An Experimental Multi-Target Tracking of AM Radio-Based Passive Bistatic Radar System via Multi-Static Doppler Shifts

This paper presents a description of recent research and the multi-target tracking in experimental passive bistatic radar (PBR) system taking advantage of numerous non-cooperative AM radio signals via multi-static doppler shifts. However, it raises challenges for use by multiple spatially distributed AM radio illuminators for multi-target tracking in PBR system due to complex data association hypotheses and no directly used tracking algorithm in the practical scenario. To solve these problems, after a series of key array signal processing techniques in the self-developed system, by constructing a nonlinear measurement model, the novel method is proposed to accommodate nonlinear model by using the unscented transformation (UT) in Gaussian mixture (GM) implementation of iterated-corrector cardinality-balanced multi-target multi-Bernoulli (CBMeMBer). Simulation and experimental results analysis verify the feasibility of this approach used in a practical PBR system for moving multi-target tracking.


Introduction
Passive bistatic radar (PBR) is a subset of bistate radars receiving non-cooperative transmitters of opportunity scattered by potential targets. Research on PBR has attracted extensive attention because of well-known advantages, such as no additional frequency channel allocation, lower costs, and lower probability of being detected with respect to active radars. Although, PBR systems have a long history, there are not enough operational systems.
Of all the transmitters of opportunity available in the PBR systems, very high frequency/ultra high frequency (VHF/UHF) bands represent some of the most attractive for surveillance purposes, such as analog television (ATV) [1,2], digital television-terrestrial (DTV) [3,4], frequency modulation (FM) radio [5], digital audio/video broadcasting (DAB/DVB) [6][7][8][9][10]. However, relatively little interest has been shown in the high frequency (HF) band  due to the propagation complexity and low range resolution. Especially, the external illuminators in the HF band have excellent range coverage, propagation over the horizon, and stealth target detection. Some preliminary and pioneering HF-PBR works have been carried out. In the PBR system [11,12], Thomas et al. from University College London performed an analysis using the HF digital radio Mondiale (DRM)signal as transmitter of opportunity. The two-dimensional target localization, using a linear frequency modulated continuous waveform from a non-cooperative OTH radar located in Longreach, Australia, with a bandwidth of 10 kHz, is presented in [13].
In fact, compared with other opportunity illuminators in the HF band, commercial amplitude modulation (AM) broadcast signal sources have the advantages of high transmitter power, larger numbers, and wider coverage. Due to the propagation complexity and bandwidth limited, little attention is paid to AM radio signal for PBR system. The research lowest cost architectures; therefore, the main contribution of this paper is that the proposed multi-target tracking method can provide a reference for similar PBR systems.
The rest of this paper is organized as follows. The description of the AM Radio based PBR system and multi-target tracking formulation are described in Section 2. Section 3 provides the proposed IC-UT-GM-CBMeMBer filter. Simulation and field experimental implementation are given in Section 4. Finally, conclusion and possible future directions are drawn in Section 5.

System Description
Supposing the ionosphere is homogeneous and spherically symmetric, the bistatic plane geometry of an AM-radio-based sky-surface wave PBR system in the scenario can be simplified as shown in Figure 1 (two transmitters are shown explicitly simplistically). In the system, we exploited one receiving antenna array approximately 20 m above ground level located over-the-horizon (farther than 1000 km from the noncooperative transmitters generally) at Hubei province of China, which is equipped with a uniform circular array (UCA) with 16 antennas.
IC-UT-GM-CBMeMBer filter. The system described in this paper was constructed on one of the simplest and lowest cost architectures; therefore, the main contribution of this paper is that the proposed multi-target tracking method can provide a reference for similar PBR systems.
The rest of this paper is organized as follows. The description of the AM Radio based PBR system and multi-target tracking formulation are described in Section 2. Section 3 provides the proposed IC-UT-GM-CBMeMBer filter. Simulation and field experimental implementation are given in Section 4. Finally, conclusion and possible future directions are drawn in Section 5.

