A Sequential ESM Track Association Algorithm Based on the Use of Information Theoretic Criteria

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1 A Sequential ESM Track Association Algorithm Based on the Use of Information Theoretic Criteria Yifeng Zhou and Jim Mickeal Radar Electronic Warfare Section Defence R&D Canada - Ottawa 371 Carling Avenue, Ontario Canada K1A Z4 Abstract In this paper, a sequential track association algorithm for multiple Electronic Support Measures (ESM) sensors is proposed based on the application of clustering techniques. Association metrics are developed based on the use of the information theoretic criteria, in particular, the Akaike Information Criterion (AIC). The proposed association algorithm is able to handle track components of differing numbers of subcomponents including incomplete and erroneous ones. It has the advantage of not requiring any subjective threshold setting in deciding a nonassociation. Computer simulation and actual ESM processors are used to demonstrate the effectiveness and performance of the proposed association approach. Keywords: ESM, track association, radar, ELINT, theoretic information criteria, AIC, clustering I. INTRODUCTION ESM systems are designed to intercept radar signals and perform emitter classification and identification for electronic warfare (EW) purposes [1]. The extracted signal parameters can be used for threat warning, assisting with radar jamming in tactical situations and collection of electronic intelligence (ELINT) data in strategic situations. Recently, there has been increasing interest in combining information from multiple ESM sensors to provide passive geolocation capability and to enhance target identification performance for command and control systems [2]. The ESM processor output is usually in the form of streamline tracks, where each track corresponds to an emitter detected by the sensor and contains parameters of the emitter such as frequency, PRI and bearing etc.. Inorder to integrate multiple ESM sensor information, tracks produced by different ESM sensors that are from a same emitter must be associated. In this paper, we focus on the problem of associating track for multiple ESM sensors. Unlike radar track association problems where the association is mainly based on positional information of the targets, ESM track association is dependent on measured parameters and attribute information of the emitters, which usually includes declarations and statements about the emitters. There are several difficulties that are encountered in ESM track association. The main difficulty is due to the capability limitations of ESM sensors, which often fail to provide accurate emitter parameters and produce correct attribute information for the emitters, particularly emitters of complex characteristics. In the presence of complex emitters with radio frequency (RF) and pulse repetition interval (PRI) agility, ESM sensors tend to produce multiple tracks representing a single emitter or tracks with incomplete or erroneous RF and PRI components. Imperfect ESM sensors also produce imperfect tracks with low purity factors, which contain pulses from multiple emitters. In addition, since ESM tracks are of different types and contain different types of variables (some are declarations and others are numerical), it is important and difficult to define appropriate metrics for tracks. We will address these difficulties in the proposed track association algorithm. The problem of ESM track association has not received much attention and open literature publications are limited probably because of its classified nature in the past. One of the few techniques of ESM track association surveyed by the authors is the one by Wright [3], which was also discussed and commented on by Hall in his book [2]. This approach is an application of clustering techniques. In his approach, Wight used a measure of correlation, which is a combination of figure of merits for track components, to assess the similarity between a pair of tracks. This approach, however, can only handle tracks with same number of components. It has limited applications for complex signals with frequency and PRI agility. In this paper, we present a sequential ESM track association algorithm based on the use of clustering techniques and the information theoretic criteria. The Akaike Information Criteria (AIC), in particular, is used as the metrics for track association. In the algorithm, ESM tracks are defined to contain several components and each component consists of a number of subcomponents. A track component has a type parameter as well as numerical parameters associated with the type. Clusters are defined to represent the association results. When a track report arrives, matching scores are evaluated for the type parameters of the components for the track and existing clusters. Association metrics are then evaluated for the track and candidate clusters that have non-zero matching scores. Based on the association metrics, an association logic will decide whether the track be associated with one of the candidate clusters or not. The association metrics take into account the special states of tie and unknown of track components. They can handle tracks with differing number of components or subcomponents, a case which also occurs when tracks contain incomplete and erroneous components. Furthermore, the association metrics also have the advantage of not requiring any subjective threshold setting in distinguishing between an association and non-association. To demonstrate

