lost sales inventory systems with a service level criterion competitive retail environments are characterized by service levels and lost sales in case of excess demand we contribute to research on lost sales models with a service level criterion in multiple ways first we study the optimal replenishment policy for this type of inventory system as well as base stock policies and r s s policies furthermore we derive lower and upper bounds on the order up to level and we propose efficient approximation procedures to determine the order up to level the procedures find values of the inventory control variables that are close to the best r s s policy and comply to the service level restriction for most of the instances with an average cost increase of 2 3 and 1 2 for the case without and with fixed order costs respectively

the bethe permanent of a nonnegative matrix it has recently been observed that the permanent of a nonnegative square matrix i e of a square matrix containing only nonnegative real entries can very well be approximated by solving a certain bethe free energy function minimization problem with the help of the sum product algorithm we call the resulting approximation of the permanent the bethe permanent in this paper we give reasons why this approach to approximating the permanent works well namely we show that the bethe free energy function is convex and that the sum product algorithm finds its minimum efficiently we then discuss the fact that the permanent is lower bounded by the bethe permanent and we comment on potential upper bounds on the permanent based on the bethe permanent we also present a combinatorial characterization of the bethe permanent in terms of permanents of so called lifted versions of the matrix under consideration moreover we comment on possibilities to modify the bethe permanent so that it approximates the permanent even better and we conclude the paper with some observations and conjectures about permanent based pseudocodewords and permanent based kernels

the cardinality balanced multi target multi bernoulli filter and its implementations it is shown analytically that the multitarget multibernoulli member recursion proposed by mahler has a significant bias in the number of targets to reduce the cardinality bias a novel multibernoulli approximation to the multi target bayes recursion is derived under the same assumptions as the member recursion the proposed recursion is unbiased in addition a sequential monte carlo smc implementation for generic models and a gaussian mixture gm implementation for linear gaussian models are proposed the latter is also extended to accommodate mildly nonlinear models by linearization and the unscented transform

a consistent metric for performance evaluation of multi object filters the concept of a miss distance or error between a reference quantity and its estimated controlled value plays a fundamental role in any filtering control problem yet there is no satisfactory notion of a miss distance in the well established field of multi object filtering in this paper we outline the inconsistencies of existing metrics in the context of multi object miss distances for performance evaluation we then propose a new mathematically and intuitively consistent metric that addresses the drawbacks of current multi object performance evaluation metrics

simultaneous identification and adaptive control of unknown systems over finite parameter sets the problem considered is one of simultaneously identifying an unknown system while adequately controlling it the system can be any fairly general discrete time system and the cost criterion can be either of a discounted type or of a long term average type the chief restriction being that the unknown parameter lies in a finite parameter set for a previously introduced scheme of identification and control based on biased maximum likelihood estimates it is shown that 1 every cesaro limit point of the parameter estimates is closed loop equivalent to the unknown parameter 2 for both the discounted and long term average cost criteria the adaptive control law cesaro converges to the set of optimal control laws and 3 in the case of the long term average cost criterion the actual cost incurred by the use of the adaptive controller is optimal and cannot be bettered even if one knew the value of the unknown parameter at the start

asymptotically optimal inventory control for assemble to order systems with identical lead times optimizing multiproduct assemble to order ato inventory systems is a long standing difficult problem we consider ato systems with identical component lead times and a general bill of materials we use a related two stage stochastic program sp to set a lower bound on the average inventory cost and develop inventory control policies for the dynamic ato system using this sp we apply the first stage sp optimal solution to specify a base stock replenishment policy and the second stage sp recourse linear program to make allocation decisions we prove that our policies are asymptotically optimal on the diffusion scale so the percentage gap between the average cost from its lower bound diminishes to zero as the lead time grows subject classifications assemble to order inventory management stochastic linear program stochastic control asymptotic optimality diffusion scale area of review stochastic models history received may 2013 revisions received july 2014 january 2015 accepted february 2015

controlled markov chains and stochastic networks controlled markov chains with average cost criterion and with special cost and transition structures are studied existence of optimal stationary strategies is established for the average cost criterion corresponding dynamic programming equations are derived a stochastic network problem that includes interconnected queues as a special case is described and studied within this framework

