Shuliang WANG,Daping BI,Huailin RUAN,Mingyang DU

College of Electronic Engineering,National University of Defence Technology,Hefei 230037,China

KEYWORDS Human visual attention;Memory;Radar Maneuvering Targets Tracking;Validation gate;Waveform selection

Abstract Radar Maneuvering Targets Tracking(RMTT)in clutter is a quite challenging issue due to the errors in the models and the varying dynamics of the processes.Modern radar tracking system calls for the adaptive signal and data processing algorithm urgently to adapt the uncertainty of the environment.The mechanism of human cognition can help persons cope with the similar difficulties in visual tracking.Inspired by human cognition mechanism,a comprehensive method for RMTT is proposed.In the method,the model transition probability in Interacting Multiple Model(IMM)and the validation gate can be adjusted dynamically with target maneuver;the waveform in radar transmitter can vary with the perception of the environment.Experimental results in cluttered scenes show that the proposed algorithm is more accurate for perceiving the environment and targets,and the waveform selection algorithm is better than that with fixed waveform.

1.Introduction

There are mainly two challenging issues in the task of Radar Maneuvering Targets Tracking(RMTT).The first challenge is caused by the changing motion of targets.To reduce the motion uncertainty,there are two main directions for motion model1,2: (A) Single model. The Constant Velocity (CV)model,Constant Acceleration(CA)model,Singer model,Jerk model and Current Statistic(CS)model,can fall under the first category. (B) Multiple models. The Interacting Multiple Model(IMM)and Varied Structure Multiple Model(VSMM),can fall under the second category.

The second challenging issue is caused by the measurementorigin uncertainty.The radar's measurements can consist of range,azimuth,elevation and other location features.The commonly used technique relies on the Mahalanobis distance metric,which is the square of the norm of the error with respect to its covariance.3According to the validation gate rule,the measurements whose distance is lower than a threshold are called candidate measurements.The typical methods include the Nearest Neighbor(NN)algorithm,the Probability Data Association(PDA)algorithm,the Joint Probability Data Association(JPDA)algorithm and so on.3,4The validation gate is an important factor affecting the radar's computing resources consumption and track loss.If the validation gate is too large,more measurements will fall into the gate to make the computing time larger.If the gate is too small,it may cause track loss when the maneuver of target happens.5

The uncertainty of state estimation depends on the predicted uncertainty and the measurement uncertainty.The measurement error covariance can be quantified by the Cramer-Rao Lower Bound(CRLB),which is derived from the curvature of the waveform ambiguity function at the origin in the time delay-Doppler plane.6When the predicted error covariance ellipsoid(e.g.,the determinant of the error covariance matrix) and measurement error covariance ellipsoid are orthogonal,the uncertainty of state estimation will be the lowest.7Furthermore,inspired by human cognition mechanism,such as the Perception-Action Cycle(PAC),memory,attention and intelligence,Haykin et al.first explicitly proposed cognitive radar.8,9The intrinsic trait of cognitive radar is to adaptively change the transmitted waveform to improve the tracking performance.10-19The determinant of estimated error covariance matrix,called perceptual information entropy,is used to describe the radar's real-time perception for target's dynamics.19

This paper presents a novel tracking framework for RMTT based on the mechanism of human cognition.This method attempts to contribute in the following three aspects:(A)Inspired by the three-stage memory mechanism of human brain,‘‘memory”is nested in IMM algorithm to overcome the tracking precision degradation problem when the model transition probability is set improperly.The model transition probability can be adaptively adjusted to weaken the bad competition of the mismatched model.(B)Inspired by the mechanism of human visual attention,an adaptive validation gate is designed.The center and volume of the validation gate are weighted by the models'interaction in IMM.The maneuvering model occupies the dominant position in the model interaction to make the maneuvering target fall into the gate.On the other hand, when the target is in weak maneuver, the nonmaneuvering model plays an important role which makes the validation gate smaller.The computing resources consumption and the tracking success rate are both improved.(C)Inspired by human PAC mechanism,radar waveform selection is also considered.Based on the criterion of minimum information entropy,19the transmitted waveform parameters can be adjusted dynamically to improve the tracking performance.

The remainder of this paper is organized as follows.The mechanism of human cognition is given in Section 2.The tracking process,especially the adaptive filtering model,adaptive validation gate,and waveform selection are described in Section 3.Then,experimental results are given in Section 4.Finally,Section 5 concludes the paper.

