Converted state equation Kalman filter for nonlinear maneuvering target tracking

We consider the problem of target tracking in a wireless sensor network (WSN) that consists of randomly distributed range-only sensors. Quantized measurements are usually adopted in such a network to attack the problem of limited power supply and communication bandwidth. Assuming that local sensor noises are mutually independent, we derive the posterior Cramer-Rao lower bound (CRLB) on the mean squared error (MSE) of target tracking in WSNs with quantized range-only measurements. Recursion of posterior CRLB on tracking based on both constant velocity (CV) and constant acceleration (CA) model for target dynamics and a general range-only measuring model for local sensors are obtained. Due to the analytical difficulties, particle filter is applied to approximate the theoretical bounds. To illustrate the posterior CRLB, an example on tracking a target with noisy circular trajectories is given.

A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous Hamiltonian system is multiplied by a set of multiplicative functions, then the general expression of the first integral can be obtained. An example is given to illustrate the application of the results.

The problem of motion modelling in the range-Doppler (R-D) plane as well as range and Doppler estimation for the Cartesian nearly constant acceleration motion, which is a common manoeuvering motion, is investigated. The temporal evolution equation is derived based on the state vector consisting of target range, Doppler and derivatives of the product of range and range rate versus time. In this way, the measurement equation of range and Doppler measurements can be maintained in a desirable linear-Gaussian structure. Based on the non-linear state equation and the linear measurement equation, the unscented Kalman filter is adopted to tackle the non-linear filtering problem. The corresponding filter initialisation method is developed based on the two-point differencing method. Explicit expressions of the initial state estimates and the initial covariance matrix are presented in analytic forms where the correlation among the state components is handled properly. The posterior Cramer–Rao lower bound (PCRLB) is provided for state estimation in the R-D plane. Comprehensive comparisons of the proposed method against the existing R-D state estimation methods using approximate models, Cartesian state estimator and PCRLB are carried out in simulations to demonstrate the validity and correctness of the proposed motion model and estimation method.

Polar coordinate system is more effective for rotational axes than Cartesian coordinate one. But most commercial motion control cards do not support the polar coordinate, so this paper presents a program module based on polar coordinate system, which can be integrated into computer numeric control (CNC) controller based on motion control cards. To access the module, a special G code is developed. The module is implemented on a custom-made CNC controller and used to machine a class of watch parts. The experimental results show that the module is effective and easy to use.

In radio astronomy, visibility data, which are measurements of wave signals from radio telescopes, are transformed into images for observation of distant celestial objects. However, these resultant images usually contain both real sources and artifacts, due to signal sparsity and other factors. One way to obtain cleaner images is to reconstruct samples into dense forms before imaging. Unfortunately, existing reconstruction methods often miss some components of visibility in frequency domain, so blurred object edges and persistent artifacts remain in the images. Furthermore, the computation overhead is high on irregular visibility samples due to the data skew. To address these problems, we propose PolarRec, a transformer-encoder-conditioned reconstruction pipeline with visibility samples converted into the polar coordinate system. This coordinate system matches the way in which radio telescopes observe a celestial area as the Earth rotates. As a result, visibility samples distribute in the polar system more uniformly than in the Cartesian space. Therefore, we propose to use radial distance in the loss function, to help reconstruct complete visibility effectively. Also, we group visibility samples by their polar angles and propose a group-based encoding scheme to improve the efficiency. Our experiments demonstrate that PolarRec markedly improves imaging results by faithfully reconstructing all frequency components in the visibility domain while significantly reducing the computation cost in visibility data encoding. The code is available at https://github.com/RapidsAtHKUSTIPolarRec.

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.

In this paper we consider the radar assignment problem for air-defense radar network to detect and track multiple stealth targets. For the purpose of selecting appropriate radar at appropriate time to optimize the detection and tracking performance under the given constraints, we propose a novel radar assignment algorithm based on posterior Cramer-Rao lower bound (PCRLB), binary particle swarm optimization (BPSO) and particle filtering (PF). A group of randomly generated particles are used to obtain the detection probability of newborn targets, while the tracking accuracy is measured by PCRLB. Moreover, the BPSO is adopted to search the surveillance region for the optimal activated radar subset. Finally, the PF outputs of activated radars are fused. Simulation results show that the proposed method can not only quickly identify newborn targets, but also can optimize the tracking performance of existing targets. Compared with traditional methods, the tracking accuracy of the radar network is improved.