long term values in markov decision processes and repeated games and a new distance for probability spaces we study long term markov decision processes mdps and gambling houses with applications to any partial observation mdps with finitely many states and zero sum repeated games with an informed controller we consider a decision maker who is maximizing the weighted sum t 1 x1d703 trt where rt is the expected reward of the t th stage we prove the existence of a very strong notion of long term value called general uniform value representing the fact that the decision maker can play well independently of the evaluations x1d703 t t 1 over stages provided the total variation or impatience t 1 x1d703 t 1 x1d703 t is small enough this result generalizes previous results of the literature that focus on arithmetic means and discounted evaluations moreover we give a variational characterization of the general uniform value via the introduction of appropriate invariant measures for the decision problems generalizing the fundamental theorem of gambling or the aumann maschler cav u formula for repeated games with incomple

approximation algorithms for stochastic inventory control models we consider two classical stochastic inventory control models the periodic review stochastic inventory control problem and the stochastic lot sizing problem the goal is to coordinate a sequence of orders of a single commodity aiming to supply stochastic demands over a discrete finite horizon with minimum expected overall ordering holding and backlogging costs in this paper we address the important problem of finding computationally efficient and provably good inventory control policies for these models in the presence of correlated nonstationary time dependent and evolving stochastic demands this problem arises in many domains and has many practical applications in supply chain management our approach is based on a new marginal cost accounting scheme for stochastic inventory control models combined with novel cost balancing techniques specifically in each period we balance the expected cost of overordering i e costs incurred by excess inventory against the expected cost of underordering i e costs incurred by not satisfying demand on time this leads to what we believe to be the first computationally efficient policies with constant worst case performance guarantees for a general class of important stochastic inventory control models that is there exists a constant c such that for any instance of the problem the expected cost of the policy is at most c times the expected cost of an optimal policy in particular we provide a worst case guarantee of two for the periodic review stochastic inventory control problem and a worst case guarantee of three for the stochastic lot sizing problem our results are valid for all of the currently known approaches in the literature to model correlation and nonstationarity of demands over time

average cost optimal policies for markov control processes with borel state space and unbounded costs abstract we show the existence of average cost optimal stationary policies for markov control processes with borel state space and unbounded costs per stage under a set of assumptions recently introduced by l i sennott 1989 for control processes with countable state space and finite control sets

discrete time controlled markov processes with average cost criterion a survey this work is a survey of the average cost control problem for discrete time markov processes the authors have attempted to put together a comprehensive account of the considerable research on this problem over the past three decades the exposition ranges from finite to borel state and action spaces and includes a variety of methodologies to find and characterize optimal policies the authors have included a brief historical perspective of the research efforts in this area and have compiled a substantial yet not exhaustive bibliography the authors have also identified several important questions that are still open to investigation

approximating the nonlinear newsvendor and single item stochastic lot sizing problems when data is given by an oracle the single item stochastic lot sizing problem is to find an inventory replenishment policy in the presence of discrete stochastic demands under periodic review and finite time horizon a closely related problem is the single period newsvendor model it is well known that the newsvendor problem admits a closed formula for the optimal order quantity whenever the revenue and salvage values are linear increasing functions and the procurement ordering cost is fixed plus linear the optimal policy for the single item lot sizing model is also well known under similar assumptions in this paper we show that the classical single period newsvendor model with fixed plus linear ordering cost cannot be approximated to any degree of accuracy when either the demand distribution or the cost functions are given by an oracle we provide a fully polynomial time approximation scheme for the nonlinear single item stochastic lot sizing problem when demand distribution is given by an oracle procurement costs are provided as nondecreasing oracles holding backlogging disposal costs are linear and lead time is positive similar results exist for the nonlinear newsvendor problem these approximation schemes are designed by extending the technique of k approximation sets and functions

analytic implementations of the cardinalized probability hypothesis density filter the probability hypothesis density phd recursion propagates the posterior intensity of the random finite set rfs of targets in time the cardinalized phd cphd recursion is a generalization of the phd recursion which jointly propagates the posterior intensity and the posterior cardinality distribution in general the cphd recursion is computationally intractable this paper proposes a closed form solution to the cphd recursion under linear gaussian assumptions on the target dynamics and birth process based on this solution an effective multitarget tracking algorithm is developed extensions of the proposed closed form recursion to accommodate nonlinear models are also given using linearization and unscented transform techniques the proposed cphd implementations not only sidestep the need to perform data association found in traditional methods but also dramatically improve the accuracy of individual state estimates as well as the variance of the estimated number of targets when compared to the standard phd filter our implementations only have a cubic complexity but simulations suggest favorable performance compared to the standard joint probabilistic data association jpda filter which has a nonpolynomial complexity