2.Mechanism of human cognition

2.1.Perception-Action Cycle(PAC)

The perception and action are the two important functions in the visual brain.9In the brain,the cortical sensory area is stimulated by cognitive tasks,and the information obtained is fed back to the cortical motion area.The cortical motion area adjusts the stimuli with the help of the existing knowledge and guidelines to better complete the cognitive task.The net result of these two functions,working together in a coordinated fashion,is the perception-action cycle.

2.2.Human memory

Memory is one of the key mechanisms of human perception,which can be divided into three levels,namely,sensory memory,short-term memory and long-term memory.As shown in Fig.1,20sensory memory refers to the retention of information input in a short time.Short-term memory refers to a memory system with a small amount of information stored in a short period of time.The information from the short-term memory is as the output and partly stored in the long-term memory. In the process, the useful information can be abstracted from the long-term memory to guide the information output.The long-term memory contains a large amount of information,such as the experience,knowledge and the rules,which can be maintained for a long time.

2.3.Human visual attention

Visual attention is another key mechanism of human perception that enables humans to effectively select the visual data with most potential interest.20,21The selective attention model that the information processing requires four stages:sensory memory,selective filter,detector and memory.The selective filter can identify the outside information based on the characteristics of the stimulus,while only allowing the information noticed into the detector,thus saving human resources.The attention is guided by two principles22: top-down and bottom-up factors. Top-down attention is driven by preknowledge,context,expectation,and current goals.On the other hand,bottom-up attention is derived solely from the perceptual data.

3.Tracking process

3.1.Target dynamic and measurement model

3.1.1.Target dynamic model

The target dynamics is modeled by a linear model1,15

where j=1,2,···,r is the dynamic model at time k.We writefor the state of the track,which represent the range,velocity and acceleration in the Cartesian coordinates respectively.F1,F2,···,Frare the state transition matrices for the different maneuvers.U1,U2,···,Urare the acceleration input matrices.are mean acceleration matrices.Process noise is denoted by W1,W2,···,Wr.The covariance matrices of the process noise are Q1,Q2,···,Qr,which are zero-mean Gaussian white noise sequences.

Fig.1 Information flow of human memory for information processing.20.

We assume the changes in target trajectory can be modeled as a Markov chain with given transition probabilities as follows:15

where M(k)is the model at timek.

3.1.2.Target measurement model

The measurement equation of the target is

A Gaussian pulse base band signal envelope is as follows6:

where,λ is the duration of the Gaussian envelope,b is the chirp rate.We use the vector θ= [λ,b ]as the waveform library parameter that will be used for waveform selection algorithm.The CRLB of measurement noise covariance(the measurement Y(k)=[rk,˙rk]T)can be achieved as

where η is signal-to-noise ratio,c is speed of electromagnetic wave,fcis the carrier frequency.Furthermore,the measurement standard error covariance of bearing β is also considered,and its expression is14

where Ψbwis the 3 dB beamwidth of the radar antenna;kmis the monopulse error slope.Then,the measurement error covariance Rθofcan be expressed as follows:

3.2.Adaptive filtering model

There are four main steps in IMM:Input interaction,Modelconditional filtering,Model probability updating,Estimation fusion.

Step 1.Input interaction

Calculate the mixed initial condition of various models Mj(k)in IMM tracking.

Step 2.Model-conditional filtering

The one-step predicted output of model j at time k areandAnd the corresponding filtering output areand

Step 3.Model probability updating

The likelihood function is

where vj(k)is the filtering residual and Sj(k,θ)is the corresponding covariance.Update the model probability as

Step 4.Estimation fusion

Estimated state and covariance matrix can be obtained as

From the above flow of IMM,the Markov model transition probability matrix πij(k)determines the degree of the input interaction.Generally,a fixed main diagonally dominant matrix is selected for IMM according to the prior information.However,the fixed transition probability matrix will bring unnecessary competition among models,and reduce the tracking accuracy.23Next,we propose a time-varying model Transition probability IMM(TIMM)with the following rule:(A)When the value λj(k)=μj(k)/μj(k-1)is bigger than 1,the contribution of the model j in IMM should be enhanced at the next time. (B) When the value λj(k)=μj(k)/μj(k-1) is smaller than 1, the contribution of model j should be weakened at the next time.The rule of modifying the model transition probability can be expressed as follows:

Considering the sum of the probability that a model is transferred to all models at each time is 1,the updated model transition probability can be obtained by the following normalization:

Fig.2 Time-varying model transition probability IMM based on human memory.

