error bounds for joint detection and estimation of a single object with random finite set observation this paper considers the performance limits for joint detection and estimation from a finite set valued observation that is stochastically related to the state or parameter of interest detection refers to inference about the existence of the state whereas estimation refers to inference about its value when detected since we need to determine the existence non existence of the state as well as its value the usual notion of euclidean distance error does not jointly capture detection and estimation error in a meaningful manner treating the state as set which can be either empty or singleton admits a meaningful distance error for joint detection and estimation we derive bounds on this distance error for a widely used class of observation models when existence of the state is a certainty our bounds coincide with recent results on cramer rao bounds for estimation only problems

geometric polar tracking from bearings only and doppler bearing measurements bearings only tracking bot and doppler bearing tracking dbt perform target motion analysis from measurements of bearings doppler and bearings respectively the state equations are simple for both the target and observer in the rectangular coordinates hence bot and dbt mostly work in that coordinate by developing the trigonometric relations between target and observer postions over time this paper first derives the pseudolinear equations for direct range and bearing estimation it then provides a generalized total least squares gtls and a maximum likelihood solution polar tracking has two advantages over rectangular first for applications that require range and bearing polar output avoids a coordinate conversion at every output instant second polar equations often have a smaller bias than rectangular consequently polar estimates can give a closer to the optimum initialization for iterative algorithms simulation results have validated the theoretical development confirming the near optimality of the gtls and maximum likelihood solutions

performance bounds for estimating vector systems we propose a unified framework for the analysis of estimators of geometrical vector quantities and vector systems through a collection of performance measures unlike standard performance indicators these measures have intuitive geometrical and physical interpretations are independent of the coordinate reference frame and are applicable to arbitrary parameterizations of the unknown vector or system of vectors for each measure we derive both finite sample and asymptotic lower bounds that hold for large classes of estimators and serve as benchmarks for the assessment of estimation algorithms like the performance measures themselves these bounds are independent of the reference coordinate frame and we discuss their use as system design criteria

generalized sliding mode control for multi input nonlinear systems the purpose of this paper is to present a framework for the design of sliding mode based controllers for multi input affine nonlinear systems in this framework the control effort goes to zero as the state approaches the sliding surface a key feature for practical implementation the sliding surface is a submanifold with codimension equal to the dimension of the involutive distribution g generated by the controlled vector fields rather than the dimension of their linear span we also allow nonzero vectors in g to be tangent to the sliding surface the singular case in sliding mode control

compensating drift vector fields with gradient vector fields for asymptotic submanifold stabilization we derive sufficient conditions on a drift vector field to let an asymptotically stable invariant submanifold of an input affine system without drift remain asymptotically stable for the system with drift in doing so we use the same feedback laws modulo control gain tuning such that no new feedback laws need to be designed for the system with drift our main assumption is that the vector field of the input affine system without drift assumes the form of a gradient vector field for given feedback laws we show how one can assess the performance of the system with drift only via knowledge about the system without drift finally we find that our results are relevant in synchronization problems and backstepping controllers for mechanical systems

bounds on achievable performance in the identification and adaptive control of time varying systems treats the identification and adaptive control of time varying linear systems for linear systems with a gauss markov parameter process a global lower bound on the mean square error is obtained which is valid for any causal parameter estimator a similar lower bound is obtained for any causal one step ahead predictor these bounds are applied to the adaptive control of time varying systems to obtain a lower bound on closed loop mean square performance for any causal control law for a specific control law mean square stability is established and through simulations it is seen that the performance nearly meets the theoretical lower bound

an input output framework for submanifold stabilization we study submanifold stabilization problems from an input output perspective where plant and controller are relations on their sets of input output signals in contrast to the classical input output approaches we consider signals whose integral p fold distance to a submanifold is finite for feedback interconnections of relations on such signals we develop a framework to show that the distance of the output of the plant to the desired submanifold remains bounded within this framework we present a small gain theorem a feedback theorem for conic relations and a feedback theorem for passive relations we connect our findings to multiplier theory and present applications to synchronization and pattern generation

