Passive sonar target tracking performance estimation method

Abstract

The invention belongs to the technical field of underwater acoustic equipment design and manufacturing, and particularly relates to a passive sonar target tracking performance estimation method. Comprising the following steps: generating a passive sonar moving target; firstly, signal simulation parameters are read, motion equation resolving is carried out, then array structure parameters are read, time delay is calculated, and simulation signals are generated; forming a beam; constructing an array flow pattern through the array structure parameters read in the step 1, and then selecting a beam forming algorithm according to the array flow pattern and a simulation signal to generate beam domain data; target tracking; a threshold value is set, a temporary track is established according to the beam domain data generated in the second step, then a target tracking algorithm is selected, and a tracking target is determined; estimating target tracking performance; and tracking the target trajectory, and evaluating the target tracking precision and the target tracking accuracy. According to the method, the target tracking precision and the target tracking accuracy can be estimated, so that the design efficiency is improved, and reliable data support is provided for sonar design.

Description

Technical Field

[0001] The invention belongs to the technical field of underwater acoustic equipment design and manufacturing, and in particular relates to a passive sonar target tracking performance estimation method. Background Art

[0002] The passive sonar detection system uses the radiation noise of the target's engine, propeller, etc. as a signal. After long-distance transmission, the target signal becomes very weak. In addition, affected by the complex underwater acoustic channel and the marine environment, the target detection results have certain errors, false alarms, and missed detections. In addition, the target detection technology is a single-frame processing technology, which has no significant correlation in time. The corresponding relationship between the detection results of the previous and next processing frames cannot be known. In each signal processing frame, the target detection result is disordered, and only the direction of the possible target can be estimated. For the above problems, although manual analysis and judgment are more intelligent, it will greatly reduce the real-time performance of the detection system. Therefore, it is necessary to establish an effective passive sonar system tracking model.

[0003] Broadly speaking, multi-target tracking involves two main research contents: data association and state filtering. The main tasks of data association are trajectory initiation, trajectory maintenance and trajectory termination, including multi-hypothesis target tracking method based on Rao-Blackwellized particle filter, probability density data association method, joint probability density data association method, etc.; filtering technology includes linear autoregressive filtering, two-point extrapolation filtering, Wiener filtering and Kalman filtering, etc. To design a passive sonar detection system, it is necessary to determine the formation and select the beamforming method that meets the index requirements, and at the same time, optimize the target tracking method to improve the target detection performance. Simulating and analyzing one by one is time-consuming and labor-intensive. Developing a method that can quickly estimate the target detection and tracking performance can greatly improve the design efficiency, provide data support for the design scheme, and increase the reliability of the design scheme. Summary of the invention

[0004] The purpose of the present invention is to overcome the above-mentioned shortcomings of the prior art. The present invention provides a passive sonar target tracking performance estimation method. To design a sonar system, it is necessary to analyze the detection performance and tracking performance of the sonar system to examine the performance of the sonar system. If different acoustic array models, different beamforming methods and target tracking methods are analyzed and verified separately, it will take a lot of effort and the efficiency is very low. At the same time, some arrays with large apertures cannot be tested for performance on lakes. Therefore, a passive sonar target tracking performance estimation method for arbitrary formations is developed to estimate the precision and accuracy of target tracking under laboratory conditions, thereby improving design efficiency and providing reliable data support for sonar design.

[0005] To solve the above technical problems, the present invention provides a passive sonar target tracking performance estimation method, comprising the following steps:

[0006] Step 1: Passive sonar moving target generation;

[0007] First, the signal simulation parameters are read and the motion equation is solved. Then, the array structure parameters are read and the delay is calculated to generate the simulation signal.

[0008] Step 2: Beam forming;

[0009] The array flow pattern is constructed by using the array structure parameters read in step 1 above, and then a beamforming algorithm is selected according to the array flow pattern and the simulation signal to generate beam domain data;

[0010] Step 3: Target tracking;

[0011] Set a threshold, establish a temporary track based on the beam domain data generated in step 2 above, and then select a target tracking algorithm to determine the tracking target;

[0012] Step 4: Target tracking performance estimation;

[0013] Track the target trajectory and evaluate the target tracking precision and target tracking accuracy.