The rule for time-varying πij(k)can be stored in the longterm memory to guide the adjustment of the filtering model structure.As shown in Fig.2,the sensory memory is used to calculate the current model probability,which is often reflected at the present time.The short-term memory is used to store the model probability at the last time.With the rule and knowledge from the long-term memory,the model transition probability is modified.Then,the model transition probability is stored in the short-term memory and also sent to the input interaction step of IMM.

3.3.Adaptive validation gate

The center and size of the validation gate at timekare determined by the one step prediction center Y(k|k -1)and the innovation covariance matrix S(k).The candidate measurement falling into the gate can be expressed as

where,γ is the threshold.The measurements play a role of‘‘bottom-up attention”.With IMM algorithm,the state of each model filter is interacted at time k-1.The predicted center and innovation covariance of each filter are obtained through one step prediction.In traditional IMM-PDA algorithm,as shown in Fig.3(a),each model uses validation gate formed by their own predicted center and innovation covariance matrix.This structure with different sub filter using different validation gate may lead to computation resources consumption large and track loss.Inspired by the mechanism of human visual attention,we propose an adaptive validation gate algorithm,24in which the sub filter uses the common gate.The structure of proposed adaptive validation gate IMM-PDA algorithm is shown in Fig.3(b).In the algorithm,the predicted center and innovation covariance are weighted according to the model predicted probability.The weighted center is

Covariance matrix of comprehensive innovation is

The center and innovation covariance play a role of‘‘upbottom attention”.The volume of the validation gate is

where nYis the dimension of measurements and cnYdepends on

Fig.3 Target state estimation process with fixed validation gate and adaptive validation gate.

3.4.Waveform selection

It can be imagined that the waveform library is a twodimensional grid,each grid of which represents an available waveform,and the location of the grid is uniquely determined.The Waveform Library(WL)of Eq.(4)can be expressed as

where min and max represent the minimum and maximum values of the designed parameters;Δ is the step values of the parameters.

From Fig.4,the information flow can be described as follows:

(1)First,the information entropycomputed with waveform library parameter from Θ and PDA algorithm is given at time k.

(2)Then,the information entropy with different waveforms are preserved in a short-term memory for the next time.It is called short-term memory because the previous value will be overwritten at the next time.

(3)Finally,the waveform parameteris selected with the optimal criterionand sent to perceive the environment and targets at the next time.

3.5.Tracking framework for RMTT and performance analysis

From the above analysis of the tracking process,the whole tracking framework for RMTT based on human cognition mechanism can be given as Fig.5.To explain the complexity of the proposed algorithm,we define the following parameters:(A)Ns:the number of model set in IMM;(B)Nv:the candidate measurements falling into the gate;(C)Ng:the waveformparameter grid size.

The IMM model contains possible model set of the target motion,which can be switched according to the target maneuver.However,there is a dilemma in the selection of model set.More models are needed to adapt the target's maneuver,but too many models may result in large computation and may even reduce the performance.23In this paper,we use CS model and CV model as the model set of IMM.In the algorithm,CS model can be used to track the high maneuvering target,and the CV model is used to overcome the lower precision of CS model for weak maneuvering target.

From Eqs.(20)and(21),the validation gate can be dynamically adjusted according to model prediction probability.If the current target is highly maneuverable,the CS model occupies the dominant position in the model interaction to make the maneuvering target fall into the gate.On the other hand,when the target is in weak maneuver,the validation gate will be reduced to obtain high tracking precision and low computation time consumption.

Fig.4 Information flow in waveform selection.

Fig.5 RMTT algorithm based on human cognition mechanism.

With the criterion of Eq.(23),the waveform selection is greedy.This strategy may lead to two aspects of the problem:(A)the computation time consumption is large;(B)the waveform may fall into local optimal area.A mixed strategy(called greedy strategy κ)is proposed.The greedy strategy κ is as follows:(A)The waveform parameteris selected randomly from the waveform library Θ with the probability of κ;(B)With the probability of 1-κ,the waveform parameteris selected based on the optimal criterion as Eq.(23).

