The PHD Filter for Extended Target Tracking With Estimable Extent Shape Parameters of Varying Size

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1 The PHD Filter for Extended Target Tracing With Estimable Extent Shape Parameters of Varying Size Anthony Swain and Daniel Clar EECE EPS Heriot Watt University Edinburgh UK and Abstract In extended target tracing targets potentially produce more than one measurement per time step. In recent random finite set RFS approaches the set of measurements obtained from an extended target is modelled as a point process. In this paper we expand on the RFS approach to extended target tracing by considering a hierarchical point process representation of multiple extended target more specifically a Poisson cluster process. This allows us to impose a geometric shape in particular an ellipse on each extended target. The set of target states which are characterised by the inematic variables and the shape parameters represents the higher level parent process and the set of points on the boundary from which measurements are generated represents the lower level daughter process. We describe the PHD filter for multiple extended targets whose extents vary in size that estimates the shape parameters of the targets jointly with their positions and velocities. The main contribution of this paper is the practical implementation we propose based on a particle-system representation for the targets shape and a Gaussian mixture formulation for the inematic state per particle. The method is demonstrated on simulated data for multiple elliptical shaped extended targets. Keywords: random finite sets PHD filters cluster processes Gaussian mixture. I. ITRODUCTIO The random finite set RFS approach to multi-target tracing has proven to be a useful method that allows the problem of estimating multiple dynamic targets in the presence of false measurements and detection uncertainty to be cast in a Bayesian filtering framewor [1]. By treating the collection of individual targets as a set-valued state and the collection of observation measurements as a set-valued observation this theoretically optimal approach is an elegant generalisation of the single-target Bayes filter. However the propagation of the posterior probability distribution in the multi-target Bayes filter is often computationally unattainable due to the high dimensionality of the target RFS. To overcome this intractability the Probability Hypothesis Density PHD filter was introduced [1] which propagates the first-order moment otherwise nown as the intensity. The PHD filter is typically implemented using a particle representation applying sequential Monte Carlo SMC techniques [2] [3] or with a Gaussian mixture formulation [4] [6] and has applications in radar [7] computer vision [8] and acoustics [9] to name but a few. In most applications including the PHD filter it is assumed that each target produces at most one measurement per timestep. In extended target tracing targets potentially produce more than one measurement per time-step. Multiple measurements per target per time-step gives rise to the possibility of estimating the target s shape and size in addition to its position and velocity. An extension of the PHD filter to handle extended targets was presented in [1] recently implemented using a Gaussian mixture formulation [11] which involved representing the measurements generated from targets as a spatial point process [12] specifically a Poisson point process. That is at each time-step a Poisson distributed number of measurements are generated spatially distributed around the target. Such a measurement model implies the target generated measurements resemble a cluster of points rather than a geometrically structured arrangement. A number of methods based on the RFS approach have been proposed for estimating the size and shape of a target [13] [14]. In [13] a direct application of the Gaussian mixture PHD filter for extended targets [11] is presented in which a method is proposed for calculating a lielihood function that relates a set of measurements potentially to a target whose structure resembles that of a rectangle or an ellipse. In [14] a partitioned state representation of an extended target is considered which consists of linear position & velocity and non-linear heading & target shape parameters components. The PHD filter is applied for jointly estimating this target state and a set of measurement