[0014] Preferably, in step 1, it is necessary to determine the specific signal form of the received signal and perform simulation design; the simulation design includes simulation of the time-frequency characteristics of ship target radiation noise, simulation of the spatial characteristics of passive sonar receiving target radiation noise, and simulation of ocean environment noise.

[0015] Preferably, the simulation of the time-frequency characteristics of the ship target radiation noise includes: modulating the broadband radiation signal generated by the low-frequency modulation signal, and superimposing a sinusoidal wave signal with a certain amplitude according to the design requirements, that is, a strong line spectrum component in the power spectrum, and finally obtaining a single-channel simulated time domain signal with broadband continuous power spectrum characteristics, modulation characteristics and line spectrum characteristics with required parameters.

[0016] Preferably, the spatial characteristic simulation of the target radiation noise received by the passive sonar includes: the spatial characteristic of the target radiation noise received by the passive sonar is mainly caused by the acoustic path difference of the target signal reaching each array element of the sound array, and after the array is determined, it can be completed by converting the acoustic path difference into the time delay between each channel, and if the time delay changes with time, the motion characteristics of the target can be simulated; the target motion trajectory is uniform linear motion, uniform circular motion or is completed by simulating other motion trajectory data.

[0017] Preferably, the ocean environment noise simulation includes: using a 4th order AR model for simulation.

[0018] Preferably, in step 2, a beamforming algorithm is used to obtain the spatial spectrum of the ship radiation noise, thereby obtaining discrete resolution units divided by azimuth information, and the spatial spectrum energy value in each resolution unit is the measurement information of the passive sonar pre-detection tracking algorithm; there are multiple preset beamforming algorithms, including a conventional beamformer, an MVDR beamformer and a SAMV beamformer.

[0019] Preferably, step 2 specifically further includes: establishing a broadband signal model; that is, performing Fourier transform on the broadband signal, dividing the frequency domain of the broadband signal into multiple narrowband components, performing CBF algorithm processing on each narrowband component, that is, obtaining the spatial spectrum of each narrowband component, combining the spatial spectra corresponding to the narrowband components to obtain the original broadband signal spatial spectrum, and combining the spatial spectra obtained by the broadband CBF algorithm at different times in chronological order to obtain the azimuth history diagram.

[0020] Preferably, in step 3, the target tracking algorithm establishes appropriate motion and observation models and utilizes filtering and data association processing to realize the proposal of false alarm targets, the completion of missed data, the division of target batches, and the filtering and smoothing of target states; there are multiple preset target tracking algorithms, including a Kalman filter tracking algorithm and a target tracking algorithm based on particle filtering.

[0021] Preferably, in step 4, the target tracking accuracy is evaluated by whether the angle root mean square error curve converges or approaches the Cramer-Rao lower bound to evaluate the performance of the algorithm, and the formula of the angle root mean square error is:

[0022]

[0023] Where N represents the number of Monte Carlo experiments; represents the true value of the target position at sampling time t in the kth Monte Carlo experiment; It represents the estimated value of the target position at sampling time t in the kth Monte Carlo experiment.

[0024] Preferably, in step 4, the target tracking accuracy specifically includes: setting the tracking target prediction sequence {f1, f2…f m}, the real target position sequence {a1,a2…a m}, at time t in the history diagram, if the target prediction value and the target true value are less than the threshold T, the target tracking is valid, otherwise it is a target tracking error recorded as mis; if the real target position value does not have the corresponding tracking target prediction value, it is a missed detection recorded as fpt; if the tracking target trajectory appears where there is no real target position trajectory, it is a false alarm, recorded as fmt; the formula for the target tracking accuracy is:

[0025] Where gt represents the number of targets that appear at time t.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] The present invention accurately simulates the target radiation noise signal according to the set ocean environment noise characteristics, the target movement trajectory of ships in the nearby sea area, and the target radiation noise characteristics; when designing the base array formation, the preset common array form can be directly selected, and other desired formations can also be obtained by loading the array element coordinate data. The present invention can set the signal parameters on the basis of the formation design, accurately simulate the array element domain data received by the array, and at the same time can select different beamforming methods, different target tracking methods, and compare the precision and accuracy of target tracking under different parameters and different algorithms, so as to facilitate the designer to optimize the sonar parameters and signal processing algorithms. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is an Ecs curve diagram in the simulation design of the time-frequency characteristics of the target radiation noise of the present invention.