2 the effectiveness and performance of the track association algorithm, a complex scenario that consists of hundreds of emitters and three ESM platforms is simulated. Simulated pulse descriptive words (PDWs) are simulated at the sites of the ESM platforms. Actual ESM processors are used to process the PDWs to generate streamline tracks for track association evaluation purpose. This paper is organized as follows. In Section II, the track association problem is formulated and the format of track reports is discussed. The ESM track association algorithm is described in Section III. In Section IV, we discuss the development of the track association metrics. Finally, in Section V, computer simulations are used to demonstrate the performance and effectiveness of the proposed algorithm. Comparisons with a baseline algorithm are also presented. ESM Sensor 1 track stream ESM Sensor 2 track stream ESM Sensor 3 track stream Figure 1. Cluster Manager cluster 1 cluster 2 cluster 3 new cluster Association Metrics Evaluation Association Logic Block diagram of the association algorithm. II. PROBLEM FORMULATION Assume that M (M = 3 is considered in this paper) distributed ESM sensors are deployed to observe a common signal environment. The environment consists of a large number of emitters. The platforms that carry the emitters include surface or airborne. The environment is mixed with friendly, unfriendly, threat and commercial platforms. The environment contains complex emitters that use agile RF/PRI and waveform modulation techniques. Many of the emitters may have similar signal characteristics such as frequency, PRI and pulse width etc.. The ESM sensors intercept emissions from the emitters, perform deinterleaving and pulse analysis, and produce streams of track reports and updates along the timeline. The objective of ESM track association is to associate track reports and updates from different ESM sensors into groups (or clusters) that represent the same emitters. A. Track Report The track report produced by an ESM processor usually consists of components such as RF, PRI, time-of-arrival (TOA) and pulse width (PW) and bearing of an emitter. It also contains emitter declarations such as track status, component type and antenna scan type etc.. The track report used in this study includes the following components. Identification (ID): a number assigned to a track by the ESM processor. Track State: a track state defines the status of the track. The track status includes active, inactive, gapped, merge and forced etc.. Time of Last Update: The time of last update is the timeof-arrival of the last pulse of the pulse trains on which the track report is based. It is synchronized to the time of arrival. Components: A track contains RF, PRI and PW component. Each component consists of a type parameter and a set of values. The RF type includes constant, agile, hopping unknown and tie while the PRI type can be one of constant, jittered, dwell, modulated, staggered, unknown and tie. A tie means that the processor can not distinguish the component type among the list of known types. The PW type can be either constant or unknown. Subcomponents: Each component may have differing numbers of subcomponents depending on the component type. For example, an RF component of constant type has only one subcomponent while the number of subcomponents of a hopping RF component is equal to the number of hops. The subcomponents are represented by their means, standard deviations and pulse counts that are used to compute the statistics. III. CLUSTERING BASED TRACK ASSOCIATION In this section, we describe the association algorithm. The detailed discussion of association metrics will be presented in the next section. Figure 1 is the block diagram of the association algorithm, where clusters are used to retain the associated tracks from different ESM sensors. Each cluster contains track reports and their updates that are considered to be a same emitter. It includes a list of tracks and a cluster center that represents the fused results of tracks from different ESM sensors. When a new track report from one of the ESM sensors arrives, the association algorithm first evaluates the matching scores for the component type parameters of the track against those of the existing clusters. Association metrics are then computed between the track and candidate clusters that have non-zero matching scores. Based on the association metrics, the association logic decides whether the track be assigned to one of the clusters or a new cluster be formed for it. The association metrics for a track and a cluster are a combination of association metrics for their components, i.e., the matching scores for their type parameters and the computation of similarity measures between the components. The matching scores for the component type parameters are computed based on a probability of agreement between the two types. For a component that has multiple subcomponents, the computation of similarity measures requires the process of subcomponent matching, which decides whether a subcomponent of the track component matches that of a cluster component. The matching is formulated as two-dimensional assignment problem [11] and