on the optimality equation for average cost markov control processes with feller transition probabilities we consider markov control processes with borel state space and feller transition probabilities satisfying some generalized geometric ergodicity conditions we provide a new theorem on the existence of a solution to the average cost optimality equation

optimality gap of constant order policies decays exponentially in the lead time for lost sales models inventory models with lost sales and large lead times have traditionally been considered intractable due to the curse of dimensionality recently goldberg and coauthors laid the foundations for a new approach to solving these models by proving that as the lead time grows large a simple constant order policy is asymptotically optimal however the bounds proven there require the lead time to be very large before the constant order policy becomes effective in contrast to the good numerical performance demonstrated by zipkin even for small lead time values in this work we prove that for the infinite horizon variant of the same lost sales problem the optimality gap of the same constant order policy actually converges exponentially fast to zero with the optimality gap decaying to zero at least as fast as the exponential rate of convergence of the expected waiting time in a related single server queue to its steady state value we also derive simple and explicit bounds for the optimality gap and demons

a note on the convergence of policy iteration in markov decision processes with compact action spaces the undiscounted unichain finite state markov decision process with compact action space is studied we provide a counterexample for a result in hordijk and puterman 1987 and give an alternate proof of the convergence of policy iteration under the condition that there exists a state that is recurrent under every stationary policy the analysis essentially uses a two term matrix representation for the relative value vectors generated by policy iteration procedure

necessary and sufficient conditions for a bounded solution to the optimality equation in average reward markov decision chains abstract we consider average reward markov decision processes with discrete time parameter and denumerable state space we are concerned with the following problem find necessary and sufficient conditions so that for arbitrary bounded reward function the corresponding average reward optimality equation has a bounded solution this problem is solved for a class of systems including the case in which under the action of any stationary policy the state space is an irreducible positive recurrent class

markov decision processes with a borel measurable cost function the average case we consider a markov decision process with a borel measurable cost function we introduce a p step contraction property for the average cost case by use of this method the validity of the optimality equation and the existence of e optimal stationary policies are proved as some applications the sequential replacement model and the inventory model are considered

average cost markov decision processes optimality conditions we are concerned in this paper with discrete time markov decision processes mdps with borel state and action spaces x and a respectively and the long run expected average cost criterion when x is a denumerable set man y necessary and or sufficient conditions for the existence of optimal control policies are known however when x is a borel space i e a borel subset of a complete separable metric space most of the available results impose on the mdp very restrictive topological conditions e g compactness and or strong recurrence assumptions such as doeblin s condition see e g 4 9 12 and their references another related work is 7 where we have studied mdps from the viewpoint of the recurrence or ergodicity properties of the state process ln the present paper however we are concerned with the existence of average optimal policies by looking at static optimization problems see condition cs in section 4 related in sorne cases equivalent to the existence of a bounded solution to the so called optimality equation see c4 in section 4 these optimization problems are dual in the sense that under appropriate conditions the existence of an optimal solution to one of the problems implies existence of an optimal

an iterative numerical method for singularly perturbed reaction diffusion equations with negative shift in this paper a numerical method based on an iterative scheme is proposed for a singularly perturbed delay differential equation of reaction diffusion type in this method the solution of the delay problem is obtained as the limit of the solutions to a sequence of the non delay problems the numerical solutions of the non delay problems are obtained by applying existing finite difference schemes and finite element method for the non delay singularly perturbed equations error estimates are derived in the supremum norm numerical results illustrating the theory are also included

a fully polynomial time approximation scheme for single item stochastic inventory control with discrete demand the single item stochastic inventory control problem is to find an inventory replenishment policy in the presence of independent discrete stochastic demands under periodic review and finite time horizon in this paper we prove that this problem is intractable and design for it a fully polynomial time approximation scheme

