Sequential Fusion based Approach for Estimating Range Gate Pull-Off Parameter in a Networked Radar System: An ECCM Algorithm

Networked radar is an emerging and effective alternative to traditional radar systems to provide improved performance by fusing information from multiple radars. Further, networked radar systems (NRS) have found numerous deployments in military and civilian infrastructures in recent years. Electronic countermeasures (ECM) like jamming, Range Gate Pull-Off (RGPO), and Velocity Gate Pull-Off (VGPO) generally pose a high risk to the radar systems by injecting intentional interference. This paper proposes networked radar to detect the RGPO ECM attack and estimate the range gate deception parameter of the deceived local track in an NRS. Each radar comprises a local tracker to provide the local estimates (updated state and updated covariance), and these estimates are then sent to the fusion node. Thereafter, a track-to-track association (T2TA) is formulated at the fusion node to detect the deceived tracks using all the available local tracks. For the deceived track, the pseudo-measurements are created using the inverse Kalman filter-based tracklets. All the local tracks except deceived track are compensated and sequentially fused to create a reference measurement. After that, the deception parameter of the deceived track is estimated by using pseudo-measurement and the reference measurement by employing the recursive least square estimator (RLSE). In addition, the proposed algorithm is analyzed for single and multiple RGPO based ECM scenarios. Further, the Cramer Rao Lower Bound (CRLB) for the proposed methodology is derived. The results are quantified with a Position Root Mean Square Error (PRMSE), CRLB, innovation test, normalized estimation error squared (NEES) test, and confidence interval. The simulation results demonstrate that the proposed estimation technique provides good performance in the presence of all the local tracks are being attacked by RGPO ECM. Besides, it is evident from the results that estimator efficiency is falling below the 5% tail probability of the chi-square distribution.