System Description
Supposing the ionosphere is homogeneous and spherically symmetric, the bistatic plane geometry of an AM-radio-based sky-surface wave PBR system in the scenario can be simplified as shown in Figure 1 (two transmitters are shown explicitly simplistically).
In the system, we exploited one receiving antenna array approximately 20 m above ground level located over-the-horizon (farther than 1000 km from the noncooperative transmitters generally) at Hubei province of China, which is equipped with a uniform circular array (UCA) with 16 antennas.
The direct wave (emitter-to-receiver) and the illumination wave (emitter-to-target) are reflected from the ionosphere, while the echo wave (target-to-receiver) was via lineof-sight (LOS) propagation in the surveillance area. To obtain multi-static Doppler measurements in the PBR system, some key techniques in array signal processing are summarized in a block diagram sketched in Figure  2. Similar to traditional passive radar, surveillance and reference channels are needed to receive target echoes and reference signal, respectively. The DOA of direct wave can be obtained by the multiple signal classification (MUSIC) algorithm from the reference channel, which is then used to clean the reference signal by using conventional beamforming (CBF) technology. After scanning the surveillance channel by normalized least mean square (NLMS) technology to obtain the echo signal, we calculated the cross-ambiguity function (CAF) of the direct path signal and the scattered signal to estimate range vs. Doppler shift of the targets. Finally, the time delay and Doppler shift of the targets after clutter removal were estimated. The direct wave (emitter-to-receiver) and the illumination wave (emitter-to-target) are reflected from the ionosphere, while the echo wave (target-to-receiver) was via line-of-sight (LOS) propagation in the surveillance area.
To obtain multi-static Doppler measurements in the PBR system, some key techniques in array signal processing are summarized in a block diagram sketched in Figure 2. Similar to traditional passive radar, surveillance and reference channels are needed to receive target echoes and reference signal, respectively. The DOA of direct wave can be obtained by the multiple signal classification (MUSIC) algorithm from the reference channel, which is then used to clean the reference signal by using conventional beamforming (CBF) technology. After scanning the surveillance channel by normalized least mean square (NLMS) technology to obtain the echo signal, we calculated the cross-ambiguity function (CAF) of the direct path signal and the scattered signal to estimate range vs. Doppler shift of the targets. Finally, the time delay and Doppler shift of the targets after clutter removal were estimated.  Furthermore, the greatest limitation on tracking target performance in the self-developed experimental PBR system is the interference and clutter in the received signal, for example, dense direct path interference and the DOA of echo signal with very low SNR under masking effects. Although the classic DOA estimation and clutter suppression methods have been studied over the past decade [22,23], most of them are unsuitable for processing HF-AM radio signal. We adopted the method of reference [24] by building a single-snapshot virtual array signal. After extending the single-snapshot virtual array signal to multi-snapshots and the MUSIC algorithm, the clutter interference could be suppressed significantly, and the desired echo signal was enhanced simultaneously. More details of signal processing and improvement can be found in [24]. Finally, the excellent Doppler shift information of targets' corresponding time can be provided on a 2-D time vs. Doppler map.

CBMeMBer Filter
The CBMeMBer filter is first introduced to solve the aforementioned tracking problem in the PBR system in this section [21].
Similarly, there are k N measurements , each taking values in an observation space at time k. In addition, the received measurement also contains a set of missing alarms or clutter that can be modeled as a Poisson RFS k Κ . Thus, multi-target observation at time k + 1 is modeled as finite sets [26]. Furthermore, the greatest limitation on tracking target performance in the self-developed experimental PBR system is the interference and clutter in the received signal, for example, dense direct path interference and the DOA of echo signal with very low SNR under masking effects. Although the classic DOA estimation and clutter suppression methods have been studied over the past decade [22,23], most of them are unsuitable for processing HF-AM radio signal. We adopted the method of reference [24] by building a single-snapshot virtual array signal. After extending the single-snapshot virtual array signal to multi-snapshots and the MUSIC algorithm, the clutter interference could be suppressed significantly, and the desired echo signal was enhanced simultaneously. More details of signal processing and improvement can be found in [24]. Finally, the excellent Doppler shift information of targets' corresponding time can be provided on a 2-D time vs. Doppler map.

