A random set theory based track-before-detect method under unknown signal-to-noise ratio

Abstract

This invention discloses a pre-detection tracking method based on random set theory for targets with unknown signal-to-noise ratios (SNR), belonging to the field of radar target detection and tracking. Pre-detection tracking is an effective technique for detecting and tracking low signal-to-noise ratio (SNR) targets. This invention proposes a solution for the case of unknown and time-varying target SNR based on a tag-based multi-Bernoulli (LMB) filter. A novel likelihood function is designed based on a second-order Taylor series expansion for the unknown target SNR. Simultaneously, a sorting update strategy is proposed to address the problem of targets sharing the same measurements when they are close to clutter. Simulation results show that this method can effectively detect and track targets under unknown target SNR conditions, with negligible performance loss compared to simulation results under known target SNR conditions.

Description

Technical Field

[0001] This invention relates to the field of multi-target detection and tracking in radar data processing, and more particularly to the field of multi-target detection and tracking under the theory of random finite sets. Background Technology

[0002] Track-Before-Detect (TBD) is a technique for weak target detection and tracking. TBD directly processes raw sensor data, utilizing the motion correlation of the target over multiple frames to accumulate target energy, thereby improving the decision signal-to-noise ratio (SNR) while suppressing irrelevant clutter. TBD is particularly suitable for weak target detection with low SNR, achieving good results through non-coherent accumulation. TBD was first applied to infrared optics, with key methods including Dynamic Programming (DP), Particle Filtering (PF), Maximum Likelihood Probabilistic Data Algorithm (ML-PDA), and Hough Transform (HT). In recent years, the emerging theory of stochastic finite sets has provided more complete modeling, offering an optimal theoretical framework for multi-target sequential estimation problems and attracting increasing attention. Random finite set theory (RFT) is a statistical theory describing finite set-type random variables. It provides methods for describing and modeling uncertainty by modeling the uncertainties of multi-source measurements, including randomness, inaccuracy, and fuzziness, and the time-varying characteristics of the unknown number of targets, within the framework of point process theory. TBD algorithms based on the RTF framework mainly include multi-Bernoulli (MB) filters, probability hypothesis density (PHD) filters, and generalized labeled multi-Bernoulli (GLMB) filters.

[0003] Currently, most research on pre-detection tracking (TBD) is based on the assumption that the target signal-to-noise ratio (SNR) is known. However, in most real-world scenarios, the target's radar cross-section (RCS) is unknown, and the echo intensity varies with the distance between the target and the radar, making the SNR variable and unknown. Existing technologies combine amplitude characteristic likelihood probability density (PHD) filters and cardinally proportional probability density (CPHD) filters for target tracking under unknown SNR. However, due to the limitations of the independent and identically distributed (IID) assumption used in PHD and CPHD filters, their performance in TBD is often unsatisfactory. Standard TBD assumes that multiple targets do not overlap in their influence range on the measurement plane (rigid body assumption), thus the likelihood functions of multiple targets are independent of each other. However, when clutter is present near the target, the clutter updates its measurements using the target's measurements, leading to false tracks and duplicate tracks. Summary of the Invention

[0004] The present invention aims to provide a pre-detection tracking method based on random set theory under unknown signal-to-noise ratio conditions, in order to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A pre-detection tracking method based on random set theory under unknown signal-to-noise ratio (SNR) conditions is proposed. The method is based on a random set filter framework, derives the likelihood function under unknown target SNR, proposes a sorting and updating strategy, and achieves multi-target detection and tracking. Specific steps include:

[0007] Step 1: Initialize system parameters, number of iteration frames, and multi-objective Bernoulli distribution;

[0008] Step 2: Update the iteration frame number frame by frame, and calculate the prior label multi-Bernoulli distribution of surviving targets and the predicted posterior label multi-Bernoulli distribution of targets based on the iteration frame number;

[0009] Step 3: Perform threshold truncation and quantity limit optimization on the components of the posterior label multi-Bernoulli distribution, remove invalid components and retain the optimal component set;

[0010] Step 4: Based on the optimized multi-Bernoulli posterior distribution, calculate the distribution cardinality and extract the target state, and output the target state estimation result for the current frame.

