Maneuvering target tracking with an adaptive Kalman filter

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.

Correct knowledge of noise statistics is essential for an effective estimator in maneuvering target tracking. In practice, however, the noise statistics are usually unknown or not perfectly known. To deal with the estimation problem in linear discrete-time systems with Markov jump parameters, where the measurement noise covariance is unknown, a novel approach is presented in this paper. This approach is based on the interacting multiple model (IMM) framework. An H ∞ filter is employed to construct a noise statistics estimator to obtain the information which is necessary for the IMM algorithm. In our approach, even the priori knowledge of noise statistics is not needed. The noise statistics loss problem is solved while the merits of IMM algorithm is reserved. The effectiveness of the proposed approach is demonstrated in comparison with single-model H ∞ filter through Monte Carlo simulation 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.

For multi-target tracking, the IMM (interactive multiple model) algorithm has been proposed. The IMM is expected to reduce tracking errors for both nonmaneuvering and maneuvering targets. However, the IMM requires a heavy computational burden, because it utilizes multiple Kalman filters in parallel. On the other hand, the Kalman filter with a turning acceleration estimator, which can adapt a maneuvering target, has been proposed. The Kalman filter with a turning acceleration estimator is a single two-stage type filter and has a problem of setting threshold for the maneuver detector. In this paper, we propose the hybrid filter with a constant-velocity (CV) filter and a turning acceleration estimation filter. The proposed filter does not require a maneuver detector, because it integrates the outputs of two filters using the likelihood of each filter. And its computational requirement is smaller than the IMM, since it consists of only two Kalman based filters. The proposed method can prevent deteriorating tracking accuracy by reducing the risk of maneuver misdetection when a target maneuvers. We evaluate the performance of the proposed filter by computer simulation, and show the effectiveness of the proposed filter, comparing with the conventional Kalman filter and the two-stage Kalman 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.

Control of the time between sawtooth crashes, necessary for ITER and DEMO, requires real-time detection of the moment of the sawtooth crash. In this paper, estimation of sawtooth crash times is demonstrated using the model-based interacting multiple model (IMM) estimator, based on simplified models for the sawtooth crash. In contrast to previous detectors, this detector uses the spatial extent of the sawtooth crash as detection characteristic. The IMM estimator is tuned and applied to multiple ECE channels at once. A model for the sawtooth crash is introduced, which is used in the IMM algorithm. The IMM algorithm is applied to seven datasets from the ASDEX Upgrade tokamak. Five crash models with different mixing radii are used. All sawtooth crashes that have been identified beforehand by visual inspection of the data, are detected by the algorithm. A few additional detections are made, which upon closer inspection are seen to be sawtooth crashes, which show a partial reconnection. A closer inspection of the detected normal crashes shows that about 42% are not well fitted by any of the full reconnection models and show some characteristics of a partial reconnection. In some case, the measurement time is during the sawtooth crashes, which also results in an incorrect estimate of the mixing radius. For data provided at a sampling rate of 1 kHz, the run time of the IMM estimator is below 1 ms, thereby fulfilling real-time requirements.

Underwater acoustic sensor networks (UASNs) play an important role in the ocean's protection. They can realize real-time data collection, monitoring, exploration, and many other underwater applications by connecting and coordinating seafloor sensors and underwater vehicles. To achieve these application objectives, such as fishes tracking in biological monitoring field and submarines tracking in military field, target tracking is one of the key techniques. This paper presents a centralized fusion algorithm based on the interacting multiple models and the adaptive Kalman filter (IMMCFAKF) for target tracking in UASNs. Specifically, by introducing an adaptive forgetting factor into the optimal centralized fusion Kalman filter algorithm, the optimal centralized fusion adaptive Kalman filter (CFAKF) algorithm is obtained first. Then, combining the superiorities of both the optimal CFAKF algorithm and the conventional IMM algorithm, the optimal IMMCFAKF is achieved. The numerical simulations are provided to demonstrate the effectiveness of the proposed optimal IMMCFAKF algorithm.

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

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

Space systems are characterized by a low-intensity process noise resulting from uncertain forces and moments. In many cases, their scalar measurement channels can be assumed to be independent, with one-dimensional internal dynamics. The nominal operation of these systems can be severely damaged by faults in the sensors. A natural method that can be used to yield fault tolerant estimates of such systems is the interacting multiple model (IMM) filtering algorithm, which is known to provide very accurate results. However, having been derived for a general class of systems with switching parameters, the IMM filter does not utilize the independence of the measurement errors in different channels, nor does it exploit the fact that the process noise is of low intensity. Thus, the implementation of the IMM in this case is computationally expensive. A new estimation technique is proposed herein, that explicitly utilizes the aforementioned properties. In the resulting estimation scheme separate measurement channels are handled separately, thus reducing the computational complexity. It is shown that, whereas the IMM complexity is exponential in the number of fault-prone measurements, the complexity of the proposed technique is polynomial. A simulation study involving spacecraft attitude estimation is carried out. This study shows that the proposed technique closely approximates the full-blown IMM algorithm, while requiring only a modest fraction of the computational cost.

According to the characteristics of Uniform motion in two-dimensional space, On the basis of the target motion model and observation model, adopted based on the Interacting Multiple Model algorithm (IMM) Kalman filter to the maneuvering target tracking. However, due to there are a lot of recursive and matrix operations in IMM algorithm, So the real time is reduced ,this also is the reason that it's works hard to achieve in project. This article through the CUDA to speed it up, Greatly improved the performance of real-time on the premise of do not affect arithmetic performance. Simulation results show that, even if when motion model is change the performance of real-time has also been improved so much, and the filtering error is also relatively small.

This paper presents mathematical procedures to calculate the Cramer-Rao lower bound (CRLB) for a target track obtained by fusing two tracks given by two interactive multiple model (IMM) trackers filtering the plots received by two radars. The target under tracking is a ballistic target (BT) in reentry phase and it is assumed that the two sensors could have a detection probabilities Pd less than 1. Accurate BT tracking is required for: (i) impact point prediction, (ii) support to the kill assessment, and (iii) threat classification. Note that, to improve the performance, the method can be extended to the fusion of more than two sensor tracks. The paper is organized as follows: the problem is introduced in section 1; section 2 briefly recalls the models of BT dynamic and of the radar measures. Section 3 presents the tracking algorithm based on the IMM approach; section 4 contains the description of the CRLB evaluation problem and section 5 the results achieved in comparing the fusion of two BT tracks (each track is obtained from the IMM algorithm described in section 4) with the CRLB; Monte Carlo simulations is also used to quantify the fused track accuracies. Section 6 is pertinent to conclusions and follows on of the activity while references are reported in section 7.

In this paper, performance evaluation for various single model nonlinear filters and nonlinear filters with interactingmultiple model (IMM) framework is carried out. A high gain (high bandwidth) filter is needed to response fast enoughto the platform maneuvers while a low gain filter is necessary to reduce the estimation errors during the uniformmotion periods. Based on a soft-switching framework, the IMM algorithm allows the possibility of using highly dynamicmodels just when required, diminishing unrealistic noise considerations in non-maneuvering situations. The IMMestimator obtains its estimate as a weighted sum of the individual estimates from a number of parallel filters matchedto different motion modes of the platform. The use of an IMM allows exploiting the benefits of high dynamic models inthe problem of vehicle navigation. Simulation and experimental results presented in this paper confirm theeffectiveness of the method.