Dynamic Ping Optimization for Surveillance in Multistatic Sonar Buoy Networks with Energy Constraints

Transcription

1 Dynamic Ping Optimizatin fr Surveillance in Multistatic Snar Buy Netwrks with Energy Cnstraints Anshu Saksena and I-Jeng Wang Abstract In this paper we study the prblem f dynamic ptimizatin f ping schedule in an active snar buy netwrk deplyed t prvide persistent surveillance f a littral area thrugh multistatic detectin The gal f ping scheduling is t dynamically determine when t ping and which ping surce t engage in rder t achieve the desirable detectin perfrmance Fr applicatins where persistent surveillance is needed fr an extended perid f time it is expected that the energy available at each ping surce is limited relative t the required system lifetime Hence efficient management f pwer cnsumptin fr pinging is imprtant t supprt the required lifetime f the netwrk while maintaining acceptable detectin perfrmance Our apprach t ping ptimizatin is based n the applicatin f apprximate Partially Observable Markv Decisin Prcess (POMDP) techniques such as the rllut algrithm T enable a practical implementatin f the plicy rllut we apply sampling-based techniques based n a simplified mdel that apprximates the detailed multistatic mdel Using high fidelity snar simulatins we evaluate the perfrmance f the prpsed apprach and cmpare it with the greedy technique in terms f detectin perfrmance and system lifetime I INTRODUCTION In this paper we derive a frmulatin f the dynamic ping ptimizatin prblem in multistatic snar buy netwrks using the framewrk f Partially Observable Markv Decisin Prcesses (POMDP) The basic perating cncept f a multistatic snar buy netwrk fr underwater surveillance is t practively ping frm an acustic surce and crrelate the ech returns (specifically time f arrivals and bearings) acrss receivers in the field t detect lcalize and track targets f interest In rder t prvide necessary cverage fr the surveillance area and sufficient diversity in multistatic gemetry fr target lcalizatin multiple receivers and acustic surces are deplyed and distributed thrughut the field The ping ptimizatin prblem cnsidered here is a specific example f sensr management in sensr netwrks which has received significant interest in recent years in generic sensr netwrk settings (see fr example [1] [2] [3]) Our wrk fcuses n the practical applicatin f existing algrithms (in particular the apprximate dynamic prgramming techniques prpsed in [3] [4]) t multistatic snar netwrks where sensing and detectin mdels are mre cmplicated than in settings cnsidered in the literature This wrk was supprted by the ONR Discvery and Inventin Prgram Anshu Saksena is with the Miltn Eisenhwer Research Center Jhns Hpkins University Applied Physics Labratry Laurel MD USA anshusaksena@jhuapledu I-Jeng Wang is with the Miltn Eisenhwer Research Center Jhns Hpkins University Applied Physics Labratry Laurel MD USA i-jengwang@jhuapledu The benefit f ptimizing ping sequences t tracking perfrmance fr multistatic snar systems has been demnstrated thrugh simulatins in [5] where a greedy apprach is presented t ptimize the expected detectin prbability during the search phase when n detectins are cnfirmed and t imprve the track with wrst quality after tracks are established In this paper we fcus n the aspects f ping surce selectin with additinal energy cnstraint during the surveillance phase The surveillance phase is defined as the stage where n specific track with sufficient cnfidence has been established based n the detectin results frm the netwrk f receivers In cntrast t [5] where cmplete absence f cnfirmed detectins is assumed we permit the existence f initial detectins in ur frmulatin The ratinale fr this unique feature is tw-fld: In practical applicatins sparse detectins are expected befre sufficient measurements are available t establish a track (the track initiatin prblem) Furthermre an apprach assuming n detectin has limited applicability since false alarms are inevitable fr mst practical scenaris The separatin f surveillance and tactical (after tracks are established) phases pstulated by existing literature is smewhat artificial In reality bth situatins exist simultaneusly since cntinuing search f new targets is desirable even after tracks are established A frmulatin