jamming is an ECM in which the enemy radar transmits a noise signal with increased strength at the radar's operating frequency, such that the signature from the target is completely melded with the interference. On the other hand, in the SOJ technique, the high-power jamming signal is transmitted from the enemy radar at a larger distance than the maximum range at which the targeted radar can detect the targets. In SSJ, jamming equipment is carried out for selfprotection, and efficient jamming geometry between victim radar and jammer is always maintained. Deception jamming techniques like RGPO and VGPO are the most productive of all the ECM techniques that generate fake targets in order to deceive target tracking systems [4]. RGPO is a sort of ECM that intercepts radar signals and retransmits a deception signal with a progressive time delay, pulling the range gate of the radar target tracker further away from the actual target over time [5]. On the other hand, VGPO is employed by injecting a frequency-shifted replica of the received radar signal; the frequency of the false return is slowly altered to interfere with the true Doppler shift [6]. Digital radio frequency memory (DRFM) devices are generally used to store and regenerate captured radar signals to confuse hostile radars [7]. In addition, because of advances in computing capability and hardware architecture, the DRFM can simultaneously process multiple captured signals, allowing a modern repeater to deploy deception jamming on multiple-radar devices [8]. The DRFM is utilized to gradually delay the deception signal, thereby "walking" the range gate away from the true target. The RGPO deception jamming produced by the DRFM system is highly coherent to the radar transmitted signal, which makes the detection of the deception jamming difficult [9].
Electronic Counter Countermeasure (ECCM) are broadly classified into signal analysis and target tracking. In signal processing, most radar systems are provided with ECCM capabilities to combat deception jamming in recent years. The ECCM techniques such as pulse diversity, polarization character, motion function, DRFM quantization error, and target detection system in the presence of interference ensure that no single radar is tricked [8], [10]- [14]. In [15], an efficient ECCM approach for countering the very high-power ECM using an orthogonal frequency division multiplexing (OFDM) radar is presented and analyzed. Here, the phase codes of the sub-carriers belonging to the OFDM pulses are tuned to limit the jamming strength to suppress range deception and combined range-velocity deception jamming [15].
Most of the sensors may not be aware of the ECM techniques; however, they are resolved using efficient target tracking. The effect of RGPO on radar target tracking with benchmark targets is studied in [16] and [17]. In particular, controlling the beam pointing of phased array radar for benchmark target tracking problems in the existence of RGPO and false alarms is investigated in [16], [17]. The impacts of target amplitude variations, beam shape, missed detections, false alarms, finite resolution, target motions, and track loss were all included in the test-bed simulation described in [16]. Further, in [18] the solution for the second Benchmark problem of tracking a maneuvering target in the existence of RGPO using variable state dimension Kalman filter is presented. Authors in [18], have deployed adaptive waveform selection and dwell revisit time selection methods and track filter coasting for handling the uncertainties introduced by false alarms, missed detection, maneuvers, and RGPO. Further, for tracking highly maneuvering targets, a comprehensive framework is presented in [3] in the presence of false alarms, SOJ, and RGPO. Mainly, the algorithms for track generation and maintenance, adaptive target revisit interval selection, waveform selection, and detection threshold; and neutralizing ECM approaches were discussed in depth in [3]. The interacting multiple model (IMM) estimator in combination with the probabilistic data association (PDA) technique is utilized for tracking the targets in [3]. Additionally, authors in [19] have suggested the solution to the benchmark target tracking, which addresses the efficient resource allocation in the presence of ECM. The resource allocation problem is solved using interacting multiple model/multiple hypothesis tracking (IMM/MHT) tracker along with target tracking [19].
In [20], to counter RGPO and Range Gate Pull-In (RGPI) jamming, an ECCM approach based on loss of balance in the range tracking loop is presented and analyzed. Further, using adaptively updated bias weight in every range tracking interval according to the error signal, which balances the energy of the early and late gates concerning the target and continues to track the target with insignificant track loss is presented in [20]. Furthermore, memory tracking and narrow gate monitoring were used to propose and assess a novel ECCM approach against deception jamming in [21]. In addition, authors in [21] have concluded that the proposed method provides significant efficacy while countering all types of RGPO. In [22], the spatial filtering technique using trilinear decomposition to overcome the effect of deception jamming is presented and analyzed. Further, authors in [23] have proposed a composite approach to estimate the location of the target and deception range for distinguishing between false targets and true targets. The data fusion-based approaches are proposed to distinguish false targets using data correlation algorithms and local radar measurements (range, angle, and Doppler information). On the other hand, signal fusionbased techniques explore the ECCM abilities of multipleradar systems by utilizing amplitude and phase information of the target echoes to provide efficient countermeasures [24]. The most generic and systematic approach for mitigating the effect of RGPO on target tracking is Decomposition and Fusion (DF) where, the deception measurements have virtually the same angles like that of true measurements [25], [26]. The fundamental steps involved in the DF technique are decomposition of validated measurements using hypothesis testing, track filtering for range deception measurements, conventional filtering, and performing a fusion of these estimates.
Considering  DRFM systems digitize the received signals and store them into the memory. Thereafter, alter the stored signals and retransmit them towards the radar to create an illusion that true target is present. DRFM consists of receivers, analogto-digital converters (ADC), electronic attack (EA) control system, digital-to-analog Converters (DAC), and transmitters [27]. The basic structure of a traditional DRFM is depicted in Fig. 1.
For deceiving a radar using a DRFM system the radar signals are captured and stored in the memory. These stored signals can be used to synthesize single or multiple false targets to intentionally misguide the radar. The input radio frequency (RF in) signal is often down-converted in frequency before being sampled with a high-speed ADC in a DRFM system. The stored samples are first altered in terms of amplitude, frequency, and phase, then processed by a DAC, up-converted, and sent back (RF out) to the victim radar so as to generate the false targets [28]. Further, a DRFM system can modify the signature of the target by altering its apparent radar cross section, range, velocity, and angle before re-transmitting the signal. There are several key DRFM based ECM techniques: 1. Generation of multiple false targets, 2. RGPO and VGPO, 3. Inverse gain and 4. Bin masking. Among these techniques, the deception jamming performed in range domain, to deceive the radar is known as RGPO. Accordingly, in this paper, we have considered countering RGPO ECM at measurement level processing using the sequential fusion based algorithm in a networked radar framework. The established RGPO measurement model presented in [29] and is represented as, where, r d (k) is the deceived false range of the target from the radar, r(k) is the actual range, and ∆r(k) = c∆t k 2 is the deviation in the range owing to RGPO ECM. Here, ∆t k is the time delay due to ECM delay line as presented in [29]. Further, t 0 is the start time of the range deception, c is the VOLUME x, xxxx speed of light and, T ca represents the length of the false target evolving time. Consider a surveillance area being monitoring by NRS, where the number of radars is greater than two. Assume that all the radars are synchronized and provides the measurements pertaining to the targets. The measurement space of the radar is range and azimuth. A deception jammer is placed in the same surveillance region and sending spurious signals to mislead either one or more radars in the given surveillance.
The measurement at the one or more radars are corrupted by range gate pull off (RGPO) ECM technique. The scenario of NRS in which one of the radar is deceived by a single RGPO jammer as shown in Fig. 2. In the first case, a single radar sensor as shown in Fig. 2, is assumed to be affected by the RGPO jamming and results in deceived track as shown in Fig. 3a. Whereas, in the second case, multiple radar sensors are considered to be affected by ECM and leads to multiple deceived tracks as shown in Fig. 3b. The target state model is represented as, where x(k) is m x dimensional state vector consisting of position and velocity of the target at the discrete time instant k. F is the state transition matrix which follows constant velocity (CV), constant turn (CT), and constant acceleration (CA) depending on the state dynamics. Γ x is noise gain matrix [30] and v(k) is the process noise that follows Gaussian PDF with covariance, Here E[.] and [.] T represents the expectation and transposition operator respectively.
The measurement model without the influence of ECM is given by, where z i (k) is the measurement vector of m z dimension (which contains range (r i ) and azimuth (θ i ) corresponding to the target). w ri (k) and w θi(k) follows Gaussian PDF with zero mean and standard deviation σ 2 ri and σ 2 θi respectively. The equivalent representation of (4) is, where H is the m z × m x measurement transition matrix and w i (k) follows Gaussian PDF with zero mean and covariance R z which can be represented as, As shown in Fig. 2, in the presence of ECM the above measurement model is as given in [2], The above (7) is equivalent to (1). Where, it is assumed that the target range information deceived by the jammer and as a result i th radar true range is displaced by a value due to RGPO deception ∆r i (k). The measurement in the presence of ECM can be modelled as, It is also assumed that the conversion will not introduce any bias. For Unbiasedness, the following condition (9) should be satisfied Then, i th radar has the measurements where, the state vector The matrix B i (k) is a nonlinear function with the true range and azimuth. Using the the measured azimuth θ m i (k) and range r m i (k) from radar i, B i (k) can be written as given in [14], In the above, superscript m represents measured value. Finally, the new covariance matrix of the measurements in Cartesian coordinates (omitting index k in the measurements for clarity) can be written as, However, one can use the observed range and azimuth as well.