3 is solved using a computationally efficient modified auction algorithm. The general procedures of the proposed ESM track association algorithm can be summarized as follows. 1. A track report update is assigned to the cluster that contains track report with the same track ID. The cluster center is updated using the track report update. 2. If the track report is a new report, it will be compared with the existing clusters. First, the component type parameters of the track are compared against those of the existing clusters, and their matching scores are evaluated. If the maximum matching score is zero, then a new cluster is formed for the track; Otherwise, association metrics will be evaluated for the track and the candidate clusters that have non-zero matching scores. Non-association metrics are also calculated under the hypothesis that the track is not associated with any of the candidate clusters. The association logic will decide whether the track be associated with the cluster that has maximum association metric or a new cluster be formed for it. 3. When a track is associated with a cluster, it is applied to update the components of the cluster center. When a track and a track update is associated with a cluster, it is applied to update the associated cluster. The component type parameters of the cluster centers are replaced by those of the track update. For each component, subcomponent matching is performed. Note that the actual implementation of subcomponent matching may not be necessary because the process is already performed in the computation of the association metrics. For matched subcomponents, their means, standard deviations and pulse counts in the cluster center are updated. For subcomponents of the track report that do not match those of the cluster, they are inserted into the cluster center. The updating of the subcomponent of a cluster center is actually a process of recalculating the sample means and variances of each subcomponent. Let X and C k denote a pair of corresponding components of the associating track and cluster, respectively. Let { c k,j, σ 2 c,k,j,n c,k,j} and { x i, σ 2 x,i,n x,i} denote the sample means, variances and pulse counts of the ith and jth subcomponents of X and C k, respectively. Let I k denote the index set of matching subcomponents. The sample means and variances are updated by σ 2 c,k,j = 1 { n (nc,k,j σ 2 c,k,j + n x,i σ 2 x,i) c,k,j +n x,i ( x x,i c k,j) 2 + n c,k,j ( c k,j c k,j) 2}, (1) where the updated pulse count is given by IV. TRACK ASSOCIATION METRICS In this section, we discuss the association metrics for assigning a track to a cluster. The metrics are a combination of association metrics for all the components of the track. For a track component, the computation of association metrics includes the computation of matching scores for the type parameters, subcomponent matching and similarity measures between subcomponents. A. Matching Score for Track Components Matching scores are defined for the type parameters of a pair of track components to measure how close the two track components are in terms of their types. A track component type parameter is similar to a categorical or nominal variable in the context of clustering [4]. A categorical variable comprises a set of mutually exclusive discrete states such that it can only take one state at a time, and has no ordering on different states. However, the type parameters of track components are slightly different in that they contain, besides a set of mutually exclusive states, the special states of tie and unknown, where the state of tie is not mutually exclusive with the rest of the states, and the state of unknown is an imprecise state. There are several measures that can be used to measure the similarities between two nominal variables. They include the simple matching coefficient, the Jaccard s coefficient, the Gower s coefficient and the measure of agreement [4] [5]. However, these measures are only applicable to nominal variables with mutually exclusive states and are not capable of handling the non-exclusive states of tie and unknown. In the following, we propose a matching score that can take into account the special states of tie and unknown for measuring the similarities between the type parameters