A Hybrid Navigation Concept Using a Spinning Satellite?Borne Interferometer and Self?Contained Equipment

This paper analyzes a hybrid navigation concept that uses signals from a radio interferometer mounted on a spinning geostationary satellite, preliminary position estimates from self-contained equipment, and stored a priori information on the past performance of this equipment. The craft-borne processor, optimum in the maximum a posteriori (MAP) sense, is designed to estimate position coordinates using only the incoming radio signals, although improved estimates result if the other two items are available. An error analysis starts with the derivation of an estimation error covariance matrix, whose elements depend on additive receiver noise and the physical parameters of the system. A minimum 1? estimation error in position is obtained by trading off these parameters. The effects of other major error sources, such as tropospheric phase fluctuations, multipath, and craft altitude uncertainty, are added to the estimation error to give a total 1? position error on the order of 3.7 to 5.6 km.     

Canonical transform for tracking with kinematic models

A canonical transform is presented that converts a coupled or uncoupled kinematic model for target tracking into a decoupled dimensionless canonical form. The coupling is due to non-zero off-diagonal terms in the covariance matrices of the process noise and/or the measurement noise, which can be used to model the coupling of motion and/or measurement between coordinates. The decoupled dimensionless canonical form is obtained by simultaneously diagonalizing the noise covariance matrices, followed by a spatial-temporal normalization procedure. This canonical form is independent of the physical specifications of an actual system. Each subsystem corresponding to a canonical coordinate is characterized by its process noise standard deviation, called the maneuver index as a generalization of the tracking index for target tracking, which characterizes completely the performance of a steady-state Kalman filter. A number of applications of this canonical form are discussed. The usefulness of the canonical transform is illustrated via an example of performance analysis of maneuvering target tracking in an air traffic control (ATC) system.     

Lock threshold deterioration induced by antenna vibration and signal coupling effects in hypersonic vehicle carrier tracking system of Ka band

The envelope of a hypersonic vehicle is affected by severe fluctuating pressure, which causes the airborne antenna to vibrate slightly. This vibration mixes with the transmitted signals and thus introduces additional multiplicative phase noise. Antenna vibration and signal coupling effects as well as their influence on the lock threshold of the hypersonic vehicle carrier tracking system of the Ka band are investigated in this study. A vibration model is initially established to obtain phase noise in consideration of the inherent relationship between vibration displacement and electromagnetic wavelength. An analytical model of the Phase-Locked Loop(PLL), which is widely used in carrier tracking systems, is established. The coupling effects on carrier tracking performance are investigated and quantitatively analyzed by imposing the multiplicative phase noise on the PLL model. Simulation results show that the phase noise presents a Gaussian distribution and is similar to vibration displacement variation. A large standard deviation in vibration displacement exerts a significant effect on the lock threshold. A critical standard deviation is observed in the PLL of Binary Phase Shift Keying(BPSK) and Quadrature Phase Shift Keying(QPSK) signals. The effect on QPSK signals is more severe than that on BPSK signals. The maximum tolerable standard deviations normalized by the wavelength of the carrier are 0.04 and 0.02 for BPSK and QPSK signals,respectively. With these critical standard deviations, lock thresholds are increased from à12 andà4 d B to 3 and à2 d B, respectively.     

GPS C/N/sub 0/ estimation in the presence of interference and limited quantization levels

The carrier-to-noise density ratio (C/N₀) is considered an important parameter describing the GPS receiver performance. This paper compares the performance of two popular coarse-acquisition (C/A) C/N₀ algorithms appearing in literature: the variance summing method (VSM) (Psiaki et al., 2003, Psiaki, 2001), and the power ratio method (PRM) (Van Dierendonck, 1996, Sayre, 2003), in terms of their estimates in 1) additive white Gaussian noise (AWGN), 2) narrowband continuous wave interference (CWI), 3) their response to quantization and saturation effects, and their 4) dynamic range. The algorithms were implemented as a part of a software receiver. Two LI GPS data sets are examined; one was obtained from a GPS raw data collection setup, while the other was obtained from a GPS signal simulator. The collected set was stored with almost constant C/N₀ level while the simulated one contained variable C/N₀ levels. The effect of adding AWGN on the C/N₀ estimate was directly proportional with the noise power. The C/N₀ estimates suffered more when the CWI frequency was closer to the IF of the receiver. The PRM suffered from saturation at higher C/N₀ levels. The VSM showed good tracking at high C/N₀ levels and better immunity to limited quantization levels, while its C/N₀ estimate suffered from rapid fluctuations in power levels when sudden power steps occurred     

The Tracking Index: A Generalized Parameter for ? ? ? and ? ? ? ? Target Trackers

A generalized, optimal filtering solution is presented for the target tracking problem. Applying optimal filtering theory to the target tracking problem, the tracking index, a generalized parameter proportional to the ratio of the position uncertainty due to the target maneuverability to that due to the sensor measurement, is found to have a fundamental role not only in the optimal steady-state solution of the stochastic regulation tracking problem, but also in the track initiation process. Depending on the order of the tracking model, the tracking index solution yields a closed form, consistent set of generalized tracking gains, relationships, and performances. Using the tracking index parameter, an initializing and tracking procedure in recursive form, realizes the accuracy of the Kalman filter with an algorithm as simple as the well-known ? ? ? filter or ? ? ? ? ? filter depending on the tracking order.     

