Tracking Filter Design Research Articles

Design and implementation of analog tracking filter for ac signal acquisition

SummaryThis paper presents an analog tracking bandpass filter that is intended to be applied in ac signal acquisition circuits to reduce measurement noise. A fast and accurate frequency tuning technique is developed based on the phase control loop. A complete derivation process is provided to build the mathematical model describing the control loop for the tracking filter. Accordingly, a zero‐crossing detector is designed to accurately extract signal phases in the proposed loop. As a closed‐loop control system, the loop dynamics such as stability, transient response, and steady‐state error are analyzed using the derived model. From both the simulations and measurements, the developed filter is found to provide excellent performance in frequency tracking, noise reduction, and linearity compared to existing work. The maximum and minimum Q value reaches 42.2 and 14, respectively, in the frequency tuning range of 34 to 107 kHz, while the frequency tracking error is less than 1.18% at 100 kHz.

Extended Kalman Filter Design for Tracking Time-of-Flight and Clock Offsets in a Two-Way Ranging System

As radio frequency (RF) hardware continues to improve, two-way ranging (TWR) has become a viable approach for high-precision ranging applications. The precision of a TWR system is fundamentally limited by estimates of the time offset T between two platforms and the time delay τ of a signal propagating between them. In previous work, we derived a family of optimal “one-shot” joint delay–offset estimators and demonstrated that they reduce to a system of linear equations under reasonable assumptions. These estimators are simple and computationally efficient but are also susceptible to channel impairments that obstruct one or more measurements. In this work, we formulate an extended Kalman filter (EKF) for this class of estimators that specifically addresses this limitation. Unlike a generic KF approach, the proposed solution specifically integrates the estimation process to minimize the computational complexity. We benchmark the proposed first- and second-order EKF solutions against the existing one-shot estimators in a MATLAB Monte Carlo simulation environment. We demonstrate that the proposed solution achieves comparable estimation performance and, in the case of the second-order solution, reduces the computation time by an order of magnitude.

Extended Kalman Filter (EKF) Design for Vehicle Position Tracking Using Reliability Function of Radar and Lidar.

Detection and distance measurement using sensors is not always accurate. Sensor fusion makes up for this shortcoming by reducing inaccuracies. This study, therefore, proposes an extended Kalman filter (EKF) that reflects the distance characteristics of lidar and radar sensors. The sensor characteristics of the lidar and radar over distance were analyzed, and a reliability function was designed to extend the Kalman filter to reflect distance characteristics. The accuracy of position estimation was improved by identifying the sensor errors according to distance. Experiments were conducted using real vehicles, and a comparative experiment was done combining sensor fusion using a fuzzy, adaptive measure noise and Kalman filter. Experimental results showed that the study’s method produced accurate distance estimations.

Tracking Filter Design for Predictive Maintenance of Jet Engine – Different Approaches and their Comparison

Abstract The aim of this paper is to design, implement, test and compare several tracking filtration methods for predictive maintenance of a jet engine. Based on literature review multiple possible methods are described. Appropriate ones selected for further implementation are peak filtration, coherent demodulation, Vold-Kalman filtration and order analysis. Methods are tested to meet criteria set by an aircraft manufacturer and compared using simulated signals.

Distributed Optimal Consensus Filter for Target Tracking in Heterogeneous Sensor Networks

This paper is concerned with the problem of filter design for target tracking over sensor networks. Different from most existing works on sensor networks, we consider the heterogeneous sensor networks with two types of sensors different on processing abilities (denoted as type-I and type-II sensors, respectively). However, questions of how to deal with the heterogeneity of sensors and how to design a filter for target tracking over such kind of networks remain largely unexplored.We propose in this paper a novel distributed consensus filter to solve the target tracking problem. Two criteria, namely, unbiasedness and optimality, are imposed for the filter design. The so-called sequential design scheme is then presented to tackle the heterogeneity of sensors. The minimum principle of Pontryagin is adopted for type-I sensors to optimize the estimation errors. As for type-II sensors, the Lagrange multiplier method coupled with the generalized inverse of matrices is then used for filter optimization. Furthermore, it is proven that convergence property is guaranteed for the proposed consensus filter in the presence of process and measurement noise. Simulation results have validated the performance of the proposed filter. It is also demonstrated that the heterogeneous sensor networks with the proposed filter outperform the homogenous counterparts in light of reduction in the network cost, with slight degradation of estimation performance.

Some Aspects on Filter Design for Target Tracking

Tracking filter design is discussed. It is argued that the basis of the present stochastic paradigm is questionable. White process noise is not adequate as a model for target manoeuvring, stochastic least-square optimality is not relevant or required in practice, the fact that requirements are necessary for design is ignored, and root mean square (RMS) errors are insufficient as performance measure. It is argued that there is no process noise and that the covariance of the assumed process noise contains the design parameters. Focus is on the basic tracking filter, the Kalman filter, which is convenient for clarity and simplicity, but the arguments and conclusions are relevant in general. For design the possibility of an observer transfer function approach is pointed out. The issues can also be considered as a consequence of the fact that there is a difference between estimation and design. The α-β filter is used for illustration.