incrprating detectins during the surveillance phase (such as the ne prpsed here) can likely be extended t address requirements fr bth search and tracking simultaneusly In Sectin II we frmally define all the necessary attributes f a POMDP fr the ping ptimizatin prblem Based n the frmulatin we discuss in Sectin III hw the plicy rllut technique can be applied t sequentially slve fr ping surce selectins by taking a nnmypic view f perfrmance ver a time hrizn int the near future This apprach serves t trade-ff the detectin perfrmance versus energy management requirement We present simulatin results t demnstrate the perfrmance f prpsed algrithms in Sectin IV Thrughut the discussin we assume that there are N s surces and N r receivers deplyed in the field and their psitins are statinary II MATHEMATICAL FORMULATION OF PING OPTIMIZATION PROBLEMS We assume a discrete time mdel and use k = t dente the kth stage with 0th stage denting the starting time We will use time k t dente the beginning f the

2 Sensr detectins Snar Buy Netwrk is the size f the grid The surveillance target state at time k is defined by Fusin Fused Measurements Fig 1 Observable States State Estimatr Psterir distributin f unbservables Cntrller Optimizatin Ping Decisin An illustratin f the POMDP fr ping ptimizatin kth stage Fllwing the standard MDP framewrk we will define the states X(k) the actin a(k) the bservatin Z(k) and its dependency n states and actins the state transitin the immediate reward r(x(k) a(k)) the hrizn H and the terminal cst r T (X(H)) if needed Given the initial state X(0) (r its distributin) the ptimizatin prblem defined by the MDP is given by V H(X(0)) = max E[r (X(0) a(0)) + a(0)a(h 1) + r (X(H 1) a(h 1)) + r T (X(H))] (1) where a(k) 0 N s } is the ping surce selectin at time k with a(k) = 0 crrespnding t the actin f nt pinging frm any surce and the maximizatin is taken ver all feasible sequences f actins Bellman s equatin prvides a characterizatin f the perfrmance f the ptimal decisins VH(X) = max Q(X a) a Q(X a) r(x a) + E X [VH 1(X )] where X is the next state after taking the actin a at state X and Q(X a) is typically referred t as the Q-value f actin a at state X Given that the states are nt fully bservable we cast the prblem as a POMDP using the cncept f the belief state r the cnditinal prbability The basic idea f the POMDP is illustrated in Figure 1 A States and Observatins The states f the ping ptimizatin can be classified int tw types f states: the target states that capture the dynamic behavirs f targets; and the sensr states that characterize the status f the sensr systems 1) Target states and bservatin: Fr the surveillance case where n credible tracks have been established it is difficult t mdel all the uncertainty including the number f targets in the field Instead f directly mdelling the target states we characterize the ptential target presence acrss the field We further discretize the field t arrive at a mre tractable frmulatin Specifically we assume that the field is discretized int a grid (x i y i ) i = 1 N g } where N g where t i (k) = X(k) = [ t 1 (k) t Ng (k) ] T 1 if there is at least 1 target at (x i y i ) at time k 0 therwise Nte that in this mdel we have made tw apprximating assumptins: (1) target lcalizatins are mapped t the grid; and (2) we make n differentiatin in ur mdels between the cases f a single target and multiple targets being at a grid pint Since n specific target tracking infrmatin has been established during the surveillance phase a randmized mdel derived frm a stchastic spatial diffusin prcess determines the randm mvement and arrival f ptential targets We define the state transitin prbability by assuming that the target dynamics are independent f each ther and nt affected by the actin taken: P (X(k + 1) X(k) a(k)) = i P (t i (k + 1) X(k)) where the individual target transitin mdel is given by a Gaussian distributin The target states are nt directly bservable but can be estimated frm the bservatin: where z i (k) = Z(k) = [ z 1 (k) z Ng (k) ] T 1 if a detectin ccurs at (x i y i ) after a(k) 0 therwise The bservatin mdel is specified by the cnditinal prbability P (Z(k) X(k) a(k)) If we assume that the detectin result at the grid pint (x i y i ) with actin a(k) is independent f bth detectin z j (k) and target presence t j (k) at ther grid pints (x j y j ) with j i at time k then P (Z(k) X(k) a(k)) = i P (z i (k) t i (k) a(k)) and P (z i (k) = 1 t i (k) = 1 a(k)) = p d (x i y i a(k)) (2) P (z i (k) = 1 t i (k) = 0 a(k)) = p fa (x i y i a(k)) (3) 2) Sensr states: In the initial frmulatin we assume that all the sensrs are statinary and fcus n mdelling the energy levels at the surces We assume a simple mdel fr the energy states: E(k) = [e 1 (k) e Ns (k)] T e i (k) 0} N where e i (k) is the remaining number f pings the surce i can supprt in the beginning f the time k befre an actin