High dynamic output feedback robust control of cascaded extended state observer

High dynamic tracking performance is a key technical index of hydraulic flight motion simulator(HFMS). However, the strong nonlinearities, various model uncertainties and measurement noise in hydraulic actuation systems limit the high dynamic performance improvement. In this paper, the outer axis frame of a HFMS is taken as a case study and its nonlinear dynamic model with consideration of strong nonlinearities, matched and mismatched uncertainties is established.A novel cascaded extended state ...     

On optimal track-to-track fusion

Track-to-track fusion is an important part in multisensor fusion. Much research has been done in this area. Chong et al. (1979, 1986, 1990) among others, presented an optimal fusion formula under an arbitrary communication pattern. This formula is optimal when the underlying systems are deterministic, i.e., the process noise is zero, or when full-rate communication (two sensors exchange information each time they receive new measurements) is employed. However, in practice, the process noise is not negligible due to target maneuvering and sensors typically communicate infrequently to save communication bandwidth. In such situations, the measurements from two sensors are not conditionally (given the previous target state) independent due to the common process noise from the underlying system, and the fusion formula becomes an approximate one. This dependence phenomena was also observed by Bar-Shalom (1981) where a formula was derived to compute the cross-covariance of two track estimates obtained by different sensors. Based on this results a fusion formula was subsequently derived (1986) to combine the local estimates which took into account the dependency between the two estimates. Unfortunately, the Bayesian derivation made an assumption that is not met. This work points out the implicit approximation made and shows that the result turns out to be optimal only in the ML (maximum likelihood) sense. A performance evaluation technique is then proposed to study the performance of various track-to-track fusion techniques. The results provide performance bounds of different techniques under various operating conditions which can be used in designing a fusion system.     

离散跟踪微分器在着舰导引滤波中的应用

介绍了自动着舰导引系统的工作原理及其滤波问题。为了抑制着舰导引系统跟踪雷达的高频噪声,并且克服常用的滤波器采用有限差分法求微分估计的弊端,采用两个二阶离散跟踪微分器串联起来,对含有噪声的雷达测量值进行滤波,并且提取其一二阶微分信息。结果表明,在仿真中使用白噪声模拟雷达噪声,跟踪微分器的滤波效果令人满意。     

Tracking Accuracies with Position and Rate Measurements

Tracking accuracies for the radial component of motion are computed for a track-while-scan radar system which obtains position and rate data during the dwell time on a target These results will be of interest to persons developing trackers for pulse Doppler surveillance radars. The normalized accuracies, computed for a two state Kalman tracking filter with white noise maneuver capability, are shown to depend upon two parameters, r = 4?0/?aT2 and s = ?dT/?0. The symbols ?0 and ?d are the position and rate measurement accuracies, respectively, ?a is the standard deviation of the white noise maneuver process and T is the antenna scan time. The scalar tracking filter equations are derived and numerical results are presented. Lower steady state tracking errors plus the earlier attainment of steady state accuracies are the direct consequence of incorporating the rate measurements into the tracking filter.     

Target racking with glint noise

In tracking targets, there can be an uncertainty associated with the measurements in addition to their inaccuracy, which is usually modeled by aDditive Gaussian noise. However, the Gaussian modeling of the noise may not be true. Noise can be non-Gaussian. The non-Gaussian noise arising in a radar system is known as glint noise. The distribution of glint noise is long tailed and will seriously affect the tracking performance. An algorithm is developed which can significantly improve the tracking performance when glint noise is present     

Bearings-only and Doppler-bearing tracking using instrumentalvariables

In bearings-only tracking (BOT) or Doppler and bearing tracking (DBT), both common passive sonar problems, the measurement equations are nonlinear. To apply the Kalman filter, it is necessary either to linearize the equations or to embed the nonlinearities into the noise terms. The former sometimes leads to filter divergence, while the latter produces biased estimates. A formulation of BOT and DBT which has a constant state vector and simplifies the tracking problem to one of constant parameter estimation is given. The solution is by the instrumental variable method. The instrumental variables are obtained from predictions based on past measurements and are therefore independent of the present noisy measurements. The result is a recursive unbiased estimator. The theoretical developments are verified by simulation, which also shows that the formulation leads to near optimal estimators whose errors are close to the Cramer-Rao lower bound (CRLB)     

Tracking an incoming ballistic missile using an extended interval Kalman filter

The important tracking problem by radar of an incoming ballistic missile system, which contains uncertainty in modeling and noise in both dynamics and measurements, is studied. The classical extended Kalman filter (EKF) is no longer applicable to such an uncertain system, and so a new extended interval Kalman filter (EIKF) is developed for tracking the missile system. Computer simulation is presented to show the effectiveness of the EIKF algorithm for this uncertain and nonlinear ballistic missile tracking problem.     