CBMeMBer Filter
The CBMeMBer filter is first introduced to solve the aforementioned tracking problem in the PBR system in this section [21].
At time k, there are N(k) target states X k = x k,1 , · · · , x k,N(k) ⊆ F (χ), which denote space of finite subsets of χ. Given a target x k at time k, it is either detected in the surveillance area with probability p D,k (x k ) and generates a Bernoulli RFS Θ k (x k ) with likelihood function g k (·|x k ) , or it is missed with probability 1 − p D,k (x k ). Given a multi-target state X k , each x k ∈ X k either continues to exist at time k + 1 with probability p S (x k+1 ) and moves to a new state x k+1 with target transition equation f k+1|k (x k ) or dies with probability 1 − p S,k (x k+1 ). Thus, given a target with state x k ∈ X k at time k, its behavior time k + 1 is modeled by the Bernoulli RFS S k+1|k (x k ), and Γ k+1 denotes the multi-Bernoulli RFS of new births at time k + 1. The multi-target state is modeled as [25].
Similarly, there are N k measurements Z k = z k,1 , . . . , z k,N k , each taking values in an observation space at time k. In addition, the received measurement also contains a set of missing alarms or clutter that can be modeled as a Poisson RFS K k . Thus, multi-target observation at time k + 1 is modeled as finite sets [26].
where Θ(x k+1 ) is a Bernoulli RFS that is generated by target state x k+1 ∈ X k+1 . A multi-Bernoulli RFS X (i) on χ is a union of a fixed number M of independent Bernoulli RFSs with existence probability r (i) and probability density p (i) , X = ∪ M i=1 X (i) . Moreover, the probability density π is [27]: The multi-target bayes recursion propagates in time [27]: where f k+1|k (·|·) is the multi-target transition density and g k+1 (·|·) is the multi-target likelihood.

Multi-Target Tracking Model
Tracking model is one of the major problems needing to be considered in the multitarget system. In this paper, we consider the target tracking scenario performed in a 2D Cartesian coordinate, with the origin point located at a single receiver antenna array; the x-axis points East and the y-axis points North. Assume that at time k, the i-th target state is represented by the state vector x is the number of targets, superscript T denotes the matrix transpose, p are the position and velocity of the target, respectively. Each target dynamic motion is followed by a nearly constant velocity model: where u k ∼ N(u; 0, Q k ) is zero-mean white Gaussian process noise with covariance Q k . We adopt: In which ∆ is the sampling interval. A 0 = 1 ∆ 0 1 , I n , and 0 n denote n × n identity and zeros matrices, respectively. In the two-dimensional surveillance area, three spatially distributed non-cooperative AM radio illuminators constantly transmit signals with a known carrier frequency f (i) c of the i-th AM radio station, i = 1 . . . 3, and the receiver places are at the original point, as illustrated in Figure 3. The direct wave and scattered waves from multiple AM broadcast stations reflected from the ionosphere (three scattered echo waves and one target are shown simplistically) reach the target and receiver simultaneously on the condition that the AM broadcast stations located at R are far away (>1000 km) from the receiver antenna array. Doppler shift measurements by i-th illumination can be generally modeled as [28]: where: → v k is the constant velocity vector of target at time k, p k = p x,k 2 + p y,k 2 , c is the is the constant velocity vector of target at time k, Multiple non-cooperative illuminators of AM radio stations (red pentacle) reflected from ionosphere received by single receiver antenna array (blue triangle) in x-y coordinate.
As the AM radio stations are typically long distance from the receiver antenna array, we approximately considered the direction of the direct wave from the i-th illuminator of AM radio station to the receiver antenna array as equal to the direction of the scattered wave from the i-th illumination to the target. According to Equation (9), the model can be approximately written as: Here, is the normalized target position relative to the receiver.
is the normalized incident direction vector of the direct wave from the i-th illuminator of the AM radio station to the receiver antenna array, which is independent on the target state and could be easily achieved from DOA estimation of the direct wave, as mentioned before.
Each Doppler-shift subset includes at most one measurement per illuminator and corresponds to the measurements made by multi-targets across all illuminators practically contaminated by false alarms and misdetections. The subsets of a partition are disjointed and comprise measurement space, which is denoted as As the AM radio stations are typically long distance from the receiver antenna array, we approximately considered the direction of the direct wave from the i-th illuminator of AM radio station to the receiver antenna array as equal to the direction of the scattered wave from the i-th illumination to the target. According to Equation (9), the model can be approximately written as: Here, → p k (i) is the normalized target position relative to the receiver. → vt k (i) is the normalized incident direction vector of the direct wave from the i-th illuminator of the AM radio station to the receiver antenna array, which is independent on the target state and could be easily achieved from DOA estimation of the direct wave, as mentioned before.
Each Doppler-shift subset includes at most one measurement per illuminator and corresponds to the measurements made by multi-targets across all illuminators practically contaminated by false alarms and misdetections. The subsets of a partition are disjointed and comprise measurement space, which is denoted as Z k is the number of the detection values, including false alarms and misdetection; z

