Multisensor deployment using PCRLBS, incorporating sensor deployment and motion uncertainties

Recently, a general framework for sensor resource deployment (Hernandez, et. al. 2004) has been shown to allow efficient and effective utilization of a multisensor system. The basis of this technique is to use the posterior Cramer-Rao lower bound (PCRLB) to quantify and control the optimal achievable accuracy of target state estimation. In the original formulation (Hernandez, et. al. 2004) it was assumed that the sensor locations were known without error. In the current paper, the authors extend this framework by addressing the issues of imperfect sensor placement and uncertain sensor movement (e.g., sensor drift). The crucial consideration is then how these two forms of uncertainty are factored into the sensor management strategy. If unaccounted for, these uncertainties will render the output of the resource manager inaccurate and overoptimistic. The authors adjust the PCRLB to account for sensor location uncertainty, and we also allow for measurement origin uncertainty due to missed detections and false alarms. The work is motivated by the problem of tracking a submarine by adaptively deploying sonobuoys from a helicopter. Simulation results are presented to show the advantages of accounting for sensor location uncertainty within this focal domain of antisubmarine warfare. The authors note that the generic nature of the technique allows it to be utilized within other problem domains, including tracking ground-based targets using unattended ground sensors (UGSs) or unmanned aerial vehicles (UAVs)     

Dynamic Cramer-Rao bound for target tracking in clutter

Recently, there have been several new results for an old topic, the Cramer-Rao lower bound (CRLB). Specifically, it has been shown that for a wide class of parameter estimation problems (e.g. for objects with deterministic dynamics) the matrix CRLB, with both measurement origin uncertainty (i.e., in the presence of false alarms or random clutter) and measurement noise, is simply that without measurement origin uncertainty times a scalar information reduction factor (IRF). Conversely, there has arisen a neat expression for the CRLB for state estimation of a stochastic dynamic nonlinear system (i.e., objects with a stochastic motion); but this is only valid without measurement origin uncertainty. The present paper can be considered a marriage of the two topics: the clever Riccati-like form from the latter is preserved, but it includes the IRF from the former. The effects of plant and observation dynamics on the CRLB are explored. Further, the CRLB is compared via simulation to two common target tracking algorithms, the probabilistic data association filter (PDAF) and the multiframe (N-D) assignment algorithm.     

Effect of bias on bearing-only target location

The influence of angle measurement bias on passive target location estimation is investigated. First the conditions for target observability are found and generalized to the non-zero-mean measurement noise case. Then the Cramer-Rao lower bound on the estimation error is derived. Numerical examples are included, illustrating the target location uncertainty in the presence of measurement bias     

Multisensor multitarget bias estimation for general asynchronous sensors

A novel solution is provided for the bias estimation problem in multiple asynchronous sensors using common targets of opportunity. The decoupling between the target state estimation and the sensor bias estimation is achieved without ignoring or approximating the crosscovariance between the state estimate and the bias estimate. The target data reported by the sensors are usually not time-coincident or synchronous due to the different data rates. 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 and sensor location biases in addition to the usual additive biases is also presented.     

Target tracking with a network of Doppler radars

By observing a Doppler signal at several points in space, it is possible to determine the position, velocity, and acceleration of a moving target. Parameter identification for a constant-acceleration motion model is studied, and the Cramer-Rao bound on motion parameter uncertainty is obtained for phaseand frequency-based estimation strategies, with the result that the preferred strategy depends upon the sensor/target geometry and target motion. Direct identification of the constant-acceleration trajectory model from the Doppler signal requires a 9-dimensional nonlinear optimization. Exploiting symmetry in the sensing geometry, a novel trajectory representation is presented which reduces the nonlinear optimization to one in 3 dimensions, with additional parameters obtained by linear identification. Baseball tracking using a network of four Doppler radars is experimentally demonstrated     

