Coordinated Turn Model Research Articles

Analytical Aircraft State and IMU Signal Generator From Smoothed Reference Trajectory

Generating aircraft position, velocity, and attitude along a reference trajectory is useful in many path and mission planning applications. In applications simulating an inertial navigation system the body-frame accelerations and angular rates are also required. This work presents a method for generating a smoothed continuous-curvature reference trajectory from a series of waypoints using line, arc, clothoid, and Fermat spiral segments in a fillet smoothing framework. The geometry of the segments are used to generate the position, velocity, and attitude of an aircraft following the reference trajectory. A primary contribution of this article is the use of the path geometry, coordinated turn model, and curvilinear motion theory to obtain analytical solutions for the body-frame accelerations and angular rates of the aircraft along the reference trajectory.

Closed-form steady-state bias error of tracking filter using coordinated turn model for constant velocity target

Closed-form steady-state bias error of tracking filter using coordinated turn model for constant velocity target

Ambiguity Resolution Between Constant Velocity and Coordinated Turn Models for Multimodel Target Tracking

Multimodel-based algorithms, such as the interacting multiple model, have been used in target estimation problems with different dynamics models. The combination of a constant velocity (CV) model and a coordinated turn (CT) model is widely used to track a maneuvering target. However, the distinction between the two models may not be distinct when the target is weakly maneuvering. In this letter, we propose a new method to resolve the ambiguity between CV and CT models that can provide a faster maneuver response and a higher estimation accuracy than traditional methods.

Higher-Order Unscented Estimator

This paper introduces a new extension of the unscented Kalman filter with asymmetric sample points and weights chosen to match third- and fourth-order moments in addition to the mean and covariance. Explicit solutions are obtained for sample points and weights, making their evaluation efficient and robust, and rigorous constraints are derived for their applicability. The use of the new filter is demonstrated with three dynamic systems (an aircraft coordinated turn model, a rotating rigid body, and a projectile with drag), and filter performance is compared with that of the conventional unscented Kalman filter and conjugate unscented transform filters. The new filter is found to be more robust in most cases where the initial distribution, process noise, and measurement noise have a high kurtosis, in that it does not generate extreme outliers in the estimation error. Also, execution times for the new filter are found to be only slightly longer than for the conventional unscented Kalman filter and significantly shorter than for the conjugate unscented transform filters.

Continuous discrete cubature quadrature Kalman filter

AbstractIn this paper, cubature quadrature Kalman filter algorithm has been reformulated for nonlinear state space model of continuous‐discrete nature. The developed method is named as continuous‐discrete cubature quadrature Kalman filter (CD‐CQKF). The formulated algorithm has been applied to track the trajectory of an aircraft. The process is described with coordinated turn model. From the simulation result, it has been observed that the developed CD‐CQKF provides better estimation compared with continuous‐discrete cubature Kalman filter.

Robust UKF-IMM Filter for Tracking an Off-road Ground Target

In this paper, the design of a robust UKF-IMM filter for tracking a fulltime off-road ground target is studied and carried out. A detailed description of the target dynamic systems with respect to motion modelling is done for a sharply maneuvering target. A four model IMM filter with two discrete white noise acceleration models and two horizontal coordinated turn models is proposed. In this IMM filter, a low noise and high noise model is proposed for the two pairs of motion models. Low noise model for non-maneuvering or slow maneuvering situations and high noise model for quick and sharp maneuvering situations. The Unscented Kalman filter is used as the base filter due to the highly nonlinear horizontal coordinated turn model with unknown turn rates along with linear Kalman filter for linear systems. Simulation is carried out and results are presented showing the performance of the proposed estimator and demonstrates its capability to perform its designed purpose. The simulated results show that the four model IMM filter can track the highly maneuvering off-road target with acceptable error margin. The error dynamics are observed to be stable with good maneuver detection characteristics. The proposed filter has a low computation complexity and therefore can be adapted to most computers.