The Proposed Multi-Target Tracking Method
The GM-CBMeMBer filter has a close-form solution under assumptions of linear Gaussian models that is difficult to implement on the nonlinear measurement models. To overcome this limitation, we extended the GM-CBMeMBer filter to a practical nonlinear measurement model by using unscented transform (UT) techniques [29]. Another straightforward extension of the single sensor CBMeMBer filters to the case of multiple illuminators can be achieved by iterating the filter update stage for each illuminator measurement set. An IC-UT-GM-CBMeMBer filter can be implemented to accommodate a multi-transmitter nonlinear Doppler model. However, this IC-CBMeMBer yields final solutions that depend on the order of the measurement set of illuminators; therefore, the development of efficient algorithms for the scenario case are left for future investigation. Hence, in this section we propose the IC-UT-GM-CBMeMBer filter for multi-target tracking in the PBR system.

IC-UK-GM-CBMeMBer Filter
We supposed that each target follows a linear Gaussian dynamical and observation mode [21], i.e., where f k+1|k (· x k ) is a transition function commonly known as Markov shift [30].N( · ; m, P) denotes a Gaussian density with mean m and covariance P, F k is the state transition matrix, Q k is the process noise covariance, g k+1 (z|x) is likelihood function, H k+1 is the observation matrix, and R k+1 is the observation noise covariance. A multi-Bernoulli RFS is characterized by a posterior distribution with parameters existence probability r (i) and probability density , which is comprised of Gaussian mixtures of the form denote the weights, means, and covariances of the j-th Gaussian component by the sample time k.
The Bernoulli filter propagates the posterior π k = r k , p k (x k ) during the whole time in "prediction" and "update" steps. This effectively means that r k and p k must be propagated.
Prediction: At time k + 1, spontaneous births are accounted for by appending a birth multi-Bernoulli RFS with components r to surviving targets. The total number of predicted hypothesized tracks is M k+1|k = M k + M Γ,k+1 . The predicted multi-target density is [21]: where: Update: In the following, based on nonlinear observations, we propose the unscented transform implementation of the IC-UK-GM-CBMeMBer filter in the update step.
At time k + 1, the updated multi-Bernoulli density π k+1 is formed by multi-Bernoulli RFS of the legacy tracks (r and measurement-corrected tracks (r U,k+1 (W), p U,k+ as follows: where: Using unscented transform extends the mean matrix and covariance matrix, respectively, We constructed a set of 2n U + 1 sigma points χ where n U is the dimension of µ k , and κ U is the scaling parameters,n U + κ U = 0.
With the i-th illuminator measurement data Z (i) k+1 , the filter is obtained by the aforementioned sequential processing of the measurement set of each illuminator with the CB-MeMBer filter corrector. The update operator Ψ k+1 is [21,31]: where a, b = χ a(x)b(x)dx denotes the inner product, and the sequential update processing is as shown where • denotes a composition.