4.Presentation of results

The radar is deployed in(0,0)m,and can provide range,range rate and the bearing measurements.An airplane,starting from(1.25×104,1.5×104)m at time t=0 s,flies for 18 s with the initial velocity(-100,-50)m/s.Then,it turns left with the turn rate ω=4.77(°)/s for 25 s.After the turn,the airplane continues with current velocity for 10 s.Then,the airplane performs right turn with the turn rate ω=4.77(°)/s for 26 s.Finally,the airplane continues with current velocity for 21 s.The sampling interval is Δt=1 s.

In the experiment,PDA algorithm is used for single target tracking in clutter,and the Extended Kalman Filter(EKF)algorithm is used for non-linear tracking.The adaptive filtering model is IMM,with the model set CV and CS.The maximum acceleration amaxin CS model is set to be 50 m/s2,and the maneuvering frequency constant is set to be 1/60.The initial model probability of the two models is assumed to be 1/2 respectively.The fixed Markov model transition probability matrix is set to be

Monte Carlo simulations are performed.To evaluate the tracking performance, we select the following criteria for tracking accuracy,efficiency and the track loss.Here,(A)range and velocity estimation Root Mean Square Error(RMSE),and the Average RMSE(ARMSE) are used to describe the accuracy;(B)the computation time is used to describe the efficiency.(C)a track is considered to be lost when the estimated target falls out of the ten-sigma region centered around the true position in the measurement space.14The Successful Tracking Rate(STR)is measured as the ratio of successful tracking number to the total Monte Carlo simulations.

4.1.Adaptive filtering model and validation gate

The measurement accuracy of range,range rate and bearing are set to be 50 m,5 m/s,and 0.1°respectively.Time-varying model TIMM algorithm is compared with the CS model and the traditional IMM algorithm.Fig.6 shows the comparison of range and velocity RMSE of the three algorithms.Fig.7 shows the model probability using IMM and TIMM algorithms.

CS model algorithm has poor performance for tracking weak maneuvering targets.26As shown in Fig.6,the IMM algorithm is used to improve the tracking accuracy of the weak maneuvering target by introducing the competition of the CV model.However,it also brings about the problem of poor tracking accuracy for strong maneuvering targets.The TIMM algorithm is used to make the model transition probability changing with the current measurements.The model with larger probability is easier to transfer to itself,thus reducing the undesirable competition of the mismatch model.As shown in Fig.7,using the TIMM algorithm,the probability is well separated from each other.

The target detection probability Pdis assumed to be 1.The validation gate is set to be ellipsoid,and its region is set to be four-sigma.The density of the clutters ρ is the false measurement number per unit volume.The adaptive filtering model is TIMM. The Adaptive validation gate TIMM-PDA(ATIMM-PDA)algorithm is compared with the traditional TIMM-PDA algorithm.Table 1 shows the STR in 100 Monte Carlo simulations.Fig.8 is the volume curve of validation gate changing with time using ATIMM-PDA algorithm.Fig.9 is the computation time histogram under different clutter density background(clutter density 1,2,3 are ρ=0.01,ρ=0.10 and ρ=0.50 respectively).

Fig.6 Comparisons of range and velocity RMSE for tracks.

Fig.7 Comparisons of model probability with IMM and TIMM algorithms.

Table 1 Comparison of performance metric for TIMM-PDA and ATIMM-PDA.

Fig.8 Validation gate volume using ATIMM-PDA algorithm.

Fig.9 Histogram of computing time in different clutter density.

From Table 1,it can be seen that when the clutter density is ρ=0.10,the STR of the TIMM-PDA algorithm is only 29%,and it has been seriously invalid.Based on ATIMM-PDA framework,the predicted center and the innovation covariance can be adjusted dynamically according to the maneuver of target(the interacting model is the compromise of CS model and CV model as shown in Fig.8).As shown in Fig.9,the traditional TIMM-PDA algorithm has a large amount of time consuming,because these two sub models use their own candidate measurements.The proposed ATIMM-PDA algorithm uses a common adaptive validation gate and the measurements in the gate.Therefore,compared to TIMM-PDA,ATIMM-PDA algorithm has lower computation time when maintaining a higher STR.

4.2.Adaptive waveform selection

The radar transmitted waveform is X band, whose carrier frequency is 10.4 GHz,and the transmitted signal is shown in Eq.(4).For simplicity,the chirp rate b is set to be 0 in the simulation. The waveform parameter library iss in Θ and the grid step-size Δλ=2×10-6s.The half power beam width of the antenna is set to be 3o.Under constant transmitted energy constraint,the SNR can be obtained from η=(r0/r)4.ris the range between the target and radar.In the simulation,r0is set to be 50 km.

