that is , is the total number of models to be interacted, represents the model mark being considered from time to time , represents the probability of the th model ( ) appearing from time to time , represents the transition probability of the model to the model , , , represents the transition probability of the model l to the model , , and let represent the estimation of the system state of the th model filter at time , let represent the error covariance matrix of the th model filter at time , represents the conditional probability, and the condition is known k ​-1 and all historical observation data prior to that time, and assuming the current k The time system is in the model i , express -1 time model State estimation.

[0033] 2) Parallel filtering by multiple filters: Based on the single-step loop algorithm steps of the Kalman filter method, combined with step 1... Interactive input of the time system model and The model can be calculated. State estimation Covariance Matrix Furthermore, we can also calculate... The likelihood function of each model at time step: ; in, Represents the probability density function. and It refers to the measurement residuals and their covariance. Let represent the probability density function of a normally distributed random variable with a mean of 0 and a covariance matrix of . , express k Observational data of the time system express k The set of data observed by the system at time -1; 3) Model probability update: Based on the probability of each model appearing in the above text, Based on the calculated results and the prior Markov probability transition matrix, we have: ; in The normalization constant is ; 4) New data fusion: The final state vector and covariance matrix of the IMM algorithm at time step can be obtained by combining the estimation results of each filter with its occurrence probability, i.e.: ; ; Among them, let express Time of the first The estimation of the system state of each model filter, let denotes the time instant error covariance matrix of each model filter, is the final state vector of the IMM algorithm, is the final covariance matrix estimate of the IMM algorithm.

[0034] By continuously iterating the above four steps, the IMM algorithm continuously predicts, updates and tracks the target.

[0035] The three-dimensional imaging single-photon laser radar based on multi-beam type eye scanning of the application has the following advantages: 1. Remote target photon point cloud acquisition (≥100m) can be realized, which provides a data support and verification platform for photon point cloud imaging and target detection and tracking; 2. Massive background point cloud can be quickly filtered out, and fast and high-precision three-dimensional imaging of the target (10Hz) can be realized; 3. High-precision target detection and high-robustness tracking can be realized (imaging range ≥6°×6°, detection success rate ≥90%).

[0036] The above-described embodiments are only descriptions of the preferred modes of the application and do not limit the scope of the application. Without departing from the design spirit of the application, various modifications and improvements to the technical solutions of the application made by those skilled in the art shall fall within the protection scope defined by the claims of the application.

Claims

1. A multi-beam class eye scan based three-dimensional imaging single-photon lidar system, characterized in that, The system includes: a laser, a DOE, a perforated mirror, a Risley scanning prism, a telescope, a detector array, a time-to-digital converter, and a two-dimensional gimbal. The laser is used to generate a laser beam as a detection beam and to transmit a transmission synchronization signal to the time-to-digital converter. The DOE is a two-dimensional laser beam splitter used to split a single incident laser beam into a two-dimensional planar array beam. The perforated reflector has a small hole in the middle to allow the two-dimensional planar array beam to exit and to reflect the echo beam back to the telescope objective lens, thus achieving coaxial transmission and reception. The Risley scanning prism is used to achieve petal-shaped scanning of a two-dimensional planar array beam and to allow echo beams to enter along the same optical axis. The telescope is used to receive the echo beam reflected by the perforated mirror and focus it onto the photosensitive surface of the detector array. The detector array is a multi-channel array detector used to receive the echo signal converged by the telescope, and after detecting a photon event, transmit an electrical signal to the time-to-digital converter. The time-to-digital converter is used to receive the synchronization signal emitted by the laser and the photon event signal of the detector array, and measure the arrival time difference of the two signals as the photon flight time. The two-dimensional gimbal is used to locate the UAV's position based on the photon time-of-flight signal, and to rotate the transmitting and receiving system to align the optical axis with the UAV, thereby enabling UAV imaging detection and tracking.

2. The system of claim 1, wherein, The laser's probe beam triggers the pin light detection module to generate a transmission synchronization signal through stray light from the perforated mirror.