3 a(k) is taken Assuming that the initial energy state E(0) is given the state transitin is defined by e i (k) 1 if a(k) = i and e i (k) 1 e i (k + 1) = e i (k) therwise In this simple mdel we assume that the energy cnsumptin fr pinging is deterministic Furthermre we assume that the energy state E(k) is directly bservable (that is can be measured withut errrs) B Belief states and estimatin T apply the POMDP technique we define the belief states and derive a recursin that enables us t estimate the belief states sequentially based n the bservatins Z(k) The belief state is defined as the cnditinal prbability f the states given the infrmatin state (all prir bservatins and actins) that is P X(k) Z(0) Z(1) Z(k 1) a(0) a(k 1)} We dente the belief state by P T (k) = [ P T (x 1 y 1 ; k) P T (x 2 y 2 ; k) P T (x Ng y Ng ; k) ] T where P T (x i y i ; k) dentes the cnditinal prbability f target presence at (x i y i ) at time k given all prir bservatins and actins The belief state P T (k) can be estimated and prpagated sequentially by a tw-step recursin Given the current belief state P T (k): 1) Bayes update: Given an actin a(k) and the resulting bservatin Z(k) cmpute the a psteriri belief state P T Z using Bayes rule P T Z(k) (x i y i ; k) = p d P T p d P T +p fa [1 P T ] if z i (k) = 1 (1 p d )P T [1 p d ]P T +[1 p fa ][1 P T ] therwise where p d p fa and P T have been written instead f p d (x i y i a(k)) p fa (x i y i a(k)) and P T (x i y i ; k) respectively fr readability 2) Diffusin: Prpagate the a psteriri belief state accrding t the transitin mdel P T (x i y i ; k+1) = 1 j ( 1 PT Z(k) (x j y j ; k)p ij ) The fllwing diagram illustrates the prpagatin f belief state: P T (k) a(k) Bayes update Z(k) P T Z(k) (k) diffusin P T (k+1) C Feasible actins and plicies An actin that meets all the cnstraints defined in the prblem is called a feasible actin An bvius cnstraint fr the ping ptimizatin prblem is that the energy level at a surce is sufficient t ping That is a i is feasible nly if e i 1 in ur frmulatin Nte that the feasibility f an actin will depend n the current state P T (k) E(k)} P T (k) E(k) } Candidate Actin a Z 1 (k) Z M (k) Fig 2 State Estimatin Mnte Carl Sampling P 1 T (k+1) P M T (k+1) E 1 (k) E M (k) Base Plicy π! a (k+1) An illustratin f the plicy rllut Q 1 Q M We dente the set f feasible actins at time k by A k 0 N s } A (Markv) plicy π is a mapping frm the states P T (k) E(k)} t an actin a(k) A plicy is feasible if π (P T (k) E(k)) A k fr all k = 0 H 1 Tw typical examples f plicy fr the ping ptimizatin prblem are: Fixed sequence plicies: One can define a feasible plicy by repeating the same sequence f ping decisins as lng as the remaining energy level at a surce is sufficient t ping The rund-rbin algrithm falls under this class f plicies Greedy plicies: The greedy plicy is a plicy that selects a decisin amng the feasible actins by maximizing the immediate reward That is π (P T (k) E(k)) = argmax a Ak E [r(p T (k) E(k) a)] III OPTIMIZATION CRITERIA AND POLICY ROLLOUT A Rewards and dynamic prgramming frmulatin Fr detectin perfrmance we define the reward functin using the average detectin prbability acrss the field: r(p T a) = 1 N g PT α (x i y i )p d (x i y i a) (4) N g i=1 where α 1 is a parameter that allws us t cntrl the search strategy T mdel the energy cnstraint we assume a simplified mdel where each ping surce has a pre-specified number f pings thrughut its lifetime Even thugh we d nt explicitly mdel energy related cnsideratins as part f the reward in POMDP it is expected that the energy cnstraint will play a rle in the perfrmance f POMDP if the selected hrizn is lng enugh relative t the available ping resurces With the reward and cnstraint defined abve we frmulate ping ptimizatin as the fllwing stchastic dynamic prgramming prblem: [ H 1 ] max E r (P T (k) a(k)) (5) a(0)a(h 1);a(k) A k k=0 where r is defined in (4) Fr ur experiments we use the frmulatin (5) in a receding hrizn setting The receding