Optimal Cooperative Sensing using a Team of UAVs

The authors investigates the joint optimal estimation of both the position and velocity of a ground moving target (GMT) using pulse Doppler radars on-board unmanned aerial vehicles (UAVs). The problem of cooperative estimation using a UAV team and the optimization of the team's configuration to achieve optimal GMT position and velocity estimates are addressed. Based on the Cramer-Rao bound, the minimum achievable error variance of the GMT position and velocity estimates is derived. The expression of the minimum achievable estimation error variance for unbiased estimation provided by the Cramer-Rao bound is minimized yielding the optimal configuration of the UAV team. Our solution is complete in that it addresses various GMT tracking scenarios and an arbitrary number of UAVs. Optimal sensor geometries for typical applications are illustrated     

KUPS: Knowledge-Based Ubiquitous and Persistent Sensor Networks for Threat Assessment

We propose a knowledge-based ubiquitous and persistent sensor network (KUPS) for threat assessment, in which "sensor" is a broad characterization. It refers to diverse data or information from ubiquitous and persistent sensor sources such as organic sensors and human intelligence sensors. Our KUPS for threat assessment consists of two major steps: situation awareness using fuzzy logic systems (FLSs) and threat parameter estimation using radar sensor networks (RSNs). Our FLSs combine the linguistic knowledge from different intelligent sensors, and our proposed maximum-likelihood (ML) estimation algorithm performs target radar cross section (RCS) parameter estimation. We also show that our ML estimator is unbiased and the variance of parameter estimation matches the Cramer-Rao lower bound (CRLB) if the radar pulses follow the Swerling II model. Simulations further validate our theoretical results.     

On joint track initiation and parameter estimation under measurement origin uncertainty

The problem of joint detection and estimation for track initiation under measurement origin uncertainty is studied. The two well-known approaches, namely the maximum likelihood estimator with probabilistic data association (ML-PDA) and the multiple hypotheses tracking (MHT) via multiframe assignment, are characterized as special cases of the generalized likelihood ratio test (GLRT) and their performance limits indicated. A new detection scheme based on the optimal gating is proposed and the associated parameter estimation scheme modified within the ML-PDA framework. A simplified example shows the effectiveness of the new algorithm in detection performance under heavy clutter. Extension of the results to state estimation with measurement origin uncertainty is also discussed with emphasis on joint detection and recursive state estimation.     

Trajectory Estimation with Uncertain and Nonassociated Data

The local behavior of a maximum likelihood estimator that adaptively weights data of uncertain origin to make a probabilistic measurement-to-track assignment is examined. The results are placed in the framework of the classic estimation theory of Fisher and Cramer. The Cramer-Rao bound is derived and the MLS error level is compared with this lower bound and the level achieved with known data association. Deterioration in performance was found to depend solely on the false-detection to valid-contact ratio, and the actual (measured) covariance matrix is a scalar multiple of the covariance matrix computed for associated data.     

空中目标传感器管理方法综述

为了避免对有限的多传感器资源的无序竞争和使用,多传感系统通常在一定约束条件下工作。传感器管理即是对传感器系统的自由度进行控制,以满足实际的约束条件并实现既定的任务目标,被大规模地应用于诸如区域目标监视、空中交通管制等各种军用与民用领域。首先,给出了传感器管理系统的概念定义与基本目标;然后,对过去及现在各种空中目标传感器管理方面的理论、方法以及应用进行了全面的综述与深入的分析,并对传感器管理领域现存的问题提出了解决思路和方法;最后,对该领域下一步的发展方向做出了展望。     

Exact multisensor dynamic bias estimation with local tracks

An exact solution is provided for the multiple sensor bias estimation problem based on local tracks. It is shown that the sensor bias estimates can be obtained dynamically using the outputs of the local (biased) state estimators. This is accomplished by manipulating the local state estimates such that they yield pseudomeasurements of the sensor biases with additive noises that are zero-mean, white, and with easily calculated covariances. These results allow evaluation of the Cramer-Rao lower bound (CRLB) on the covariance of the sensor bias estimates, i.e., a quantification of the available information about the sensor biases in any scenario. Monte Carlo simulations show that this method has significant improvement in performance with reduced rms errors of 70% compared with commonly used decoupled Kalman filter. Furthermore, the new method is shown to be statistically efficient, i.e., it meets the CRLB. The extension of the new technique for dynamically varying sensor biases is also presented.     