an efficient framework for fluid structure interaction using the lattice boltzmann method and immersed moving boundaries this paper presents a serial computational framework that hydrodynamically couples the lattice boltzmann method lbm and the discrete element method dem for the solution of particle suspension problems in two and three dimensions the single relaxation time bhatnagar gross krook lbgk form of the lattice boltzmann equation is employed with an immersed moving boundary method for the fluid structure interaction similar algorithms have been previously reported in the literature however this work deliberately utilizes solution options that minimize the computational overheads of the framework to facilitate simulations of multibody structural fields in large fluid domains in particular mixed boundary conditions are employed which combine the simple bounce back technique with the immersed moving boundary method and the relatively inexpensive d3q15 lattice is employed for 3d solutions the fundamentals of the lbm are briefly discussed followed by a review of the coupling techniques available for fsi using the lbm options for mapping solid obstacles to the lbm grid are presented and an algorithm for automatic dynamic subcycling of the two explicit solution schemes is outlined the lbm dem framework is then validated and benchmarked against previously published lbm results with comments made where appropriate on the comparative accuracy and convergence characteristics finally a multi particle suspension simulation is presented to qualitatively assess the performance of the framework when a large number of dynamic contacts exist

a novel power bearing approach and asymptotically optimum estimator for target motion analysis the problem of target motion analysis tma has been extensively investigated using bearing only bo doppler bearing db and other measurement data for radio frequency rf emitters signal powers follow the well known path loss law that can be utilized to aid localization and target tracking in bo tma leading to the novel power bearing pb approach as proposed in this paper our main contribution lies in the proof of the asymptotic optimality of the total least squares tls algorithm for pb tma under some mild condition the cramer rao lower bound crlb is employed to demonstrate the performance improvements of the pb tma over the bo tma our work shows the promise of the pb tma approach for rf signals

combined three dimensional lattice boltzmann method and discrete element method for modelling fluid particle interactions with experimental assessment a general algorithmic framework is established in this paper for numerical simulations of three dimensional fluid particle interaction problems with a large number of moving particles in turbulent flows using a combined lattice boltzmann method lbm and discrete element method dem in this approach the fluid field is solved by the extended three dimensional lbm with the incorporation of the smagorinsky turbulence model while particle interactions are modelled by the dem the hydrodynamic interactions between fluid and particles are realized through the extension of an existing two dimensional fluid particle hydrodynamic interaction scheme the main computational aspects comprise the lattice boltzmann formulation for the solution of fluid flows the incorporation of a large eddy simulation based turbulence model within the framework of the three dimensional lbm for turbulent flows the moving boundary condition for hydrodynamic interactions between fluid and moving particles and the discrete element modelling of particle particle interactions to assess the solution accuracy of the proposed approach a much simplified laboratory model of vacuum dredging systems for mineral recovery is employed the numerical results are compared with the experimental data available it shows that the overall correspondence between numerical results and experimental measurements is good and thus indicates to a certain extent the solution accuracy of the proposed methodology copyright 2009 john wiley sons ltd

cramer rao bound for nonlinear filtering with pd 1 and its application to target tracking the paper investigates the cramer rao bound for discrete time nonlinear filtering in the case where the probability of detection of a sensor is less than unity the theoretical formula involves the evaluation of exponentially growing number of possible miss detection sequences an approximation of the theoretical bound for practical applications such as target tracking where the number of sensor scans is large is proposed an application of the developed techniques to the well known filtering problem of tracking a re entry ballistic object is also presented

on the central difference algorithm in discrete element modelling of impact the paper provides a comprehensive analysis of the accuracy and stability of the central difference scheme when applied to simulate a simple impact problem in the context of the discrete element approach it is revealed that the algorithm exhibits some different behaviour due to the inherent nonlinearity discontinuity of the impact system particularly for an elastic or slightly inelastic impact the stable unstable region governing the selection of a maximum time step size is essentially different from that defined by the conventional linear stability criterion and thus a smaller time step should be employed in order to reduce the possible occurrence of an unexpected numerical instability