of a pair of track components. Let X denote a track component. The number of mutually exclusive states that the type parameter of X may fall into is denoted by s x. Define a state vector, η x, of length given by s x. When the type parameter of X falls into one of its exclusive states, the corresponding field of the state vector is set to 1; otherwise, it is zero. When the type parameter of X is tie, all the fields of η x are set to 1/s x, implying that the type parameter of X can take any of the mutually exclusive states equally. When the type parameter of X is unknown, all the fields of the state vector are set to zeros, meaning that the knowledge is imprecise and no decision on matching should be made. The values of the state vector can be interpreted as probabilities that the type parameter falls into the corresponding states. Define C k as a component of the kth cluster. The number of mutually exclusive states that the type parameter of C k mayfallintoisgivenbys c,k.letη c,k denote the state vector for the type parameter of C k. The matching score for X and C k is defined as P (X, C k )=η T x η c,k, (2) where {i, j} I k. n c,k,j = n c,k,j + n x,i which can be verified to lie in the range of [, 1]. We can interpret P (X, C k ) as the probability that the type parameters of X and C k fall into the same state. The overall matching

4 score for all the components of a pair of track and cluster can be evaluated as a product of the matching scores for each component by assuming that their type parameters are detected independently. A cluster and a track are said to match if the overall matching score is non-zero; otherwise, it is a nonmatch. B. Subcomponent Matching When a track matches a clusters, their components need to be compared and similarity measures be evaluated. However, when a component has multiple subcomponents, we need to match the subcomponents of the track with those of the cluster. As shown previously, subcomponent matching is also required when updating the cluster centers. Subcomponent matching is necessary because a track component may be incomplete contain erroneous subcomponents due to limitations of ESM processors. We formulate subcomponent matching as a two-dimensional assignment problem [11], where a subcomponent of a track component is assigned to either one subcomponent of the cluster component or a dummy according to a minimized cost criterion. The dummy is added to a cluster component to represent the state of no matching. A subcomponent assigned to the dummy means that it does not match any subcomponents. A modified auction algorithm is used for solving the assignment problem. The cost of matching a pair of subcomponents is defined based on the information theoretic criteria, in particular, the Akaike information criteria (AIC) [7]. The information theoretic criteria take into account both the goodness-of-fit (likelihood) of a model and the number of parameters used to achieve that fit. Denote I and J k as the numbers of subcomponents of a track and a cluster component, respectively. Let x i and c k,j be the ith and j th subcomponents of the track and the kth cluster, respectively. Let X = {x i ; i = 1, 2,...,I} and C k = {c k,j ; j =, 1, 2,...,J k },wherec k, denotes the dummy subcomponent. The pulse counts for x i and c k,j are denoted by n x,i and n c,k,j, respectively. Let { x i, σ x,i 2 } and { c k,j, σ c,k,j 2 } denote the sample means and variances of x i and c k,j, respectively. The cost that x i matches c k,j is defined as the AIC under the hypothesis that they share a common mean. Under the Gaussian assumption, it can be verified that the AIC is given by a ij = n c,k (ln 2π +lnˆσ 2 +1)+ξ ij (ln n c,k +1), (3) where ξ ij = J k +1 is the number of adjustable parameters and ˆσ 2 = 1 n c,k,j σ n c,k,j, 2 c,k j The same procedures are repeated for i =1, 2,...,I and j = 1, 2,...,J k to obtain all combinations of i and j. Thecost that x i matches the dummy in C k is given by the AIC under the hypothesis that x i does not match any subcomponents of C k, which can be computed using (3) by letting j =and using the variance estimate ˆσ 2 = 1 (n c,k,j σ c,k,j 2 + n x,i σ n x,i). 2 c,k j Note that the number of free adjustable parameters becomes ξ i = J k +2. The subcomponent matching is formulated as a 2-D assignment problem, which is to find the optimum α ij, i =1, 2,..., and j =, 1, 2,...,J k that minimizes the following min α ij α ij a ij, (4) ij subject to J k j= α ij =1,i=1, 2,...,I,whereα ij = {, 1} and a, =. The optimization (4) can be solved by using the modified auction algorithm described as follows. First, the matching costs are modified as a ij = a ij + a i for i =1, 2,...,J k and any subcomponent pairs with negative costs will be discarded. Define the subcomponents of the track and the cluster components as bidders and objects, respectively. Each bidder bids for a best object that provides the bidder with maximum profits. The auction algorithm iterates over unassigned bidders and terminates when either all the