CMOS on-chip active RF tracking filter for digital TV tuner ICs

A full frequency band active RF tracking filter design for a digital TV tuner is implemented for the first time. By combined control of the Gm and C values in the biquad of the Gm - C filter, the proposed tracking bandpass filter satisfies full frequency band tuning while maintaining narrow bandwidth. The Gm cell of the tracking filter is based on a dynamic source degenerated differential pair with optimised transistor size ratio, which provides good linearity and high-frequency operation. The fabricated tracking filter based on a 0.13 μm CMOS process shows 48 780 MHz tracking range with 15 60 MHz bandwidth, more than 50 dB of third-order harmonic rejection, 14 dB unwanted signal rejection at N + 6 channel offset, and a maximum IIP3 of 3.8 dBm at 4.7 dB gain while drawing 30 mA from a 1.2 V supply.

Filter Design for Steady-State Tracking of Maneuvering Targets with LFM Waveforms

Modern radars employ linear frequency modulated (LFM) waveforms for target tracking as the range-Doppler coupling enables better track accuracy in range. This paper derives expressions for the sensor-noise only (SNO) covariance matrix and the position and velocity lags during maneuvers for an alphabeta-filter processing measurements from LFM waveforms. These expressions were confirmed through computer simulations. An analysis of the maximum root-mean-square error (RMSE) in position and velocity estimates is performed, and the gains that minimize the maximum RMSE in either position or velocity are plotted versus the tracking index. For deterministic maneuvers, the paper introduces the concept of the deterministic tracking index and shows its relation to the typical tracking index generally used for random maneuvers. Using these relations, the paper also proposes a method to calculate the optimal process noise variance to be used in the tracking filter for a deterministic tracking index.

Effective Evolutionary Algorithms for Many-Specifications Attainment: Application to Air Traffic Control Tracking Filters

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper addresses a real-world engineering design requiring the application of effective and global optimization techniques. The problem it deals with is the design of nonlinear tracking filters under up to several hundreds of performance specifications. The suitability of different evolutionary computation techniques for solving multiobjective problems is explored, contrasting the performance achieved with recent multiobjective evolutionary algorithm (MOEAs) proposals and different aggregation schemes. In particular, a new scheme is proposed to build a fitness function based on an operator that selects worst cases of multiple specifications in different situations. They have been evaluated in the design of an air traffic control (ATC) tracking filter that should accomplish a specific normative with 264 specifications. Results show their performance in terms of effectiveness and computational load, comparing their capability to scale the problem with respect to problem size. </para>

Robust Filter Design for Tracking of Time-varying Mobile Radio Channels

In this paper, we deal with the problem of tracking smoothly time-varying parameters of linear regression channel models occurring in mobile radio communications. The system under consideration is subjected to time-varying coefficient uncertainties with bounded covariances and noises with inexplicit statistical characteristics. The objective of the tracking problem is to find the filter parameters such that the tracking performance, defined as the least mean square of the tracking error, is optimized. The key to the addressed problem is that the tracking problem is transformed into a filtering one and using a projection formula. A polynomial approach based solution for the tracking will be developed. The robust filter design proposed in this paper may have slightly higher computational complexity than the standard optimal filter designed for systems without random coefficient uncertainties. However, the tracking performance is improved.

Design of bearing-only vision-based tracking filters

We investigate tracking filters in electro-optical target-tracking systems with bearing-only measurements and a stationary tracker. In passive tracking, for maintaining the target in the camera field of view, two tracking angles should be controlled. To extract the target position, there is at least one frame period latency resulting from time duration required for image processing. Three filtering methods, a simple Kalman filter, a novel filtering approach based on curve fitting on time series data, and an interactive multiple model filter, are studied. Since target range is neither available nor observable, in the all mentioned techniques, instead of applying filters to the target states (position and velocity in the space), each filter is directly applied to the tracking angles. The performance of each filter in this approach is evaluated by tracking angles error with two maneuvering targets.

Application of Evolution Strategies to the Design of Tracking Filters with a Large Number of Specifications

This paper describes the application of evolution strategies to the design of interacting multiple model (IMM) tracking filters in order to fulfill a large table of performance specifications. These specifications define the desired filter performance in a thorough set of selected test scenarios, for different figures of merit and input conditions, imposing hundreds of performance goals. The design problem is stated as a numeric search in the filter parameters space to attain all specifications or at least minimize, in a compromise, the excess over some specifications as much as possible, applying global optimization techniques coming from evolutionary computation field. Besides, a new methodology is proposed to integrate specifications in a fitness function able to effectively guide the search to suitable solutions. The method has been applied to the design of an IMM tracker for a real-world civil air traffic control application: the accomplishment of specifications defined for the future European ARTAS system.