generating points defined on the boundary of each target s geometrically structured shape rectangle and implemented using a Rao-Blacwellized particle filter as demonstrated for the Simulation Localisation and Mapping SLAM problem in [15]. Other proposed approaches for extended target size and shape estimation include a Random Hypersurface Model method [16] that assumes varying measurement sources which lie on scaled versions of shape boundaries and a novel SMC approach [17] that considers target generated measurements bounded by a circular region which is estimated jointly with the target s inematic state. In this paper we consider an alternative approach whereby multiple extended targets are modelled as a hierarchical point process as proposed in [18]. Hierarchical point processes nown as cluster point processes have been previously exploited in the group target tracing problem [19] [2] the SLAM problem [21] and more recently in sensor registration 1111

2 [22]. In this paper we specifically consider a Poisson cluster point process representation of multiple extended targets which allows us to impose a geometric shaped extent on each target where the centres of each target s extent represent the higher level parent process on which a dynamic model can be specified and the set of points on the boundary of each target s extent represents the lower level daughter process from which the measurements are generated. In the PHD filter for this approach to extended target tracing the inematic states and the shape parametric variables are estimated jointly via the first-order moment. The remainder of the paper is organised as follows: Sections II and III present the proposed methodology and implementation. The PHD recursion in Section II can easily be derived using a general chain rule and Gateaux differentials [23] [25]. Section IV details a multiple extended target tracing example whose extents are elliptical in shape and vary in size over time. The estimation results from the PHD filter implementation for this example using simulated data are then discussed followed by concluding remars in Section V. II. EXTEDED TARGET TRACKIG USIG CLUSTER PROCESSES In this wor we model multiple extended targets whose extents have a geometrically shaped structure and vary in size as a doubly-stochastic point process. In particular we suppose the multiple extended targets have a Poisson cluster process representation defined by X {X 1 Ξ 1...X n Ξ n } where for i 1...nthe state X i [ ] T x i s i consists of the random vector x i defining the inematic state and the random vector s i defining the shape parameter variables for target i. TheRFS Ξ i { 1... ni } represents the points on the boundary of the extent for target i. Theparent process is represented by the RFS of target states X i with which there corresponds a daughter process represented by the RFS Ξ i conditioned on X i fori 1...n. In addition we consider a measurement model defined by the RFS Z that taes into account detection uncertainty and false measurements clutter and is formed by the union of target generated measurements Θ X and clutter K i.e. Z K Θ X. 1 In recent RFS approaches [1] [11] [13] [14] the set of false measurements K is modelled as a Poisson point process the probability density for which is p K exp λz dz λz 2 z K where λz is the intensity of the clutter process. An integral part of extended target tracing with the PHD filter is the partitioning of the measurement set. A partition π is defined as a division of the RFS Z into subsets denoted as φ such that φ π φ Z. We denote the set of all possible partitions of Z as Π Z. To assist the partitioning operation instead of the false measurement model given by the probability density in 2 we model K as a Poisson cluster point process the probability density for which is p K exp λ 1 u φκ du φκ λ 1 u φκ φ κ exp λ 2 z u φκ dz λ 2 z u φκ κ 3 where λ 1 u φκ is the intensity of the parent process whose state u φκ is the centroid of the measurements in subset φ κ and λ 2 z u φκ is the intensity of the daughter process. With the clutter process modelled in this way the assumption is that the measurements appear in clusters. Let p X Z 1: be the posterior probability distribution of the Poisson cluster process representation of the multiextended target state X given a time sequence of measurement sets denoted by Z 1: Z 1...Z. The Bayesian filter recursion for estimating the posterior p X Z 1: involves computing set integrals [26] due to the RFS of target states X i representing the parent process as well as the RFS definition of Ξ i for i 1...n. The set integrals in this recursion involve multiple infinite sums over all possible posterior distributions at different cardinalities in the parent and daughter processes which maes implementing the Bayes filter computationally intractable for variable numbers of targets X and corresponding boundary points. Instead we propagate the first-order moment approximation of the posterior p X Z 1: an approach proposed for multi-target tracing under the name of the Probability Hypothesis Density PHD filter in [1]. The PHD filter for multiple extended targets modelled as a Poisson cluster process with geometric shaped target extents jointly propagates the inematic state and shape parametric via the first-order moment or intensity. Throughout the PHD filter recursion the propagation of the inematic state will depend on the shape parametric since the RFS Ξ of boundary points from which measurements are generated updating the inematic state are partly determined by the shape parameters. Therefore the joint prior PHD can be factorized as follows M 1 s x M 1 s M 1 x s 4 where M 1 s M 1 s 1 is the intensity of the shape parametric and M 1 x s M 1 x 1 s 1 is the intensity of the inematic state. ow suppose that the targets positions and shapes evolve independently of one another so that dynamics can be factorized as f 1 X X f 1 s s f 1 x x where f 1 s s is the Marov transition density for the shape parametric and f 1 x x is the Marov transition density for the inematic state. This is representative of a scenario in which the targets shape parametrics do not include the orientations of the shapes which are instead determined by the targets velocities that are incorporated into the inematic state. The PHD prediction equation is then M 1 s x M 1 s M 1 x s

3 where the predicted intensity of the shape parametric is M 1 s M 1 s f 1 s s ds 6 where the predicted intensity of the inematic state is M 1 x s γ x s+ p S x f 1 x x M 1 x sdx 7 and γ x s is the intensity for birth targets. The probability of survival p S x is also assumed to be shape independent. Given a new set of measurements Z and under the assumption that the daughter process can be approximated with a Poisson point process the PHD update equation is M s x L Z s x M 1 s M 1 x s LZ s x M 1 s M 1 x sds dx where the joint pseudo-lielihood is L Z s x e μ[1 sx] + ω π π Π Z φ π with partition weight given as Λφ+M 1 [Υ φ ] ω π φ π π Π Z φ π 8 Υ φ s x Λφ+M 1 [Υ φ ] 9 Λφ +M 1 [Υ φ ] 1 given the following denotations μ[1 s x] μ s x d M 1 [Υ φ ] Υ φ s x M 1 x s dx 11 Υ φ s x exp μ s x d μ s x l z x d for daughter process intensity μ s x and singlemeasurement lielihood l z x. The clutter term is given by Λφ λ 1 u φ e λ2[1 uφ] λ 2 z u φ 12 for false measurements modelled as a Poisson cluster process whose probability density is defined by 3. The lielihood L Z s x updates both the shape parametric s and inematic state x and involves the summation over all possible partitions Π Z of the measurement set. The number of partitions Π Z for a measurement set of size Z n equates to the nth Bell number B n for n respectively. Consequently the operation of summing over all possible partitions in 9 is very computationally demanding. If a single partition denoted as π is nown the joint pseudo-lielihood reduces to L Z s x e μ[1 sx] + φ π Υ φ s x Λφ+M 1 [Υ φ ]. 13 The study into appropriate partitioning methods is beyond the scope of this paper. However we assume for the remainder of the paper that such a partition π exists for each measurement set. Finally the presence of the lone exponential term in 13 can be accounted for by the Poisson point process approximation of the daughter process and the possible occurrence of an empty measurement set attributing to missed detected targets. Hence this term can be regarded as the probability of missed detection which for a daughter process with Poisson rate greater than 3 is less than.5 and can be interpreted in the following way that the more boundary points on a target s extent the more measurements are liely to be generated resulting in a low probability of missed detection. III. IMPLEMETATIO We implement the PHD filter for the multiple extended target model described in Section II using a Dirac mixture model for the intensity of the target shape. Each component of this mixture