A tutorial on Yau-Yau nonlinear filtering algorithm: from model-driven to data-driven

Radar systems are used for estimating the position and velocity of aircraft and ships from range and bearing measurements. In this article, we consider two motion models for a civilian aircraft: a constant velocity model and a coordinated turn model. Both kinematics models are written in state-space terms, where the velocity perturbations are modeled by a white noise acceleration model. In order to estimate the aircraft states given noisy measurements obtained from sensor outputs, we follow a Bayesian statistical approach that calculates the estimators of the unknown states. In our simulation, we recreate an air traffic control scenario and implement two nonlinear filtering algorithms in order to perform target tracking of the aircraft. The nonlinear Bayesian-based filters for this target tracking problem are the unscented Kalman filter and the Gauss-Hermite Kalman filter. Finally, the performance of both nonlinear filters is evaluated with a performance metric, root mean squared error, in Monte-Carlo runs.KeywordsTarget trackingUnscented Kalman filterGauss-Hermite Kalman filter

LIDAR (Laser Integrated Radar) is an engineering problem of great practical importance in environmental monitoring sciences. Signal processing for LIDAR applications involves highly nonlinear models and consequently nonlinear filtering. Optimal nonlinear filters, however, are practically unrealizable. In this paper, the Lainiotis′s multi‐model partitioning methodology and the related approximate but effective nonlinear filtering algorithms are reviewed and applied to LIDAR signal processing. Extensive simulation and performance evaluation of the multi‐model partitioning approach and its application to LIDAR signal processing shows that the nonlinear partitioning methods are very effective and significantly superior to the nonlinear extended Kalman filter (EKF), which has been the standard nonlinear filter in past engineering applications.

In this paper, a fast convergent nonlinear adaptive algorithm for narrow-band interference rejection in direct sequence spread spectrum (DS-SS) systems is proposed. The new algorithm can significantly increase the convergence rate of the nonlinear adaptive filter by computer simulations.

A nonlinear active noise control algorithm using the FEWT and channel-reduced recursive Chebyshev filter

Nonlinear filtering algorithm is the key technology for dealing with complex systems in sensor data processing. To improve the filtering accuracy of the nonlinear filtering algorithm in the non‐Gaussian case, an improved version of the Gaussian sum algorithm, the Gaussian sum adaptive sparse grid quadrature filter (GSASQF), is proposed. The proposed algorithm overcomes the challenges by introducing the Gaussian sum principle, which converts the non‐Gaussian state and noise in the system into the form of weighted sum of Gaussian components. Based on the Bayesian filtering framework, a three‐level sparse grid sampling rule is introduced, with the sparse grid orthogonal filtering algorithm serving as the sub‐filter. By determining the sampling point parameters, the filtering process for each combination of Gaussian components is implemented, thereby ensuring the filtering accuracy of each group. In addition, in combination with the ideal of data‐driven, the weight of each Gaussian component combination is adaptively updated inversely by the values of the sensor measurement, which improves the global filtering accuracy of nonlinear system under non‐Gaussian noise. The combination of these three improvements enables high‐precision filtering of non‐Gaussian non‐linear systems. Theoretical analysis and simulation confirm that the proposed GSASQF algorithm provides advantages in filtering accuracy for nonlinear non‐Gaussian filtering problems.

The application of matrix differential calculus for the derivation of simplified expressions in approximate non-linear filtering algorithms

In radar tracking guidance, intelligent video surveillance, robot vision system, the parameters of position and velocity and steering state often need to get the target of interest, based on the motion characteristics of the target and further to control it. The filtering method is used to estimate the desired state parameters based on the functional relationship between the measured values and the state variables. This method is also called target tracking technique. At present, there are many target tracking technologies for different systems, but there is a big gap between the robustness and real-time requirements of the actual system. In order to solve the problem of large computation and bad real-time performance of Particle Filters, a real-time target tracking algorithm based on nonlinear mean shift and Particle Filters is proposed. The distribution of particles is closer to the actual posterior distribution by selecting the important probability density function. Furthermore, the nonlinear mean shift algorithm is integrated into the Particle Filters, so that the particles are further clustered into the real distribution. Finally, the algorithm is applied in the traffic video surveillance, and the effective tracking of the target motorcycle and vehicle is realized.