[0029] Figure 2 The present invention is a flowchart of a passive sonar target tracking performance estimation method. DETAILED DESCRIPTION

[0030] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. The advantages and features of the present invention will become more apparent from the following description. It should be noted that the accompanying drawings are in very simplified form and in non-precise proportions, and are only used to conveniently and clearly assist in explaining the purpose of the embodiments of the present invention.

[0031] like Figure 1 and Figure 2 As shown, the embodiment of the present invention specifically provides a passive sonar target tracking performance estimation method, which specifically includes the following contents:

[0032] Step 1: Generation of passive sonar moving targets;

[0033] The receiving signal of passive sonar is different from that of active sonar. The receiving signal of passive sonar comes from the noise emitted by the tracking target itself or after reflection and the background noise in the ocean. Therefore, it is necessary to determine the specific signal form of the receiving signal and perform simulation design.

[0034] (1) Simulation design of the time-frequency characteristics of target radiation noise;

[0035] The continuous spectrum model of ship radiation noise power spectrum adopts the following mathematical model, that is, the Ecs curve description, and its autocorrelation function is:

[0036] R(τ)=e -α|τ|(cos(ω0τ)+Gsin(ω0|τ|))

[0037] Where α≥0, G is a real number, τ is the delay, let α=2πf m ,ω0=2πf0; then the corresponding power spectrum density function is

[0038]

[0039] like Figure 1 The ECS curve is shown in Figure 1. f0 determines the peak position of G(f). m Determine the sharpness and height of the peak by changing f m , f0, and G parameters can be used to obtain the target radiation noise power spectrum that meets the requirements.

[0040] The generation of time domain digital signal adopts autoregressive model method (AR model), and the system function of this model is

[0041]

[0042] Where p is the system order, where Z = e jω , ω is a real number; in the embodiment of the present invention, the value is taken according to experience, α k is the AR model coefficient, and the parameters in the above autocorrelation function are used to solve it through the YW equation. The time series with continuous power spectrum characteristics can be expressed as:

[0043]

[0044] n(t) is Gaussian white noise with flat power spectral density.

[0045] After obtaining the time series that meets the continuous spectrum characteristics, the periodic modulation envelope is designed according to the set ship target and other parameters.

[0046]

[0047] Among them, b k is the modulation depth, which can be set to a fixed value or a random variable with a certain probability distribution. k is the modulation frequency, f s Target frequency, is the initial phase.

[0048] The low-frequency modulation signal is used to modulate the broadband radiation signal, and a sine wave signal with a certain amplitude, i.e., a strong line spectrum component in the power spectrum, is superimposed according to the design requirements. Finally, a single-channel simulation time domain signal with broadband continuous power spectrum characteristics, modulation characteristics, and line spectrum characteristics with the required parameters is obtained.

[0049] (2) Simulation of spatial characteristics of target radiation noise received by passive sonar;

[0050] The spatial characteristics of the target radiation noise received by the sonar are mainly caused by the acoustic path difference of the target signal reaching each array element of the sound array. After the array is determined, the acoustic path difference can be converted into the time delay between each channel. If the time delay changes with time, the motion characteristics of the target can be simulated. The target motion trajectory can be uniform linear motion, uniform circular motion, or can be simulated through other motion trajectory data.

[0051] (3) Ocean environmental noise simulation;

[0052] Considering that the spectrum of ocean ambient noise is relatively flat, the fourth-order AR model is selected for simulation.

[0053] The calculation formula for ocean ambient noise is:

[0054]

[0055] Where n(t) is a Gaussian white noise with a mean of 0 and a variance of 1, σ n is the energy adjustment factor, the coefficient b0 is the same as b when k = 1 k The same setting is used in k The calculation method is the same as the solution method introduced above, using the YW equation for solution.

[0056] Step 2: beam forming;

[0057] Passive sonar tracking systems are generally pure azimuth tracking. In the present invention, beamforming technology is used to obtain the spatial spectrum of ship radiation noise, thereby obtaining discrete resolution units divided by azimuth information. The spatial spectrum energy value in each resolution unit is the measurement information of the passive sonar pre-detection tracking algorithm.