C. NOISE JAMMING
The jamming to signal ratio can be obtained as derived in [31]: The received power at the radar can be expressed as, where, P tx is the peak transmitted power in watts, G tx is the gain of the transmit antenna, G rx is the gain of the receive antenna, λ x is the carrier wavelength in meters, σ x is the radar cross section of the target in square meters, R x is the range from the radar to the target in meters, and L s is the total receiver system losses. The total power received at the radar from the jammer is given by, where, P jx is the peak transmitted jammer power in watts, G jx is the gain of the jammer antenna, G jr is the gain of the radar antenna in the direction of the jammer, λ x is the carrier wavelength in meters, R j is the range from jammer to the radar in meters, and L jr is the total jammer related losses.
Considering the ratio of jammer power (P jr ) to radar received power (P rx ), the jamming to signal ratio (JSR) can be written as, The received noise power at the radar under noise jamming is given by, where, kT 0 B n is the thermal noise of the radar receiver and P jr is the received jammer power which can be computed using (14). Here, k is the Boltzmann's constant (1.3803 × 10 23 J/K), T 0 is the absolute temperature in Kelvin, and B n is the noise bandwidth. The increased level in the received jamming power at the radar receiver results in the raise of the noise floor and subsequently leads to the missed detections [29]. When noise power of the jammer is sufficiently higher, it yields false measurements which can be written as, where, M indicates the number of false alarms. Each false alarm's range value is determined by the range bin at which noise power exceeds the threshold provides false detection. Effective signal processing techniques such as space time adaptive processing [32], [33], adaptive beamforming [34], waveform matching [35] and other advanced filtering techniques [36] are proposed in the literature for the detection and suppression of the noise jamming. In this work, it is assumed that noise jamming is suppressed at signal processing level and measurements are corrupted by RGPO deception jamming only.
Generally, the jamming power will be higher compared to the radar signal power, which helps the jammer to deceive the radar. Few signal processing based techniques like waveform diversity method and singular spectrum analysis for countering the RGPO ECM are presented in [37], [38]. This work aimed at estimating the range deception parameter in a networked radar scenario by using sequential fusion based approach and correct the local tracks by providing feedback information from the fusion center. Instead of detecting the attack, this work aimed to estimate the true target tracks from the falsified track information.

