KEYWORDS: Missiles, Protactinium, Monte Carlo methods, Navigation systems, Mathematical modeling, Motion estimation, Motion models, Statistical analysis, Optimization (mathematics), Signal to noise ratio
This work deals with the following question: using passive (line-of-sight angle) observations of a multistage
surface to air missile from an aircraft, how can one infer that the missile is or is not aimed at the aircraft. The
observations are assumed to be made only on the initial portion of the missile's trajectory. The approach is to
model the trajectory of the missile with a number of kinematic and guidance parameters, estimate them and
use statistical tools to infer whether the missile is guided toward the aircraft or not. A mathematical model is
presented for a missile under pure proportional navigation with a changing velocity (direction change as well
as speed change), to intercept a nonmaneuvering aircraft. A maximum likelihood estimator (MLE) is used for
estimating the missile's motion parameters and a goodness-of-fit test is formulated to test if the aircraft is the
aim or not. Using measurement data from several realistic missiles - single stage as well as multistage - aimed
at an aircraft, it is shown that the proposed method can solve this problem successfully. The key to the solution,
in addition to the missile model parametrization, is the use of a reliable global optimization algorithm with a
hierarchical search technique for the MLE. The estimation/decision algorithm presented here can be used for an
aircraft to decide, in a timely manner, whether appropriate countermeasures are necessary.
KEYWORDS: Missiles, Protactinium, Motion estimation, Mathematical modeling, Motion models, Statistical analysis, Solids, Monte Carlo methods, 3D modeling, Signal to noise ratio
This work deals with the following question: using passive (line-of-sight angle) observations of a missile from an aircraft, how can one infer that the missile is or is not aimed at the aircraft. The observations are assumed to be made only on the initial portion (about 1/4) of the missile's trajectory. The approach is to model the trajectory of the missile with a number of kinematic and guidance parameters, estimate them and use statistical tools to infer whether the missile is guided toward the aircraft. A mathematical model is constructed for a missile under pure proportional navigation with a changing velocity (direction change and speed change), to intercept a nonmaneuvering aircraft. A maximum likelihood estimator is presented for estimating the missile's motion parameters and a goodness-of-fit test is formulated to test if the aircraft is the aim or not. Using measurement data from a realistic missile aimed at an aircraft shows that the proposed method can solve this problem successfully. The estimation/decision algorithm presented here can also be used for an aircraft to decide whether appropriate countermeasures are necessary.
KEYWORDS: Sensors, Error analysis, Filtering (signal processing), Device simulation, Detection and tracking algorithms, Sensor fusion, Data fusion, Signal processing, Data processing, Systems modeling
In this paper, multisensor-multitarget tracking performance with bias estimation and compensation is investigated when only moving targets of opportunity are available. First, we discuss the tracking performance improvement with bias estimation and compensation for synchronous biased sensors, and then a novel bias estimation method is proposed for asynchronous sensors with time-varying biases. The performance analysis and simulations show that asynchronous sensors have a slightly degraded performance compared to the "equivalent" synchronous ones. The bias estimates as well as the corresponding Cramer-Rao Lower Bound (CRLB) on the covariance of the bias estimates, i.e., the quantification of the available information on the sensor biases in any scenario are also given. Tracking performance evaluations with different sources of biases --- offset biases, scale biases and sensor location uncertainties, are also presented and we show that tracking performance is significantly improved with bias estimation and compensation compared with the target tracking using the original biased measurements. The performance is also close to the lower bound obtained in the absence of biases.