matrix crlb scaling due to measurements of uncertain origin in many estimation situations measurements are of uncertain origin this is best exemplified by the target tracking situation in which at each scan of a radar sonar or electro optical sensor a number of measurements are obtained and it is not known which if any of these is target originated the source of extraneous measurements can be false alarms especially in low snr situations that force the detector at the end of the signal processing chain to operate with a reduced threshold or spurious targets in several earlier papers the surprising observation was made that the cramer rao lower bound crlb for the estimation of a fixed parameter vector e g initial position and velocity that characterizes the target motion for the special case of multidimensional measurements in the presence of additive white gaussian noise is simply a multiple of that for the case with no uncertainty that is there is a scalar information reduction factor this is particularly useful as it allows comparison in terms of a scalar in this paper we explore this result to determine how wide the class of such problems is it turns out to include many non gaussian situations simulations corroborate the analysis

a tracking filter for maneuvering sources an adaptive filter that is based on the pontryagin minimum principle and the method of invariant imbedding is introduced and applied to the problem of tracking maneuvering sources the major advantages of this approach are 1 no model for the target dynamics is required and 2 the signal to noise ratio of the observation and stations need to be known the performance of the proposed approach with unknown system dynamics is compared to that of the extended kalman filter with known system dynamics for the maneuvering reentry vehicle examples are given for different target scenarios

analysis and computation of limit cycles for systems with separable nonlinearities the variational system obtained by linearizing a dynamical system along a limit cycle is always non invertible this follows because the limit cycle is only a unique modulo time translation it is shown that questions such as uniqueness robustness and computation of limit cycles can be addressed using a right inverse of the variational system small gain arguments are used in the analysis

weiss weinstein lower bounds for markovian systems part 1 theory being essentially free from regularity conditions the weiss weinstein estimation error lower bound can be applied to a larger class of systems than the well known crameacuter rao lower bound thus this bound is of special interest in applications involving hybrid systems i e systems with both continuously and discretely distributed parameters which can represent in practice fault prone systems however the requirement to know explicitly the joint distribution of the estimated parameters with all the measurements makes the application of the weiss weinstein lower bound to markovian dynamic systems cumbersome a sequential algorithm for the computation of the crameacuter rao lower bound for such systems has been recently reported in the literature along with the marginal state distribution the algorithm makes use of the transitional distribution of the markovian state process and the distribution of the measurements at each time step conditioned on the appropriate states both easily obtainable from the system equations a similar technique is employed herein to develop sequential weiss weinstein lower bounds for a class of markovian dynamic systems in particular it is shown that in systems satisfying the crameacuter rao lower bound regularity conditions the sequential weiss weinstein lower bound derived herein reduces for a judicious choice of its parameters to the sequential crameacuter rao lower bound

posterior cramer rao bounds for discrete time nonlinear filtering a mean square error lower bound for the discrete time nonlinear filtering problem is derived based on the van trees 1968 posterior version of the cramer rao inequality this lower bound is applicable to multidimensional nonlinear possibly non gaussian dynamical systems and is more general than the previous bounds in the literature the case of singular conditional distribution of the one step ahead state vector given the present state is considered the bound is evaluated for three important examples the recursive estimation of slowly varying parameters of an autoregressive process tracking a slowly varying frequency of a single cisoid in noise and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation

proteus a direct forcing method in the simulations of particulate flows a new and efficient direct numerical method for the simulation of particulate flows is introduced the method combines desired elements of the immersed boundary method the direct forcing method and the lattice boltzmann method adding a forcing term in the momentum equation enforces the no slip condition on the boundary of a moving particle by applying the direct forcing scheme proteus eliminates the need for the determination of free parameters such as the stiffness coefficient in the penalty scheme or the two relaxation parameters in the adaptive forcing scheme the method presents a significant improvement over the previously introduced immersed boundary lattice boltzmann method ib lbm where the forcing term was computed using a penalty method and a user defined parameter the method allows the enforcement of the rigid body motion of a particle in a more efficient way compared to the bounce back scheme used in the conventional lbm the direct forcing method provides a smoother computational boundary for particles and is capable of achieving results at higher reynolds number flows by using a set of lagrangian points to track the boundary of a particle proteus eliminates any need for the determination of the boundary nodes that are prescribed by the bounce back scheme at every time step it also makes computations for particles of irregular shapes simpler and more efficient proteus has been developed in two as well as three dimensions this new method has been validated by comparing its results with those from experimental measurements for a single sphere settling in an enclosure under gravity as a demonstration of the efficiency and capabilities of the present method the settling of a large number 1232 of spherical particles is simulated in a narrow box under two different boundary conditions it is found that when the no slip boundary condition is imposed at the front and rear sides of the box the particles motion is significantly hindered under the periodic boundary conditions the particles move faster the simulations show that the sedimentation characteristics in a box with periodic boundary conditions at the two sides are very close to those found in the sedimentation of two dimensional circular particles

pattern generation and the control of nonlinear systems many important engineering systems accomplish their purpose using cyclic processes whose characteristics are under feedback control examples involving thermodynamic cycles and electromechanical energy conversion processes are particularly noteworthy likewise cyclic processes are prevalent in nature and the idea of a pattern generator is widely used to rationalize mechanisms used for orchestrating movements such as those involved in locomotion and respiration in this paper we develop a linkage between the use of cyclic processes and the control of nonholonomic systems emphasizing the problem of achieving stable regulation the discussion brings to the fore characteristic phenomena that distinguish the regulation problem for such strongly nonlinear systems from the more commonly studied linear feedback regulators finally we compare this approach to controlling nonholonomic systems to another approach based on the idea of an open loop approximate inverse as discussed in the literature

filtering predictive and smoothing cramer rao bounds for discrete time nonlinear dynamic systems cramer rao lower bounds for the discrete time nonlinear state estimation problem are treated the cramer rao bound for the mean square error matrix of a state estimate is particularly important for quality evaluation of nonlinear state estimators as it represents a limit of cognizability of the state recursive relations for filtering predictive and smoothing cramer rao bounds are derived to establish a unifying framework for several previously published derivation procedures and results lower bounds for systems with unknown parameters are newly provided computation of filtering predictive and smoothing cramer rao bounds their mutual comparison and utilization for quality evaluation of some nonlinear filters are shown in numerical examples

coupled lattice boltzmann method and discrete element modelling of particle transport in turbulent fluid flows computational issues this paper presents essential numerical procedures in the context of the coupled lattice boltzmann lb and discrete element de solution strategy for the simulation of particle transport in turbulent fluid flows key computational issues involved are 1 the standard lb formulation for the solution of incompressible fluid flows 2 the incorporation of large eddy simulation les based turbulence models in the lb equations for turbulent flows 3 the computation of hydrodynamic interaction forces of the fluid and moving particles and 4 the de modelling of the interaction between solid particles a complete list is provided for the conversion of relevant physical variables to lattice units to facilitate the understanding and implementation of the coupled methodology additional contributions made in this work include the application of the smagorinsky turbulence model to moving particles and the proposal of a subcycling time integration scheme for the de modelling to ensure an overall stable solution a particle transport problem comprising 70 large particles and high reynolds number around 56 000 is provided to demonstrate the capability of the presented coupling strategy copyright 2007 john wiley sons ltd

the recursive form of error bounds for rfs state and observation with p_d this paper presents recursive performance bounds for dynamic estimation and tracking problems in both single and multiple target cases within the framework of finite set statistics because the targets can appear and disappear when the detection probability of a sensor is less than unity pd 1 we must determine the existence or nonexistence of the state as well as its value following the possible detection miss sequences within the framework of a random vector possible observation sets sequences are first defined based on these sequences the performance bounds can be represented by a multivariate function of some time based auxiliary elements recursive relations for all the auxiliary elements are derived rigorously for the multitarget case this recursive estimated bound can be applied without data association applications are analyzed through simulations to verify our theoretical results and show that our bounds are tighter than all other bounds for the case where detection probability pd 1