D. OBSERVATIONS
We can clearly see that the range measurement of radar-i is deceived. This deception results in a false track, as shown in Fig. 3a, after performing the distributed tracking. The objectives of the proposed research work are: 1) The measurements are being processed by the local tracker and provide the local estimates (estimated state and covariance). At the fusion center, only local estimates are available, and no other data is available from the radar or tracker. Hence, we need to recreate the measurements at the fusion center by using the local tracks. This recreation of measurements is possible by evaluating the tracklets [39]. 2) One needs to formulate a method to associate the local tracks pertaining to the same target so that those tracks can be utilized as a reference to estimate the deception occurrence in other tracks. This association can be formulated as a track-to-track association and can be solved using S-Dimensional (S-D) assignment [40].
3) The deception parameter of the RGPO ECM track is to be estimated by using un-corrupted local tracks. These uncorrupted local tracks can be fused to generate a reference measurement.

III. DISTRIBUTED TRACKING AND TRACK-TO-TRACK ASSOCIATION A. DISTRIBUTED TRACKING
All radars are deployed with local trackers as shown in Fig. 2. The radar is ignorant about the measurement pertaining to the target, whether it is a true measurement or false measurements due to ECM. The tracker works with the converted measurements. For the acquired measurement, the local tracker provides the local estimates (estimated state and covariance). Given the previous state estimatex i (k|k), the KF state prediction for i = 1, . . . .N radars is written as, This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and content may change prior to final publication.  where k is the discrete time instant and F is a state transition matrix. Similar to the state prediction, for the given covariance P(k|k) at the k th instant, the predicted covariance at the k + 1 th instant is represented as, where Q x is the process noise covariance and Γ is the noise gain matrix as given in [41]. The measurement prediction is, The innovation of the filter is, The updated state is designated as, where, W i (k + 1) is the Kalman gain and is computed as, where, S i is the innovation covariance and is represented as, Here R z is the measurement covariance matrix. Finally, the updated covariance matrix is given by, (25) In a single RGPO ECM case, out of all the local tracks, only one track (local track-i) is falsified by the RGPO ECM as illustrated in Fig. 3a. Here, we can see that the local track corresponding to local track-i is deviated by ∆r i from its true position as comprehensively derived in [42]. One has to perform track-to-track association to all local tracks, and it should report that all local tracks correspond to same-origin except i th track. In another case, if N jammers are employed to deceive all the local tracks, the local tracks appear as Fig. 3b. In this case, one should report that all the tracks are from a different origin. The track-to-track association is presented in the subsequent section to address this issue.

B. TRACK-TO-TRACK ASSOCIATION (T2TA)
The fusion of target tracks from multiple sensors is an essential block in the sensor fusion field. The information from multiple sensors has the potential to significantly improve tracking accuracy and target acquisition rates. Out of all the variants of track-to-track associations [43], the hypothesis based track-to-track association is popular and can provide improved tracking accuracy even with less target detection probability and high false alarm rates. The N radars will have their own number of tracks in the form of target estimatex i ni with their errors distributed as zero-mean Gaussian with covariance P i ni . The i = 1, 2, . . . , N , represents radar number and n i = 1, 2, . . . , T represents number of tracks that the each radar generates. To find out the tracks that represents the same target, it is required to perform the likelihood ratio test, given by where, Λ(H 1 n1,n2,...,n N ) represents the likelihood hypothesis of tracks having the common origin, Λ(H 0 n1,n2,...,n N ) represents the likelihood hypothesis of tracks coming from the different origin.
Calculating the likelihood hypothesis of tracks having a common origin is as follows: The (27) can also be written conditioned on the track estimate of the first radar, given by, The p(x 1 n1 |H 1 ) is independent of H 1 n1,n2,...,n N , hence it can be relaxed. Also, it is assumed to follow uniform distribution, which is a valid assumption in the presence of lack of information. i.e., Substituting, (29) into (28) results in Consider the two radar (i, j) case having two tracks (n i , n j ) as common target origin. Under the Gaussian assumption, if the tracksx i ni andx j nj at radar i and radar j results from the same target, the likelihood function of the two tracks is given by, where, N (x;x, P ) represents Gaussian distribution of variable x has mean and covariance asx, P , respectively. Similar to (31), the generalized likelihood function of all the common tracks (zero error tracks) n 1 , n 2 , . . . , n N for all N radars is given by Here, where,x ij represents the difference of the estimates resulted from the same target at i th and j th radar, given bỹ The diagonal elements of P is given by, wherex ij is defined in (34).
The diagonal elements of P is given by, Similar to (32), the likelihood hypothesis of tracks coming from different origins follows the same procedure as above, given by Similar to (29), the p(x 1 n1 |H 0 n1,n2,...,n N ) is assumed as diffuse prior given by, whereas, p(x N n N , . . . ,x 2 n2 |H 0 ,x 1 n1 ) is assumed to follow Poisson distribution in the state space having the spatial density λ. Therefore, substituting (38) into (37) yields Finally, from (26), (32), (39), the likelihood ratio test is given by, where, χ(H 1 : H 0 ) is the likelihood ratio given in (