[0058] For general far-field signals, there is an acoustic path difference when the same signal reaches different array elements. This acoustic path difference causes differences in the received signals between the receiving array elements. We compensate for this difference so that the desired signals of each array element are superimposed in the same direction. This is the process of beamforming.

[0059] Here, narrowband signals are used to describe the beamforming process. First, consider K far-field narrowband signals incident on a certain array in space. After each array element receives the signal, it is sent to the processor through its own transmission channel. Under the assumption of narrowband signals, it can be expressed as:

[0060]

[0061] Where u i (t) represents the amplitude of the signal received by the i-th element at time t, represents the phase of the signal received by the i-th array element at time t, and w0 is the frequency of the received signal.

[0062] Under the condition of narrowband far-field signal source, there is

[0063]

[0064] From the above two formulas, we can get

[0065] Then, the signal received by the mth array element is

[0066]

[0067] In the formula, g mi is the gain of the mth array element to the ith signal, n m (t) represents the noise of the mth array element at time t, τ mi It represents the time delay of the i-th signal reaching the m-th array element relative to the reference array element.

[0068] Arrange the signals received by M array elements at a specific time into a column vector, and we can get

[0069]

[0070] Assuming that the array elements are isotropic and the channels are consistent, and there is no mutual coupling, it can be simplified to

[0071]

[0072] The array receives the signal x(t) = [x1(t)x2(t)…x M (t)] T , s(t)=[s1(t)s2(t)…s M (t)] T , n(t)=[n1(t)n2(t)…n M (t)] T

[0073] Then the vector form of the multi-target received signal is

[0074] x(t)=As(t)+n(t)

[0075] Where A is the array flow matrix, A=[a1(w0)a2(w0)…a K (w0)], the steering vector is

[0076]

[0077] From the above, once the delay expression between array elements is known, the array manifold of a specific spatial array can be obtained, and then the beam output result can be obtained. After the delay expression between spatial array elements is derived, we can get

[0078]

[0079] Where θ is the horizontal angle is the pitch angle, and x, y, z are the coordinates of the target in three-dimensional space.

[0080] Since the receiving signal of passive sonar is usually ship radiation noise, which is generally a broadband signal, it is also necessary to establish a broadband signal model.

[0081] In the frequency domain, a broadband signal can be regarded as a superposition of multiple non-overlapping narrowband components. Therefore, the broadband signal can be Fourier transformed. After dividing its frequency domain into multiple narrowband components, each narrowband component is processed by the CBF algorithm to obtain the spatial spectrum of each narrowband component. On this basis, the spatial spectrum corresponding to each narrowband component is combined to obtain the original broadband signal spatial spectrum. The spatial spectra obtained by the broadband CBF algorithm at different times are combined in time order to obtain the azimuth history map.

[0082] In the present invention, the receiving signal array model has been determined in the process of simulating the signal, and the same model is used for beamforming processing. In the present invention, a variety of beamformers are preset, including conventional beamformers, MVDR beamformers, and SAMV beamformers. In addition, other beamforming algorithms can also be loaded through the interface.

[0083] Step 3: Passive sonar target tracking;

[0084] Target detection technology is a single-frame processing technology. There is no significant correlation in time. The corresponding relationship between the detection results of the previous and next processing frames cannot be known, and there are certain errors, false alarms and missed detections in the detection results. Underwater multi-target tracking technology is used to give continuous and accurate target trajectories. It establishes appropriate motion and observation models, uses filtering technology and data association technology, realizes the proposal of false alarm targets, the completion of missed detection data, the division of target batches, and the filtering and smoothing of target states.

[0085] The present invention takes the automatic tracking method of a passive sonar intersecting target as an example to explain the tracking process of the target tracking method.

[0086] The input of the Kalman filter tracker algorithm in the present invention is the beam domain data after beamforming. The specific algorithm flow is as follows:

[0087] First, set the detection threshold, receive the first frame of azimuth information data, search for the maximum point of the power spectrum greater than the threshold, and mark the azimuth as θ0 and establish a temporary track; if the power spectrum maximum point θ of consecutive p frames of data is greater than the threshold, the azimuth is marked as θ0 and a temporary track is established; p Satisfy the condition |θ p -θ0|<α, where α is the set gate width, then it is confirmed that this is one of the targets to be tracked

[0088] Secondly, determine whether the target disappears. During the automatic target tracking process, if the peak value of the mth target is not detected within the t time period, the "virtual" detection value of the target at the current moment is predicted by fitting historical data. When the target measurement value cannot be detected for t consecutive moments, the target is determined to have disappeared.