model has associated with it a Gaussian mixture formulation for the intensity of the inematic state conditioned on that particular shape component. At each iteration of the filter we start with the following prior intensities M 1 s 1 i1 j1 π i 1 δs si 1 14 i J 1 M 1 x s i 1 ω j i 1 x si 1 ; mj i 1 Pj i The notation x ; m P is used to denote a Gaussian distribution with mean vector m and covariance matrix P and δs denotes the Dirac delta distribution centred at s. The mixture in 14 defines a particle representation of M 1 s which can be expressed as the set of weighted particles {π i 1 si 1 } 1 i1. A. Gaussian mixture formulation Following the derivation of the Gaussian mixture PHD filter for single measurement targets in [4] and the single-group PHD filter in [2] a Gaussian mixture formulation can be attained for the predicted intensity of the inematic state in 7 and the updated intensity of the inematic state defined by M x s i L Z s i x M 1x s i 16 where L Z s i x is the joint pseudo-lielihood given in 9 for each particle s i. 1113

4 For the predicted intensity M i Gaussian dynamic model given by 1 x we assume a linear f 1 x x x ; Fx Q 17 where F is the state transition matrix and Q is the process noise covariance matrix. In addition suppose the probability of survival is state independent i.e. p S x p S and the intensity for the birth targets is a Gaussian mixture of the form γ x s i i γ J j1 ω j i γ x si ; mj i γ Pj i γ 18 where J i γ ωj γ mj i γ and P j i γ for j 1...J i γ are given model parameters that determine the shape of the birth intensity for a particular particle i. The prediction for the inematic state is then the same as that for the standard Gaussian mixture PHD filter M 1 x s i i J 1 j1 ω j i 1 x si ; mj i 1 Pj i 1 where for birth targets we have ω j i 1 ωj i γ mj i m j i γ Pj i γ for persistent targets 1 Pj i ω j i 1 p S ω j i 1 m j i 1 Fmj i 1 Pj i 1 FPj i 1 FT + Q and J i i i 1 J γ + J 1. For the updated intensity M x s i given in 16 we assume a separable linear Gaussian single-measurement lielihood given by l z x z ; H R 1 z ; Ĥx R 2 21 where z ; H R 1 is the lielihood that the measurement z is related to the point on the boundary of the target s shape with projection matrix H and observation noise covariance matrix R 1 and z ; Ĥx R 2 is the lielihood that the measurement z relates to the state vector x with projection matrix Ĥ and observation noise covariance matrix R 2. In addition suppose the intensity of the daughter process is a mixture of conditional Gaussian functions of the form μ s i j i J x l1 υ l si ; ml ij 1 Pl ij 1 22 where the mean and covariance are given by 1 m l ij 1 ml ij + P l ij 12 P j i 1 x m j i 1 1 T P l ij 1 Pl ij 11 P l ij 12 P j i 1 P l ij The Gaussian components in 22 are conditional Gaussian [ realisations from joint Gaussians with mean m l ij matrix m j i 1] T and covariance given by the bloc for j 1...J i 1 P j i 1 m l ji Pl ij 11 P l ij 12 P l ij 12 T P j i 1 24 and l 1...Jj i where m j i are the predicted means and covariances from 19 1 P l ji 11 are the means and covariances from the corresponding marginal Gaussian for the daughter process and P l ji 12 are the covariances that describe the relationship between parent and daughter. As a consequence of the Gaussian mixture formulation for the daughter intensity in the joint pseudo-lielihood given in μ[1 si 13 we have e x] e α denoting the expected j i J number of boundary points as α l1 υl and in Υ φ s x we have μ[l z s i x] z ; Ĥx R 2 J j i υ l z si ; Hml ij 1 R l ij 25 l1 where for brevity we denote R l ij HP ȷ ı ij 1 HT + R 1. This product of Gaussian mixtures can be expanded for ȷ ı 1...J j i and ı 1... φ to give the following sum of Gaussian products ȷ 1... ȷ φ φ ı1 υ ȷ ı z ı ; Ĥx R 2 z ı s i ; Hm ȷ ı ij 1 R ȷ ı ij. 26 ow for further brevity we denote ȷ 1... ȷ φ then the measurement update for the inematic state is M x s i φ π J i 1 j1 e α M 1 x s i + 27 ω ȷ1: φ j i φ x s i where for 1 ı φ the means m ȷ1: ıj i in the Gaussian components are P ȷ1: ıj i m ȷ1: ıj i P ȷ1: ıj i ; mj i P j i and covariances m ȷ1: ıj i + K ȷ1: ıj i z ı Ĥ m ȷ1: ıj i I K ȷ1: ıj i Ĥ P ȷ 1: ıj i