IV. DECEPTION PARAMETER ESTIMATION ALGORITHM
The block diagram for the overall flow of the proposed algorithm is as shown in Fig. 4. As observed in the previous section, in case of all the local tracks are deceived, there is no availability of local tracks to fuse and form a reference track.
In the first step of the algorithm, measurement recreation is carried out for deceived track in the tracklets framework. On the other hand, the tracklets are computed for the rest of the tracks. These tracklets are compensated using previously estimated deception parameters (In the Fig. 4 the feedback of previous estimates is shown in dotted lines). Next, the sequential update algorithm is applied to the compensated local tracks to obtain the fused states and covariance. Using the fused states, the fused measurement (reference measurement) is recreated. Further, perform RLSE by utilizing the recreated measurement of deceived track and the reference measurement.  The local tracker provides the updated states and covariances. However, the measurements are being corrupted by the deception parameter. Hence, one needs to recreate the measurements. Once the measurement covariance is known or estimated (i.e.R z ), we can rewrite the Kalman gain (23) as,Ŵ
The (23) can be rewritten as, where, y(k + 1) is the recreated measurement. Here on the right hand side, gain matrix should be taken to the left side and perform the pseudo inversion as, Upon rearranging, the recreated measurement can be found as, (46) At this stage, to successfully recreate the measurements, we needR z . To estimate theR z , we are using Tracklets framework [44]. This method constructs the approximately uncorrelated equivalent measurements and the associated covariance matrices from the local tracks. The inverse Kalman filter-based tracklet method from [45] is used. Based on this method, the equivalent measurement vector u(k + 1, k) and measurement covariance U(k + 1, k) can be found using Algorithm-1, Algorithm 1 Measurement recreation using tracklets 1: inputs:x(k|k), P(k|k), x(k + 1|k + 1), P(k + 1|k + 1)  The detailed derivation of the tracklets is presented in the [46] and [47]. We constructed equivalent measurement vector u(k+1, k) and its error covariance matrix U(k+1, k). Note that, in order to calculate u(k + 1, k) usingx f (k + 1|k) and P f (k + 1|k), one needs the estimated target statex(k|k) and its covariance matrix P(k|k).

B. CORRECTION OF DECEPTION PARAMETER AMONG ALL TRACKS
Consider a case, where N RGPO ECM jammers are employed to perform RGPO ECM to all the N local tracks and results in N deceived local tracks. Here, all tracks gets altered due to RGPO ECM and the deception parameter for each track has to be estimated. In this case, the trackto-track association reports all the tracks are unique and they are not from the same origin. Therefore, each track is to be first compensated with the estimated range deception parameter (∆r i ) obtained in the previous scans and fuse the compensated tracks to get a fused state and covariance. The equivalent measurement isû = [x,ŷ]. Since the equivalent measurement is in Cartesian, one can get the measurement in polar by applying transformation. Therefore, compensate the range in the converted equivalent measurement as Here, ∆r(k) is the previous estimate and c indicates the corrected measurement.
θ c (k + 1) = arctan ŷ(k + 1) x(k + 1) These corrected polar measurements can be again transformed to Cartesian by standard coordinate conversion without bias as x m (k + 1) = b −1 r c (k + 1) cos(θ c (k + 1)) y m (k + 1) = b −1 r c (k + 1) sin(θ c (k + 1)) where, b e −σ 2 θc /2 . Now these x m and y m serve as the local tracker information without being effected by the ECM. Hence in this case, to find the deception of track-i, all the tracks are compensated except i th track. Therefore, the sequential fusion runs for N − 1 tracks.