bidders are assigned or the objects have received bids. In the context of subcomponent matching, unassigned track subcomponents are assigned to the dummy of the cluster component, and, similarly, unassigned cluster subcomponents are assigned to the dummy of the track component. Unassigned cluster subcomponent means that either the cluster component has erroneous subcomponents or the track component is incomplete. If both the track and cluster components are singleton, i.e., both contain only one subcomponent, the matching process reduces to a simple test that compares the association and non-association costs. The subcomponents associate when the association cost is less than the non-association cost; otherwise, they are not associated. C. Association Metrics for Track Components After the subcomponents are matched, the association metrics for the components will be evaluated. The association metrics are based on the application of the AIC and are used to quantify the similarity measures between a pair of track components. Assume that there are K candidate clusters and a track is associated with the k th cluster. Let m k denote the number of matching subcomponents of C k. Under a Gaussian assumption and the hypothesis that x i is associated with C k, the AIC is given by AIC(X, C k )=N(ln 2π +lnˆσ 2 +1)+ξ k [ln N +1], (5) where

5 ˆσ 2 = 1 N + k,k k j,j I k n c,k,j σ c,k,j 2 + j i,i/ I k n x,i σ 2 x,i n c,k,j ˆσ2 c,k,j, (6) and ξ k = k j J k,j +(I m k )+1 is the number of free adjustable parameters under the hypothesis. The association metrics for a pair of track/cluster components combines the matching score 2lnP (X, C k ) AIC(X, C k ). (7) The non-association metric is evaluated under the hypothesis that X is not associated with any of candidate clusters. It can be verified that the non-association AIC is also given by (6) letting k =, where the variance is estimated by ˆσ 2 = 1 n z,k,j σ z,k,j 2 N + n x,i σ 2 x,i, k j i and ξ = j J k,j + I +1. D. Association Metrics for Track and Clusters The overall association metrics for associating a track and a candidate cluster are evaluated based on the metrics for each component, and are obtained by averaging the metrics for all the components. The non-association metric is also averaged for all the components. The association logic compares the AIC association and non-association metrics and searches for the minimum one. It associates the track with the cluster that has the minimum AIC association metric. If the nonassociation metrics turn out to be the minimum, the association logic will form a new cluster to contain the track. V. PERFORMANCE ANALYSIS Computer simulations are used to demonstrate the performance of the proposed ESM track association algorithm. The testbed consists of three ESM sensors: two shipborne and one airborne. In the scenario, about 3 emitters were simulated, which includes ships and aircraft. Both complex and simplex emitters were simulated with a large number of th emitters having similar parameters (navigation radars). Emitter PDWs are computed at the ESM platform sites and antenna/receiver models were applied. Isotropic antennas were used in the model. The receiver sensitivity was set to be 7 dbm. In the receiver model, Gaussian distributed noises with zero means and pre-set variances were added to the detected PDWs to simulate the receiver noise. The variances used by the receiver model are listed in Table I for each frequency band. Performance measures were developed for evaluating the effectiveness of the track association algorithms, which include cluster purity, collective score, detected emitter ratio and fragmentation ratio. Cluster Purity is the ratio of the peak to total pulse count of each cluster. The collective score is a Table I STANDARD DEVIATIONS FOR RECEIVER MODEL PARAMETERS RF Bearing TOA PW Power Band (MHz) (degrees) (ns) (ns) (dbm) 1 (1-2) GHz (2-6) GHz (6-12) GHz (12-18) GHz weighted sum of constructed track ratio, correct correlation, cluster purity and ambiguity (percent of pulses lost). The smaller the collective score, the better the performance. The detected emitter Ratio is the ratio of the number of correlated cluster to the total number of ground truth emitters. A value of 1 is ideal. Finally, the Fragmentation Ratio is defined as the ratio of the number of clusters that are not correlated to any ground truth cluster to the total number of clusters. The evaluation of the performance metrics requires a correlation of the clusters and the ground truth emitters. However, since real ESM processors with imperfect deinterleaving are used, the output track reports are not pure, i.e., each track report often contains pulses from more than one emitter. Obviously, impure track reports will result in impure clusters. In the presence of impure clusters, correlating a cluster with an emitter becomes a non-trivial task. We proposed an algorithm for correlating tracks and clusters with ground truth emitters based on a peak pulse count principle. Clusters that contain