State Extraction and Cardinality Biass
Extract multi-target states are the same as that of the GM-MB filter; for more details see [21]. The number of targets is estimated by: For completeness, the key steps of the proposed filter are summarized as a block diagram of the processing algorithm in Table 1.
construction of birth target Gaussian components using Equation (13) end update the legacy tracks for i = 1:M k+1|k r (i) each component constructs a set of sigma points and weights using Equation (22) to generate: end compute (r U,k+1 , p U,k+1 ) using Equations (18) and (19) end prune tracks end state extraction and cardinality bias using Equation (37) end

Experimental Configuration
We developed the PBR system in Huazhong University of Science and Technology by tracking a close-in civilian airplane whose working frequency band is 6-30 MHz. The system is configured to work in multi-transmitter and receiver-only mode. The experiment was carried out in December 2014, in which three AM radio broadcast stations were selected as the noncooperative transmitters, namely, Tx1, Tx2, and Tx3, respectively. The specific parameters can be obtained from the International Telecommunication Union (ITU) Radiocommunication Sector [32,33] listed in Table 2, including carrier frequency (f c ), transmitting power, distance with respect to the receiver, and so on. The ground distance between the AM radio broadcast station and the receiver antenna array is over 800 km. Thus, the transmitted signals are reflected by the ionosphere to reach targets over-the-horizon away. Figure 4 shows the geographical distribution of the illuminators and the receiver station. The noncooperative targets in the experiment are two civil aircrafts in the surveillance area with flight numbers CCAXXXX and CSNXXXX, respectively, namely, Target 1 and Target 2. The civil aircrafts parameters were broadcast by the automatic dependent surveillance-broadcast (ADS-B) system within a short interval of time. The data sets, including position, velocity, and so on, are the reference to verify the tracking method, which is recorded by a ground-based AirNav Radar Box. The two real trajectories of the civil aircrafts during the experiment are plotted in Figure 5a  The noncooperative targets in the experiment are two civil aircrafts in the surveillance area with flight numbers CCAXXXX and CSNXXXX, respectively, namely, Target 1 and Target 2. The civil aircrafts parameters were broadcast by the automatic dependent surveillance-broadcast (ADS-B) system within a short interval of time. The data sets, including position, velocity, and so on, are the reference to verify the tracking method, which is recorded by a ground-based AirNav Radar Box. The two real trajectories of the civil aircrafts during the experiment are plotted in Figure 5a  The noncooperative targets in the experiment are two civil aircrafts in the surveillance area with flight numbers CCAXXXX and CSNXXXX, respectively, namely, Target 1 and Target 2. The civil aircrafts parameters were broadcast by the automatic dependent surveillance-broadcast (ADS-B) system within a short interval of time. The data sets, including position, velocity, and so on, are the reference to verify the tracking method, which is recorded by a ground-based AirNav Radar Box. The two real trajectories of the civil aircrafts during the experiment are plotted in Figure 5a