5 P ȷ1: ıj i and K ȷ1: ıj i the Gaussian components are ω j i φ where Ĥ T Λφ+ J i 1 φ L j i s i υ ȷ ı ı1 S ȷ ı ij 2 1. The weights of ω j i 1 e α L j i s i ω j i j1 1 e α L j i s i q ı ȷ1: ıj i 1 z ı s i 29 q ı ȷ1: ıj i 2 z ı s i in which we have q ı ȷ1: ıj i 1 z ı s i z ı s i ; b ȷ1: ı ij 1 S ȷ1: ı ij 1 q ı ȷ1: ıj i 2 z ı s i z ı s i ; Ĥ m ȷ1: ıj i 1 and denoting A ȷ ı ij HP ȷ ı ij 12 P 1 j i b ȷ1: ı ij 1 Hm ȷ ı ij S ȷ1: ı ij 1 A ȷ ı ij Σ ȷ1: ıj i + A ȷ ı ij η ȷ1: ı ij S ȷ1: ı ij ȷ1: ıj i 2 Ĥ P Ĥ T + R 2. Furthermore for 1 ı φ m ȷ1: ıj i η ȷ1: ı ij + I where P ȷ1: ıj i K ȷ1: ıj i η ȷ1: ı ij Σ ȷ1: ıj i 3 S ȷ1: ı ij 2 31 m j 1 A ȷ ı ij T + R ȷ ı ij K ȷ1: ıj i z ı b ȷ1: ı ij 1 ȷ1: ıj i K A ȷ ı ij Σ ȷ1: ıj i Σ ȷ1: ıj i A ȷ ı ij T 1 S ȷ1: ı ij 1 and { m j 1 for ı 1 m ȷ1: ı 1j i for 1 < ı φ { j P 1 for ı 1 P ȷ1: ı 1j i for 1 < ı φ. 34 The resulting mixture in 27 has J i i 1 + π J 1 φ J j i components and left uncheced the size of the parent process mixture would grow at an approximately exponential rate with every time step. Many of these come from low-lielihood measurement associations and contribute little to the updated intensity in 27. There are a couple of Gaussian mixture reduction procedures we employ to then eliminate and merge such low-weight components. The first is a measurement gating procedure as described in [27] which we apply to determine how many boundary points are related to measurements z φ for each φ π hence reducing the number of components in the mixture within the product given in 25. The other procedure is the pruning and merging one presented in [4]. Applying both procedures help maintain a more manageable approximation of the inematic state intensity. B. Particle representation To implement the Gaussian mixture formulation in Section III-A we sample 1 particles from the Marov transition density for the particle representation of M s i.e. for i sample s i π 1 s s i 1. The weights of the Dirac mixture can be updated then as follows π i 1 i1 L Z s i πi L Z s i 1 35 where L Z s i can be determined from the updated intensity for the process L Z s i e α J i 1 j1 ω j i 1 + φ π J i 1 j1 ω ȷ1: φ j i φ 36 such that ω j i φ is as defined in 29. A resampling procedure is then applied which maes copies of particles { π i si } 1 i1 and eliminates low-weighted particles to give {π i si } i1. IV. SIMULATED EXAMPLE The methodology and implementation detailed in Sections II & III apply to extended targets with any structural shape in general. In this section we present a multiple extended target tracing example in which the extents are specifically elliptical in shape that the proposed implementation has been tested on using simulated data. The generated target trajectories are shown in Fig. 1 along with the elliptical shapes parameterized by the major and minor axes which gradually reduce in size over 1 iterations for each target. The target trajectories are also shown plotted against time along with the simulated measurements in Fig. 2. In the following subsection we first provide precise details of the simulation set-up before presenting the simulation results in Section IV-B. A. Set-up The target state X consists of the inematic state variable x [ x 1 x 2 x 3 x 4 ] T 37 where [ ] T x 1 x 3 is the position vector centre of the ellipse and [ ] T x 2 x 4 is the velocity vector at time-step and shape parametric variable s [ s 1 s 2 s 3 s 4 ] T 38 where s 1 is the magnitude of the major axis and s 3 is the magnitude of the minor axis of the ellipse while s 2 & s 4 are the rates of change in the major and minor axes magnitudes respectively. Targets follow the linear Gaussian dynamic model 17 with [ ] F F 2 Q σ 2 F x 2 Γ Γ T

6 y coordinate in m 3 2 y coordinate in m 3 2 y coordinate in m x coordinate in m x coordinate in m x coordinate in m a Trajectory 1 b Trajectory 2 c Trajectory 3 Figure 1: The multiple target trajectories line and size varying elliptical extents. Starting positions are indicated by the blue filled diamonds at times a 1b 26c 51and terminal positions are indicated by the blue filled squares at times a 1 b 125 c x in m y in m Figure 2: Measurements green and target trajectories line. such that F [ ] 1 τ Γ 1 [ / ] τ 2 T 2 τ τ 2/ 4 2 τ where 2 denotes the 2 2 zero matrix τ 1sisthesampling period and σ x 2 m/s 2 is the standard deviation of the process noise. The probability of survival is p S.9. The point measurements z [ ] T z 1 z 2 Z relate to points on the ellipse according to the lielihood z ; H R 1 in 21 with H I 2 and R 1 σ1i 2 2 where σ 1 5m. They relate to the target state x according to the lielihood z ; Hx R 2 in 21 with [ ] 1 Ĥ 41 1 and R 2 σ 2 2I 2 where σ 2 5m. The average number of observed points on the ellipse is α 5. The clutter term in the PHD update is