C. CONSTRUCTING THE REFERENCE MEASUREMENT
Now the goal is to create reference measurement by fusing N − 1 tracks, which are compensated by the previously estimated deception parameters. The sequential update algorithm is performed in the fusion step. Although it is not an optimal approach for fusing the local tracks, it is computationally inexpensive than parallel update method [48]. In addition, it is independent of previous equivalent measurements at time instant k. Therefore, the index for sequential fusion is j = 1, . . . .N − 1/i. Which means j runs for all tracks rather than effected track i. After calculating the Algorithm 2 Sequential update algorithm 1: inputs: x j (k|k), P j (k|k) The state update is given by, The gain is given by, The covariance is given by, : end for 10: The final updated state estimate and covariance values arex f (k + 1|k + 1) =x N −1 (k + 1|k + 1) P f (k + 1|k + 1) = P N −1 (k + 1|k + 1) equivalent measurements for all the (N − 1) local tracks, we get u(k + 1) j , U(k + 1) j N −1 j=1 . This tracklet computation using Algorithm-1. It is assumed that fused state and covariance at k th instant is available asx f (k|k) andP f (k|k) respectively. The sequential updation algorithm is presented in Algorithm-2. In the algorithm, all N − 1 local tracks are sequentially updated to provide x f (k + 1|k + 1) and P f (k + 1|k + 1). One of the advantages of this sequential fusion approach is that in each "for loop" (step-5 in Algorithm-2) only a low dimensional Kalman filter that is independent of the size of the stacked RGPO vector and number of the sensors is needed. Furthermore, the fusion of local tracks can be accomplished by adding one sequential update for the latest corrected measurement of sensor j to the previously fused track. In the sequential fusion algorithm, it is also important to note that, there is no constraint on the rate at which local tracks are being received from the individual sensors. VOLUME x, xxxx

D. DECEPTION PARAMETER ESTIMATION ALGORITHM
The algorithm for estimating the deception parameter is presented in Algorithm-3. Also, the block diagram representation of deception parameter estimation is shown in Fig. 4. Recreate measurements: The tracklets for the deceived track are computed and then recreate the measurements corresponding to local tracks-i using (45),we obtain y i as

5:
Calculate the fused weight as

6:
Reference measurement Therefore, by providing the fused covariance in (46), we get y i * as Compute RLSE: The new measurement using reference measurement and re-created track is recursively solve using the last updates in recursive least squares estimation (RLSE) framework [48]. 8: end for

A. INNOVATION TEST
Innovation test is used for testing the efficiency of RLS estimator. The measurement is given by, y(k) = H(k)∆r(k) +w(k) (49) where, H(k) measurement transition matrix and the measurement noise covariance is The innovation covariance is represented as, The gain and the residual is calculated as The range gate estimate and its covariance are, The innovation test [49] is given as, where, ξ 2 nr (1 − q) is the chi square value with n r degree of freedom and tail probability of q.

B. CRAMER RAO LOWER BOUND
The Cramer Rao Lower Bound (CRLB) on the mean square error of unbiased estimator is a frequently used metric for determining the correctness of parameter estimate based on a set of data [50]. The CRLB of the algorithm provides the criterion to know the minimum value of error, that can be achieved by the algorithm.
From the measurement equation of the RLS estimator, where ∆r i (k) is the range gate vector to be estimated and the measurement noise covariance of w i (k) is given as is the measurement noise of i th local track and R * i (k) is the measurement noise obtained by fusing rest of the local tracks.
The covariance matrix of an unbiased estimator is bounded as below [30] and [51]: Here, E is the estimation operator and J z is the Fisher Information Matrix(FIM) and is given as [∇ ln p(ȳ(k) | ∆r(k))] ∆r(k)=∆rt (58) 10 VOLUME x, xxxx This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and where, ∆r t is the true value of the range gate parameter and ∇ is the gradient operator. Also, p(y(k) | ∆r(k)) is the likelihood function, which is given as below: (59) Substituting λ y = − ln p(z(k) | ∆r(k)), (60) Upon further simplification, which gives, The FIM at K is also the recursive form of CRLB is represented as,

C. NEES TEST AND CONFIDENCE INTERVAL TEST
In simulation frameworks, the normalised estimation error squared (NEES) test can be used to determine if the estimator is efficient, that is, whether the error matches the covariance provided by the CRLB [52]. The error matrix provided by the CRLB is J z . For an estimated deception parameter ∆r(k), there exist a ground truth r(k). The estimation error is given by, ∆r(k) = ∆r(k) − ∆r(k) The NEES value for the parameter ∆r is written as, The confidence interval of a deception parameter is evaluated for ∆r(k). The squared norm of the error should be constrained by the estimate if the estimator is efficient [53].
The confidence for the parameter ∆r(k) is, which follows chi square distribution with degree of freedom equal to n r .