Specific Features of IMM Tracking Filter Design

The Interacting Multiple Model (IMM) estimator is a suboptimal hybrid filter that has been shown to be one of the most cost-effective hybrid state estimation schemes. The model of hybrid system and the IMM algorithm, initially proposed by Blom, may serve as a basis for synthesis of more efficient filters for tracking maneuvering aircraft. In this paper we present a number of specific features of the IMM design procedure. In section 2 we briefly describe the hybrid system (aircraft dynamics), hybrid estimation and the principle of the IMM algorithm. The models used in the IMM configuration to describe different flight phases and the measurement model used for our application are presented in sections 3 and 4 respectively. Section 5 provides a detailed discussion on the specific features of the IMM algorithm design. Finally, some examples of IMM tracking filter design and performance evaluation are presented in section 6.

Negative correlation and optimal tracking with Doppler measurements

In target tracking systems that utilize Doppler radar (or sonar), the measurements consist of range, range rate, and one or two angles, When multiple sensors are used in the proper geometry, the final accuracy is determined primarily by each sensor's range estimation accuracy. In this case it is particularly important to extract the most accurate state estimate in the range direction by processing optimally the range and range rate measurements. The usual assumption in the design of tracking filters is that the measurement errors in range and range rate are uncorrelated. However, in the case of the commonly used upsweep chirp (linear FM) waveforms, there can be a significant negative correlation between the range and range rate measurement noises. The purpose of this note is to quantify the performance improvement one can obtain when this correlation is present, as it is in certain waveforms, and accounted for.

Improved Kalman filter design for three-dimensional radar tracking

The problem of three-dimensional (3D) radar tracking is considered. The usual tracking filter design relying on first-order (or linear) approximations leads to poor convergence and erratic filter behavior in highly nonlinear situations. Simple filter algorithms that can overcome these ill effects are developed for two different types of 3D radar measurement. For each type of radar measurement, an accurate expression for the measurement covariance is obtained by evaluating inherent nonlinearities of radar measurements via coordinate transformation. Then algebraic manipulations and reasonable approximations are employed to yield a simple filter formulation based on the expression. The resulting filter equations are similar to the extended Kalman filter (EKF) and provide some useful insights into the behavior of linearized Kalman filters designed with radar measurements. Finally, simulation results show that the proposed approach is very effective in accounting for the measurement nonlinearities.

Robust Estimation with Application to Processing of GPS-data

A new globally, asymptotically stable variable structure observer is derived. The result extends known approaches which are limited to a small class of tracking loops with input-output dynamics of relative degree one. The approach discussed here seems promising for the design of robust tracking filters for purposes of guidance and navigation. A stochastic version of the observer is compared with an adaptive extended Kalman filter for an example of motion tracking from GPS measurements

Observability analysis for target maneuver estimation via bearing-only and bearing-rate-only measurements

The implementation of modern guidance laws requires the design of tracking filters that provide information about the target maneuver. Because of the nonlinearity of the tracking problem, the stability of extended Kalman filters in tracking applications involving bearing-( rate-) only observations is highly dependent on the intercept geometry. This is due mainly to the lack of observability in the absence of range measurements. In this paper, the observability of target maneuvers via bearing-( rate-) only measurements is discussed. Intercept scenarios that result in the loss of observability are identified. They play an important role for both the initialization of tracking filters and the design of missile guidance laws based on bearing-( rate-) only measurements.

Design of near-optimal linear digital tracking filters with colored input

Design of near-optimal linear digital tracking filters with colored input

Improved extended Kalman filter design for passive tracking

Extended Kalman filters are here modified for coordinate estimation of a stationary object using bearing measurements taken from a moving platform. The modifications improve significantly the coordinate estimation on the initial period of data collection when otherwise the performance is far from optimal. The modifications are to the nonlinearities and could, in some instances, be implemented by the introduction of a time decreasing amplitude dither signal in the extended Kalman filter prior to the output nonlinearity. A bound on a Lyapunov function decay rate is also given which assists in the design of the modified nonlinearities and in the selection of an appropriate coordinate basis to be used in the extended Kalman filter.

Kalman filter design for target tracking

The problem of solving the matrix Riccati differential equation in the design of Kalman filters for the target tracking problem is considered. An algebraic transformation method is used to reduce the order of the Riccati differential equation and to obtain explicit expressions for the filter gains (in terms of the interceptor /target separation range) which results in a substantial reduction of the computer burden involved in estimating the target states. The applicability of the transform technique is demonstrated for the receiver thermal noise and the target glint noise cases.