This paper presents a joint trajectory smoothing and tracking framework for a specific class of targets with smooth motion. We model the target trajectory by a continuous function of time (FoT), which leads to a curve fitting approach that finds a trajectory FoT fitting the sensor data in a sliding time-window. A simulation study is conducted to demonstrate the effectiveness of our approach in tracking a maneuvering target, in comparison with the conventional filters and smoothers. Note to Practitioners —Estimation, such as automatically tracking and predicting the movement of an aircraft, a train, or a bus, plays a key role in our daily life. In this paper, we provide a new approach for the online estimation of the target trajectory function by means of fitting the time-series observation, which accommodates the lack of quantifiable knowledge about the target motion and of the statistical property of the sensor observation noise. The resulting trajectory function can be used to infer either the past or the present state of the target. Engineering-friendly strategies are provided for computationally efficient implementation. The proposed approach is particularly appealing to a broad range of real-world targets that move in smooth courses, such as passenger aircraft and ships.
Maneuvering target tracking is a challenge. Target’s sudden speed or direction changing would make the common filtering tracker divergence. To improve the accuracy of maneuvering target tracking, we propose a tracking algorithm based on spline fitting. Curve fitting, based on historical point trace, reflects the mobility information. The innovation of this paper is assuming that there is no dynamic motion model, and prediction is only based on the curve fitting over the measured data. Monte Carlo simulation results show that, when sea targets are maneuvering, the proposed algorithm has better accuracy than the conventional Kalman filter algorithm and the interactive multiple model filtering algorithm, maintaining simple structure and small amount of storage.  In underwater target tracking applications, measurement uncertainty and inaccuracies are usually modeled as additive Gaussian noise. The Gaussian model of noise may not be appropriate in many practical systems. The non-Gaussian noise and the model non-linearity arising in a tracking system will seriously affect the tracking performance. This paper discusses one way to create a robust version of the extended Kalman filter for enhanced underwater target tracking. State estimation in the filter is done through the robust regression approach and Welsch's proposal is used in the regression process. Monte Carlo simulation results with heavy-tailed contaminated observation noise demonstrate the robustness of the proposed estimation procedure. > Abstract In many applications, bearings are measured to a moving object with the goal of estimating the object's course of movement. If movement is appropriately modeled as a smooth deterministic curve in the plane, then a cubic spline is a reasonable representation of the curve. Maximum likelihood estimators are presented for parameters of regression splines, assuming that observation errors follow a Von Mises distribution. Location estimates are obtainable even when data are sparse. Path estimation error, number and placement of knots, and outlier detection are discussed. Examples, including both simulated paths and observations from a wildlife radio-tracking study, are presented. We describe a Bayesian method, for fitting curves to data drawn from an exponential family, that uses splines for which the number and locations of knots are free parameters. The method uses reversible jump Markov chain Monte Carlo to change the knot configurations and a locality heuristic to speed up mixing. For nonnormal models, we approximate the integrated likelihood ratios needed to compute acceptance probabilities by using the Bayesian information criterion, BIC, under priors that make this approximation accurate. Our technique is based on a marginalised chain on the knot number and locations, but we provide methods for inference about the regression coefficients, and functions of them, in both normal and nonnormal models. Simulation results suggest that the method performs well, and we illustrate the method in two neuroscience applications. A curve fitting algorithm for batch ship trajectory estimation that employs Bayesian statistical inference for non-parametric regression is presented. It assumes no knowledge about the ship motion model while only assuming standard ship maneuvers. The trajectory is thought to be well represented by a cubic spline with an unknown number of knots in two-dimensional Euclidean plane. The function estimate is determined from positional measurements which are assumed to be received in batches at irregular time intervals. As the measurements are often delivered by different sensors the measurement errors are assumed to be heteroscedastic and correlated. A fully Bayesian approach is adopted by defining the prior distributions on all unknown parameters: the spline coefficients as well as the number and the locations of knots. The quality of the estimator algorithm is evaluated statistically using several simulated scenarios. The results suggest that the algorithm represents efficient methodology for trajectory estimation in maritime surveillance, especially in the absence of prior knowledge of the motion model. Tracking of highly maneuvering targets with unknown behavior is a difficult problem in state estimation. This paper presents an interacting multiple model algorithm (IMM) utilizing adaptive turn rate models to track a maneuvering target. The turn rate is calculated at each step form the estimator of velocity and the radius of curvature of the trajectory of the target by using Least Square (LS) and curve fitting theory. Simulation in different scenario proves that the turn-rate estimation techniques in this adaptive framework can significantly solve the problem of tracking maneuvering targets. Ground-based aircraft trajectory prediction is a critical issue for air traffic management. A safe and efficient prediction is a prerequisite for the implementation of automated tools that detect and solve conflicts between trajectories. Moreover, regarding the safety constraints, it could be more reasonable to predict intervals rather than precise aircraft positions . In this paper, a standard point-mass model and statistical regression method is used to predict the altitude of climbing aircraft. In addition to the standard linear regression model, two common non-linear regression methods, neural networks and Loess are used. A dataset is extracted from two months of radar and meteorological recordings, and several potential explanatory variables are computed for every sampled climb segment. A Principal Component Analysis allows us to reduce the dimensionality of the problems, using only a subset of principal components as input to the regression methods. The prediction models are scored by performing a 10-fold cross-validation. Statistical regression results method appears promising. The experiment part shows that the proposed regression models are much more efficient than the standard point-mass model. The prediction intervals obtained by our methods have the advantage of being more reliable and narrower than those found by point-mass model.