The robotic manipulators which are actively interacting with humans should be able to emulate the characteristics and performance of human body systems. Among various approaches to this end, this paper introduces a novel coordination system to control a two link manipulator in a more intuitive and human-friendly way: the polar coordinate system to describe the motions of a two-link manipulator and a biarticular actuation mechanism. The kinematics and dynamics of the two-link manipulator are analyzed utilizing the biarticular actuation mechanism and the polar coordinate system for an effective and convenient expression of the equation of motion inspired by the musculoskeletal structure of humans, which enables the sophisticated and intuitive control of an end-effector of a two-link manipulator. The dynamic equation with the proposed coordinate system and biarticular actuation mechanism is formalized into a state space equation, and the state feedback controller is designed based on the derived state space dynamics (1) to reject undesired dynamic couplings caused by the inherent mechanical structure and (2) to realize the desired dynamic characteristics at the end-effector. As applications of the proposed method, a position tracking controller is designed for the end-effector. In addition, for implementation of the proposed method, a kinematic Kalman filter is utilized for the best estimation of state variables. The experimental verifications of the proposed method are given in this paper.

Basic mathematical tools in electrical engineering: coordinates systems, scalars, phasors, and vectors

The deformation problem of elasticity theory with regard to nonlinear deformations is examined. The expressions of deformations through displacements in the orthogonal curvilinear coordinate system are recorded. The relations for finite deformations in cylindrical and polar coordinate systems are derived. Physical relations for finite deformations and corresponding generalized stresses are recorded.

Diffraction of Plane SH Waves by a Cylindrical Cavity in an Infinite Wedge

Optical analog computing prevails over digital computing in several aspects, such as processing speed and power consumption. Optical differentiation, as a main branch, can be particularly significant in image recognition. Various differentiators have been developed to realize the two-dimensional differentiation in Cartesian coordinates. Here, we propose the optical differentiation in a polar coordinate system, which can be factorized into the radial differentiation and the angular differentiation. Experimental results demonstrate that the variations along radial and angular directions can be, respectively, highlighted by the two kinds of differentiation, which suggests that employing polar coordinates may be more intuitive and informative in practical use. This work is probable to enrich the content of optical differentiation and extend potential applications in image recognition.

Kalman filter and its families have played an important role in information gathering, such as target tracking. Data association techniques have also been developed to allow the Kalman filter to track multiple targets simultaneously. This paper revisits the principle and applications of the Kalman filter for single target tracking and multiple hypothesis tracking (MHT) for multiple target tracking. We present the brief review of the Bayes filter family and introduce a brief derivation of the Kalman filter and MHT. We show examples for both single and multiple targets tracking in simulation to illustrate the efficacy of Kalman filter-based algorithms in target tracking scenarios.

In order to realize high-speed laser writing arbitrary patterns, we establish a set of high-speed polar coordinate laser writing system. Although the polar coordinate laser writing system is generally suitable for fabricating circular symmetric patterns, there are challenges when dealing with arbitrary patterns. Here, we propose an effective method to solve this problem by converting the pattern data from Cartesian coordinates to polar coordinates for high-speed laser writing of arbitrary patterns. Several types of arbitrary patterns are written on chalcogenide thin films with a minimum pattern linewidth of 700 ± 70 nm and a maximum writing speed of approximately 10 m/s, which corresponds to more than 600 mm2/min at 1.0 μm linewidth. This writing speed is ten times faster than that of the conventional x-y type Cartesian coordinate laser writing system.

ABSTRACTLocation information of sensor nodes is of vital importance for most applications in wireless sensor networks (WSNs). This paper proposes a new range-free localisation algorithm using support vector machine (SVM) and polar coordinate system (PCS), LSVM-PCS. In LSVM-PCS, two sets of classes are first constructed based on sensor nodes’ polar coordinates. Using the boundaries of the defined classes, the operation region of WSN field is partitioned into a finite number of polar grids. Each sensor node can be localised into one of the polar grids by executing two localisation algorithms that are developed on the basis of SVM classification. The centre of the resident polar grid is then estimated as the location of the sensor node. In addition, a two-hop mass-spring optimisation (THMSO) is also proposed to further improve the localisation accuracy of LSVM-PCS. In THMSO, both neighbourhood information and non-neighbourhood information are used to refine the sensor node location. The results obtained verify that the proposed algorithm provides a significant improvement over existing localisation methods.