A. SINGLE RADAR SENSOR JAMMING
In this case, a single radar effected by jamming (RGPO ECM) is considered among the three radars present in the surveillance region. All the radars are static and synchronous in time with t s = 1s. The radars are located at r s and θ s with reference to the origin. The range and azimuth measurements are corrupted with the noise with a standard deviation of σ r and σ θ , respectively. A single target is considered in the surveillance region, and all the radars are comprises of the local tracker to provide local estimates about the target. A single jammer is considered in this simulation, and it influences the single radar equipped with local tracker-1. Since the local track-1 generated from the tracker-1 is deceived with the RGPO ECM measurements, this yields a range displacement of ∆r 1 . The positions, measurement standard deviation, and deception parameters are tabulated in the Table-I. Moreover, the scenario is depicted in Fig. 5. The target is located at a range of 3000m and the azimuth of 1.5 rad from the origin. The target moves with a speed of 40m/s, and 80 deg heading throughout the simulation time of 1000s. The target follows a constant velocity model, and the state transition matrix is represented as,

1) Tracking Accuracy
A GNN association based EKF filter is used for target tracking. Two-point initialization method [54] is used to initialize the filter. The range-azimuth measurements r(0) and θ(0) at zero instant are considered to form a converted measurements as x(0) and y(0). Similarly, the first instant measurements are used to form the converted measurements as x(1) and y(1). Hence, the two-point initialization is given by, The measurement conversion follows the unbiased conversion by using, Here λ = exp − σ 2 θ 2 . This unbiased conversion is valid for initialization, since it follows the necessary criteria of rσ 2 θ σr 0.4. The covariance is initialized using, where, The tracking is performed with the help of an extended Kalman filter (EKF). The tunable parameters like process noise covariance and measurement noise covariances as Q x and R z , respectively are represented as, The tracking performance is evaluated using the PRMSE.
The tracking performance of all the local trackers is depicted in Figs. 6a-6c. It is observed from Fig. 6a that the local track-1 PRMSE is around 1000 ± 8m because of the range deception of 1000m affected by the RGPO ECM jamming. Moreover, the PRMSE of the local track-2 and local track-3 are also depicted in the Fig. 6b and Fig. 6c. The PRMSE of local track-2 and local track-3 is lesser than the local track-1; this is because the RGPO jamming is un-influencing local track-2 and local track-3. This tracking performance can be directly reflected in the fusion module.

2) Sequential Fusion Performance
The sequential fusion is performed on the compensated equivalent measurements. The correction is performed at k in the polar coordinates with the help of the estimated deception parameter at k − 1 time instant. For the time stamp of k = 1, since there are no previously fused estimates are available, the local track's updated state is considered as the fused state estimate i.e., x f (k|k) = x(k|k) and P f (k|k) = P(k|k) at k = 1. It can be seen from the Figs. 6d-6f that, the PRMSE of local track-1 fused estimate is equal to the PRMSE of local track-1 for the initial scan. After that, the deception parameter estimation converges over time and improves the PRMSE of the sequential fusion block. Therefore, we observed that, the local track-1 fusion PRMSE decreases over time, and the similar procedure holds true for local track-2 and local track-3 performance. Since the deception parameter is kept at 1000m for local track-1, the sequential fusion PRMSE starts at 1000m and finally diminishes to 10 m accuracy. The sequential fusion provides sub-optimal solution, but it is a significant technique importance due to its reduced computational requirement. It is also worth noting that the sequential fusion is only dependent on the compensated equivalent measurements to compute the fused state and covariance estimates at a given scan.

3) Deception Parameter Evaluation
The deception parameter is calculated in the RLSE framework. In this framework, measurement i corresponds to the deceived local track i. whereas, the reference measurement is generated by the compensation and fusion of all local tracks except i. That is the sequential fusion block runs for i * ∈ 1, · · · N /i. The initial state and covariance of the RLSE is ∆r(0|0) = 0 and Σ(0|0) = 1000 2 . There is no prior information regarding the deception parameter and its associated covariance at k = 0. The deception parameter of the deceived local track-1 is estimated, and its corresponding PRMSE is plotted in Fig. 7. Initially, the deception is considered as zero, and hence PRMSE at initial state is equal to 1000 m which is the deception created by the RGPO ECM. Along with the estimated deception parameter, we also plotted the Batch CRLB ( √ B − CRLB), Recursive CRLB ( √ R − CRLB) and the diagonal of the covariance estimate ( √ Σ). From Fig. 7, it can be observed that the estimator is working effectively, and the estimated deception parameter is coming closer the CRLB value. We have plotted on logy scale for better visualization, keeping the deception parameter changing from 10 3 to unity.