a mixed value and policy iteration method for stochastic control with universally measurable policies we consider stochastic optimal control models with borel spaces and universally measurable policies for such models the standard policy iteration is known to have difficult measurability issues and cannot be carried out in general we present a mixed value and policy iteration method that circumvents this difficulty the method allows the use of stationary policies in computing the optimal cost function in a manner that resembles policy iteration it can also be used to address similar difficulties of policy iteration in the context of upper and lower semicontinuous models we analyze the convergence of the method in infinite horizon total cost problems for the discounted case where the one stage costs are bounded and for the undiscounted case where the one stage costs are nonpositive or nonnegative for undiscounted total cost problems with nonnegative one stage costs we also give a new convergence theorem for value iteration that shows that value iteration converges whenever it is initialized with a f

randomized and past dependent policies for markov decision processes with multiple constraints the markov decision problem of locating a policy to maximize the long run average reward subject to k long run average cost constraints is considered it is assumed that the state and action spaces are finite and the law of motion is unichain that is every pure policy gives rise to a markov chain with one recurrent class it is first proved that there exists an optimal stationary policy with a degree of randomization no greater than k consequently it is never necessary to randomize in more than k states a linear program produces the optimal policy with limited randomization for the special case of a single constraint we also address the problem of finding optimal nonrandomized but nonstationary policies we show that a round robin type policy is optimal and conjecture the same for a steering policy that depends on the entire past history of the process but whose implementation requires essentially no more storage than that of a pure policy

control of markov chains with long run average cost criterion the dynamic programming equations the long run average cost control problem for discrete time markov chains on a countable state space is studied in a very general framework necessary and sufficient conditions for optimality in terms of the dynamic programming equations are given when an optimal stable stationary strategy is known to exist e g for the situations studied in stochastic differential systems stochastic control theory and applications ima vol math app 10 springer verlag new york berlin 1988 pp 57 77 a characterization of the desired solution of the dynamic programming equations is given in a special case also included is a novel convex analytic argument for deducing the existence of an optimal stable stationary strategy when that of a randomized one is known

markov decision processes with sample path constraints the communicating case we consider time average markov decision processes mdps which accumulate a reward and cost at each decision epoch a policy meets the sample path constraint if the time average cost is below a specified value with probability one the optimization problem is to maximize the expected average reward over all policies that meet the sample path constraint the sample path constraint is compared with the more commonly studied constraint of requiring the average expected cost to be less than a specified value although the two criteria are equivalent for certain classes of mdps their feasible and optimal policies differ for many nontrivial problems in general there does not exist optimal or nearly optimal stationary policies when the expected average cost constraint is employed assuming that a policy exists that meets the sample path constraint we establish that there exist nearly optimal stationary policies for communicating mdps a parametric linear programming algorithm is given to construct nearly optimal stationary policies the discussion relies on well known results from the theory of stochastic processes and linear programming the techniques lead to simple proofs of the existence of optimal and nearly optimal stationary policies for unichain and deterministic mdps respectively

some monotonicity results for partially observed markov decision processes this paper provides sufficient conditions for the optimal value in a discrete time finite partially observed markov decision process to be monotone on the space of state probability vectors ordered by likelihood ratios the paper also presents sufficient conditions for the optimal policy to be monotone in a simple machine replacement problem and in the general case for the optimal policy to be bounded from below by an easily calculated monotone function

fixed dimensional stochastic dynamic programs an approximation scheme and an inventory application we study fixed dimensional stochastic dynamic programs in a discrete setting over a finite horizon under the primary assumption that the cost to go functions are discrete l convex we propose a pseudo polynomial time approximation scheme that solves this problem to within an arbitrary prespecified additive error of e 0 the proposed approximation algorithm is a generalization of the explicit enumeration algorithm and offers us full control in the trade off between accuracy and running time the main technique we develop for obtaining our scheme is approximation of a fixed dimensional l convex function on a bounded rectangular set using only a selected number of points in its domain furthermore we prove that the approximation function preserves l convexity finally to apply the approximate functions in a dynamic program we bound the error propagation of the approximation our approximation scheme is illustrated on a well known problem in inventory theory the single product problem with lost sales and lead times we demonstrate the practical value of our scheme by implementing our approximation scheme and the explicit enumeration algorithm on instances of this inventory problem

