cyclic codes and sequences from generalized coulter matthews function in this paper we will study the exponential sum sigmaxisinfq x alphax pk 1 2 betax that is related to the generalized coulter matthews function x pk 1 2 with k gcd as applications we obtain the following the correlation distribution of a p ary m sequence and a decimated m sequence of degree pk 1 2 the weight distribution of the cyclic code whose dual has two zeros pi 1 and pi pk 1 2

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

mistuning based control design to improve closed loop stability margin of vehicular platoons we consider a decentralized bidirectional control of a platoon of n identical vehicles moving in a straight line the control objective is for each vehicle to maintain a constant velocity and inter vehicular separation using only the local information from itself and its two nearest neighbors each vehicle is modeled as a double integrator to aid the analysis we use continuous approximation to derive a partial differential equation pde approximation of the discrete platoon dynamics the pde model is used to explain the progressive loss of closed loop stability with increasing number of vehicles and to devise ways to combat this loss of stability if every vehicle uses the same controller we show that the least stable closed loop eigenvalue approaches zero as o 1 n2 in the limit of a large number n of vehicles we then show how to ameliorate this loss of stability by small amounts of mistuning i e changing the controller gains from their nominal values we prove that with arbitrary small amounts of mistuning the asymptotic behavior of the least stable closed loop eigenvalue can be improved to o 1 n all the conclusions drawn from analysis of the pde model are corroborated via numerical calculations of the state space platoon model

multiobject tracking for generic observation model using labeled random finite sets this paper presents an exact bayesian filtering solution for the multiobject tracking problem with the generic observation model the proposed solution is designed in the labeled random finite set framework using the product styled representation of labeled multiobject densities with the standard multiobject transition kernel and no particular simplifying assumptions on the multiobject likelihood computationally tractable solutions are also devised by applying a principled approximation involving the replacement of the full multiobject density with a labeled multi bernoulli density that minimizes the kullback leibler divergence and preserves the first order moment to achieve the fast performance a dynamic grouping procedure based implementation is presented with a step by step algorithm the performance of the proposed filter and its tractable implementations are verified and compared with the state of the art in numerical experiments

a family of m sequences with five valued cross correlation finding the cross correlation between two m sequences st and sdt of the same period 2m 1 that differ by a decimation d has been a popular research problem since the 1960s many cases with three and four valued correlation have been determined several values of d are known to lead to five valued cross correlation but their exact correlation distribution has been open the correlation distribution is completely determined for one of these families with five valued cross correlation by using evaluations of certain exponential sums including kloosterman sums the decimation considered is the special decimation d 22k 1 2k 1where m is odd and k 1 i e d 5 3 the paper introduces some techniques that may be useful to obtain further results on related decimations

cross correlation of m sequences of different lengths we consider the distribution of the cross correlation between m sequences of period 2 sup m 1 where m 2k and m sequences of shorter period 2 sup k 1 we present some general properties of the cross correlation between these m sequences and we find some decimations with 3 valued cross correlation we further present some numerical results and open problems

distributed averaging via lifted markov chains motivated by applications of distributed linear estimation distributed control and distributed optimization we consider the question of designing linear iterative algorithms for computing the average of numbers in a network specifically our interest is in designing such an algorithm with the fastest rate of convergence given the topological constraints of the network as the main result of this paper we design an algorithm with the fastest possible rate of convergence using a nonreversible markov chain on the given network graph we construct such a markov chain by transforming the standard markov chain which is obtained using the metropolis hastings method we call this novel transformation pseudo lifting we apply our method to graphs with geometry or graphs with doubling dimension specifically the convergence time of our algorithm equivalently the mixing time of our markov chain is proportional to the diameter of the network graph and hence optimal as a byproduct our result provides the fastest mixing markov chain given the network topological constraints and should naturally find their applications in the context of distributed optimization estimation and control

derivation of new and existing discrete time kharitonov theorems based on discrete time reactances digital signal processing the author first uses a discrete time reactance approach to give a second proof of existing discrete time kharitonov type results 1979 he then uses the same reactance language to derive a new discrete time kharitonov type theorem which in some sense is a very close analog to the continuous time case he also points out the relation between discrete time reactances and the technique of line spectral pairs lsp used in speech compression

a new family of four valued cross correlation between m sequences of different lengths the cross correlation function between m sequences of period 2m 1 where m 6k and m sequences of shorter period 2m 2 1 is investigated the first infinite family of pairs of m sequences with four valued cross correlation is constructed and the complete correlation distribution of this family is determined

joint detection and estimation of multiple objects from image observations the problem of jointly detecting multiple objects and estimating their states from image observations is formulated in a bayesian framework by modeling the collection of states as a random finite set analytic characterizations of the posterior distribution of this random finite set are derived for various prior distributions under the assumption that the regions of the observation influenced by individual objects do not overlap these results provide tractable means to jointly estimate the number of states and their values from image observations as an application we develop a multi object filter suitable for image observations with low signal to noise ratio snr a particle implementation of the multi object filter is proposed and demonstrated via simulations