[0011] Optionally, step 1 includes:

[0012] Step 11: Initialize the radar monitoring range; the radar monitoring range includes radar range resolution, radar Doppler velocity resolution, radar scan period, and total number of observation frames;

[0013] Step 12: Initialize the number of iteration frames Initialize multi-objective Bernoulli distribution and order ,in Represents the target label set space of the current frame; Indicates the first The probability of a target continuing to survive. Indicates the first The probability density function of each surviving target; initialization of the multi-objective likelihood function and target survival probability. And the single-target transition probability density function.

[0014] Optionally, step 2 includes:

[0015] Step 21: Set the number of iteration frames , No. New target births occur in frames. Target birth information is obtained through event triggering or passive reconnaissance. The set of new target components and the multi-Bernoulli distribution of the tags are represented as follows:

[0016] ;

[0017] ;

[0018] in, Represents the set of new target components. This indicates the status of the first new target. This indicates the status of the second new target. Indicates the first The state of a new student's goal. Indicates the number of new target students. This indicates a multi-Bernoulli distribution of the target labels for newborns. Indicates the first The probability of the existence of a new target. Indicates the first The probability density function of a new target. A set of labels representing the goals of new students; Indicates the first The target state of the frame;

[0019] Step 22: Calculate the survival target number The prior labels of the frames are distributed in a multi-Bernoulli pattern.

[0020] Step 23: Calculate the predicted target number The posterior label of the frame is a multi-Bernoulli distribution.

[0021] Optionally, step 22 includes:

[0022] Step 221: Given Posterior label multi-Bernoulli distribution of the target in the frame , ,in, express Frame time The probability of a target continuing to survive. express Frame time The probability density function of the remaining surviving targets. express Frame-time target label set space;

[0023] Step 222: Calculate the first... The first goal in The probability of a frame continuing to exist and the corresponding probability density function :

[0024] ;

[0025] ;

[0026] Among them, mathematical symbols Representation function and The inner product, i.e.: ; Indicates the first The single-target transfer probability density function.

[0027] Optionally, step 23 includes:

[0028] Step 231: Given Frame prediction of multi-Bernoulli distribution For each of the target labels By sorting the birth times in ascending order, the first predicted Bernoulli distribution is obtained. ;

[0029] Step 232: For the first predicted Bernoulli distribution The existence probability of each target is sorted from largest to smallest to obtain the second prediction Bernoulli distribution. ;

[0030] Step 233: Based on the second predicted Bernoulli distribution According to the Bayesian update equation, calculate the first... The first goal in posterior existence probability of a frame and the corresponding posterior probability density function :

[0031] ;

[0032] ;

[0033] in, The likelihood function is defined when the target signal-to-noise ratio is unknown. The likelihood function is designed as follows:

[0034] ;

[0035] in, Represents the target state The set of pixel unit indices that can be affected; Represents pixel grid The corresponding measured power; Indicates the probability of a false alarm. , where T represents the threshold;

[0036] Step 234: Update the first After obtaining the posterior state of the first target, it will be used to update the second target. Measurement data for each target were removed from the original measurements.

[0037] Optionally, step 3 includes:

[0038] Step 31: Include components of the posterior label multi-Bernoulli distribution with a probability less than the threshold. The components are removed;

[0039] Step 32: Include items with a probability greater than the threshold. Sort the components of the posterior label multi-Bernoulli distribution from largest to smallest, and take the top... The components of a posterior-labeled Bernoulli distribution, where... This represents the maximum value of the new target.