singular perturbation analysis of boundary value problems for differential difference equations a study is made of a class of boundary value problems for linear second order differential difference equations in which the highest order derivative is multiplied by a small parameter consideration of the exact solution of simple model equations provides insight into the appropriate use of singular perturbation techniques for more general problems the resulting analysis leads to several novel features which are not present in problems without differences

markov decision problems and state action frequencies consider a controlled markov chain with countable state and action spaces basic quantities that determine the values of average cost functionals are identified under some regularity conditions these turn out to be a collection of numbers one for each state action pair describing for each state the relative number of uses of each action these conditional frequencies which are defined pathwise are shown to determine the state action frequencies that in the finite case are known to determine the costs this is extended to the countable case allowing for unbounded costs the space of frequencies is shown to be compact and convex and the extreme points are identified with stationary deterministic policies conditions under which the search for optimality in several optimization problems may be restricted to stationary policies are given these problems include the standard markov decision process as well as constrained optimization both in terms of average cost functionals and variability sensitive optimization an application to a queueing problem is given where these results imply the existence and explicit computation of optimal policies in constrained optimization problems the pathwise definition of the conditional frequencies implies that their values can be controlled directly moreover they depend only on the limiting behavior of the control this has immediate application to adaptive control of markov chains including adaptive control under constraints

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

asymptotic optimality of constant order policies for lost sales inventory models with large lead times lost sales inventory models with large lead times which arise in many practical settings are notoriously difficult to optimize due to the curse of dimensionality in this paper we show that when lead times are large a very simple constant order policy first studied by reiman performs nearly optimally the main insight of our work is that when the lead time is very large such a significant amount of randomness is injected into the system between when an order for more inventory is placed and when the order is received that being smart algorithmically provides almost no benefit our main proof technique combines a novel coupling for suprema of random walks with arguments from queueing theory

a scalable algorithm for tracking an unknown number of targets using multiple sensors we propose an algorithm for tracking an unknown number of targets based on measurements provided by multiple sensors our algorithm achieves low computational complexity and excellent scalability by running belief propagation on a suitably devised factor graph a redundant formulation of data association uncertainty and the use of augmented target states including binary target indicators make it possible to exploit statistical independencies for a drastic reduction of complexity an increase in the number of targets sensors or measurements leads to additional variable nodes in the factor graph but not to higher dimensions of the messages as a consequence the complexity of our method scales only quadratically in the number of targets linearly in the number of sensors and linearly in the number of measurements per sensor the performance of the method compares well with that of previously proposed methods including methods with a less favorable scaling behavior in particular our method can outperform multisensor versions of the probability hypothesis density phd filter the cardinalized phd filter and the multi bernoulli filter

a weighted markov decision process the two most commonly considered reward criteria for markov decision processes are the discounted reward and the long term average reward the first tends to neglect the future concentrating on the short term rewards while the second one tends to do the opposite we consider a new reward criterion consisting of the weighted combination of these two criteria thereby allowing the decision maker to place more or less emphasis on the short term versus the long term rewards by varying their weights the mathematical implications of the new criterion include the deterministic stationary policies can be outperformed by the randomized stationary policies which in turn can be outperformed by the nonstationary policies an optimal policy might not exist we present an iterative algorithm for computing an e optimal nonstationary policy with a very simple structure

a numerical method based on finite difference for boundary value problems for singularly perturbed delay differential equations abstract a boundary value problem for second order singularly perturbed delay differential equation is considered when the delay argument is sufficiently small to tackle the delay term the researchers m k kadalbajoo k k sharma numerical analysis of singularly perturbed delay differential equations with layer behavior appl math comput 157 2004 11 28 r e o malley jr singular perturbation methods for ordinary differential equations springer verlag new york 1991 used taylor s series expansion and presented an asymptotic as well as numerical approach to solve such type boundary value problem but the existing methods in the literature fail in the case when the delay argument is bigger one because in this case the use of taylor s series expansion for the term containing delay may lead to a bad approximation in this paper to short out this problem we present a numerical scheme for solving such type of boundary value problems which works nicely in both the cases i e when delay argument is bigger one as well as smaller one to handle the delay argument we construct a special type of mesh so that the term containing delay lies on nodal points after discretization the proposed method is analyzed for stability and convergence to demonstrate the efficiency of the method and how the size of the delay argument and the coefficient of the delay term affects the layer behavior of the solution several test examples are considered