The Fixed Waveform(FW)algorithm is with four different waveforms,which are λ=4×10-6s in θ1,λ=10×10-6s in θ2,λ=12×10-6s in θ3and λ=20×10-6s in θ4respectively.The Waveform Selection(WS)algorithm selects the waveform parameter from the librarys in Θ.The greedy parameter is set to be κ=10%.Table 2 shows the STR in 100 Monte Carlo simulations.

Table 2 Comparison of performance metric for FW and WS algorithms.

Fig.10 Comparisons of range and velocity RMSE for tracks.

Table 3 Comparisons of performance metrics for FW and WS algorithms.

Then,assume the density of clutter is ρ=0.01,the tracking performance comparison for the WS algorithm with 10%-greedy and FW algorithm is shown in Fig.10.The FW algorithm chooses the waveform parameter θ1and θ2respectively.Table 3 shows the tracking ARMSE with different algorithms.The dynamic selection of pulse duration time in one Monte Carlo simulation for the proposed algorithm is given in Fig.11.The comparison of tracking uncertainty is shown in Fig.12.

It can be seen from Table 2 that the WS algorithm significantly improves the tracking performance in STR metrics.Using the minimum information entropy criterion,the WS algorithm is greedy,it may fall into the local optimal region,and lead to more track losses.WS algorithm 10%-greedy has 10%random waveform,which can make WS algorithm jump out of the local area.Therefore,it has a higher STR than the WS algorithm.

Fig.11 Dynamic selection of Pulse duration time.

It can be seen from Fig.10 and Table 3 that the range RMSE of waveform 2 is worse than that of waveform 1.The velocity RMSE of waveform 2 is better than the velocity RMSE of waveform 1.Considering all the waveform in the waveform library,the computation time of WS algorithm is larger than the FW algorithm and the WS algorithm 10%-greedy.The range and velocity ARMSE of the WS algorithm is similar to the range and velocity ARMSE of the 10%-greedy algorithm,both of which are obviously better than the FW algorithm.It can be seen from Fig.11 that the WS with 10%-greedy algorithm can dynamically select waveform parameters to continuously balance the measurement error covariance of range and range rate(λ=2×10-6s is selected with the probability 60%approximately;λ=20×10-6s is selected with the probability 30%approximately;the last 10%is for the random selection).

Fig.12 Tracking uncertainty of three algorithms.

From the comparison of tracking uncertainty in Fig.12,we can find that the algorithm with waveform 1 is better than that with waveform 2,and the waveform selection algorithm is much better than that with fixed waveform.Meanwhile,the tracking stability of WS algorithm with 10%-greedy is superior and robust.

5.Conclusions

Intelligence is the main function of human cognition,and also an important direction for the development of next generation radar.In this paper,radar signal and data adaptive processing based on human cognitive mechanism is an important exploration of this trend.The main conclusions of this paper are as follows:

(1)The time-varying model transition probability IMM is an adaptive filtering model for RMTT.The ratio of model probability with current time and the last time is used to adjust the transition probability.This mechanism makes the cooperation and competition among models more proper to improve the tracking performance.

(2)Adaptive validation gate is very similar to the selective attention in human cognition,which can capture the target of attention with the least computing resources.When the target is maneuvering,the validation gate becomes larger and the target is dropped into the gate.Similarly,when the target maintains a constant velocity,the validation gate becomes smaller, which reduces the candidate measurements in the gate to improve tracking accuracy and efficiency.Clutter environment adaptability with adaptive validation gate is far better than that with fixed validation gate.

(3)Waveform selection algorithm includes perception of environment and adapting actions to environment.This is very similar to the mechanism of human Perception of Action Cycle (PAC). In this algorithm, the information entropy of different waveforms is stored in short-term memory by online learning from the environment.Then,according to a certain criterion,the appropriate waveform can be extracted to change the measurement noise covariance to adapt to the changing environment.

(4)The greedy strategy κ for waveform selection has two aspects of advantages:(A)The optimal selected waveform makes the tracking performance better than that with the fixed waveform. (B) The random selection makes sure that it can easily jump out of the local optimal region.The computational resources are also allocated properly.

Acknowledgements

This study was co-supported by the National Natural Science Foundation of China(No.61671453)and the Anhui Province Natural Science Fund Project, China (No.1608085MF123).