given by 12 with λ 1 u φ κ 1 Uu φ and λ 2 z u φ κ 2 z ; u φ R κ where Uu φ is the uniform density over the observation region κ 1 2is the average number of false measurement clusters over the region κ 2 1 is the average number of measurements per cluster and R κ 5 I 2. The filter is initialised with the birth intensity γ x s i at time-step 1. Birth targets are measurement driven a technique applied for the PHD filter in [28]. That is in 18 for measurements in each cluster subset φ π and j 1...J i i γ where J γ π wehave m j i γ [ 1 φ z 1 1 φ T z 2 ] 42 with covariance P j i γ σ2i 2 4 and weight ω j i γ.1 for each particle i. The sampling distribution for the particle representation of a target s shape is a linear truncated Gaussian. That is 1116

7 x m 2 x m 2 x m y m 2 y m 2 y m Figure 3: Position estimates blue circles uncertainty grey shaded area and target trajectories line Major axis m Major axis m Major axis m Minor axis m Minor axis m Minor axis m Figure 4: Shape estimates blue circles uncertainty grey shaded area and true shape variation line. for persistent targets we sample s i f 1 s s i 1 s ; Fs i 1 Q such that s i lies within the interval a b where a [ ] T [ b ] T 43 F is as defined in 39 and Q Γ Σ s Γ T Σ s diag[σ 2 s1σ 2 s2σ 2 s3σ 2 s4] 44 for σ s1 2m σ s2.2m σ s3 1m σ s4.1m and Γ as defined in 4. For new targets we sample c i [ ] T c i 1 c i 2 c ; bnew Σ new such that c i lies within the interval a new b new where a new [ ] T bnew [ ] T & Σnew diag[σs1σ 2 s3] 2 so that we have s i [ T c i 1 c i 2 ]. Finally the daughter process for each particle i and inematic state j has the conditional Gaussian mixture form given in 22 with J j i α υ l 1 m l ij P l ij Ĥmj i 1 + tl ij 1 12 βσ 1 P j i 1 Pl ij 11 R P j i for all l 1...J j i where t l ij 1 [ s i 1 cosθ lcosφ j i 1 + si 3 sinθ lsinφ j i 1 1 s i 1 cosθ lsinφ j i 1 si 3 sinθ lcosφ j i 46 given θ l 2πl/α φ j i 1 arctanmj i 14 /mj i 12 denoting m j i 1n as the nth element of mean vector m j i 1 and P j i 1 n m as the n m element of the covariance matrix P j i 1. Finally we set β.4 where β 1 relates to the correlation between parent and daughter. B. Results The estimation results shown in Fig. 3 & 4 are from a simulation run with 5 particles for each target. Tracs are maintained by labelling each corresponding particle set. The state and error estimates are obtained by applying a similar clustering technique as demonstrated in [28] whereby the weights and means within the sum φ π in 27 are re-indexed as ω n i φ and m n i φ for n 1... φ where φ J i j i 1 φ J. Then for each cluster subset φ we compute W φ 1 φ i1 n1 ωn i φ and if W φ T for some threshold T we calculate the position and shape ] 1117

8 estimates respectively as ˆm φ 1 i1 φ n1 ω n i φ mn i φ ŝ φ 1 i1 and the corresponding errors are calculated as ˆP φ ŝ err φ 1 i1 φ n1 +m n i φ 1 i1 φ n1 ω n i φ P n i φ φ n1 ω n i φ ˆm φ m n i φ ˆm φ T ω n i φ si ŝ φ s i ŝ φ T si From the early simulation trials it can be seen in Fig. 3 & 4 that the extracted estimates for both position and shape parameters are accurate even when the uncertainty is high. The exception being when the targets approach the perimeter of the observation region towards the end of their existence in which case the extents are only partly visible. V. COCLUSIO The paper presented a hierarchical point process approach to tracing an extended target which gives rise to a structured set of measurements per time-step in the form of a geometric shape. The implementation of the corresponding PHD filter for the compound state consisting of the target s shape parametric and inematic state was based on a particle representation and a Gaussian mixture formulation respectively. The novelty of the approach is that it s non-shape specific and is applicable for structured sets of target generated measurements which tae the form of any geometric shape that can be parameterised in a two-dimensional observation space. Demonstrated on a multiple extended target example where the extents are elliptical in shape and variable in size early simulation results are promising. VI. ACKOWLEDGEMETS Anthony Swain is funded by an EPSRC Industrial CASE Award PhD Studentship with SELEX Galileo Ltd. Daniel Clar is a Royal Academy of Engineering/EPSRC Research Fellow. The authors would lie to than eil Cade SELEX Galileo Ltd for his advice in contribution to this paper. REFERECES [1] R. P. S. 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