Mixed-model multiple-hypothesis tracking of targets in clutter

Variable Structure Multiple Model (VSMM) estimation generalizes Multiple Model (MM) estimation by assuming that the set of models used for MM estimation is time varying. By using VSMM estimation, a large model set which may cover all possible target maneuvers can be used without significant increase of computational load, while maintaining a reasonable estimation accuracy. Various implementable VSMM algorithms, like Model Group Switching (MGS), Likely Model Set (LMS) and Minimal Sub-Model-Set Switching (MSMSS) using the Interacting Multiple Model (IMM) algorithm with a sub-model-set adaptation logic have appeared in the recent literature. However, the use of these algorithms for tracking maneuvering target in clutter has not been explored. In presence of clutter, one need to use data association technique to differentiate target originated measurement from clutter. The probabilistic data association (PDA) has been popularly adopted to many algorithms for tracking in clutter. In this paper, we integrate PDA technique with MSMSS and propose a VSIMM-PDA algorithm for maneuvering target tracking in clutter. A new grating technique to account for potential model errors is used. A numeric example via multiple Monte Carlo runs, which compares the performance of the new algorithm to a standard IMM-PDA in terms of Root Mean Squared error (RMS) and percentage of track loss, is presented.© (2003) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

In this paper, a self-tuning hierarchical controller in which a Fuzzy logic controller supervises the control actions of a conventional PID has been proposed, implemented and presented. The controller has been applied to a control study of Fluid Catalytic Cracking (FCC) unit riser temperature, and regenerator temperature respectively. Performance comparison of the proposed Fuzzy-PID controller and the conventional PID was made in simulation studies of regulatory and servo performances of the two controller types. Six performance measures: Percent overshoot (OS), settling time (ST), integral absolute error (IAE), integral square error (ISE), integral time absolute error (ITAE) and integral time square error (ITSE) were employed as the tools for performance comparison between the conventional PID and the Fuzzy-PID controller. For the tracking of riser temperature with a set point at 524oC, the performance indicators under PID control gave the following results overshoot (14.5%); settling time (40 seconds) Integral absolute error (8.246), integral square error (3.3); integral time absolute error(1762);integral time square error (43.77) while for the same indicators under Fuzzy-PID control the following values: overshoot (3.3%); settling time (40 seconds) ;Integral absolute error (8.811); integral square error (14.5); integral time absolute error(280),;integral time square error (31.11) .The results allude to the superiority of the fuzzy-PID scheme over the PID scheme in tracking the optimal set point of riser temperature. More so, for tracking the regenerator set point temperature of 746oC, comparative study of step response under the two schemes gave the following results in six performance indicators: overshoot (PID(12.6%)/Fuzzy-PID(6%)); settling time (PID(80 seconds)/Fuzzy-PID(20seconds));Integral absolute error(PID(14.29)/Fuzzy-PID(8.63)); integral square error(PID(6.713).Fuzzy-PID(4.506)); integral time absolute error(PID(2858)/Fuzzy-PID(305.9)), integral time square error (PID(77.55)/Fuzzy-PID(33.05)).Moreover, the fuzzy-PID controller also showed superior performance over the conventional PID controller in terms disturbance rejection (regulatory response) of both riser and regenerator temperature. The results from this study suggest that the application of fuzzy-PID scheme to temperature control offers good promise of improved fluid catalytic cracking unit (FCCU) operations.

By integrating the cardinality balanced multitarget multi-Bernoulli (CBMeMBer) filter with the interacting multiple models (IMM) algorithm, an MM-CBMeMBer filter is proposed in this paper for tracking multiple maneuvering targets in clutter. The sequential Monte Carlo (SMC) method is used to implement the filter for generic multi-target models and the Gaussian mixture (GM) method is used to implement the filter for linear-Gaussian multi-target models. Then, the extended Kalman (EK) and unscented Kalman filtering approximations for the GM-MM-CBMeMBer filter to accommodate mildly nonlinear models are described briefly. Simulation results are presented to show the effectiveness of the proposed filter.

This paper extends the smoothing algorithm based on integrated probabilistic data association to track multiple maneuvering targets by applying smoothing to joint integrated probabilistic data association (JIPDA). The proposed algorithm utilizes smoothing data association to obtain smoothing prediction which is needed to calculate the smoothing data association probabilities, the smoothing target trajectory state estimates and the smoothing target existence probability. The smoothing data association probabilities are used to update and propagate the forward tracks for tracking multiple maneuvering targets in clutter. This algorithm is called fixed-interval smoothing JIPDA (JIPDAS). Simulation is carried out to show improved false track discrimination performance over the existing algorithms for tracking multiple maneuvering targets in a heavy cluttered environment.