some new results on the cross correlation of m sequences the determination of the cross correlation between an m sequence and its decimated sequence has been a longstanding research problem considering a ternary m sequence of period 33r 1 we determine the cross correlation distribution for decimations d 3r 2 and d 32r 2 where gcd r 3 1 meanwhile for a binary m sequence of period 22lm 1 we make an initial investigation for the decimation d 22lm 1 2m 1 2s where l 2 is even and 0 s 2m 1 it is shown that the cross correlation takes at least four values furthermore we confirm the validity of two famous conjectures due to sarwate et al and helleseth in this case

chebyshev polynomials in distributed consensus applications in this paper we analyze the use of chebyshev polynomials in distributed consensus applications it is well known that the use of polynomials speeds up the convergence to the consensus in a significant way however existing solutions only work for low degree polynomials and require the topology of the network to be fixed and known we propose a distributed algorithm based on the second order difference equation that describes the chebyshev polynomials of first kind the contributions of our algorithm are three i since the evaluation of chebyshev polynomials is stable there is no limitation in the degree of the polynomial ii instead of the knowledge of the whole network topology it only requires a partial knowledge or an approximation to it iii it can be applied to time varying topologies in the paper we characterize the main properties of the algorithm for both fixed and time varying communication topologies theoretical results as well as experiments with synthetic data show the benefits of using our algorithm compared to existing methods

niho type cross correlation functions via dickson polynomials and kloosterman sums suppose that n 2k is even we study the cross correlation function between two m sequences for niho type decimations d 2 sup k 1 s 1 we develop a new technique to study the value distribution of these cross correlation functions which makes use of dickson polynomials as a first application we derive here the distribution of the six valued cross correlation function for s 3 and odd k up to a term which depends on kloosterman sums in addition applying simpler methods we prove a theorem providing niho type decimations with four valued cross correlation functions and their distribution we conjecture that the latter result actually covers all such decimations

ternary m sequences with three valued cross correlation function new decimations of welch and niho type we show that the cross correlation between two ternary m sequences of period 3 sup n 1 that differ by the decimation d 2 spl middot 3 sup m 1 where n 2m 1 takes on three different values we conjecture the same result for the decimation d 2 spl middot 3 sup r 1 where n is odd and r is defined by the condition 4r 1 spl equiv 0 mod n these two new cases form in a sense ternary counterparts of two previously confirmed binary cases the conjectures of welch and niho 1972

visual tracking in background subtracted image sequences via multi bernoulli filtering this correspondence presents a novel method for simultaneous tracking of multiple non stationary targets in video our method operates directly on the video data and does not require any detection we propose a multi target likelihood function for the background subtracted grey scale image data which admits multi target conjugate priors this allows the multi target posterior to be efficiently propagated forward using the multi bernoulli filter our method does not need any training pattern or target templates and makes no prior assumptions about object types or object appearance case studies from the caviar dataset show that our method can automatically track multiple targets and quickly finds targets entering or leaving the scene

graph diameter eigenvalues and minimum time consensus we consider the problem of achieving average consensus in the minimum number of linear iterations on a fixed undirected graph we are motivated by the task of deriving lower bounds for consensus protocols and by the so called definitive consensus conjecture which states that for an undirected connected graph g with diameter d there exist d matrices whose nonzero pattern complies with the edges in g and whose product equals the all ones matrix our first result is a counterexample to the definitive consensus conjecture which is the first improvement of the diameter lower bound for linear consensus protocols we then provide some algebraic conditions under which this conjecture holds which we use to establish that all distance regular graphs satisfy the definitive consensus conjecture

some new three valued crosscorrelation functions for binary m sequences in 1972 niho gave various conjectures about the crosscorrelation between a binary maximum length linear shift register sequence and a decimation of that sequence by an integer d we prove that the crosscorrelation function for two new values of d takes on precisely three values and thereby confirm two of niho s conjectures

polynomial filtering for fast convergence in distributed consensus in the past few years the problem of distributed consensus has received a lot of attention particularly in the framework of ad hoc sensor networks most methods proposed in the literature address the consensus averaging problem by distributed linear iterative algorithms with asymptotic convergence of the consensus solution the convergence rate of such distributed algorithms typically depends on the network topology and the weights given to the edges between neighboring sensors as described by the network matrix in this paper we propose to accelerate the convergence rate for given network matrices by the use of polynomial filtering algorithms the main idea of the proposed methodology is to apply a polynomial filter on the network matrix that will shape its spectrum in order to increase the convergence rate such an algorithm is equivalent to periodic updates in each of the sensors by aggregating a few of its previous estimates we formulate the computation of the coefficients of the optimal polynomial as a semidefinite program that can be efficiently and globally solved for both static and dynamic network topologies we finally provide simulation results that demonstrate the effectiveness of the proposed solutions in accelerating the convergence of distributed consensus averaging problems