A nonlinear filtering algorithm for multi-dimensional finite element pollutant advection schemes

: The research under this grant centered upon two distinct but complementary approaches to the problem of developing implementable non-diverging nonlinear filtering algorithms: decentralized linear filtering approach, and adaptive extended Kalman filtering approach.

Nonlinear filtering using the wavelet transform

Presents the results obtained in our research about application of modern nonlinear filtering techniques to GPS based position estimation. The stand-alone GPS based position estimation problem using GPS pseudo-range and Doppler shifts measurements are described. A model for position and velocity estimation are developed. The model is nonlinear and has variable measurement number for coping with an arbitrary number of satellites. Over the last 20-30 years, the extended Kalman filter (EKF) has become the algorithm of choice in numerous nonlinear estimation and machine learning applications. In this work the use of an alternative filter: the unscented Kalman filter (UKF) is proposed. The first experimental results that comprise the comparison of estimation results obtained with a simple model using different filters are then presented. Future research directions are also discussed.

The trajectory estimation of a highly maneuvering target is a challenging problem and has practical applications. The interacting multiple model (IMM) filter is a well-established filtering algorithm for the trajectory estimation of maneuvering targets. In this study, we present an overview of IMM filtering algorithms for tracking a highly-maneuverable fighter aircraft using an air moving target indicator (AMTI) radar on another aircraft. This problem is a nonlinear filtering problem due to nonlinearities in the dynamic and measurement models. We first describe single-model nonlinear filtering algorithms: the extended Kalman filter (EKF), unscented Kalman filter (UKF), and cubature Kalman filter (CKF). Then, we summarize the IMM-based EKF (IMM-EKF), IMM-based UKF (IMM-UKF), and IMM-based CKF (CKF). In order to compare the state estimation accuracies of the IMM-based filters, we present a derivation of the posterior Cramér-Rao lower bound (PCRLB). We consider fighter aircraft traveling with accelerations 3g, 4g, 5g, and 6g and present numerical results for state estimation accuracy and computational cost under various operating conditions. Our results show that under normal operating conditions, the three IMM-based filters have nearly the same accuracy. This is due to the accuracy of the measurements of the AMTI radar and the high data rate.

In order to diagnose and predict the contaminant transport process in large scale geosystems using a nonlinear filtering strategy the state space model has been derived from simulating horizontal contaminant dispersion by extending the discrete vortex method. The dispersion area S and the dispersion rate S have been taken into account for evolving the state space model of the horizontal contaminant transport process. Eventually, S/S has been found to be represented by a function composed of exponential decay terms, which is transformed to the autonomous state equation and serves as the state space model accompanied with the observation equation. The state equation is extended to involve a noise process corresponding to disturbances such as viscous diffusion and inhomogeneity of the vortex strength as observed in real systems. The parameters involved in the state equation are adaptively estimated from the current state observations using a non-linear filtering algorithm. The state space model has been verified by a series of numerical demonstrations carried out using the discrete vortex method.

A novel virtual error approach is proposed for fully adaptive feedforward compensation/equalization, which is useful in nonlinear active noise control and predistortion for nonlinear high power amplifier (HPA). To attenuate the compensation error, two kinds of virtual error are introduced and are forced into zero by adjusting three nonlinear adaptive filters in an on-line manner. It is shown that the convergence of the compensation error to zero can be assured by forcing the virtual errors to zero separately. The proposed method can adjust the predistorter directly without identification of a post-inverse model of HPA as adopted in previous predistortion methods. The effectiveness of the proposed virtual error approach is validated in numerical simulation with comparison to an ordinary nonlinear filtered-x algorithm in the adaptive predistortion for nonlinear HPA used in OFDM communication systems.

This paper first proposes nonlinear spline adaptive filter based on the robust Geman-McClure estimator (SAF-RGM). The proposed algorithm is obtained by minimizing the cost function relied on the Geman-McClure estimator. Since the Geman-McClure estimator can remove outliers with large amplitude from dataset, the proposed algorithm can obtain the excellent performance in the impulsive noise. Moreover, the mean and mean square behaviors of the SAF-RGM algorithm are analyzed. Simulations are conducted to confirm that the proposed SAF-RGM algorithm achieves better performance than the existing spline nonlinear adaptive filtering algorithms. Besides, simulation results validate the theoretical conclusions.