Iterative statistical linear regression for Gaussian smoothing in continuous-time non-linear stochastic dynamic systems

Abstract This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary Gaussian process. Two methods are developed based on (1) taking the limit of statistical linear regression of the discretised process and (2) minimising an upper bound to a cost functional. Their difference is manifested in the diffusion of the approximate processes. This in turn gives novel derivations of pre-existing Gaussian smoothers when Method 1 is used and a new class of Gaussian smoothers when Method 2 is used. Furthermore, based on the aforementioned development the iterative Gaussian smoothers in discrete-time are generalised to the continuous-time setting by iteratively re-linearising the stochastic differential equation with respect to the current Gaussian process approximation to the smoothed process. The method is verified in two challenging tracking problems, a reentry problem and a radar tracked coordinated turn model with state dependent diffusion. The results show that the method has competitive estimation accuracy with state-of-the-art smoothers.

Improved IMM Filter for Tracking a Highly Maneuvering Target with Mixed System Noises

We propose a method of improving tracking filter performance of a highly maneuvering target with mixed system noises in this paper. A case study of an off-road high speed moving target is considered. The system noises consist of white Gaussian noises generated from target motion models and additional colored noises arising from the effect of rough and uneven terrain profile. we design the colored noise first order discrete Markov dynamic system representing terrain conditions. Tracking is done by using an IMM filter with discrete white noise acceleration and horizontal coordinated turn models. The designed colored noise dynamic model is augmented with each of the motion models. We use Kalman filter for linear DWNA model while extended and unscented Kalman filters are used for nonlinear HCT model. A test scenario is setup and simulations are carried out. For filter performance comparison purposes, two more cases are considered i.e., systems with white noncorrelated system noises and the system correlated noise cases. Results show that the proposed method outperforms the traditional error treatment methods in terms of robustness, small mean square error, and acceptable computation load and data processing time.

Tracking and detecting highs maneuvering weak targets

Modern military targets as aircraft are able to perform high maneuvers due to their complex design. This ability of maneuvers includes sudden changes in acceleration and high-G turns that are not achievable from traditional military targets. Moreover, recent military targets generally have a low radar cross-section or low signal-to-noise ratio (SNR) profile, which makes the detection and tracking of those maneuvering targets a complicated dynamic state estimation problem. In this case, the track-before-detect filter (TBDF) that uses unthresholded measurements is considered as an effective method for tracking and detecting a single maneuvering target under low SNR conditions. Nevertheless, the performance of the algorithm will be affected by severe loss because of the mismatching of target model during maneuver. To resolve the target maneuvers, we propose an application of particle filtering, which depends on TBD. We employ the constant acceleration model and coordinate turn model. Our simulation results show that the detection and tracking of maneuvering target performance of TBDF has been improved using the proposed algorithm.

Passively Track WiFi Users With an Enhanced Particle Filter Using Power-Based Ranging

Passive positioning systems produce user location information for third-party providers of positioning services. In this paper, we provide a passive tracking system for WiFi signals with an enhanced range-only particle filter using fine-grained power. Our proposed particle filter, WVT-bootstrap particle filter, provides improved observation likelihood and is equipped with a single coordinated turn model to address the challenges in passive positioning. The anchor nodes for WiFi signal sniffing use software defined radio techniques to extract channel state information for multipath mitigation and a non-linear regression method is used for the path-loss model. Our tracking system produces measured positioning errors that, in the 80th percentile, are equal to or less than 2 m; this represents a 33% improvement over the traditional bootstrap particle filter. Additionally, it requires (0.12 s for 1000 particles) only half of the computation efforts as a multi-model particle filter.

Tracking of manoeuvring targets using fuzzy information fusion filter

ABSTRACTThe paper discusses the tracking of a manoeuvring target using fuzzy information fusion filters (FIFFs), based on bearing only measurements received from multiple sensors. While a number of tracking filters including the Kalman filters have been proposed and demonstrated successfully for tracking, the information filter has been reported to be capable of estimating the state of a target even without an initial estimate. However, the estimate is often seen to diverge after a short period. A FIFF has been shown to track small manoeuvres in target following a constant velocity model but is not effective when the target switches to a coordinated turn model. In this paper, the idea of using the FIFF for tracking manoeuvring target is proposed and demonstrated. The filter uses only the bearing measurements in tracking the target and also for detecting the manoeuvre. Using an adaptive turn rate model, the turning rate of the moving target is estimated from the range rate. Here, the range rate is also computed directly from bearing measurements. The detection of the onset of manoeuvre is on the basis of consistent change in the turning rate of the target. A number of different scenarios involving manoeuvring targets are given to demonstrate the efficacy of this approach.

