Cooperative Localization of AUVs Using Moving Horizon Estimation

This paper studies the localization problem of autonomous underwater vehicles (AUVs) constrained by limited size, power and payload. Such AUVs cannot be equipped with heavy sensors which makes their underwater localization problem difficult. The proposed cooperative localization algorithm is performed by using a single surface mobile beacon which provides range measurement to bound the localization error. The main contribution of this paper is twofold: 1) The observability of single beacon based localization is first analyzed in the context of nonlinear discrete time system, deriving a sufficient condition on observability. It is further compared with observability of linearized system to verify that a nonlinear state estimation is necessary. 2) Moving horizon estimation is integrated with extended Kalman filter (EKF) for three dimensional localization using single beacon, which can alleviate the computational complexity, impose various constraints and make use of several previous range measurements for each estimation. The observability and improved localization accuracy of the localization algorithm are verified by extensive numerical simulation compared with EKF.      

On the use of observability measures for sensor location in tubular reactor

In this paper we discuss the choice of sensor positions for a tubular reactor with a preset number of sensors. Different observability measures, based on the observability matrix (Kailath, Linear Systems, Prentice Hall, Englewood Cliffs, NJ, 1980; Callier and Desoer, Linear System Theory, Springer-Verlag, Berlin, 1991: Damak et al., DYCORD '92, 1992, pp. 315–320), the observability gramian (Callier and Desoer, 1991) as well as on the Popov-Belevitch-Hautus rank test (Kailath. 1980) will be considered for locating optimal sensor positions. The analysis is carried out on the reduced finite-dimensional model of the process. The results of these investigations will be illustrated in simulation and put in perspective with the modal observability properties of the original infinite-dimensional model.     

A method of robust multi-rate state estimation

The inadequacy of the standard notions of detectability and observability to ascertain robust state estimation is shown. The notion of robust state estimation is defined, and for a class of processes the conditions under which the robust state estimation is possible, are given. A method of robust, nonlinear, multi-rate, state estimator design is presented. It can be used to improve robustness in an existing estimator or design a new robust estimator. Estimator tuning guidelines that ensure the asymptotic stability of the estimator error dynamics are given. To ensure that estimation error does not exceed a desired limit, the sampling period of infrequent measurements should be less than an upper bound that depends on factors such as the size of the process dominant time constant, the magnitude of measurement noise, and the level of process–model mismatch. An expression that can be used to calculate the upper bound on the sampling period of infrequent measurements, is presented. The upper bound is the latest time at which the next infrequent measurements should arrive to ensure that estimation error does not exceed a desired limit. The expression also allows one to calculate the highest quality of estimation achievable in a given process. A binary distillation flash tank and a free-radical polymerization reactor are considered to show the application and performance of the estimator.     

Observability-based Optimization of Coordinated Sampling Trajectories for Recursive Estimation of a Strong, Spatially Varying Flowfield

Autonomous vehicles are effective environmental sampling platforms whose sampling performance can be optimized by path-planning algorithms that drive vehicles to specific regions of the operational domain containing the most informative data. In this paper, we apply tools from nonlinear observability, nonlinear control, and Bayesian estimation to derive a multi-vehicle control algorithm that steers vehicles to an optimal sampling formation in an estimated flowfield. Sampling trajectories are optimized using the empirical observability gramian, which quantifies the sensitivity of output measurements to variations of the flowfield parameters. We reconstruct the parameters of the flowfield from noisy flow measurements collected along the sampling trajectories using a recursive Bayesian filter.     

A Kalman Filter-Based Algorithm for IMU-Camera Calibration: Observability Analysis and Performance Evaluation

Vision-aided inertial navigation systems (V-INSs) canprovide precise state estimates for the 3-D motion of a vehicle when no external references (e.g., GPS) are available. This is achieved bycombining inertial measurements from an inertial measurement unit (IMU) with visual observations from a camera under the assumption that the rigid transformation between the two sensors is known. Errors in the IMU-camera extrinsic calibration process cause biases that reduce the estimation accuracy and can even lead to divergence of any estimator processing the measurements from both sensors. In this paper, we present an extended Kalman filter for precisely determining the unknown transformation between a camera and an IMU. Contrary to previous approaches, we explicitly account for the time correlation of the IMU measurements and provide a figure of merit (covariance) for the estimated transformation. The proposed method does not require any special hardware (such as spin table or 3-D laser scanner) except a calibration target. Furthermore, we employ the observability rank criterion based on Lie derivatives and prove that the nonlinear system describing the IMU-camera calibration process is observable. Simulation and experimental results are presented that validate the proposed method and quantify its accuracy.      