[0089] Again, when the target tracks intersect, that is, when the difference between the detected azimuth values ​​of two adjacent targets is less than the gate width, the "virtual" detection value is used to replace the detected target azimuth until the difference between the two target azimuths is greater than the gate width. The "virtual" detection value algorithm (Kalman filter processing) is as follows:

[0090] Assume that the target's motion model within T time (T < 30s) can be approximately regarded as uniform linear motion. The "virtual" measurement value of the current t moment θ(t) = A + B(t) is linearly fitted using the measurement value of the previous T moments, and weighted linear fitting is used for estimation. The expressions of coefficients A and B are as follows:

[0091]

[0092] In the formula, Here, α is set based on experience.

[0093] The present invention presets a variety of target tracking algorithms, including Kalman filter tracking algorithm, target tracking algorithm based on particle filter, etc. In addition, other target tracking algorithms can also be loaded through the interface.

[0094] Step 4: Track performance estimation;

[0095] In a multi-target tracking system, the accuracy of target number estimation (target tracking accuracy) and the precision of target state estimation are often the main indicators for evaluating tracking performance.

[0096] (1) Target tracking accuracy evaluation;

[0097] The performance of an algorithm is usually evaluated by whether the root mean square error curve converges or approaches the Cramer-Rao lower bound. Therefore, the root mean square error is a very important indicator in the study of pure bearing target motion analysis in passive sonar.

[0098] The angle root mean square error is defined as

[0099]

[0100] Where N represents the number of Monte Carlo experiments; represents the true value of the target position at sampling time t in the kth Monte Carlo experiment; It represents the estimated value of the target position at sampling time t in the kth Monte Carlo experiment.

[0101] (2) Evaluation of the number of tracked targets (target tracking accuracy evaluation);

[0102] The number of tracked targets refers to the number of continuously tracked targets displayed in the tracking interface. This number is dynamic and changes over time, including the appearance, disappearance, and continuous tracking of targets.

[0103] Evaluating the accuracy of the tracking number means evaluating the ability of the tracking algorithm to track the consistency of the trajectory generated by the target over time, that is, in the entire orientation process, the trajectory of each target is unique, and the trajectory of the target is correctly tracked, and each target generates a trajectory.

[0104] At sampling time t, under the condition of setting the tracking threshold (the tracking accuracy is considered accurate tracking within a range), calculate the number of targets missed due to the lack of tracking target position; calculate the number of false alarm targets where the tracking target position exists but there is actually no target; calculate the number of targets where target tracking has incorrect matching (this situation generally occurs when the targets are in cross motion).

[0105] Set the tracking target prediction sequence {f1,f2…f m}, the real target position sequence {a1,a2…a m}, at time t in the history graph, if the target prediction value and the target true value are less than the threshold T, the target tracking is valid, otherwise it is a target tracking error recorded as mis; if the real target position value does not have the corresponding tracking target prediction value, it is a missed detection recorded as fpt; if the tracking target trajectory appears where there is no real target position trajectory, it is a false alarm, recorded as fmt, gt represents the number of targets appearing at time t, and the tracking accuracy is described as

[0106]

[0107] The above description is only a description of the preferred embodiments of the present invention, and is not intended to limit the scope of the present invention. Any changes or modifications made by a person skilled in the art in the field of the present invention based on the above disclosure shall fall within the scope of protection of the claims.

Claims

1. A passive sonar target tracking performance estimation method, characterized in that: The steps include: Step 1: Passive sonar moving target generation; First, the signal simulation parameters are read and the motion equation is solved. Then, the array structure parameters are read and the delay is calculated to generate the simulation signal. Step 2: Beam forming; The array flow pattern is constructed by using the array structure parameters read in step 1 above, and then a beamforming algorithm is selected according to the array flow pattern and the simulation signal to generate beam domain data; Step 3: Target tracking; Set a threshold, establish a temporary track based on the beam domain data generated in step 2 above, and then select a target tracking algorithm to determine the tracking target; Step 4: Target tracking performance estimation; Track the target trajectory and evaluate the target tracking precision and target tracking accuracy.