4) Estimator Performance Evaluation
The performance of the proposed algorithm is validated using the NEES test, innovation test, and confidence interval test. In all three tests, we have considered chi-square distribution as where q is tail probability. We have taken q as 1% and 5% and is plotted in the Fig. 8. It is evident from the results that the NEES values are falling within the chisquare distribution with a tail probability of 5% which infers 12 VOLUME x, xxxx This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and that the proposed estimator is efficient. The NEES for the estimator along with the chi-square distribution is shown in Fig. 8a. Further, it can be observed from Fig. 8b that the innovation test is inbound with the Raleigh distribution, and it is falling within the 95% confidence interval of the chisquare distribution with a degrees of freedom equal to two. Further, we examined the confidence area of the parameter to associated confidence interval, which intuitively specifies whether the estimated parameter and the estimated parameter covariance are agreeing with each other. From Fig. 8c it is evident that the confidence region of the estimated parameter is well within the specified range. That is the estimated covariance and R-CRLB are almost equal. Therefore, we can state that the proposed estimator neither optimistic nor pessimistic.

B. MULTI-SENSOR JAMMING
In this scenario, we considered three radars present in the surveillance region and all are affected by RGPO ECM. All the three radars are assumed to be static and synchronous in time. The radars are located at r s i and θ s with respect to origin. The range and azimuth measurements are corrupted with white Gaussian noise with zero mean and standard deviations of σ ri and σ θi respectively. A single target is considered, and all local trackers provide updated state and covariance to the fusion center. Unlike the single jammer three jammers are considered, and this yields a range displacement of ∆r i to each local track. The locations, standard deviation of measurements, and deception parameters of each of the local track are tabulated in Table-II.

1) Tracking Accuracy
A two-point initialization method is adapted to initialize the filter, the extended Kalman filter is used to filter the measurements. The tracking PRMSE of all the three local tracks is depicted in Figs. 9a-9c. Since all the three local tracks are affected by the jamming, we can observe that the local VOLUME x, xxxx 13 This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and content may change prior to final publication.

2) Sequential Fusion Performance
Each track is compensated with the estimated range deception parameter ∆r i , and then the sequential fusion is performed. Similar to the single jammer case, the initialization of the fused track is performed by using local tracks. That is, x f (k|k) = x(k|k) and P f (k|k) = P(k|k) at k = 1. It can be seen from Figs. 9d-9f that, for all the local tracks fused estimate is equal to the tracking PRMSE of the initial scan at k = 1. Similar to the single jammer case, we observed that all the local track's fusion PRMSE decreases over time. This indicates that, the deception parameter compensation followed by sequential fusion brings all the fused tracks together. Since the deception parameter is 1000m for local track-1, 1500m for local track-2, and 2000m for local track-3, the sequential fusion PRMSE starts around the same value and finally reduces to minimum value. Henceforth, one can visualize that the local tracks converges to a single track over time, after performing the deception parameter compensation.

3) Deception Parameter Evaluation
The deception parameter of all the local tracks is estimated, and its corresponding PRMSE is plotted in Fig. 10. Initially, the deception parameter is zero, and hence PRMSE at k = 1 is higher and equal to the value of the deception parameter. Along with the estimated deception parameter, we also plotted the √ B − CRLB, √ R − CRLB and √ Σ. Here, we can observe that the estimator is working effectively, and the estimated deception is coming closer to the CRLB value.

4) Estimator Performance Evaluation
To evaluate the performance of the estimator we have considered the similar tests as that of single jammer case. Figs. 11a-11c provides the plots corresponding to the innovation test, whereas Figs. 11d-11f depicts the NEES test, and finally Figs. 11g-11i shows the plots corresponding to the confidence interval test. From the plots, it is evident that the value of the estimated parameter falls within chi-square distribution of 5% tail probability.

VII. CONCLUSION
This paper presents a deception parameter estimation algorithm for countering RGPO ECM in a networked radar scenario. The RGPO attack is detected, and the range gate deception parameter is estimated for the deceived local track. A track-to-track association is formulated at the fusion node to detect the deceived tracks using all the available local tracks. Once the attack is detected, the weight matrix, pseudo-measurement, pseudo-measurement covariance at the fusion center are recreated by utilizing the tracklet framework (using updated state and updated covariance from the local tracker). Moreover, all the local tracks except deceived track is compensated and sequentially fused to create a reference measurement. The deception parameter of the deceived track is estimated by deploying a recursive least squares framework with the help of the pseudo-measurement and reference measurement. Further, the proposed algorithm was analyzed for single and multiple RGPO ECM scenarios and is validated by using tracker accuracy, fusion accuracy, and estimator accuracy. Besides, the estimated deception parameter is in