Computer selection and criteria for computer performance evaluation

Computer evaluation, comparison, and selection is essentially a decision process. The decision making is based on a number of worth indicators, including various computer performance indicators. The performance indicators are obtained through the computer performance measurement procedure. Consequently, in this environment the measurement procedure should be completely conditioned by the decision process. This paper investigates various aspects of the computer performance measurement and evaluation procedure within the context of the computer evaluation, comparison, and selection process based on the Logic Scoring of Preference method. A set of elementary criteria for performance evaluation is proposed and the corresponding set of performance indicators is defined. The necessary performance measurements are based on a standardized set of synthetic benchmark programs and include three separate measurements: monoprogramming performance measurement, multiprogramming performance measurement, and multiprogramming efficiency measurement. Using the proposed elementary criteria, the measured performance indicators can be transformed into elementary preferences and then aggregated with other nonperformance elementary preferences obtained through the evaluation process. The applicability of presented elementary criteria is illustrated by numerical examples.     

Estimation of dynamical-varying parameters by the internal modelprinciple

A novel design method of recursive algorithms for identification of linear deterministic SISO stable discrete systems with dynamical-varying parameters is presented. An algorithm for parameter identification of such systems, based on the known internal model principle and on the recursive least squares parameter estimation, is proposed. The system parameters are assumed to satisfy a linear difference equation with constant coefficients. A persistent excitation condition of the measurement vector automatically guarantees exponential stability and therefore there is no need to use any resetting procedures. This condition is similar in form to the observability gramian property of a linear time-varying system. Simulation and practical application of the algorithm on an experimental robot system show good tracking even when the parameters vary drastically and in an abrupt manner     

Road‐Centered Map‐Aided Localization for Driverless Cars Using Single‐Frequency GNSS Receivers

Accurate localization with high availability is a key requirement for autonomous vehicles. It remains a major challenge when using automotive sensors such as single‐frequency Global Navigation Satellite System (GNSS) receivers, a lane detection camera, and proprioceptive sensors. This paper describes a method that enables the estimation of stand‐alone single‐frequency GNSS errors by integrating the measurements from a forward‐looking camera matched with lane markings stored in a digital map. It includes a parameter identification method for a shaping model, which is evaluated using experimental data. An algebraic observability study is then conducted to prove that the proposed state vector is fully observable in a road‐oriented frame. This observability property is the basis to develop a road‐centered Extended Kalman filter (EKF) that can maintain the observability of every component of the state vector on any road, whatever its orientation. To accomplish this, the filter needs to handle road changes, which it does using bijective transformations. The filter was implemented and tested intensely on an experimental vehicle for driverless valet parking services. Field results have shown that the performance of the estimation process is better than solutions based on EKF implemented in a fixed working frame. The proposed filter guarantees that the drift along the road direction remains bounded. This is very important when the vehicle navigates autonomously. Furthermore, the road‐centered modeling improves the accuracy, consistency, and robustness of the localization solver.     

基于伪测量法的直链式N体空间绳系系统约束状态估计

针对直链式N体空间绳系系统（STS）,将系绳绳长作为先验信息,在仅使用2个GPS（全球定位系统）传感器的条件下,提出了一种基于伪测量法的约束状态估计方法。首先,基于Udwadia-Kalaba方法建立了一种新颖的直链式N体STS通用动力学模型。然后,针对GPS传感器更新频率低和非线性系统模型线性化过程中雅可比矩阵计算复杂的问题,开发了一种改进的平方根无迹卡尔曼滤波（IUKF）算法。同时,基于李导数的局部弱可观的秩判据方法严格证明了本文估计方法的可观性。最后,仿真验证了本文方法的有效性。仿真结果表明所提方法能够保证系统状态估计精度和跟踪实时性。     

Model reduction using impulse-response gramians: a frequency-domain approach

A frequency domain model reduction technique based on the impulse-response gramian is proposed. Two new methods for evaluation of the impulse-response gramian in the frequency domain are also presented. The Routh technique relies on a Routh table to evaluate energy integrals of the type found on the impulse-response gramian diagonal, while the second approach uses an Inners determinant technique. Off diagonal elements are computed via system Markov parameters and knowledge of diagonal values. The model reduction technique, involving truncation of the impulse-response gramian, is a variation on that presented by Agathoklis and Sreeram (1990 a). The proposed method evaluates the transfer function of the reduced-order model directly rather than producing a state space representation. Algorithms outlining the steps involved in impulse-response gramian evaluation, plus those for model reduction, are given. Each is supported by a numerical example     

Magnetic sensor-based simultaneous state and parameter estimation using a nonlinear observer