void probabilities and cauchy schwarz divergence for generalized labeled multi bernoulli models the generalized labeled multi bernoulli glmb is a family of tractable models that alleviates the limitations of the poisson family in dynamic bayesian inference of point processes in this paper we derive closed form expressions for the void probability functional and the cauchy schwarz divergence for glmbs the proposed analytic void probability functional is a necessary and sufficient statistic that uniquely characterizes a glmb while the proposed analytic cauchy schwarz divergence provides a tractable measure of similarity between glmbs we demonstrate the use of both results on a partially observed markov decision process for glmbs with cauchy schwarz divergence based reward and void probability constraint

a generalization of kharitonov s four polynomial concept for robust stability problems with linearly dependent coefficient perturbations kharitonov s four polynomial concept is generalized to the case of linearly dependent coefficient perturbations and more general zero location regions to this end a specially constructed scalar function of a scalar variable is instrumental to the robustness analysis the present work is motivated by two fundamental limitations of kharitonov s theorem namely 1 the theorem only applies to polynomials with independent coefficient perturbations and 2 it only applies to zeros in the left hand plane

cphd filtering with unknown clutter rate and detection profile in bayesian multi target filtering we have to contend with two notable sources of uncertainty clutter and detection knowledge of parameters such as clutter rate and detection profile are of critical importance in multi target filters such as the probability hypothesis density phd and cardinalized phd cphd filters significant mismatches in clutter and detection model parameters result in biased estimates in practice these model parameters are often manually tuned or estimated offline from training data in this paper we propose phd cphd filters that can accommodate model mismatch in clutter rate and detection profile in particular we devise versions of the phd cphd filters that can adaptively learn the clutter rate and detection profile while filtering moreover closed form solutions to these filtering recursions are derived using beta and gaussian mixtures simulations are presented to verify the proposed solutions

multiple object tracking in unknown backgrounds with labeled random finite sets this paper proposes an online multiple object tracker that can operate under unknown detection profile and clutter rate in a majority of multiple object tracking applications model parameters for background processes such as clutter and detection are unknown and vary with time hence the ability of the algorithm to adaptively learn these parameters is essential in practice in this paper we detail how the generalized labeled multibernoulli filter a tractable and provably bayes optimal multiobject tracker can be tailored to learn clutter and detection parameters on the fly while tracking provided that these background model parameters do not fluctuate rapidly compared to the data rate the proposed algorithm can adapt to the unknown background yielding better tracking performance

labeled random finite sets and multi object conjugate priors the objective of multi object estimation is to simultaneously estimate the number of objects and their states from a set of observations in the presence of data association uncertainty detection uncertainty false observations and noise this estimation problem can be formulated in a bayesian framework by modeling the hidden set of states and set of observations as random finite sets rfss that covers thinning markov shifts and superposition a prior for the hidden rfs together with the likelihood of the realization of the observed rfs gives the posterior distribution via the application of bayes rule we propose a new class of rfs distributions that is conjugate with respect to the multiobject observation likelihood and closed under the chapman kolmogorov equation this result is tested on a bayesian multi target tracking algorithm

some discrete time counterparts to kharitonov s stability criterion for uncertain systems in 1 kharitonov gave an elegant and simple stability criterion for continuous time systems this note reports on similar results for discrete time systems

analysis of accelerated gossip algorithms gossiping is a distributed process whose purpose is to enable the members of a group of n 1 autonomous agents to asymptotically determine in a decentralized manner the average of the initial values of their scalar gossip variables this paper analyzes the accelerated gossip algorithms first proposed in cao spielman and yeh 2006 in which local memory is exploited by installing shift registers at each agent for the two register case the existence of the desired convergence is established under a symmetry assumption by separately studying the convergence in expectation and in mean square in particular the optimal rate of convergence in expectation is derived which is faster than that of the standard gossip algorithm and a sufficient condition on the adjustable parameter for the convergence in mean square is provided these theoretical results are validated for some classes of networks by comparison with existing empirical data more general multi register cases are also discussed

adding a single state memory optimally accelerates symmetric linear maps previous papers have proposed to add memory registers to the dynamics of discrete time linear systems in order to accelerate their convergence in particular it has been proved that adding one memory slot per agent allows faster convergence towards average consensus we here prove that this situation cannot be improved by adding more memory slots when the knowledge about the self adjoint linear map to be accelerated reduces to bounds on its extreme eigenvalues

binary m sequences with three valued crosscorrelation a proof of welch s conjecture we prove the long standing conjecture of welch stating that for odd n 2m 1 the power function x sup d with d 2 sup m 3 is maximally nonlinear on gf 2 sup n or in other terms that the crosscorrelation function between a binary maximum length linear shift register sequence of degree n and a decimation of that sequence by 2 sup m 3 takes on precisely the three values 1 1 spl plusmn 2 sup m 1

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

cross correlation distribution of p ary m sequence of period p 4k 1 and its decimated sequences by left p 2k 1 over 2 right 2 for an odd prime p n 4k and d p2k 1 2 2 there are p2k 1 2 distinct decimated sequences s dt l 0lesl p2k 2 of a p ary m sequence s t of period pn 1 because gcd d pn 1 p2k 1 2 in this paper it is shown that the cross correlation function between s t and s dt l 0lesl p2k 1 2 takes the values in 1 1 radic pn 1 radic pn 1 2radic pn and their cross correlation distribution is also derived