4 hrizn setting can ptentially reduce the impact f mdel inaccuracy n the predictin f future detectin perfrmance in dynamic prgramming B Plicy Rllut Technique T address the cmplexity f the dynamic prgramming frmulated fr the ping ptimizatin prblem we apply the plicy rllut technique [9] The basic idea f the plicy rllut algrithm is t use the perfrmance resulting frm a base plicy π t estimate the Q-value fr making the decisin Given the cmplexity f the underlying mdels it is difficult t directly estimate the perfrmance f a base plicy Hence we apply a sampling-based apprach similar t the nes used in [3] [4] t this estimatin prblem The sampling-based apprach relies n the utcme f multiple Mnte Carl simulatins with the base plicy t estimate the Q-value f each feasible actin Cnsider the traces f states frm M independent Mnte Carl runs by taking an actin a and fllwing a feasible base plicy π afterward: P T (k) E(k)} a Z i (k) P i T (k + 1) E i (k + 1)} a π (k+1) P i T (k + 2) E i (k + 2)} a π (H 1) P i T (H) E i (H)} i = 1 M Nte that the specific actins taken fllwing the base plicy will generally differ amng the traces since they depend n the specific belief and energy state trajectry P i T Ei } btained in each Mnte Carl run Frm each sample path we btain a sample f the Q-value fr the base plicy π as Q i (P T (k) a) = r (P T (k) a) + r ( P i T (k + 1) a π (k + 1) ) + + r ( P i T (H 1) a π (H 1) ) An estimate f the Q-value fr the actin a at the belief state P T (k) dented by Q (P T (k) a) can be btained as the empirical average ver these Mnte Carl runs Fllwing the plicy rllut strategy the actin at time k is chsen based n a (k) = argmax a Ak Q (PT (k) a) In this paper we cnsider the fllwing apprximatin mdel fr simulatins f Z(k) in plicy rllut: z i (k) = 1 with prbability p d P T + p fa (1 P T ) where P T p d and p fa are again used as shrthand fr P T (x i y i ; k) p d (x i y i a(k)) and p fa (x i y i a(k)) respectively fr the sake f readability IV HIGH FIDELITY SIMULATION RESULTS A Snar Mdels In rder t test perfrmance ver a range f envirnmental settings and cnditins numerical mdeling was used t simulate the mtin f a target thrugh a distributed TABLE I TOTAL PROBABILITY OF DETECTION FOR TARGET 1 Mean Std dev Num scenaris Rund-rbin Greedy Rllut H= Rllut H= Rllut H= TABLE II TOTAL PROBABILITY OF DETECTION FOR TARGET 2 Mean Std dev Num scenaris Rund-rbin Greedy Rllut H= Rllut H= Rllut H= sensr netwrk The signal excess fr eches assciated with surce-receiver pairs was determined fr each event in a ping schedule using a physics-based mdel Clutter was established statistically frm a measured characteristic distributin Transmissin lss calculatins are perfrmed using APLNM a range-dependent cupled nrmal mde cde Sund velcity prfiles bathymetry and bttm prperties are extracted frm standard databases Backgrund interference was calculated using a pwer sum f an assumed spectral ambient nise level (NL) and a calculated spectral reverberatin level (RL) The RL was calculated by assuming a cnstant sund speed with an equitime ellipse f reverberant patches (RV B) cnstrained by the signal bandwidth The receiver beam pattern is included directly in establishing RL with a single directivity index applied t the N L Bth N L and RV B are determined in units f intensity and are assumed cnstant ver the bandwidth f the signal Ptential clutter events are established using a unifrm density f events fr each receiver beam (eg ne event per secnd) These events are drawn randmly frm a generalized gamma distributin having mean standard deviatin and skewness parameters fit t represent measured clutter statistics frm at-sea experiments B Evaluatin with Simulated Data Our simulatins are based n a snbuy field cnsisting f 16 receivers arranged in a 4x4 grid and 4 active snar surces lcated within the grid f receivers as shwn in Figure 3 Each surce begins with enugh energy t ping 150 times The first target enters the field at stage 15 and TABLE III SYSTEM LIFETIME Mean Min Max Num scenaris Rund-rbin Greedy Rllut H=

