Parameter adjustment in the turn rate models in the interacting multiple model algorithm to track a maneuvering target

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.

<div class="section abstract"><div class="htmlview paragraph">Safety is the cornerstone for Advanced Driver Assistance Systems (ADAS) and Autonomous Driving Systems (ADS). To assess the safety of a traffic situation, it is essential to predict motion states of traffic participants in the future with mathematic models. Accurate vehicle trajectory prediction is an important prerequisite for reasonable traffic situation risk assessment and appropriate decision making. Vehicle trajectory prediction methods can be generally divided into motion model based methods and maneuver model based methods. Vehicle trajectory prediction based on motion models can be accurate and reliable only in the short term. While vehicle trajectory prediction based on maneuver models present more satisfactory performance in the long term, these maneuver models rely on machine learning methods. Abundant data should be collected to train the maneuver recognition model, which increases complexity and lowers real-time performance. In this paper, a vehicle trajectory prediction method based on motion model and maneuver model fusion with Interactive Multiple Model (IMM) is proposed. Firstly, Constant Turn Rate and Acceleration (CTRA) motion model and Unscented Kalman Filter (UKF) are used to predict vehicle trajectory with uncertainty in the future. Then, vehicle trajectory prediction based on simplified maneuver recognition model is conducted, using temporal and spatial relationship between vehicle historical trajectory and lane lines. After that, vehicle trajectory prediction by integrating motion model and maneuver model with IMM is conducted. Finally, the proposed method is compared with CTRA motion model based vehicle trajectory prediction and lane keeping model (LKM) based vehicle trajectory prediction in two simulation test scenarios. The simulation results indicates that the IMM-based method achieves both excellent prediction accuracy and appropriate prediction uncertainty in the whole prediction horizon. This research can be used to support decision making for Advanced Driver Assistance Systems (ADAS) and Autonomous Driving Systems and leads to improvement of traffic safety.</div></div>

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.

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.

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.

This paper addresses the problem of data fusion for joint multiple manoeuvring target tracking and classification where centralised versus decentralised architectures are contrasted. The proposal advocates the use of a hybrid approach combining a particle filter (PF) like method to deal with system nonlinearities, Fitzgerald's cheap joint probabilistic data association filter (CJPDAF) for the purpose of data association/target estimation problems and multiple model filter (MMF) to handle the issue of target manoeuvrability, yielding CJPDA-MMPF algorithm. The feasibility and the performances of the proposal have been demonstrated using complex scenarios involving a set of Monte Carlo simulations dealing with four crossing targets with different operations modes. Constant velocity model and constant turn rate model were employed to generate the manoeuvres. The results of the simulations demonstrate the feasibility and the superiority of the centralised fusion architecture approach when combined with multiple model particle filter and cheap joint data association filter.

In this paper, we present an efficient filtering algorithm to perform accurate estimation in jump Markov nonlinear systems, in case of multi-target tracking. With this paper, we aim to contribute in solving the problem of model-based body motion estimation by using data coming from visual sensors. The interacting multiple model (IMM) algorithm is specially designed to track accurately targets whose state and/or measurement (assumed to be linear) models changes during motion transition. However, when these models are nonlinear, the IMM algorithm must be modified in order to guarantee an accurate track. In this paper we propose to avoid the extended Kalman filter because of its limitations and substitute it with the unscented Kalman filter which seems to be more efficient especially according to the simulation results obtained with the nonlinear IMM algorithm (IMM-UKF). To resolve the problem of data association, we propose to use a Fuzzy approach. The later is then combined with the IMM-UKF algorithm; the derived algorithm is called fuzzy-IMM-UKF.

Estimation of 3D piecewise coordinated turn target maneuvers with unknown turning rates is considered. The State Dependent Differential-Difference Riccati Equation (SDDRE) and the Interacting Multiple Model (IMM) approaches are compared. The comparison is kept as simple as possible and effort is made to perform it on a common basis. The SDDRE uses a non-linear modeling of the target's equations of motion that takes into account the rotation of the velocity and acceleration vectors as the target maneuvers. The IMM implements two models: a constant acceleration target model and a simple uncoupled coordinated turn maneuver model using the average-expected turn rate. The simulated trajectory is a combination of constant velocity trajectory segments and coordinated turn segments. The simulations show advantages and disadvantages of each of the approaches. It is demonstrated that the SDDRE approach filter is not sensitive to the trajectory orientation and that it has faster transient thus demonstrates a kind of adaptivity to the turning rate level. The IMM approach filter has the advantages that when the target trajectory is close to one of the hypotheses it has better performance than the SDDRE based filter.

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.

in estimating the vertical velocity of the aircraft which influences altitude prediction. Altitude prediction is important in conflict alarm systems. This problem is investigated and several Bayesian estimators, including the Interacting Multiple Model (IMM) algorithm, are tuned and tested on real measurement data for a performance comparison. It is shown that a single model filter with maneuver handling using the Unscented Kalman Filter is superior to IMM estimators and Kalman filters for long term predictions.

Recently, targets tracking plays an important role in the rapidly expanding field of autonomous driving. With the presentation of vehicle-to-vehicle (V2V) communication standards and the improvement of Global Navigation Satellite System (GNSS) technology, the accuracy of cooperative vehicle tracking should be greatly improved. However, high-precision positioning suffers from a number of vulnerabilities and is unstable in clutter environment. In this paper, a modified approach using particle filter (PF) integrated with Interacting Multiple Models (IMM) algorithm is proposed to improve the accuracy of cooperative vehicle tracking in changing V2V environment. This paper focuses on a novel framework for cooperative vehicle tracking and implementation of data fusion originating from positioning information receiving from radars and connected vehicles. The simulations on scenarios of single vehicle and multi-vehicle tracking were implemented by utilizing Matlab. The performance of the proposed modified IMM-PF algorithm was evaluated. The results demonstrated that the proposed approach can adapt to a changing accuracy of positioning information and significantly reduce the tracking errors by approximately 50% compared with traditional methods. Consequently, the proposed method can effectively enhance the security and reliability of autonomous driver assistance systems, and its application has potential to support urban planning for smart cities.

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.

Tracking targets in clutter, with the inherent data association problem, naturally leads to a Gaussian mixture representation of the probability density function (pdf) of the target state vector, conditioned on the measurements observed. Online trackers require reduction of the number of components in the mixture on each processing cycle, and the integral square error (ISE) based mixture reduction algorithm (MRA) significantly outperforms known alternative algorithms. Moreover, to handle target maneuver onset and changing trajectory characteristics, one can use multiple model adaptive estimation in the form of either multiple model adaptive estimation (MMAE) or interacting multiple model (IMM) algorithms. For maneuvering targets in clutter, one can replace each Kalman filter within a conventional MMAE or IMM with an ISE-based MRA, or better yet, replace each Kalman filter within an ISE-based algorithm with an MMAE or IMM, to yield superior tracking of aggressive maneuvers in deep clutter. Such an ISE-based algorithm of MMAEs is seen to have performance attributes significantly superior to that of a current state-of-the-art tracker.

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