Bounds on Time-Delay Estimation for Monochromatic Signals

Time-delay estimation (TDE) of monochromatic signals,observed by spatially separated sensors, is widely used for sourcelocalization in radar/sonar applications. We use lower bounds tostudy the accuracy of TDE as a function of signal to noise ratio(SNR), frequency, and sensor separation. We show that the Cramer-Rao bound, which is frequently used as a standard ofreference, yields optimistic predictions in many cases.     

Posterior Cramer-Rao bounds for multi-target tracking

This study is concerned with multi-target tracking (MTT). The Cramer-Rao lower bound (CRB) is the basic tool for investigating estimation performance. Though basically defined for estimation of deterministic parameters, it has been extended to stochastic ones in a Bayesian setting. In the target tracking area, we have thus to deal with the estimation of the whole trajectory, itself described by a Markovian model. This leads up to the recursive formulation of the posterior CRB (PCRB). The aim of the work presented here is to extend this calculation of the PCRB to MTT under various assumptions.     

Explicit formulas for two state Kalman, H/sub 2/ and H/sub /spl infin// target tracking filters

The continuous time, two state, target tracking problem is considered from the Kalman, H/sub 2/, and H/sub /spl infin// filter viewpoint. While previous treatments were numerical in nature, analytic transient responses and infinite horizon solutions with analytic performance expressions are presented here. Tracking indices, involving the maneuver and measurement uncertainties, are shown to have a role for both the steady state and transient responses. In addition, the H/sub /spl infin// tracker has a sensor index involving the performance bound and measurement uncertainty, which, along with the tracking index, plays a significant role in the H/sub /spl infin// tracker expressions. Analytical expressions for the probability of target escape, the probability that the target position will be outside the radar beamwidth (BW), are developed not only to compare the performance of various trackers, but also as a design tool to meet tracking specifications. Examples illustrate the performance of the target trackers as a function of the error gain upper bound.     

Sequence comparison techniques for multisensor data fusion andtarget recognition

A new class of techniques for multisensor fusion and target recognition is proposed using sequence comparison by dynamic programming and multiple model estimation. The objective is to fuse information on the kinematic state and “nonkinematic” signature of unclassified targets, assessing the joint likelihood of all observed events for recognition. Relationships are shown to previous efforts in pattern recognition and state estimation. This research applies “classical” speech processing-related and other sequence comparison methods to moving target recognition, extends the efforts of previous researchers through improved fusion with kinematic information, relates the proposed techniques to Bayesian theory, and applies parameter identification methods to target recognition for improved understanding of the subject in general. The proposed techniques are evaluated and compared with existing approaches using the method of generalized ambiguity functions, which lends to a form of Cramer-Rao lower bound for target recognition     

基于决策不确定性的多目标跟踪传感器管理

针对高杂波、电子干扰环境,在量测驱动的多目标滤波框架下提出了一种基于决策不确定性的传感器管理方法。首先,根据部分可观测马尔科夫决策过程的理论,给出了基于Rényi信息增量的传感器管理一般方法。其次,综合考虑决策过程的信息完整性、信息质量、信息的内涵等因素,在量测驱动的自适应滤波框架下,基于目标运动态势评估多目标决策不确定性水平,并选取最大决策不确定性目标。最后,以最大决策不确定性目标的信息增量最大化为准则进行传感器分配方案的求解。仿真实验表明所提方法能够有效抑制电子干扰、杂波对多目标跟踪及传感器分配的影响,与基于威胁的传感器管理方法相比,所提方法的平均最优子模式分配（OSPA）距离及平均计算时长均显著降低,且在高杂波、电子干扰情形下具有较高的可靠性。     