5 the secnd enters at stage 250 We cmpare detectin perfrmance f three surce selectin plicies: the rund-rbin plicy the greedy plicy and plicy rllut using the greedy plicy as the base plicy Plicy rllut ptimized the decisin at each stage based n the average f up t 50 Mnte Carl simulatins f the bservatins At each stage there are 5 pssible actins: ping frm ne f the 4 surces r d nt ping frm any surce We measure surveillance perfrmance by summing the prbability f detecting each target ver each simulatin run A number f different target track scenaris were run using rund-rbin greedy and plicy rllut strategies with their results summarized in Table I fr the first target entering the field and in Table II fr the secnd Plicy rllut was run with hrizn lengths f and 20 stages with the results fr each listed in the table separately Since target 1 is tracked with sufficient energy reserves predictin accuracy ver the hrizn is gverned by the uninfrmed diffusin target mtin mdel the lnger hrizns seem t have verextended the relevance f thse predictins Since target 2 arrived later the end game f limited resurces becmes mre f a factr Lnger hrizns may be beneficial in this case since predictin f energy depletin is accurate even ver lng hrizns While these trends seem reasnable the statistics f these results preclude us frm cncluding that any f these plicies perfrms better r wrse than any ther The system lifetime defined as the time after which all surces have exhausted their energy is shwn in Table III With the exceptin f the first stage when there are n targets believed t be in the area and ur implementatin selects nt t ping the greedy plicy pings at every stage until surce energies are exhausted at stage 601 The rundrbin plicy als pings at every stage and thus als has a lifetime f 600 Hwever lnger lifetimes result frm plicy rllut s anticipatin f the scarcity and subsequent ratining f energy Hwever there was ne scenari that Latitude Time 300 Time 600 Time Time 900 Time 1200 Lngitude Fig 3 Simulated scenari: asterisks indicate acustic surces circles receivers lines shw target tracks and circles indicate the time at which the target is at that pint f the track Targets enter the field frm the Nrthwest turn East and leave Surce 1 Surce 2 Surce 3 Surce Fig 4 Plt f the energy reserves in the number f pings remaining n each surce as a functin f time under the greedy surce selectin plicy Surce 1 Surce 2 Surce 3 Surce Fig 5 Plt f the energy reserves in the number f pings remaining n each surce as a functin f time under the rllut surce selectin plicy with hrizn length f 20 never exhausted its energy fr any f the plicy rllut hrizn lengths This large lifetime dminates the mean f each algrithm but since the number f scenaris increases with increasing hrizn length the effect f the utlying scenari decreases creating an apparent trend f decreasing lifetime Remving this utlier frm each data set prduces the results in Table?? The p-values shwn are fr cmparisn t the lifetime f the greedy algrithm Of curse t be fair an extreme value n the ther end f the distributin shuld als be remved but that wuld nly imprve the statistics ver thse shwn in Table?? Therefre each implementatin f plicy rllut prduces a significantly lnger system lifetime than greedy r rund-rbin a key result fr persistent surveillance withut sacrificing detectin perfrmance significantly We nw briefly present mre detailed data frm ne scenari t illustrate the perfrmance f plicy rllut with hrizn length 20 versus the greedy algrithm Figure 3 shws an example f the simulated tracks that was used t generate the plts presented here Figure 4 shws the energy reserves f each surce as a functin f time fr the greedy plicy and Figure 5 shws this fr plicy rllut giving an idea f hw judiciusly each plicy makes use f each surce