3. The system of claim 1, wherein, A rapid 3D imaging method for UAVs is used to obtain the 3D image of the UAV by using photon point cloud fusion method that integrates motor angle signals and photon event signals and spatiotemporal information. Among them, the motor angle signal is calculated by accumulating the ABZ signal output by the photoelectric encoder using FPGA; The process of obtaining a UAV's 3D image using a fast 3D imaging method that fuses spatiotemporal information from photon point clouds includes: Construct a background-tree for the background frame point cloud and a current-tree for the current frame point cloud; Perform a difference operation between the current frame point cloud and the background tree to obtain a preliminary set of foreground point clouds. ; Foreground attractions cloud collection For each point in the background tree, calculate its distance to the center of the nearest leaf node in the background tree. ; Based on distance Based on voxel side length The distance threshold is used to determine whether there are motion misjudgments. Based on the assessment results, 3D reconstruction and imaging were performed using the foreground points.

4. The system according to claim 3, characterized in that, Based on distance Based on voxel side length The process of determining whether there is a motion misjudgment, based on a distance threshold, includes: If distance If the point is a background point that has shifted to other nodes due to sensing error or edge disturbance, it should be discarded. If distance If the foreground is positive, it is considered a valid foreground point and is retained for target identification and tracking.

5. The system according to claim 4, characterized in that, The system uses adaptive clustering and interactive multi-model detection to detect UAV targets, combined with Kalman filters to predict the UAV target trajectory, and controls a two-dimensional gimbal to track the UAV target.

6. The system according to claim 5, characterized in that, The process of detecting UAV targets using adaptive clustering and interactive multi-model approaches includes: S1: For any unvisited point in the input point cloud Determine about this point Parameters, and set the minimum number of points. , Defined as: ； in, This represents the average angular resolution of the lidar. S2: Calculate the distance from this point that is less than or equal to... Number of all points ,like If so, then this point is considered the core point, and a point cloud cluster is established. This includes the point and all its neighboring points. S3: In point cloud clusters Select another unvisited data point and repeat S1 and S2 until no new data points are added to the cluster. ; S4: Repeat S1, S2 and S3 until all points are classified.

7. The system according to claim 6, characterized in that, The process of predicting the drone target trajectory using a Kalman filter and controlling a 2D gimbal to track the drone target includes: S5: Calculate the value of each filter. Interactive input at any time will Time model The input is denoted as Then we have: ； ； ； in, Represents conditional probability. Representation Model To model Interaction probability, Indicates corresponding to The covariance matrix is ​​given by the model probability at the initial time step, which is derived from the Markov matrix, i.e.: , The total number of models to be interacted with. Indicates from Time's up The model flag being considered at any given time. Indicates the first The model is from Time's up The probability of occurrence at time 1. Representation Model To model The transition probability, , , Representation Model l To model The transition probability, , express Time of the first Estimation of the system state of a model filter, express Time of the first The error covariance matrix of each model filter, Represents conditional probability. express -1 time model State estimation; S6: Based on the single-step loop algorithm steps of the Kalman filter method, combined with the steps in S5... Interactive input of the time system model and Computational model State estimation Covariance Matrix At the same time, further find The likelihood function of each model at time step: ； in, Represents the probability density function. and It refers to the measurement residuals and their covariance. Let represent the probability density function of a normally distributed random variable with a mean of 0 and a covariance matrix of . , express k Observational data from the time system express k The set of data observed by the system at time -1; S7: Based on the probability of each model appearing... Based on the calculated results and the prior Markov probability transition matrix, we have: ； in The normalization constant is ； S8: Obtained by combining the estimation results and occurrence probabilities of each filter. The estimation of the final state vector and covariance matrix of the IMM algorithm at time step: ； ； Among them, let express Time of the first The estimation of the system state of each model filter, let express Time of the first The error covariance matrix of each model filter, This represents the final state vector of the IMM algorithm. This is an estimate of the final covariance matrix of the IMM algorithm; By continuously iterating through S5, S6, S7, and S8, the IMM algorithm continuously predicts, updates, and tracks the target.

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