Field Experimental Results
The targets are observed in the surveillance region with dimensions [−40, 40]km × [−40, 40]km. The single-target transition model is a linear Gaussian process given by Equation (11), in which ∆ = 1 s is the sampling period, and σ v = 0.1m/s 2 is the standard deviation of the process noise.
The birth process is multiBernoulli with density . The probability of target survival is p S,k = 0.95. The probability of target detection is p D,k = 0.5.
After the aforementioned signal processing, we obtained the DOA estimation of each direct wave and the Doppler shift measurement data, including the false alarms and misdetections. Figure 6 shows the detected Doppler vs. time obtained from the surveillance areas using three AM broadcast stations with the carrier frequency of 17.7 MHz, 15.37 MHz, and 15.5 MHz, respectively. The Doppler measurement sets have clutter and the missing alarm. Then, the noisy three stations Doppler-shift measurement sets Z (I) 1:80 , are passed to the tracking filter, as plotted in Figure 7. The parameters of the tracking filter are set as follows: observation noise covariance R k = σ 2 ε I 1 , where σ ε = 1Hz is the standard deviation of the measurement noise. Clutter parameter is Poisson with intensity κ k (z) = λ c Vu(z), where u(z) is a uniform probability density over the surveillance region, V = 1600 km 2 is the "volume" of the surveillance region, and the clutter intensity is λ

Field Experimental Results
The targets are observed in the surveillance region with dimensions  The initial density of the target state 0 ( ) p x is the Gaussian mixture of the form:  Figures 8 and 9, which show the estimated target traces and four estimated components of the state vector: px, py, vx, vy change vs time compared with the true trajectories, respectively. At ending time instants, short discontinuities occur in the tracks owing to the missing alarm of the Doppler measurement. Notice that the number of targets suffers from latency problem at the beginning of tracking in Figure 10, because the initial points are located arbitrarily.   The initial density of the target state 0 ( ) p x is the Gaussian mixture of the form:  Figures 8 and 9, which show the estimated target traces and four estimated components of the state vector: px, py, vx, vy change vs time compared with the true trajectories, respectively. At ending time instants, short discontinuities occur in the tracks owing to the missing alarm of the Doppler measurement. Notice that the number of targets suffers from latency problem at the beginning of tracking in Figure 10, because the initial points are located arbitrarily.      Different numbers of illuminators are a problem in multi-target tracking performance when only Doppler measurements are used. To study this, the filter is implemented under the conditions of AM radio broadcast stations Ns = 2,1, corresponding to stations with serial numbers of I = {1, 2}, {1}, respectively. The optimal subpattern assignment (OSPA) is used to evaluate the tracking miss-distance. The OSPA distances (for c = 20 and p = 1) vs. time on conditions of various number of broadcast stations compared with the results on the condition of Ns = 3, I = {1, 2, 3} is shown in Figure 11. Particularly, the OSPA distances vs. the time between 6s and 32s is plotted. It can be seen that the estimated largest OSPA distances are approximately 2880 m, 2922 m, and 5712 m on the condition of Ns = 3, Ns = 2, and Ns = 1, respectively. The obvious error in the period time from k = 27 to 56 is due to the missing detections and clutter of the Doppler measurements and the number of illuminators. Therefore, we believe that the more numerous the AM radio broadcast stations that are exploited, the more accurate the tracking trajectories are. Different numbers of illuminators are a problem in multi-target tracking performance when only Doppler measurements are used. To study this, the filter is implemented under the conditions of AM radio broadcast stations Ns = 2,1, corresponding to stations with serial numbers of I = {1, 2}, {1}, respectively. The optimal subpattern assignment (OSPA) is used to evaluate the tracking miss-distance. The OSPA distances (for c = 20 and p = 1) vs. time on conditions of various number of broadcast stations compared with the results on the condition of Ns = 3, I = {1, 2, 3} is shown in Figure 11. Particularly, the OSPA distances vs. the time between 6s and 32s is plotted. It can be seen that the estimated largest OSPA distances are approximately 2880 m, 2922 m, and 5712 m on the condition of Ns = 3, Ns = 2, and Ns = 1, respectively. The obvious error in the period time from k = 27 to 56 is due to the missing detections and clutter of the Doppler measurements and the number of illuminators. Therefore, we believe that the more numerous the AM radio broadcast stations that are exploited, the more accurate the tracking trajectories are.