[0040] Optionally, in step 4, the following formula can be used for calculation. The cardinality of the Bernoulli posterior distribution of each frame is determined, and the state of the corresponding target is extracted as... Frame target state estimation results:

[0041] ;

[0042] in, Indicates the first The number of targets estimated in the frame. This indicates rounding. Indicates the first The probability of the existence of each target; This indicates the maximum number of new target cells.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] This invention achieves multi-target pre-detection tracking when the target signal-to-noise ratio is unknown by using a likelihood function modeling scheme under the condition of unknown target signal-to-noise ratio and by using a sorting update strategy to solve the problem of the target and clutter sharing the same measurement when they are close to each other.

[0045] In addition, this invention is based on the LMB filter tracking framework, which has high algorithm robustness and can be applied to robust target tracking in weak target scenarios; the algorithm has high accuracy and can achieve high-precision target tracking; and it can effectively solve the problems of shared measurement and unknown target signal-to-noise ratio when the target and clutter are close together. Attached Figure Description

[0046] Figure 1 A flowchart of a pre-detection tracking method based on random set theory under unknown signal-to-noise ratio provided by the present invention;

[0047] Figure 2 The trajectories of the three targets (RVs) are shown.

[0048] Figure 3 The diagram shows the OSPA (Optimal Sub-Pattern Assignment) results from the experimental simulation, where a represents the results of missed detections, b represents the results of distance error, and c represents the results of cardinality error. Detailed Implementation

[0049] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments:

[0050] The specific implementation process is as follows:

[0051] Reference Figure 1 As shown, this embodiment provides a pre-detection tracking method based on random set theory under unknown signal-to-noise ratio. This method is based on the numerical implementation of random set filters, specifically particle filtering, but is not limited to other numerical implementation methods. The implementation steps include:

[0052] Step 1: Initialize system parameters, number of iteration frames, and multi-objective Bernoulli distribution.

[0053] Specifically, it includes: Step 11: Initialize the radar monitoring range; the radar monitoring range includes radar range resolution, radar Doppler velocity resolution, radar scan period, and total number of observation frames;

[0054] Step 12: Initialize the number of iteration frames Initialize multi-objective Bernoulli distribution and order ,in Represents the target label set space of the current frame; Indicates the first The probability of a target continuing to survive. Indicates the first The probability density function of each surviving target; initialization of the multi-objective likelihood function and target survival probability. And the single-target transition probability density function.

[0055] Step 2: Update the iteration frame number frame by frame, and calculate the prior label multi-Bernoulli distribution of surviving targets and the posterior label multi-Bernoulli distribution of predicted targets based on the iteration frame number.

[0056] Specifically, this includes step 21: Let , No. A new target is born.

[0057] In this embodiment, target birth information is obtained through event triggering or passive reconnaissance, and the set of newborn target components and the multi-Bernoulli distribution of the tags are represented as follows:

[0058] ;

[0059] ;

[0060] in, Represents the set of new target components. This indicates the status of the first new target. This indicates the status of the second new target. Indicates the first The state of a new student's goal. Indicates the number of new target students. This indicates a multi-Bernoulli distribution of the target labels for newborns. Indicates the first The probability of the existence of a new target. Indicates the first The probability density function of a new target. A set of labels representing the goals of new students; Indicates the first The target state of the frame;

[0061] Step 22: Calculate the survival target number The prior labels of the frames are distributed by a multi-Bernoulli distribution.

[0062] In this embodiment, step 221 is included: given Posterior LMB distribution of Frame Survival Targets , ,in, express Frame time The probability of a target continuing to survive. express Frame time The probability density function of the remaining surviving targets. express Frame-time target label set space.

[0063] Step 222: Calculate the first... The first goal in The probability of a frame continuing to exist and the corresponding probability density function :

[0064] ;

[0065] ;

[0066] Among them, mathematical symbols Representation function and The inner product, i.e.: ); Indicates the first The single-target transfer probability density function.