utilization of modified polar coordinates for bearings only tracking previous studies have shown that the cartesian coordinate extended kalman filter exhibits unstable behavior characteristics when utilized for bearings only target motion analysis tma in contrast formulating the tma estimation problem in modified polar mp coordinates leads to an extended kalman filter which is both stable and asymptotically unbiased exact state equations for the mp filter are derived without imposing any restrictions on own ship motion thus prediction accuracy inherent in the traditional cartesian formulation is completely preserved in addition these equations reveal that mp coordinates are well suited for bearings only tma because they automatically decouple observable and unobservable components of the estimated state vector such decoupling is shown to prevent covariance matrix ill conditioning which is the primary cause of filter instability further investigation also confirms that the mp state estimates are asymptotically unbiased realistic simulation data are presented to support these findings and to compare algorithm performance with respect to the cramer rao lower bound ideal as well as the cartesian and pseudolinear filters

stabilization of bilinear sparse matrix control systems using periodic inputs abstract in this brief paper using results from the theory of averaging of bilinear systems we provide a graph theoretic characterization for the existence of periodic control inputs that stabilize a sparse matrix system to the origin in particular we introduce a class of extensions to the directed graph corresponding to a given sparse matrix system which when contains a stable sparse matrix system implies that the original system is stabilizable using periodic inputs when this condition holds we provide a systematic procedure for designing such controllers our technical approach combines ideas from the theory of bilinear control systems and averaging theory with graph theoretic results

regular article an accurate curved boundary treatment in the lattice boltzmann method the lattice boltzmann equation lbe is an alternative kinetic method capable of solving hydrodynamics for various systems major advantages of the method are due to the fact that the solution for the particle distribution functions is explicit easy to implement and natural to parallelize because the method often uses uniform regular cartesian lattices in space curved boundaries are often approximated by a series of stairs that leads to reduction in computational accuracy in this work a second order accurate treatment of the boundary condition in the lbe method is developed for a curved boundary the proposed treatment of the curved boundaries is an improvement of a scheme due to o filippova and d hanel 1998 j comput phys 147 219 the proposed treatment for curved boundaries is tested against several flow problems 2 d channel flows with constant and oscillating pressure gradients for which analytic solutions are known flow due to an impulsively started wall lid driven square cavity flow and uniform flow over a column of circular cylinders the second order accuracy is observed with a solid boundary arbitrarily placed between lattice nodes the proposed boundary condition has well behaved stability characteristics when the relaxation time is close to 1 2 the zero limit of viscosity the improvement can make a substantial contribution toward simulating practical fluid flow problems using the lattice boltzmann method

improved coupling of time integration and hydrodynamic interaction in particle suspensions using the lattice boltzmann and discrete element methods this paper introduces improvements to the simulation of particle suspensions using the lattice boltzmann method lbm and the discrete element method dem first the benefit of using a two relaxation time trt collision operator instead of the popular bhatnagar gross krook bgk collision operator is demonstrated second a modified solid weighting function for the partially saturated method psm for fluid solid interaction is defined and tested results are presented for a range of flow configurations including sphere packs duct flows and settling spheres with good accuracy and convergence observed past research has shown that the drag and consequently permeability predictions of the lbm exhibit viscosity dependence when used with certain boundary conditions such as bounce back or interpolated bounce back and this is most pronounced when the bgk collision operator is employed the improvements presented here result in a range of computational viscosities and therefore relaxation parameters within which drag and permeability predictions remain invariant this allows for greater flexibility in using the relaxation parameter to adjust the lbm timestep which can subsequently improve synchronisation with the time integration of the dem this has significant implications for the simulation of large scale suspension phenomena where the limits of computational hardware persistently constrain the resolution of the lbm lattice c 2018 elsevier ltd all rights reserved