This paper presents an observer design technique for a newly developed non-intrusive position estimation system based on magnetic sensors. Typically, the magnetic field of an object as a function of position needs to be represented by a highly nonlinear measurement equation. Previous results on observer design for nonlinear systems have mostly assumed that the measurement equation is linear, even if the process dynamics are nonlinear. Hence, a new nonlinear observer design method for a Wiener system composed of a linear process model together with a nonlinear measurement equation is developed in this paper. First, the design of a two degree-of-freedom nonlinear observer is proposed that relies on a Lure system representation of the observer error dynamics. To improve the performance in the presence of parametric uncertainty in the measurement model, the nonlinear observer is augmented to estimate both the state and unknown parameters simultaneously. A rigorous nonlinear observability analysis is also presented to show that a dual sensor configuration is a sufficient and necessary condition for simultaneous state and parameter estimation. Finally, the developed observer design technique is applied to non-intrusive position estimation of the piston inside a pneumatic cylinder. Experimental results show that both position and unknown parameters can be reliably estimated in this application.     

A New Parametrization of Rational Inner Functions of Fixed Degree: Schur Parameters and Realizations

We present a new parametrization of inner functions based on the Schur algorithm. We make use of state space formulas (in practice we obtain a new parametrization of observable pairs). The main advantage of our parametrization is that for each chart the observability gramian is constant: this leads to very good behavior in some approximation problems. Date received: July 22, 1997. Date revised: February 1, 2000.     

Collaborative target tracking in WSNs using the combination of maximum likelihood estimation and Kalman filtering

Target tracking using wireless sensor networks requires efficient collaboration among sensors to tradeoff between energy consumption and tracking accuracy. This paper presents a collaborative target tracking approach in wireless sensor networks using the combination of maximum likelihood estimation and the Kalman filter. The cluster leader converts the received nonlinear distance measurements into linear observation model and approximates the covariance of the converted measurement noise using maximum likelihood estimation, then applies Kalman filter to recursively update the target state estimate using the converted measurements. Finally, a measure based on the Fisher information matrix of maximum likelihood estimation is used by the leader to select the most informative sensors as a new tracking cluster for further tracking. The advantages of the proposed collaborative tracking approach are demonstrated via simulation results.     

A maximum-likelihood Kalman filter for switching discrete-time linear systems

State estimation is addressed for a class of discrete-time systems that may switch among different modes taken from a finite set. The system and measurement equations of each mode are assumed to be linear and perfectly known, but the current mode of the system is unknown. Moreover, additive, independent, normally distributed noises are assumed to affect the dynamics and the measurements. First, relying on a well-established notion of mode observability developed “ad hoc” for switching systems, an approach to system mode estimation based on a maximum-likelihood criterion is proposed. Second, such a mode estimator is embedded in a Kalman filtering framework to estimate the continuous state. Under the unique assumption of mode observability, stability properties in terms of boundedness of the mean square estimation error are proved for the resulting filter. Simulation results showing the effectiveness of the proposed filter are reported.     

Bearings only multi-sensor maneuvering target tracking

This paper presents a solution to target trajectory estimation when multiple asynchronous passive bearings only sensors with uncertain positions are employed. Asynchronous target position triangulation is achieved. Gaussian mixture measurement presentation, together with a track splitting algorithm allows space/time integration of the target position uncertainty with a simple algorithm. Gaussian mixture measurement presentation incorporates sensor position uncertainty, as well as the spatial uncertainty brought by bearings only measurement. Each sensor detects the target emissions independently, and the measurements are incorporated into track as they arrive. Measurements by arbitrary number of sensors can be incorporated, provided that the triangulation observability criterion is satisfied. The approach is verified by a single target, two sensors, two-dimensional surveillance simulation experiment.     

Product property and production rate control of styrene polymerization

A multivariable multi-rate nonlinear model predictive control (NMPC) strategy is applied to styrene polymerization. The NMPC algorithm incorporates a multi-rate Extended Kalman Filter (EKF) to handle state variable and parameter estimation. A fundamental model is developed for the styrene polymerization CSTR, and control of polymer properties such as number average molecular weight (NAMW) and polydispersity is considered. These properties characterize the final polymer distribution and are strong indicators of the polymer qualities of interest. Production rate control is also demonstrated. Temperature measurements are available frequently while laboratory measurements of concentration and molecular weight distribution are available infrequently with substantial time delays between sampling and analysis. Observability analysis of the augmented system provides guidelines for the design of the augmented disturbance model for use in estimation using the multi-rate EKF. The observability analysis links measurement sets and corresponding observable disturbance models, and shows that measurements of moments of the polymer distribution are essential for good estimation and control. The CSTR is operated at an open-loop unstable steady state. Control simulations are performed under conditions of plant-model structural mismatch and in the presence of parameter uncertainty and disturbances, and the proposed multi-rate NMPC algorithm is shown to provide superior performance compared to linear multi-rate and nonlinear single-rate MPC algorithms. The major contributions of this work are the development of the multi-rate estimator and the measurement design study based on the observability analysis.     

