Multiple model nonlinear filtering for low signal ground target applications

Trackers for Ground Moving Target Indicator (GMTI) radar have to be benchmarked in order to yield good results. For many benchmarking purposes, the usage of real data may become expensive and in-feasible. It may also lack of knowledge of the ground truth. Simulating GMTI situations is a less-expensive alternative to real measurements. In order to get a realistic scenario, the motion and radar cross section (RCS) of ground targets, the motion of sensor platforms and the properties of GMTI sensors have to be simulated. In this paper, considerations for a realistic motion and sensor model are presented. Then, an implementation of a framework for simulation is shown, together with first experiences in tracker benchmarking using this framework.

This paper addresses the numerical solution of a fractional evolution equation with a weakly singular kernel. The temporal discretization is carried out by the Crank–Nicolson (CN) method based on graded time steps, while the spatial discretization is carried out using an alternating direction implicit (ADI) finite difference method. Stability and convergence rate are also discussed. The convergence rate is $ O(k^2+h_x^2+h_y^2) $, where $ k $ is a parameter of the maximal time steps and $ h_x $, $ h_y $ are the uniform grid steps in space. Three numerical examples are employed to demonstrate the errors and convergence behavior in practice.

In this work, we propose a new ground moving target indicator (GMTI) radar based ground vehicle tracking method which exploits domain knowledge. Multiple state models are considered and a Monte-Carlo sampling based algorithm is preferred due to the manoeuvring of the ground vehicle and the non-linearity of the GMTI measurement model. Unlike the commonly used algorithms such as the interacting multiple model particle filter (IMMPF) and bootstrap multiple model particle filter (BS-MMPF), we propose a new algorithm integrating the more efficient auxiliary particle filter (APF) into a Bayesian framework. Moreover, since the movement of the ground vehicle is likely to be constrained by the road, this information is taken as the domain knowledge and applied together with the tracking algorithm for improving the tracking performance. Simulations are presented to show the advantages of both the new algorithm and incorporation of the road information by evaluating the root mean square error (RMSE).

Current out-ofsequence measurement (OOSW filtering algorithms belong to two distinct classes, Kalman filter (U) or extended KF (EKF) based and particle filter (PF) based. This paper compares the performances of the multiple-lag I@ and PF based OOSMJiltering algorithms for a number of scenarios with linear dynamic and measurement models with additive Gaussian noisesjrst. The KF with in-sequence measurements represents an optimal estimator. Therefore, for this case, we compare the performances of the OOSMjltering algorithms relative to the KF with in-sequence measurements. Numerical results show that the KF OOSMaIgorithm used in this study is optimal. Next, we evaluate the multiple-lag KF/EU and PF based 0OSMf;rtering algorithms using realistic Ground Moving Target Indicator (GMTI) sensor measurements. We use estimation accuracy and statistical consistency for comparison.

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Incorporating standard high-order spatial approximations in the alternating-direction implicit (ADI) finite-difference time-domain method does not suffice for improving the technique’s accuracy, as these operators are capable of reducing spatial errors only. We herein develop an alternative design procedure, which results in the construction of finite-difference expressions that ameliorate the combined space–time flaws. In essence, it is shown that three error formulas are derived from the individual implicit equations, provided that the ADI updates are treated as a single-step process. Then, more efficient spatial expressions can be extracted through proper manipulation of these formulas and subsequent application of error-controlling concepts.

In this paper, we present an easy-hardware-implementation multiple model particle filter (MMPF) for maneuvering target tracking. In the proposed filter, the sampling importance resampling (SIR) filter typically used for nonlinear and/or non-Gaussian application is extended to incorporating multiple models that are composed of a constant velocity (CV) model and a "current" statistical (CS) model, and the Independent Metropolis Hasting (IMH) sampler is utilized for the resampling unit in each model. Compared with the bootstrap MMPF, the proposed MMPF requires no knowledge of models and model transition probabilities for different maneuvering motions, and keeps a constant number of particles per model at all times. This allows a regular pipelined hardware structure and can be implemented in hardware easily. Furthermore, using the IMH sampler for the resampling unit avoids the bottleneck introduced by the traditional systematic resampler and reduces the latency of the whole implementation. Simulation results indicate that the proposed filter has approximately equal tracking performance with the bootstrap MMPF. Hardware architecture of the IMH sampler and its corresponding sample unit are presented, and a parallel architecture consisting of CV model processing element (PE), CS model PE and a central unit (CU) is described. The proposed architecture is evaluated on a Xilinx Virtex-II Pro FPGA platform for a maneuvering target tracking application and the results show many advantages of the proposed MMPF over existing approaches in terms of efficiency, lower latency, and easy hardware implementation.