High manoeuvre target tracking in coordinated turns

In target tracking, most tracking algorithms are model based, and serious errors can arise when the models fail to fit the physical target motions, especially during coordinated turns. To address this problem, a two-step tracking algorithm is proposed. First, considering the diversity of the target manoeuvres, five elemental Singer models with carefully designed parameter α interact with each other in an interacting multiple model (IMM) algorithm to accomplish the tracking and estimate the target's kinematic parameters. Second, if a turn motion occurs, then it discriminates the turn motion into a horizontal turn or a three-dimensional (3D) turn; and the real-time turn rate is calculated to refine the corresponding model for tracking. Since the filtering stage is important in estimating the kinematic parameters, sparse-grid quadrature Kalman filter is employed to improve the filtering capability. The proposed algorithm is exemplified by simulation tests and data tests in 3D, and is compared with that of an IMM algorithm utilising constant velocity, constant acceleration and 3D coordinated turn models. All of the test results demonstrate that the proposed algorithm is effective and has higher accuracy.

Tracking Algorithm Design and Comparison of High Speed High Maneuvering Target

Aiming at the problem that the traditional tracking method cannot track high speed high maneuvering target effectively, one modified fixed structure multiple model algorithm (M-FSMM) and one modified variable structure multiple model (M-VSMM) algorithm were proposed. The Constant Velocity (CV) model, Current Statistical (CS) and Modified Coordinate Turn (MCT) model were adopted in the M-FSMM algorithm, by means of Connected Graph (CG) thinking, the model connected graph was made up by models that can describe possible motion, the connected relation was set up and model self-adapting was designed to carry out the variable structure tracking that can quickly jump between models. Monte Carlo simulation results show that the two methods can track high speed high maneuvering target effectively, the computational quantum of M-FVMM algorithm is larger but the tracking accuracy and stability are better than the M-FSMM algorithm. They can be used to track near space hypersonic targets.

Interacting Multiple Mode Tracking Algorithm Based on Modified Coordinate Turn Model

The continuing success of near space hypersonic aircraft flight test has become a real threat to China's space attack-defense system, In view of the problem that the single model cannot track such target effectively, an interacting multiple model (IMM) tracking algorithm based on modified cornering model (MCT) was proposed. First the characteristics of near space hypersonic target were analyzed, and then the target real-time angular velocity according to the target motion equation was estimated, finally the near space hypersonic target tracking through the IMM was carried out. The Monte Carlo simulation results show that the IMM tracking algorithm can effectively track near space hypersonic target, and the tracking accuracy and stability are superior to single model, it has certain practical significance.

Bearing-Only Maneuvering Mobile Tracking With Nonlinear Filtering Algorithms in Wireless Sensor Networks

Mobile node localization is important to offer wireless services in vehicular communication applications. Some typical methods realize the mobile node tracking through data fusion from time of arrival (TOA) and received signal strength (RSS) measurements provided by sensor nodes or base stations (BSs). Although the TOA/RSS method is not expensive under a concern of cost, it is very sensitive to multipath signal propagation effects. As the technology of angle of arrival (AOA) antennas is showing a rapid progress, we turn to consider AOA estimation. In this paper, the nonlinear extended Kalman filter (EKF) and the particle filter (PF) along with a three-model interacting multiple model (IMM) algorithm are utilized and compared for maneuvering mobile station (MS) tracking with bearing-only measurements. A coordinated turn model is used to improve the tracking performance since the MS frequently turns in the streets. We also propose an efficient method for resampling particles to alleviate the degeneracy effect of particle propagation in the interacting multiple model particle filter (IMMPF) algorithm. Moreover, a BS sensor selection scheme is also exploited for the long-haul MS tracking case which often changes BSs in a wireless vehicular sensor network. Numerical simulations show that the three-model IMMPF algorithm outperforms the interacting multiple model extended Kalman filter algorithm and achieves a root-mean-square tracking performance which is quite close to the posterior Cramer-Rao lower bound.