6 V CONCLUSIONS AND FUTURE WORK In this paper we present a mathematical frmulatin f the dynamic ping ptimizatin prblem fr snar buy netwrks with energy cnstraints We develp an implementatin f the sampling-based plicy rllut t ptimize the average detectin perfrmance Even with a much simplified mdel used in plicy rllut the apprximate dynamic prgramming apprach leads t a lnger system lifetime while achieving detectin perfrmance similar t the greedy apprach as illustrated by the experimental results using high-fidelity snar simulatins As an immediate future wrk we will cnsider applying state aggregatin techniques t further imprve the efficiency f plicy rllut We address the energy cnstraint by defining a hrizn lng enugh in stchastic dynamic prgramming One might cnsider explicitly mdelling the energy cnsideratin t enable a receding hrizn frmulatin with shrter hrizn (and hence reducing the cmputatinal csts f plicy rllut) Theretically the mst apprpriate metric fr energy management is the lifetime f the system Hwever directly using the lifetime as the reward will lead t a difficult POMDP A gd alternative is t use a lad-balancing type f metric t capture the fairness f energy cnsumptin acrss the field Given the energy levels E = [e 1 e Ns ] T define the deviatin f energy level at surce i as σi e (E) = e i ē ē where ē is the average amng e i } We can then use the energy deviatins t either define the reward r define a cnstraint N s r(p T E a) = σi e (E ) (6) i=1 σ e i (E ) ρ(e) < 1 fr all i = 1 N s (7) where E is the resulting energy levels after the actin a is taken given current energy levels E and ρ(e) is defined t ensure the existence f a feasible actin while maintaining a desirable level f lad balancing Finally since we cnsider the detectins during the surveillance in ur frmulatin it is straightfrward t incrprate the utcme f tracking algrithms int ur frmulatin with an apprpriate expansin f the state space t include the current target curse and speed etc In essence the state estimatin prcess we discussed in Sectin II-B is a simple Bayesian tracking algrithm with the prbabilistic diffusin as its underlying dynamic mdel Amng the existing tracking appraches the Prbability Hypthesis Density (PHD) filter [10] [11] is perhaps the mst natural ne t cnsider The PHD filter recursins prpagate the intensity f the target states in a way that is very similiar t the prpagatin f the belief state cnsidered in ur frmulatin A key challenge in incrprating tracking utcmes in ping ptimizatin is t devise a perfrmance metric that adequately addresses the peratinal pririty regarding the trade-ff between cntinuing tracking f cnfirmed targets and persistent surveillance f the entire field One pssible apprach is t experiment with the chice f parameter α in the average detectin reward defined in (4) t cntrl the preference f future detectin n lcatins with higher target presence belief where established tracks wuld be VI ACKNOWLEDGEMENTS The authrs gratefully acknwledge the wrk f Jeff Dunne in develping the snar simulatins and the cntributins f Dennis Lucarelli t the develpment f the frmulatin f ur prblem Bth are f the Jhns Hpkins University Applied Physics Labratry REFERENCES [1] V Krishnamurthy Algrithms fr ptimal scheduling f hidden Markv mdel sensrs IEEE Transactins n Signal Prcessing vl 50 n 6 pp [2] C M Kreucher A O Her III K D Kastella and M R Mrelande An infrmatin-based apprach t sensr management in large dynamic netwrks Prceedings f the IEEE vl 95 n 5 May 2007 [3] Y Li L W Krakw E K P Chng and K N Grm Apprximate stchastic dynamic prgramming fr sensr scheduling t track multiple targets Digital Signal Prcessing t appear [4] E K P Chng C Kreucher and A O Her III POMDP apprximatin methds based n heuristics and simulatin Chapter 8 in Fundatins and Applicatins f Sensr Management A O Her D Castann D Cchran and K Kastella Eds Chapter 5 Springer 2008 ISBN: pp [5] D W Krut M A El-Sharkawi W J L Fx and M U Hazen Intelligent ping sequencing fr multistatic snar systems th Internatinal Cnference n Infrmatin Fusin 2006 [6] W A Albersheim A Clsed-Frm Apprximatin t Rbertsn s Detectin Characteristics Prceedings f the IEEE Vl 69 N 7 July 1981 [7] A Saksena L Benmhamed J Dunne D Lucarelli I-J Wang Imprving System-wide Detectin Perfrmance fr Snar Buy Netwrks using In-Netwrk Fusin MILCOM 2007 Unclassified Prceedings Orland FL [8] A C Cn Spatial crelatin f detectins fr impulsive ech ranging snar Jhns Hpkins APL Technical Digest vl 18 n1 pp [9] D P Bertsekas and D A Castañn Rllut algrithms fr stchastic scheduling prblems Jurnal f Heuristics vl 5pp [10] R Mahler Multi-target Bayes filtering via first-rder multi-target mments IEEE Trans Aersp Electrn Syst vl 39 n 4 pp [11] B-N V and W-K Ma The Gaussian mixture prbability hypthesis denisty filter IEEE Transactins n Signal Prcessing vl 54 n11 pp