The focus of this research is to provide methods for generating precise parameter estimates in the face of potentially significant parameter variations such as system component failures. The standard multiple model adaptive estimation (MMAE) algorithm uses a bank of Kalman filters, each based on a different model of the system. Parameter discretization within the MMAE refers to selection of the parameter values assumed by the elemental Kalman filters, and dynamically redeclaring such discretization yields a moving-bank MMAE. An online parameter discretization method is developed based on the probabilities associated with the generalized Chi-squared random variables formed by residual information from the elemental Kalman filters within the MMAE. This algorithm is validated through computer simulation of an aircraft navigation system subjected to interference/jamming while attempting a successful precision landing of the aircraft.

In this paper, we consider the problem of radar detector threshold optimization for maneuvering targets in clutter. In the earlier works, the problem was studied in the context of the probabilistic data association filter (PDAF) for non-maneuvering targets. In this study, we have extended the ideas, which were applied to the PDAF, to the interacting multiple model PDAF (IMM-PDAF) for maneuvering targets. The proposed optimization problem and its solution show better results over the traditional approaches in terms of track loss percentage and RMS position error criteria.

For maneuvering target tracking, general interacting multiple model (IMM) algorithms have a fixed structure. It has been overlooked that how the performance of these algorithms depends on the set of models used. The use of too many models is as bad as that of too few models. Therefore, a variable structure IMM (VSIMM) was presented and applied to ground target tracking. This algorithm eliminates the need for carrying all the possible models throughout the entire tracking period as in the standard IMM estimator, significantly improving performance and reducing computational load. But it is difficult to apply the VSIMM to other scenario (for example, aerial target) without auxiliary information such as map for ground target. This paper then presents a model set multiple hypotheses IMM algorithm (MS-MHIMM) which leads to a systematic treatment of model-set adaptation without using any additional auxiliary information. The new approach is illustrated in detail with an aerial complex maneuvering target tracking example.

Data truncation is a commonly accepted method of dealing with initialization bias in discrete-event simulation. An algorithm for determining the appropriate initial-data truncation point for multivariate output is proposed. The technique entails averaging across independent replications and estimating a steady-state output model in a state-space framework. A Bayesian technique called Multiple Model Adaptive Estimation (MMAE) is applied to compute a time varying estimate of the output's steady-state mean vector. This MMAE implementation features the use, in paralle, of a bank of Kalman filters. Each filter is constructed under a different assumption concerning the output's steady-state mean vector. One of the filters assumes that the steady-state mean vector is accurately reflected by an estimate, called the “assumed steady-state mean vector”, taken from the last half of the simulation data. As the filters process the output through the effective transient, this particular filter becomes more likely (in a Bayesian sense) to be the best filter to represent the data and the MMAE mean estimator is influenced increasingly towards the assumed steady-state mean vector. The estimated truncation point is selected when a norm of the MMAE mean vector estimate is within a small tolerance of the assumed steady-state mean vector. A Monte Carlo analysis using data from simulations of open and closed queueing models is used to evaluate the technique. The evaluation criteria include the ability to construct accurate and reliable confidence regions for the mean response vector based on the truncated sequences.

This paper presents a simple yet efficient adaptive Kalman filter for tracking targets expected to perform varying turn maneuvers. The process noise covariance level of a second order Kalman filter is adjusted at each time step according to the calculated turn rate. The turning rate is estimated from the magnitude of the calculated acceleration divided by the estimated speed of the target. At each scan the previous and current velocity estimates are used to calculate the acceleration. The comparison of the performance of the proposed algorithm is made with that of an interacting multiple model (IMM) algorithm, employing three models with different levels of process noise covariance and also to that of a second order Kalman filter. Two different assumptions have been made for selecting the process noise values for the the IMM and Kalman filter algorithms, in the first case it was assumed that there was no prior information about the target motion whereas in the second case it was assumed that the largest turn rate that the target of interest could perform was known. The IMM algorithm utilizing three models gives slightly better estimates during the nonmaneuvering periods, but the proposed algorithm is superior to the IMM algorithm during maneuvering periods in terms of estimation errors. Also the proposed algorithm requires 78% less computation, almost the same number of calculations required by a single fixed process noise Kalman filter, than the IMM algorithm.

This research aims at improving Detect and Avoid (DAA) functions in Unmanned Aircraft Systems (UAS) using a Multiple Model Estimation algorithm to track maneuvering intruders. This research builds on previous work that used predefined aircraft encounter trajectories. An established encounter model generates the intruder trajectories while a multiple model algorithm is introduced to improve intruder dynamics estimation. A new method based on the Kalman prediction phase inside the Interactive Multiple Model (IMM) algorithm is presented to estimate time to closest point of approach, horizontal miss distance, and vertical separation. An analysis of the sensor error on the algorithm estimation and the sensor field of regard requirement from the Air-to-Air Radar Minimum Operational Performance Standards (MOPS) is performed. The efficiency of the trajectory estimation has direct implication on the estimation of the intruder trajectory in relation to the own aircraft. The methods described in this research can aid a certification authority in determining if a DAA system is sufficient for safely integration of UAS into the National Airspace System.