Clutter Rejection using Peak Curvature

A typical tracking algorithm takes its input from a peak detector or plot extractor. This process reduces the sensor image data to point measurements and reduces the volume of data that the tracker must process. However, useful information can be lost. This paper shows how the clutter of a peak can be a useful feature for discriminating false alarms and valid detections. The benefit obtained by using this feature is quantified through false track rate on recorded sensor data. On recorded data with difficult clutter conditions, approximately sixty percent of false tracks are rejected by exploiting peak curvature     

Altitude Estimation Using Asynchronous ? - ? Tracking Filters

In the analysis of the ?-? tracking filter it is usually assumed that the tracking filter and data source operate in synchronism at a constant data rate. However, in a multisensor environment in which the tracking algorithm operates at fixed intervals, the tracking filter cannot be synchronized with the sensors. An analytical solution is obtained for the case in which the tracking filter and data source operate asynchronously with a ?time-correction? process used to approximate the synchronous operation of the tracking filter. An example is given in which the effects of data quantization on the performance of an altitude tracking filter for air traffic control are examined. It is shown that the asynchronous operation of the tracking filter in the example without the time-correction process will result in significant errors in the predicted altitude.     

K-Band Tracking System for Domestic Satellite Communication System

System design and operational results of a tracking system for a K-band Earth station antenna with a diameter of 11.5 m are discussed. Monopulse tracking technique using higher order waveguide modes is utilized. An investigation was conducted to clarify the rainfall effect and the effect of oscillator phase noise on the tracking receiver. An autotrack system is to be manufactured on the basis of these studies. Experiments were performed using the medium capacity communications satellite. No cross coupling was seen in the pull-in patterns. Sufficiently good results were obtained in tracking accuracy: less than 0.005° (peak value) under normal conditions, and less than 0.01° under an average wind velocity of more than 20 m/s.     

Monopulse Estimation of the Centroid of an Ensemble of Radar Scatterers

The use of data obtained by a monopulse radar to estimate the location of the radar cross-section centroid of an ensemble of scatterers is discussed. Both dish and phased-array antenna radars are treated. Expressions for the bias and variance of the centroid estimates are presented, including the effects of the radar receiver and beam pattern characteristics, receiver noise, and the video waveform sampling granularity, as well as the target properties. The monopulse tracking approach discussed here is contrasted with a raster scan approach presented previously.     

Optimum Steady State Position, Velocity, and Acceleration Estimation Using Noisy Sampled Position Data

A one-dimensional tracking filter based on the Kalman filtering techniques for tracking of a dynamic target such as an aircraft is discussed. The target is assumed to be moving with constant acceleration and is acted upon by a plant noise which perturbs its constant acceleration motion. The plant noise accounts for maneuvers and/or other random factors. Analytical results for estimating optimum steady state position, velocity, and acceleration of the target are obtained.     

Modeling and analysis for the GPS pseudo-range observable

In this paper, a digital system for the Global Positioning System (GPS) pseudo-range observable is modeled and analyzed theoretically. The observable is measured in a GPS receiver by accurately tracking the pseudorandom noise (PRN) code phase of the input GPS signal using a digital energy detector and a digital delay lock loop (DDLL). The following issues are presented: (1) mathematical modeling of the digital PRN code acquisition and tracking system, (2) the closed-form expression derivation for the detection and false-alarm probabilities of the acquisition process and for the variance of code phase tracking error, and (3) the linear and nonlinear performance analysis of the DDLL for optimizing the receiver structures and parameters with tradeoff between the tracking errors due to receiver dynamics and due to input noise     

Mahalanobis distance-based fading cubature Kalman filter with augmented mechanism for hypersonic vehicle INS/CNS autonomous integration

Inertial Navigation System/Celestial Navigation System(INS/CNS) integration, especially for the tightly-coupled mode, provides a promising autonomous tactics for Hypersonic Vehicle(HV) in military demands. However, INS/CNS integration is a challenging research task due to its special characteristics such as strong nonlinearity, non-additive noise and dynamic complexity.This paper presents a novel nonlinear filtering method for INS/CNS integration by adopting the emerging Cubature Kalman Filter(C...     

Radar Measurement Noise Variance Estimation with Several Targets of Opportunity

A number of methods exist to track a target's uncertain motion through space using inherently inaccurate sensor measurements. A powerful method of adaptive estimation is the interacting multiple model (IMM) estimator. In order to carry out state estimation from the noisy measurements of a sensor, however, the filter should have knowledge of the statistical characteristics of the noise associated with that sensor. The statistical characteristics (accuracies) of real sensors, however, are not always available, in particular for legacy sensors. A method is presented of determining the measurement noise variances of a sensor, assumed to be constant, by using multiple IMM estimators while tracking targets whose motion is not known---targets of opportunity. Combining techniques outlined in [2] and [6], the likelihood functions are obtained for a number of IMM estimators, each with different assumptions on the measurement noise variances. Then a search is carried out over a varying grid of IMMs to bracket the variances of the sensor measurement noises. The end result consists of estimates of the measurement noise variances of the sensor in question.