Improved Adaptive Grid Interactive Multiple Model Algorithm based on Maneuverability Division

The results of an investigation into the use of the adaptive interactive multiple model (AIMM) algorithm, in which the sampling rate was adaptively selected among a predetermined set, for the benchmark problem of the beam pointing control of a phased array radar for tracking maneuvering targets is presented. The results of the AIMM algorithm where a fixed sampling rate policy was used has also been given for the same problem for comparison purposes. (8 pages)

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.

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 paper considers the decline problem of tracking accuracy caused by acceleration estimation inaccuracy in hybrid grid multiple model (HGMM) algorithm. A new improved tracking algorithm of maneuvering targets based on CSHGMM is proposed. Grid partition is performed by estimation of the acceleration mean in current statistic (CS) model, where a fading factor is adopted to improve tracking accuracy by adjusting the gain matrix under the condition of the abrupt change of acceleration. Then possible model sets of the target are generated online, and interactive multiple model algorithm is adopted to estimate the target state. The proposed algorithm performance is tested and compared in general and strong maneuvering scenarios, and simulation results demonstrate that the proposed algorithm not only improves the accuracy for maneuvering target tracking, but also can be applied to most of the tracking scenarios.

The extended Kalman filter (EKF) as a primary integration scheme has been applied in the Global Positioning System (GPS) and inertial navigation system (INS) integrated system. Nevertheless, the inherent drawbacks of EKF contain not only instability caused by linearization, but also massive calculation of Jacobian matrix. To cope with this problem, the adaptive interacting multiple model (AIMM) filter method is proposed to enhance navigation performance. The soft-switching characteristic, which is provided by interacting multiple model algorithm, permits process noise to be converted between upper and lower limits, and the measurement covariance is regulated by Sage adaptive filtering on-line Moreover, since the pseudo-range and Doppler observations need to be updated, an updating policy for classified measurement is considered. Finally, the performance of the GPS/INS integration method on the basis of AIMM is evaluated by a real ship, and comparison results demonstrate that AIMM could achieve a more position accuracy.

Combining the interacting multiple model (IMM) and the unscented particle filter (UPF), a new multiple model filtering algorithm is presented. Multiple models can adapt to targets’ high maneuvering. Particle filter can deal with the nonlinear or non-Gaussian problems and the unscented Kalman filter (UKF) may improve the approximate accuracy. Compared with other interacting multiple model algorithms in the target tracking simulations, the results demonstrate the validity of the new filtering method, that is, particle filter with the UKF proposal.

In this paper we investigate an adaptive interacting multiple model (AIMM) tracker using the extended Kalman filter. This adaptive algorithm is based on the interacting multiple model (IMM) tracking technique with the addition of an adaptive acceleration model to track behavior that falls in between the fixed model dynamics. In previous research, we found that the adaptive model matches more closely the true system dynamics when the target kinematics lie in between the fixed models, thus improving the overall performance of the tracking system. We also showed that the AIMM outperforms other existing adaptive approaches while reducing computational complexity. In this paper, we further investigate these superior qualities of the AIMM by considering a more realistic radar-tracking scenario where monopulse radar range, azimuth, and elevation measurements are processed using extended Kalman filters in the AIMM. Here a more complex 3D simulation is implemented instead of the simplified 2D problem considered in our previous research. Again, the result how that the AIMM outperforms the classical IMM when the target is maneuvering.

The Interacting Multiple Model (IMM) algorithm has been used in various applications with good performance. However, to the best of our knowledge, stability conditions of the IMM algorithm have not been shown in the control literature. This technical note presents a sufficient condition for the exponential stability of the IMM algorithm for a class of Markov jump linear systems. We derive a lower bound and an upper bound for the error covariances of the IMM algorithm, and then derive the stability condition by the Lyapunov approach.

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 the paper, we consider an application of the genetic approach to improve the performance of the trajectory tracking procedure. Our aim is to reduce the horizontal position estimation errors. The procedure is based on the well known Interacting Multiple Model algorithm and has many parameters to be adjusted, e.g., elements of the transition probability matrix. A genetic tuning algorithm is elaborated and some numerical experiments on simulated aircraft trajectories are made.

An interacting Fuzzy-Fading-Memory-based Augmented Kalman Filtering method for maneuvering target tracking

The interacting multiple model (IMM) algorithm is specially designed to track accurately targets whose state and measurement models changes during motion transition. However, when these models are nonlinear, the IMM algorithm must be modified in order to guarantee an accurate track. Recently, the cubature Kalman filter (CKF) has been proposed to estimate the nonlinear system, and could perform better than unscented Kalman filter (UKF). In this paper, the IMM algorithm CKF based (IMM-CKF) is presented to track the maneuvering target using angular measurements. The simulation results demonstrate the improved performance of IMM-CKF over IMM-UKF, and the execution time of the former algorithm is shorter than the latter.

An algorithm to estimate the tangential and normal accelerations directly using the Doppler radar measurement in an online closed loop form is proposed. Specific works are as follows: first, the tangential acceleration and normal acceleration are taken as the state variables to establish a linear state transition equation; secondly, the decorrelation unbiased conversion measurement Kalman filter (DUCMKF) algorithm is proposed to deal with the strongly nonlinear measurement equation; thirdly, the geometric relationship between the range rate and the velocity direction angle is used to obtain two estimators of the velocity direction angle; finally, the interactive multiple model (IMM) algorithm is used to fuse the estimators of the velocity direction angle and then the adaptive IMM of current statistical model based DUCMKF (AIMM-CS-DUCMKF) is proposed. The simulation experiment results show that the accuracy and stability of DUCMKF are better than the sequential extended Kalman filter algorithm, the sequential unscented Kalman filter algorithm, and converted measurement Kalman filter algorithms; on the other hand they show that the AIMM-CS-DUCMKF can obtain the high accuracy of the tangential and normal accelerations estimation algorithm.

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.

Online displacement extraction and vibration detection based on interactive multiple model algorithm