KEYWORDS: Sensors, Monte Carlo methods, Filtering (signal processing), Error analysis, Computer engineering, Sensor fusion, Detection and tracking algorithms, Signal processing, Systems modeling, Data communications
This paper provides the exact solution for the bias estimation problem in multiple asynchronous sensors using common targets of opportunity. The target data reported by the sensors are usually not time-coincident or synchronous due to the different sampling times. We consider here the case when the sensors obtain the measurements at the same rate but with a phase difference. Since the bias estimation requires time-coincident target data from different sensors, a novel scheme is used to transform the measurements from the different times of the sensors into pseudomeasurements of the sensor biases with additive noises that are zero-mean, white and with easily calculated covariances. These results allow bias estimation as well as the evaluation of the Cramer-Rao Lower Bound (CRLB) on the covariance of the bias estimate, i.e., the quantification of the available information about the biases in any scenario. Monte Carlo simulation results show that the new method is statistically efficient, i.e., it meets the CRLB. The use of this technique for scale biases in addition to the usual additive (offset) biases is also presented.
KEYWORDS: Sensors, Error analysis, Data analysis, Statistical analysis, Monte Carlo methods, Radar, Computer engineering, Data processing, Optical tracking, Computing systems
This paper provides a solution for sensor bias estimation based on local tracks at a single time without a priori association for a decentralized multiple sensor tracking system. Each local tracker generates its own local state estimates ignoring the bias. The fusion center then performs track-to-track fusion occasionally after estimating the sensor biases based on the common targets tracked by different sensors. The likelihood function of the bias in a multisensor-multitarget scenario is derived. Using this likelihood, it is shown that the difference of the local estimates is the sufficient statistic for estimating the biases. A least squares solution of the bias estimates and corresponding Cramer-Rao Lower Bound (CRLB) are presented assuming uncorrelatedness as well as accounting for the crosscorrelation between the local estimation errors. Two approaches to estimate the sensor biases in the absence of known track-to-track association, namely, the Maximum Likelihood estimator combined with Probabilistic Data Association (ML-PDA) and an estimator based on soft data association, are proposed. These methods are compared with the baseline solution with known (perfect) track-to-track association by Monte Carlo simulations. The experimental results indicate that the bias estimator based on the soft data association provides nearly optimal performance and has less computational load than the one using ML-PDA.
In this paper we consider a nonlinear bearing-only target tracking problem using three different methods and compare their performances. The study is motivated by a ground surveillance problem where a target is tracked from an airborne sensor at an approximately known altitude using depression angle observations. Two nonlinear suboptimal estimators, namely, the extended Kalman Filter (EKF) and the pseudomeasurement tracking filter are applied in a 2-D bearing-only tracking scenario. The EKF is based on the linearization of the nonlinearities in the dynamic and/or the measurement equations. The pseudomeasurement tracking filter manipulates the original nonlinear measurement algebraically to obtain the linear-like structures measurement. Finally, the particle filter, which is a Monte Carlo integration based optimal nonlinear filter and has been presented in the literature as a better alternative to linearization via EKF, is used on the same problem. The performances of these three different techniques in terms of accuracy and computational load are presented in this paper. The results demonstrate the limitations of these algorithms on this deceptively simple tracking problem.
This paper presents an Interacting Multiple-Model (IMM) estimator based approach to navigation using the Global Positioning System (GPS). The “soft-switching” IMM estimator obtains its estimate as a weighted sum of the individual estimates from a number of parallel filters matched to different motion modes of the platform, e.g., nearly constant velocity and maneuvering. The goal is to obtain the maximum navigation accuracy from an inexpensive and light GPS-based system, without the need for an inertial navigation unit, which would add both cost and weight. In the case of navigation with maneuvering, for example, with accelerations and decelerations, the IMM estimators can substantially improve navigation accuracy during maneuvers as well as during constant velocity motion over a conventional (extended) Kalman Filter (KF), which is, by necessity, a compromise filter. This paper relies on a detailed modeling of GPS and presents the design of a navigation solution using the IMM estimator. Two different IMM estimator designs are presented and a simulated navigation scenario is used for comparison with two baseline KF estimators. Monte Carlo simulations are used to show that the best IMM estimator significantly outperforms the KF, with about 40-50% improvement in RMS position, speed and course errors.
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