We address the problem of training data corruption in space-time adaptive processing (STAP) for ground moving target indication (GMTI) radar scenarios characterized by high densities of ground targets. A site-specific clutter simulation is used to demonstrate the impact that target signals in the training data have on STAP performance. Measured MCARM data results are presented that reveal similar performance trends as those observed in the simulations. A strategy for mitigating the deleterious effects of targets in the training data using a priori knowledge of the radar environment (e.g., locations of roads) to edit the training data is presented.

We have developed and tested a new algorithm, which we call the filter, that solves the nonlinear filtering problem with discrete-time measurements by solving the Fokker-Planck equation for the conditional probability density function using a split-step technique. The wave filter uses fast convolution to compute the effect of process noise at discrete times. Between measurements, the conditional density is propagated by solving a system of ordinary differential equations. Measurement update is carried out via Bayes' rule. We propose the adjoint method to reduce the computational complexity of the algorithm by adaptively varying the mesh size.

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

A two-dimensional numerical solution for pulsed laser transformation hardening is developed using the finite difference method (FDM). The FDM has been developed using Crank-Nicolson scheme which solved by using alternating-direction implicit method. If this present model was compared to the analytical solution, then the Crank-Nicolson scheme showed better results in terms of accuracy, consistency, stability, convergence, and performance than to the explicit scheme. The longer heating duration, higher laser beam intensity, and greater number of pulse had influences on increasing the maximum temperature. The repetitive heating had influences on extending the heat duration and increasing the initial temperature of domain. The shorter cooling duration in repetitive pulse produced higher maximum temperature. The thinner material’s thickness increased the cooling rate, which finally increased the possibility of austenite to transform into martensite phase. In addition, it was also found that the higher maximum temperature always reduced the cooling rate value when temperature cools down toward to the starting temperature of martensite formation. It reduced the possibility of martensite formation. It was also seen that the heat was conducted more effective to the axial direction than to the radial direction.

This paper presents a computational acceleration of image inpainting using parallel processing based on Graphics Processing Unit (GPU) Compute Unified Device Architecture (CUDA). We use parabolic partial differential equation (PDE) called heat equation as the model equation. The heat equation is discretized numerically using Finite Difference method. Semi-algebraic equation that formed then solved by using Alternating-Direction Implicit (ADI) scheme. The numerical algorithm is implemented in GPU CUDA parallel computing to speed up the computational time. The computational process of the inpainting can be done using larger time-step. The computational time can be accelerated to 5.86 times faster using an image with 2736×1824 resolution.

In this paper, a novel compact alternating direction implicit (ADI) scheme is proposed for solving the time-fractional subdiffusion equation in two space dimensions. The established scheme is based on the modified L1 method in time and the compact finite difference method in space. The unique solvability, unconditionally stability and convergence of the scheme are proved. The derived compact ADI scheme is coincident with the one for 2D integer order parabolic equation when the , where is the order of the Riemann–Liouville derivative operator. In addition, the novel ADI scheme is used to solve the 2D modified fractional diffusion equation, and the corresponding stability and convergence results are also given. Numerical results are provided to verify the theoretical analysis.

ABSTRACTHeat transfer at microscale plays an important role in microtechnology applications. First, this paper is concerned with the numerical solution of a two-dimensional (2D) heat transfer equation at microscale through a second-order alternating direction implicit (ADI) method. By the discrete energy method, it is shown that the ADI solution converges to the exact solution with a convergence order of in L2-norm. Second, the ADI method is generalized to numerically solve the three-dimensional (3D) problem, and provides numerical solutions of order two in both time and space. Finally, numerical results testify the temporal and spatial accuracy of the ADI method.

We evaluate the use of a probability hypothesis density (PHD) filter in a bearings-only tracking application. The main feature of a PHD filter is that it propagates the first-order statistical moment of a multisource posterior distribution. Multisource estimation using a PHD filter has been shown to reliably track multiple simulated targets in the bearings-only case. In this paper we evaluate the utility of the sequential Monte-Carlo PHD filter for tracking surface ships using bearings-only data acquired from a Bluefin-21 unmanned underwater vehicle in Boston Harbor. The unmanned underwater vehicle was equipped with a rigidly mounted planar hydrophone array that measures the bearing angle to sources of acoustic noise, of which shipping traffic is the dominant source. We further evaluate several target maneuvering models, including clockwise and counter-clockwise coordinated turns. The combination of the coordinated turn models with a constant velocity model is used in a multiple model PHD filter. The results of the multiple model PHD filter are compared to the results of a PHD filter using only a constant velocity model.