具有非完整约束移动机器人的超宽带-惯导-里程计融合定位与能观测性分析

为解决现有超宽带-惯导组合定位系统在轮式移动机器人的定位精度低、依赖高精度IMU等问题,提出了一种采用误差状态卡尔曼滤波融合超宽带-惯导-里程计的定位算法,利用里程计的线速度测量和由非完整约束隐含的伪测量,提高了移动机器人的位置和姿态估计精度.同时,对于由多传感器测量模型组成的非线性系统,通过基于李导数的能观性秩条件分析方法对该系统的能观测性进行了详细的理论分析与数学证明,得到了系统局部弱可观的条件,从而确定了系统状态可以被无偏估计所需要的测量输出以及控制输入.仿真结果表明,在满足能观测性条件时,本文提出的方法能够有效地获得移动机器人较准确的六自由度位姿,且相比传统方法显著提升了定位精度.     

Reconstruction of measurements in state estimation strategy against deception attacks for cyber physical systems

Without the known state equation, a new state estimation strategy is designed to be against malicious attacks for cyber physical systems. Inspired by the idea of data reconstruction, the compressive sensing (CS) is applied to reconstruction of residual measurements after the detection and identification scheme based on the Markov graph of the system state, which increases the resilience of state estimation strategy against deception attacks. First, the observability analysis is introduced to decide the triggering time of the measurement reconstruction and the damage level from attacks. In particular, the dictionary learning is proposed to form the over completed dictionary by K singular value decomposition (K SVD), which is produced adaptively according to the characteristics of the measurement data. In addition, due to the irregularity of residual measurements, a sampling matrix is designed as the measurement matrix. Finally, the simulation experiments are performed on 6 bus power system. Results show that the reconstruction of measurements is completed well by the proposed reconstruction method, and the corresponding effects are better than reconstruction scheme based on the joint dictionary and the traditional Gauss or Bernoulli random matrix respectively. Especially, when only 29% available clean measurements are left, performance of the proposed strategy is still extraordinary, which reflects generality for five kinds of recovery algorithms.     

Estimation of message source and destination from network intercepts

We consider the problem of estimating the endpoints (source and destination) of a transmission in a network based on partial measurement of the transmission path. Possibly asynchronous sensors placed at various points within the network provide the basis for endpoint estimation by indicating that a specific transmission has been intercepted at their assigned locations. During a training phase, test transmissions are made between various pairs of endpoints in the network and the sensors they activate are noted. Sensor activations corresponding to transmissions with unknown endpoints are also observed in a monitoring phase. A semidefinite programming relaxation is used in conjunction with the measurements and linear prior information to produce likely sample topologies given the data. These samples are used to generate Monte Carlo approximations of the posterior distributions of source/destination pairs for measurements obtained in the monitoring phase. The posteriors allow for maximum a posteriori (MAP) estimation of the endpoints along with computation of some resolution measures. We illustrate the method using simulations of random topologies.     

Integrity-directed sequential state estimation: Assessing high reliability requirements via safe confidence intervals

This study deals with the problem of dynamic state estimation of continuous-time systems from discrete-time measurements in the context of high-integrity applications. The objective of integrity-directed estimation is to provide confidence intervals for the state with an extremely low risk of error. We suppose that the process noise can be modelled by Gaussian sequences, and that the measurement noise is Gaussian in the normal operating mode of the sensors. The evolution of the posterior probability distribution of the system’s state is deduced from recursive linear MMSE estimation. The estimation scheme presented here is equivalent to the Kalman filter, with the difference that the data is not processed directly, but collected in sets in preparation for an ulterior, slightly delayed, grouped processing. This strategy is particularly suitable for fault detection, because the estimator naturally takes into account the cross-correlations of close-in-time measurements and the decisions can be based on more data. Next, we introduce dynamic tools for detecting faults and sensor failures. A full Bayesian modelling of the sensors leads to the derivation of a dynamic multiple-model estimator performing the linear MMSE state estimation under various fault hypotheses. This estimator provides estimates of the posterior density function of the state, on which safe confidence intervals certifying very high-integrity levels can be fixed. In practice, the exponential growth of the complexity of the multiple-model estimator requires the simplification of the posterior mixture distributions. A new method for limiting the complexity of the posterior distributions in an integrity-oriented context is presented. Unlike the known mixture simplification strategies (GPB, IMM), the present method has the property to quantify and minimize the loss in integrity of the process of simplification of the distributions. Finally, the estimator is tested on a typical rail navigation problem.