The existing multiple-model adaptive estimation approach is able to detect faults quickly. However, there are three main problems when it is used for fault detection and diagnosis: false alarms, requirement of designing additional models to identify the faults, and slow response to detect the removal of the faults. In this paper, a novel selective-reinitialization multiple-model adaptive estimation approach is proposed. This approach introduces a state augmentation strategy that can identify the faults without designing additional models, as well as reduce false alarms. The major contribution of this approach is that three selective-reinitialization algorithms are proposed that can improve the performance of the multiple-model adaptive estimation significantly. The selective-reinitialization multiple-model adaptive estimation approach eliminates false alarms and is quick to detect the removal of the faults. The performance of the proposed approach is compared with the multiple-model adaptive estimation and the interacting multiple model with an example of the fault diagnosis of the inertial measurement unit and air data sensors for a Cessna Citation II aircraft. The simulation results suggest that the selective-reinitialization multiple-model adaptive estimation outperforms the multiple-model adaptive estimation and interacting multiple model in effectiveness and efficiency.

Previous papers (1997, 1999, 2000) have described a tracking approach which utilized a Combined Kalman Filter (CKF), adaptive tracking for maneuver tracking, and the JVC association algorithm for reports to tracks, for use in Airborne Early Warning (AEW) applications. In this paper we present our incorporation of Interacting Multiple Model (IMM) tracking. First our previous AEW tracking approach is briefly reviewed as most of this approach is still utilized and forms our baseline. The new IMM approach and equations are then described. Then the two IMM tracking approaches used are discussed. One involves a two model IMM containing two constant velocity models, one a low process noise and the other a high process noise model. The other approach involves three IMM filter models, a coordinated turn filter model, and the same two constant velocity filter models as in the two model IMM approach. Results for both IMM approaches and the baseline tracker are shown. The results presented involve a 120 target scenario with two second update time with simulated radar data. In addition computer timing results are presented. These results indicate that while the three model IMM approach provides the best tracking results, it does so at a substantial computational cost. The two model IMM provides comparable tracking improvement but at a far less computational cost.

The interacting multiple model (IMM) algorithm is a widely accepted state estimation scheme for solving maneuvering target tracking problems, which are generally nonlinear. During the IMM filtering process, serious errors can arise when a Gaussian mixture of posterior probability density functions is approximated by a single Gaussian. Particle filters (PFs) are effective in dealing with nonlinearity and non-Gaussianity. This work considers an IMM algorithm that includes a constant velocity model, a constant acceleration model and a 3D turning rate (3DTR) model for tracking three-dimensional (3D) target motion, using various combinations of nonlinear filters. In existing literature on combining IMM and particle filtering techniques to tackle difficult target maneuvers, a PF is usually used in every model In comparison, simulation results show that by using a computationally economical PF in the 3DTR model and Kalman filters in the remaining models, superior performance can be achieved with significant reduction in computational costs.

Hybrid systems consist of both continuous state evolutions and discrete state (or mode) transitions. In many hybrid systems, mode transitions are governed by guard conditions that are dependent on the continuous state. These kind of mode transitions can be described by continuous-state-dependent mode transition probabilities. However, most multiple model Kalman filter based algorithms, such as the well-known interacting multiple model (IMM) algorithm, assume constant mode transition probabilities. We propose a hybrid estimation algorithm based on the IMM approach for the stochastic hybrid systems with continuous-state-dependent transitions. We first develop two models to describe the guard conditions for various stochastic hybrid systems. From the models of the guard conditions, we derive the corresponding continuous-state-dependent mode transition probabilities, which are expressed in terms of Gaussian probability density functions (pdfs) or Gaussian cumulative density functions (cdfs). We then propose a hybrid estimation algorithm for the stochastic hybrid systems based on the IMM algorithm. Like the IMM algorithm, our algorithm utilizes Gaussian distributions to represent the continuous state pdfs which are updated analytically at each time step. We also use analytical integration methods to reduce the computational cost of updating the mode probabilities. As a result, the proposed algorithm is computationally efficient and is applicable to high-dimensional problems. The performance of the proposed algorithm is illustrated with two examples in air traffic control tracking applications.

A maneuver target interception algorithm based on multiple model adaptive estimator (MMAE) is researched and a modified differential game guidance law is given. The efficiency of this simplified MMAE algorithm lies mainly in the exploitation of the special structure of the evader maneuver command hypothesis space to reduce the number of MMAE elemental filters running in parallel and to realize the reduction of the computational load. To realize the reduction of the miss distance resulting from the estimation delay, the modified differential game guidance law increases the lateral acceleration command for small values of time-to-go of the pursuer to the maximum available value by enhancing the gain of the command. The Monte Carlo simulations are carried out for the homing performance comparison and the results demonstrate the superiority and effective of the proposed methods.