Combining the interacting multiple model method with particle filters for manoeuvring target tracking with a multistatic radar system

Practical problems on target localisation and tracking arise in many military and civilian applications. This study investigates a problem on locating and tracking a manoeuvring target for a multistatic radar system. An approach that combines the interacting multiple model (IMM) method with variants of particle filters is implemented. The IMM method accounts for mode switching, whereas the particle filters account for non-linearity and/or non-Gaussianity in the dynamic system models for the posed problem. The approach consists of a constant velocity model, a constant acceleration model and a coordinated turn model. This work considers six combinations of extended Kalman filters (EKFs), unscented Kalman filters (UKFs) and particle filters for the models. A simulation study is carried out to evaluate the implemented IMM algorithm variants. Based on the test results obtained, IMM variants that use computationally efficient particle filters in the coordinated turn models, with EKFs and/or UKFs in the remaining models possess potential to achieve superior accuracy in state estimation for problems with significant non-linearity and/or non-Gaussianity.

Bearing only Tracking of Maneovuring Targets Using a Single Coordinated Turn Model

The passive tracking of manoeuvring objects using line of sight (LOS) angle measurements only is an important field of research in the application areas of submarine tracking, aircraft surveillance, autonomous robotics and mobile systems. In this paper, the tracking of target dynamics is treated as a system identification problem. We propose to use the coordinated turn (CT) model along with extended Kalman filter to track all possible dynamics such as velocity, acceleration and coordinated turn of manoeuvring targets. Simulations are used to demonstrate the effectiveness of this approach and the results obtained are promising .

Continuous-Time Tracking Filters for the Coordinated Turn Model

Continuous-time tracking filters based on the coordinated turn model are discussed. By a coordinate transformation, the four-state filter design is reduced to design of two-state filters. An observer approach is applied, including pole placement and transfer function analysis. Deterministic steady-state errors for a circular turn are obtained as analytical expressions in target acceleration, filter bandwidth, and the actual and assumed turn rates. It is seen that no errors are obtained if the turn rate is known. If it is unknown, performance could still be better than with independent filters, if the assumed turn rate is not too erroneous. Even a first order transfer function can be formulated from which the steady-state errors are easily obtained. An interpretation in terms basic two-state filters is given of filters based on the coordinate turn model. Furthermore, the Kalman filter for a stochastic coordinated turn model is given in closed form and compared to the observers.

An interacting multiple model particle filter for manoeuvring target location

A constant velocity model, a constant acceleration model and a coordinated turn model are used for manoeuvring target. However, high location precision of the target could not be obtained with any one of these models. In this paper, an interacting multiple model particle filter (IMMPF) algorithm is proposed to estimate the target location with several models. Besides similar mixing and interaction to those in a traditional interaction multiple model (IMM) estimator, a standard particle filter runs in every model and the number of particles in every model is fixed. Compared through a target location example, the proposed algorithm is better than the traditional IMM.

Tracker and signal processing for the benchmark problem with unresolved targets

Radar signal processing is particularly important in tracking closely spaced targets and targets in the presence of sea-surface-induced multipath. Closely spaced targets can produce unresolved measurements when they occupy the same range cell of the radar. These issues are the salient features of the benchmark problem for tracking unresolved targets combined with radar management, for which this paper presents the only complete solution to date. In this paper a modified version of a recently developed maximum likelihood (ML) angle estimator, which can produce two measurements from a single (unresolved) detection, is presented. A modified generalized likelihood ratio test (GLRT) is also described to detect the presence of two unresolved targets. Sea-surface-induced multipath can produce a severe bias in the elevation angle measurement when the conventional monopulse ratio angle extractor method is used. A modified version of a recently developed ML angle extractor, which produces nearly unbiased elevation angle measurements and significantly improves the track accuracy, is presented. Efficient radar resource allocation algorithms for two closely spaced targets and targets flying close to the sea surface are also presented. Finally, the IMMPDAF (interacting multiple model estimator with probabilistic data association filter modules) is used to track these targets. It is found that a two-model IMMPDAF performs better than the three-model version used in the previous benchmark. Also, the IMMPDAF with a coordinated turn model works better than the one using a Wiener process acceleration model. The signal processing and tracking algorithms presented here, operating in a feedback manner, form a comprehensive solution to the most realistic tracking and radar management problem to date.