[0067] Step 23: Calculate the predicted target number The posterior label of the frame is a multi-Bernoulli distribution.

[0068] In this embodiment, step 23 includes:

[0069] Step 231: Given Frame prediction of multi-Bernoulli distribution For each of the target labels By sorting the birth times in ascending order, the first predicted Bernoulli distribution is obtained. ;

[0070] Step 232: For the first predicted Bernoulli distribution The existence probability of each target is sorted from largest to smallest to obtain the second prediction Bernoulli distribution. ;

[0071] Step 233: Based on the second predicted Bernoulli distribution According to the Bayesian update equation, calculate the first... The first goal in posterior existence probability of a frame and the corresponding posterior probability density function :

[0072] ;

[0073] ;

[0074] in, Let represent the likelihood function when the target signal-to-noise ratio is unknown. In this invention, the likelihood function when the target signal-to-noise ratio is unknown is designed as follows:

[0075] ;

[0076] in, Represents the target state The set of pixel unit indices that can be affected; Represents pixel grid The corresponding measured power; Indicates the probability of a false alarm. , where T represents the threshold.

[0077] Step 234: Update the first After obtaining the posterior state of the first target, it will be used to update the second target. Measurement data for each target were removed from the original measurements.

[0078] Finally, repeat steps 233 and 234 until all predicted components have been updated.

[0079] Step 3: Perform threshold truncation and quantity limitation optimization on the components of the posterior label multi-Bernoulli distribution, remove invalid components and retain the optimal component set.

[0080] In this embodiment, step 3 includes:

[0081] Step 31: Include components of the posterior label multi-Bernoulli distribution with a probability less than the threshold. The components are removed.

[0082] Step 32: Include items with a probability greater than the threshold. Sort the components of the posterior label multi-Bernoulli distribution from largest to smallest, and take the top... The components of a posterior-labeled Bernoulli distribution, where... This represents the maximum value of the new target.

[0083] Step 4: Based on the optimized multi-Bernoulli posterior distribution, calculate the distribution cardinality and extract the target state, and output the target state estimation result for the current frame.

[0084] In this embodiment, the following formula is used for calculation. Cardinality of the frame LMB posterior distribution:

[0085] ;

[0086] in, Indicates the first The number of targets estimated in the frame. This indicates rounding. Indicates the first The probability of the existence of a target.

[0087] Finally, extract the following respectively. The state of each objective, as Frame target state estimation results.

[0088] The following section provides a detailed explanation of the beneficial effects of this invention by comparing simulation data.

[0089] Reference Figure 2 , Figure 2 This diagram illustrates the trajectories of three targets moving in the range-Doppler velocity domain. The experimental parameters are as follows: target SNR = 9dB, and the noise level during target motion is 0.2 m / s². 2 The particle sampling quantity is 1000, the range resolution unit is 5m, the Doppler velocity resolution unit is 0.05m / s, and the radar scan period is... Total number of observation frames Frame, the survival probability of the target in frame k. After steps 2 to 4 of this invention, the following can be obtained after 100 Monte Carlo experiments: Figure 3 a- Figure 3 The OSPA results are shown in c. From... Figure 3 a- Figure 3 It can be concluded that the missed detections, distance errors, and cardinality errors are basically the same in both cases with known and unknown signal-to-noise ratios. Simulation results verify the effectiveness of the proposed algorithm in the case of unknown signal-to-noise ratio, and its performance loss compared with the algorithm in the case of known signal-to-noise ratio is negligible.