peak pulse counts corresponding to the same ground truth emitter are considered as fragmented. Among them, the cluster that has the maximum pulse count is correlated with the ground truth emitter, and the rest are considered not correlated with any of the ground truth emitters. A baseline algorithm based on the use of statistical distance measures is implemented for comparison [1]. Figure 2 shows the pulse count distribution of the emitter clusters versus the ground truth pulse index. For each cluster, the pulse counts of the ground truth emitters that are contained in the cluster is plotted. It can be seen that, due to the imperfectness of the ESM processors and the track association algorithm, the clusters contain pulses from more than one emitter, and pulses from one ground truth emitter are scattered into more than one cluster. Table II lists some of the performance metrics for the proposed and the baseline algorithm, which include cluster purity, the collective score, detected emitter ratio and fragmentation ratio. From the table, it can be seen that the proposed algorithm has better track purity and detected emitter ratio than the baseline algorithm. However, its fragmentation is slightly higher than that of the baseline algorithm, which in turn results in a slightly higher collective score. It should be the noted that the baseline algorithm requires subjective threshold settings, which is usually difficult in practice. Figure 3 is a cluster purity comparison for the proposed and the baseline algorithm. In the figure, the number of clusters that contain a specific number of ground truth emitters

6 3.5 x Proposed algorithm Alternate algorithm Pulse count Number of clusters Ground truth emitter index Cluster index Ground truth emitter count Figure 2. Cluster pulse count versus ground truth emitters. Figure 3. Distribution of clusters versus the number of ground truth emitters. Table II PERFORMANCE OF THE ASSOCIATION ALGORITHMS Proposed algorithm Baseline algorithm Cluster Collect. Detected Frag. Purity Score Track Ratio Ratio Proposed Baseline is counted, and plotted versus the number of ground truth emitters. The number of ground truth emitters corresponding to cluster count zero represents the number of emitters that are not detected by any ESM sensor. The proposed algorithm is shown to be able to produce more emitter clusters that contain one and only one ground truth emitter. Figure 4 is a track count histogram comparison. The figure shows the distribution of clusters that contain differing numbers of tracks for the two algorithms. It can be seen that the proposed algorithm produced more clusters that contain only one track, meaning that the proposed algorithm is more likely to form a new cluster to contain tracks. The total of number of clusters that contain two or three tracks are similar for both algorithms. VI. CONCLUSIONS In this paper, a sequential track association algorithm has been presented for multiple ESM sensors based clustering techniques and the application of the information theoretic criteria. The algorithm is capable of handling incomplete and erroneous track subcomponents and does not require any subjective threshold setting. A complex signal environment was simulated and actual ESM processors were used to produce track streams for demonstrating the performance of the proposed association algorithm. Performance metrics were proposed and it was shown that the proposed algorithm was able to produce reasonably good results when applied to imperfect tracks obtained from actual ESM processors with imperfect deinterleaving capabilities. The association results were also compared with a baseline algorithm based statistical distance measures. It was shown that the proposed algorithm Number of clusters Track count Figure 4. Track count histogram comparison. outperformed the baseline algorithm in terms of track purity. However, it had a slightly higher fragmentation track ratio than the baseline algorithm. It should be noted that the baseline algorithm requires subjective threshold settings in order to achieve the optimal performance. REFERENCES [1] R.G.Wiley,Electronic Intelligence: The Analysis of Radar Signals, 2nd Ed., Artech House, Norwood, MA, 1993 [2] D. L. Hall, Mathematical techniques in multisensor data fusion, Artech House, Norwood, MA, 1992 [3] F. L. Wright, The fusion of multi-source data, Signal, vol. no. pp , October 198 [4] M. R. Anderberg, Cluster Analysis for Application, Academic Press, New York, 1973 [5] A. D. Gordon, Classification: Method for the exploration analysis of multivariate data, Chapman and Hall, New York, 1981 [6] D. P. Bertsekas, Auction algorithms for network flow problem: A tutorial introduction, Computational Optimization and Applications, vol. 1, pp. 7-66, 1992 [7] H. Akaike, A new look at the statistical model identification, IEEE Trans. AC, vol. 6, pp , 1974 [8] J. Rissanen, Modeling by the shortest description, Automatica, vol. 14, pp , 1978

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