2. A passive sonar target tracking performance estimation method as claimed in claim 1, characterized in that: In the step 1, it is necessary to determine the specific signal form of the received signal and perform simulation design; the simulation design includes simulation of the time-frequency characteristics of the ship target radiation noise, simulation of the spatial characteristics of the passive sonar receiving target radiation noise, and simulation of the ocean environment noise.

3. A passive sonar target tracking performance estimation method as claimed in claim 2, characterized in that: The simulation of the time-frequency characteristics of the ship target radiation noise includes: modulating the broadband radiation signal generated by the low-frequency modulation signal, and superimposing a sinusoidal wave signal with a certain amplitude, that is, a strong line spectrum component in the power spectrum according to the design requirements, and finally obtaining a single-channel simulation time domain signal with broadband continuous power spectrum characteristics, modulation characteristics and line spectrum characteristics with the required parameters.

4. A passive sonar target tracking performance estimation method as claimed in claim 2, characterized in that: The spatial characteristic simulation of the target radiation noise received by the passive sonar includes: the spatial characteristic of the target radiation noise received by the passive sonar is mainly caused by the acoustic path difference between the target signal and each array element of the sound array. After the array is determined, it can be completed by converting the acoustic path difference into the time delay between each channel. If the time delay changes with time, the motion characteristics of the target can be simulated; the target motion trajectory is uniform linear motion, uniform circular motion or is completed by simulating other motion trajectory data.

5. A passive sonar target tracking performance estimation method as claimed in claim 2, characterized in that: The ocean environment noise simulation includes: selecting a 4th order AR model for simulation.

6. A passive sonar target tracking performance estimation method as claimed in claim 1, characterized in that: In step 2, a beamforming algorithm is used to obtain the spatial spectrum of the ship radiation noise, thereby obtaining discrete resolution units divided by azimuth information. The spatial spectrum energy value in each resolution unit is the measurement information of the passive sonar pre-detection tracking algorithm. There are multiple preset beamforming algorithms, including conventional beamformers, MVDR beamformers and SAMV beamformers.

7. A passive sonar target tracking performance estimation method as claimed in claim 6, characterized in that: The step 2 specifically also includes: establishing a broadband signal model; that is, performing Fourier transform on the broadband signal, dividing the frequency domain of the broadband signal into multiple narrowband components, performing CBF algorithm processing on each narrowband component, that is, obtaining the spatial spectrum of each narrowband component, combining the spatial spectra corresponding to each narrowband component to obtain the original broadband signal spatial spectrum, and combining the spatial spectra obtained by the broadband CBF algorithm at different times in chronological order to obtain the azimuth history diagram.

8. A passive sonar target tracking performance estimation method as claimed in claim 1, characterized in that: In step 3, the target tracking algorithm establishes appropriate motion and observation models and utilizes filtering and data association processing to realize the proposal of false alarm targets, the completion of missed data, the division of target batches, and the filtering and smoothing of target states; there are multiple preset target tracking algorithms, including a Kalman filter tracking algorithm and a target tracking algorithm based on particle filtering.

9. A passive sonar target tracking performance estimation method as claimed in claim 1, characterized in that: In step 4, the target tracking accuracy is evaluated by whether the angle root mean square error curve converges or approaches the Cramer-Rao lower bound to evaluate the performance of the algorithm. The formula of the angle root mean square error is: Where N represents the number of Monte Carlo experiments; represents the true value of the target position at sampling time t in the kth Monte Carlo experiment; It represents the estimated value of the target position at sampling time t in the kth Monte Carlo experiment.

10. A passive sonar target tracking performance estimation method as claimed in claim 1, characterized in that: In step 4, the target tracking accuracy specifically includes: setting the tracking target prediction sequence {f1, f2…f m }, the real target position sequence {a1,a2…a m }, at time t in the history diagram, if the target prediction value and the target true value are less than the threshold T, the target tracking is valid, otherwise it is a target tracking error recorded as mis; if the real target position value does not have the corresponding tracking target prediction value, it is a missed detection recorded as fpt; if the tracking target trajectory appears where there is no real target position trajectory, it is a false alarm, recorded as fmt; the formula for the target tracking accuracy is: Where gt represents the number of targets that appear at time t.

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