Simulation Results
In this subsection, the performance of the proposed method is verified via simulation under similar scenarios to those aforementioned under the situation of cross trajectories, in consideration that it usually occurs in real data processing on a 2D Cartesian coordinate. Three AM broadcast stations were chosen, the same as Table 2. The two targets' motion is assumed to be a nearly constant model adjusted for civil aircrafts, and the flight parameters are listed in Table 3. The false alarms are uniformly distributed in the field of view with range −30 Hz to 30 Hz, and the number of false alarms at each scan follows the Poisson distribution with a mean of 10. The parameters of the tracking filter are set the same as in Section 4.2. As shown in Figure 12, despite the intersection points, the two targets can follow their trajectories, respectively. In Figure 13, the OSPA metric (p = 1, c = 20) shows the track

Simulation Results
In this subsection, the performance of the proposed method is verified via simulation under similar scenarios to those aforementioned under the situation of cross trajectories, in consideration that it usually occurs in real data processing on a 2D Cartesian coordinate. Three AM broadcast stations were chosen, the same as Table 2. The two targets' motion is assumed to be a nearly constant model adjusted for civil aircrafts, and the flight parameters are listed in Table 3. The false alarms are uniformly distributed in the field of view with range −30 Hz to 30 Hz, and the number of false alarms at each scan follows the Poisson distribution with a mean of 10. The parameters of the tracking filter are set the same as in Section 4.2. As shown in Figure 12, despite the intersection points, the two targets can follow their trajectories, respectively. In Figure 13, the OSPA metric (p = 1, c = 20) shows the maintenance quality of the proposed method. However, the instantaneous peaks are observed from times k = 59 to k = 81 due to corresponding intersection point and track termination latency. The simulation results indicate that the proposed method can deal with relatively complex tracking problems.

Conclusions
In this paper, we propose a multi-target tracking filter in a self-developed PBR system by using spatially distributed multiple AM broadcast stations. Multiple non-cooperative illuminators with different carrier frequencies located over-the horizon and one receiver in the surveillance area are involved in the practical system. The direct wave and the illumination wave are reflected from the ionosphere received by a uniform circular maintenance quality of the proposed method. However, the instantaneous peaks are observed from times k = 59 to k = 81 due to corresponding intersection point and track termination latency. The simulation results indicate that the proposed method can deal with relatively complex tracking problems.

Conclusions
In this paper, we propose a multi-target tracking filter in a self-developed PBR system by using spatially distributed multiple AM broadcast stations. Multiple non-cooperative illuminators with different carrier frequencies located over-the horizon and one receiver in the surveillance area are involved in the practical system. The direct wave and the illumination wave are reflected from the ionosphere received by a uniform circular

Conclusions
In this paper, we propose a multi-target tracking filter in a self-developed PBR system by using spatially distributed multiple AM broadcast stations. Multiple non-cooperative illuminators with different carrier frequencies located over-the horizon and one receiver in the surveillance area are involved in the practical system. The direct wave and the illumination wave are reflected from the ionosphere received by a uniform circular array located over the horizon, while the echo wave (target-to-receiver) is via LOS propagation in the surveillance area. After some techniques in array signal processing, the Doppler measurement sets, including clutter and the missing alarm with corresponding time, can be collected. To overcome linear Gaussian models, we propose the tracking model and extend the GM-CBMeMBer filter to a practical nonlinear measurement model by using unscented transform (UT) techniques by iterating the filter update stage for each illuminator measurement set in this practical scenario. Three AM broadcast stations were selected as the non-cooperative illuminators. Two non-cooperative civil aircrafts were chosen as tracking targets, whose flight parameters were recorded by a ground-based AirNav Radar Box set. Considering the clutter and missing alarm in the measurement sets, the OSPA distances are acceptable. Moreover, the performance of simulation has verified the feasibility of the proposed tracking method. In future work, the unknown clutter rate and detection probability under unknown background in this practical scenario will be taken into consideration. Maneuvering target tracking is also worthy of study.