[0090] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or technical improvements to the embodiments in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A pre-detection tracking method based on random set theory under unknown signal-to-noise ratio, characterized in that, include: Step 1: Initialize system parameters, number of iteration frames, and multi-objective Bernoulli distribution; Step 2: Update the iteration frame number frame by frame, and calculate the prior label multi-Bernoulli distribution of surviving targets and the predicted posterior label multi-Bernoulli distribution of targets based on the iteration frame number; Step 3: Perform threshold truncation and quantity limit optimization on the components of the posterior label multi-Bernoulli distribution, remove invalid components and retain the optimal component set; Step 4: Based on the optimized multi-Bernoulli posterior distribution, calculate the distribution cardinality and extract the target state, and output the target state estimation result for the current frame; Step 2 includes: Step 21: Set the number of iteration frames , No. New target births occur in frames. Target birth information is obtained through event triggering or passive reconnaissance. The set of new target components and the multi-Bernoulli distribution of the tags are represented as follows: ； ； in, Represents the set of new target components. This indicates the status of the first new target. This indicates the status of the second new target. Indicates the first The state of a new student's goal. Indicates the number of new target students. This indicates a multi-Bernoulli distribution of the target labels for newborns. Indicates the first The probability of the existence of a new target. Indicates the first The probability density function of a new target. A set of labels representing the goals of new students; Indicates the first The target state of the frame; Step 22: Calculate the survival target number The prior labels of the frames are distributed in a multi-Bernoulli pattern. Step 23: Calculate the predicted target number The posterior label of the frame is a multi-Bernoulli distribution; Step 22 includes: Step 221: Given Posterior label multi-Bernoulli distribution of live targets in frames , ,in, express Frame time The probability of a target continuing to survive. express Frame time The probability density function of the remaining surviving targets. express Frame-time target label set space; Step 222: Calculate the first... The first goal in The probability of a frame continuing to exist and the corresponding probability density function : ； ； Among them, mathematical symbols Representation function and The inner product, i.e.: ; Indicates the first Single-target transfer probability density function; Step 23 includes: Step 231: Given Frame prediction of multi-Bernoulli distribution For each of the target labels By sorting the birth times in ascending order, the first predicted Bernoulli distribution is obtained. ; Step 232: For the first predicted Bernoulli distribution The existence probability of each target is sorted from largest to smallest to obtain the second prediction Bernoulli distribution. ; Step 233: Based on the second predicted Bernoulli distribution According to the Bayesian update equation, calculate the first... The first goal in posterior existence probability of a frame and the corresponding posterior probability density function : ； ； in, The likelihood function is defined when the target signal-to-noise ratio is unknown. The likelihood function is designed as follows: ； in, Represents the target state The set of pixel unit indices that can be affected; Represents pixel grid The corresponding measured power; This represents the probability of a false alarm. , where T represents the threshold; Step 234: Update the first After obtaining the posterior state of the first target, it will be used to update the second target. Measurement data for each target were removed from the original measurements.

2. The pre-detection tracking method according to claim 1, characterized in that, Step 1 includes: Step 11: Initialize the radar monitoring range; the radar monitoring range includes radar range resolution, radar Doppler velocity resolution, radar scan period, and total number of observation frames; Step 12: Initialize the number of iteration frames Initialize multi-objective Bernoulli distribution and order ,in Represents the target label set space of the current frame; Indicates the first The probability of a target continuing to survive. Indicates the first The probability density function of each surviving target; initialization of the multi-objective likelihood function and target survival probability. And the single-target transition probability density function.

3. The pre-detection tracking method according to claim 1, characterized in that, Step 3 includes: Step 31: Include components of the posterior label multi-Bernoulli distribution with a probability less than the threshold. The components are removed; Step 32: Include items with a probability greater than the threshold. Sort the components of the posterior label multi-Bernoulli distribution from largest to smallest, and take the top... The components of a posterior-labeled Bernoulli distribution, where... This represents the maximum value of the new target.

4. The pre-detection tracking method according to claim 1, characterized in that, In step 4, calculate according to the following formula The cardinality of the Bernoulli posterior distribution of each frame is determined, and the state of the corresponding target is extracted as... Frame target state estimation results: ； in, Indicates the first The number of targets estimated in the frame. This indicates rounding. Indicates the first The probability of the existence of each target; This indicates the maximum number of new target cells.

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