Pursuer identification and time-to-go estimation using passive measurements from an evader

We present an algorithm for identifying the parameters of a proportional navigation guidance missile (pursuer) pursuing an airborne target (evader) using angle-only measurements from the latter. This is done for the purpose of classifying the missile so that appropriate counter-measures can be taken. Mathematical models are constructed for a pursuer with a changing velocity, i.e., a direction change and a speed change. Assuming the pursuer is launched from the ground with fixed thrust, its motion can be described by a four-dimensional parameter vector consisting of its proportional navigation constant and three parameters related to thrusting. Consequently, the problem can be solved as a parameter estimation problem, rather than state estimation and we provide an estimator based on maximum likelihood (ML) to solve it. The parameter estimates obtained can be mapped into the time-to-go until intercept estimation results are presented for different scenarios together with the Cramer-Rao lower bound (CRLB), which quantifies the best achievable estimation accuracy. The accuracy of the time-to-go estimate is also obtained. Simulation results demonstrate that the proposed estimator is efficient by meeting the CRLB.     

Estimation near "Zero Information" points: angle-of-arrival near the endfire

We examine large-sample properties of the maximum- likelihood estimator (MLE) in the vicinity of points where the Fisher information measure (FIM) equals zero. Under mild regularity conditions the MLE is asymptotically efficient and therefore lower bounded by the Cramer-Rao lower bound (CRLB) [5], which diverges for such points. When a linear sensor array is used for angle-of-arrival (AOA) estimation, the CRLB diverges as the AOA approaches pi/2. We provide new results characterizing the MLE performance in the AOA problem.     

Passive ranging of a low observable ballistic missile in agravitational field

In this paper we present an estimation algorithm for tracking the motion of a low-observable target in a gravitational field, for example, an incoming ballistic missile (BM), using angle-only measurements. The measurements, which are obtained from a single stationary sensor, are available only for a short time. Also, the low target detection probability and high false alarm density present a difficult low-observable environment. The algorithm uses the probabilistic data association (PDA) algorithm in conjunction with maximum likelihood (ML) estimation to handle the false alarms and the less-than-unity target detection probability. The Cramer-Rao lower bound (CRLB) in clutter, which quantifies the best achievable estimator accuracy for this problem in the presence of false alarms and nonunity detection probability, is also presented. The proposed estimator is shown to be efficient, that is, it meets the CRLB, even for low-observable fluctuating targets with 6 dB average signal-to-noise ratio (SNR). For a BM in free flight with 0.6 single-scan detection probability, one can achieve a track detection probability of 0.99 with a negligible probability of false track acceptance     

Optimal sensor selection strategy for discrete-time stateestimators

A novel sensor selection strategy is introduced, which can be implemented on-line in time-varying discrete-time system. We consider a case in which several measurement subsystem are available, each of which may be used to drive a state estimation algorithm. However, due to practical implementation constraints (such as the ability of the on-board computer to process the acquired data), only one of these subsystems can actually by utilized at a measurement update. An algorithm is needed, by which the optimal measurement subsystem to be used is selected at each sensor selection epoch. The approach described is based on using the square root V-Lambda information filter as the underlying state estimation algorithm. This algorithm continuously provides its user with the spectral factors of the estimation error covariance matrix, which are used in this work as the basis for an on-line decision procedure by which the optimal measurement strategy is derived. At each sensor selection epoch, a measurement subsystem is selected, which contributes the largest amount of information along the principal state space direction associated with the largest current estimation error. A numerical example is presented, which demonstrates the performance of the new algorithm. The state estimation problem is solved for a third-order time-varying system equipped with three measurement subsystem, only one of which can be used at a measurement update. It is shown that the optimal measurement strategy algorithm enhances the estimator by substantially reducing the maximal estimation error