a contribution to the control of the non holonomic integrator including drift in this paper a three dimensional non holonomic integrator ni with drift terms is considered for this type of plant the question how to obtain desired piecewise constant output functions with minimum norm control inputs is explored it is shown that this can be achieved by a nonlinear controller that provides simultaneous modulation of both the amplitude and the frequency of the harmonic input vector the internal states are implicitly forced to follow natural periodic orbits satisfying the non holonomic constraints of the plant global asymptotic stability and high dynamics in the output response are achieved the problem of singularity at zero initial state is solved by a time optimal control scheme for the internal states by combining the nonlinear controller and the time optimal controller using an appropriate switching strategy a powerful control concept can be established the torque control of an induction machine is considered as an illustrative example for the application of the control scheme experimental results of the closed loop feedback control system are presented

hybrid invariant manifolds in systems with impulse effects with application to periodic locomotion in bipedal robots motivated by the problem of controlling walking in a biped with series compliant actuation this paper develops two main theorems relating to the stabilization of periodic orbits in systems with impulse effects the first main result shows that when a periodic orbit of a system with impulse effects lies within a hybrid invariant manifold there exist local coordinate transforms under which the jacobian linearization of the poincare return map has a block upper triangular structure one diagonal block is the linearization of the system as restricted to the hybrid invariant manifold also called the hybrid zero dynamics the other is the product of two sensitivity matrices related to the transverse dynamics one pertaining to the impact map and the other pertaining to the closed loop vector field when either of these sensitivity matrices is sufficiently close to zero the stability of the return map is determined solely by the stability of the hybrid zero dynamics the second main result of the paper details the construction of a hybrid invariant manifold such as that required by the first main theorem forward invariance follows from the methods of byrnes and isidori and impact invariance is achieved by a novel construction of impact updated control parameters in addition to providing impact invariance the construction allows entries of the impact sensitivity matrix of the transverse dynamics to be made arbitrarily small a simulation example is provided where stable walking is achieved in a 5 link biped with series compliant actuation

a new continuous discrete particle filter for continuous discrete nonlinear systems abstract the continuous discrete version of particle filter cd pf for continuous discrete nonlinear systems is proposed in this paper firstly the continuous discrete extended kalman filter cd ekf and the cd pf are described in detail then some comparisons of these two methods are carried out the simulation results show that the performance of the cd pf is better than that of the cd ekf then higher order stochastic runge kutta schemes are proposed to improve the stability and precision of the filter furthermore the cd pf is applied to nonlinear systems with nongaussian noise finally some simulations are provided to illustrate the effectiveness of the proposed filter

a comparison of two crame spl acute r rao bounds for nonlinear filtering with p sub d 1 the paper presents a comparative study of two recently reported crame spl acute r rao lower bounds crlbs for nonlinear filtering both applicable when the probability of detection is less than unity the first bound is the information reduction factor crlb the second is the enumeration method crlb the enumeration method is accurate but computationally expensive we prove in the paper that the information reduction factor bound is overoptimistic being always less than the enumeration crlb the theory is illustrated by two target tracking applications ballistic object tracking and bearings only tracking the simulations studies confirm the theory and reveal that the information reduction factor crlb rapidly approaches the enumeration crlb as the scan number increases

asymptotic stabilization of submanifolds embedded in riemannian manifolds we study control problems in which systems whose states spaces are riemannian manifolds must be steered towards embedded submanifolds of their state spaces in a stable fashion i e feedback laws rendering the given submanifold asymptotically stable are sought bringing the closed loop to the form of a gradient system with drift we find that the gradient part can be scaled in a fashion so as to guarantee asymptotic stability of the desired submanifold under this circumstance we show that solutions of the system can be brought to an arbitrarily small neighborhood of the submanifold in arbitrary time thereafter we derive an algebraic condition under which the control vector fields can be brought to the desired form lastly we recast our algebraic condition in terms of vertical and horizontal spaces for the case that the submanifold is an equivalence class