a 2 approximation algorithm for stochastic inventory control models with lost sales in this paper we describe the first computationally efficient policies for stochastic inventory models with lost sales and replenishment lead times that admit worst case performance guarantees in particular we introduce dual balancing policies for lost sales models that are conceptually similar to dual balancing policies recently introduced for a broad class of inventory models in which demand is backlogged rather than lost that is in each period we balance two opposing costs the expected marginal holding costs against the expected marginal lost sales cost specifically we show that the dual balancing policies for the lost sales models provide a worst case performance guarantee of two under relatively general demand structures in particular the guarantee holds for independent not necessarily identically distributed demands and for models with correlated demands such as the ar 1 model and the multiplicative autoregressive demand model the policies and the worst case guarantee extend to models with capacity constraints on the size of the order and stochastic lead times our analysis has several novel elements beyond the balancing ideas for backorder models

labeled random finite sets and the bayes multi target tracking filter an analytic solution to the multi target bayes recursion known as the delta generalized labeled multi bernoulli delta glmb filter has been recently proposed by vo and vo in labeled random finite sets and multi object conjugate priors ieee trans signal process vol 61 no 13 pp 3460 3475 2014 as a sequel to that paper the present paper details efficient implementations of the delta glmb multi target tracking filter each iteration of this filter involves an update operation and a prediction operation both of which result in weighted sums of multi target exponentials with intractably large number of terms to truncate these sums the ranked assignment and k th shortest path algorithms are used in the update and prediction respectively to determine the most significant terms without exhaustively computing all of the terms in addition using tools derived from the same framework such as probability hypothesis density filtering we present inexpensive relative to the delta glmb filter look ahead strategies to reduce the number of computations characterization of the l 1 error in the multi target density arising from the truncation is presented

optimal stationary policies in general state space markov decision chains with finite action sets the result of sennott 9 on the existence of optimal stationary policies in countable state markov decision chains with finite action sets is generalized to arbitrary state space markov decision chains the assumption of finite action sets occurring in a global countable action space allows a particularly simple theoretical structure for the general state space markov decision chain two examples illustrate the results example 1 is a system of parallel queues with stochastic work requirements a movable server with controllable service rate and a reject option example 2 is a system of parallel queues with stochastic controllable inputs a movable server with fixed service rates and a reject option

correlation decay in random decision networks we consider a decision network on an undirected graph in which each node corresponds to a decision variable and each node and edge of the graph is associated with a reward function whose value depends only on the variables of the corresponding nodes the goal is to construct a decision vector that maximizes the total reward this decision problem encompasses a variety of models including maximum likelihood inference in graphical models markov random fields combinatorial optimization on graphs economic team theory and statistical physics the network is endowed with a probabilistic structure in which rewards are sampled from a distribution our aim is to identify sufficient conditions on the network structure and rewards distributions to guarantee average case polynomiality of the underlying optimization problem additionally we wish to characterize the efficiency of a decentralized solution generated on the basis of local information we construct a new decentralized algorithm called cavity expans

on the convergence of policy iteration in finite state undiscounted markov decision processes the unichain case we study the convergence of policy iteration for the undiscounted finite state discrete time markov decision problem with compact action space and unichain transition structure using a newton method type representation for policy iteration we establish the existence of a solution to the optimality equation we show that to find an average optimal policy it is sufficient to solve the optimality equation on the recurrent set of the maximizing policy under the additional assumption of a unique maximizing policy at each stage of the policy iteration procedure we show that the iterates are convergent and the resulting policy is blackwell optimal

the labeled multi bernoulli filter this paper proposes a generalization of the multi bernoulli filter called the labeled multi bernoulli filter that outputs target tracks moreover the labeled multi bernoulli filter does not exhibit a cardinality bias due to a more accurate update approximation compared to the multi bernoulli filter by exploiting the conjugate prior form for labeled random finite sets the proposed filter can be interpreted as an efficient approximation of the delta generalized labeled multi bernoulli filter it inherits the advantages of the multi bernoulli filter in regards to particle implementation and state estimation it also inherits advantages of the delta generalized labeled multi bernoulli filter in that it outputs labeled target tracks and achieves better performance