Trajectory Synthesis for Fisher Information Maximization

Estimation of model parameters in a dynamic system can be significantly improved with the choice of experimental trajectory. For general, nonlinear dynamic systems, finding globally "best" trajectories is typically not feasible; however, given an initial estimate of the model parameters and an initial trajectory, we present a continuous-time optimization method that produces a locally optimal trajectory for parameter estimation in the presence of measurement noise. The optimization algorithm is formulated to find system trajectories that improve a norm on the Fisher information matrix. A double-pendulum cart apparatus is used to numerically and experimentally validate this technique. In simulation, the optimized trajectory increases the minimum eigenvalue of the Fisher information matrix by three orders of magnitude compared to the initial trajectory. Experimental results show that this optimized trajectory translates to an order of magnitude improvement in the parameter estimate error in practice.Comment: 12 page

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

A Robust Carrier Frequency Offset Estimation Algorithm in Burst Mode Multicarrier CDMA based Ad Hoc Networks

The future wireless communication systems demand very high data rates, anti-jamming ability and multiuser support. People want large amount of data to be continuously accessible in their personal devices. Direct Sequence (DS) spread spectrum based techniques such as Code Division Multiple Access (CDMA) fulfil these requirements but, at the same time, suffer from the Intersymbol Interference (ISI). Multicarrier CDMA (MC-CDMA) is an emerging technology to be used in mobile devices operating in an ad hoc setting due to its immunity towards ISI and having all the advantages of spread spectrum communication. One of the major problems with MC-CDMA is the high sensitivity towards carrier frequency offsets caused due to the inherent inaccuracy of crystal oscillators. This carrier frequency offset destroys the orthogonality of the subcarriers resulting in Intercarrier Interference (ICI). In this paper, we propose a computationally efficient algorithm based on Fast Fourier Transform (FFT) and biquadratic Lagrange interpolation. The FFT is based on the use of overlapping windows for each frame of the data instead of non-overlapping windows. This gives a coarse estimate of the frequency offset which is refined by the successive application of Lagrange quadratic interpolation to the samples in the vicinity of FFT peak. The proposed algorithm has been applied to the multiuser ad hoc network and simulated in Stanford University Interim (SUI) channels. It has been shown by simulations that the proposed algorithm provides better performance of almost 1~2 dB as compared to the well-known algorithms

Methods Studies on System Identification from Transient Rotor Tests

Some of the more important methods are discussed that have been used or proposed for aircraft parameter identification. The methods are classified into two groups: Equation error or regression estimates and Bayesian estimates and their derivatives that are based on probabilistic concepts. In both of these two groups the cost function can be optimized either globally over the entire time span of the transient, or sequentially, leading to the formulation of optimum filters. Identifiability problems and the validation of the estimates are briefly outlined, and applications to lifting rotors are discussed

MIMO Radar Target Localization and Performance Evaluation under SIRP Clutter

Multiple-input multiple-output (MIMO) radar has become a thriving subject of research during the past decades. In the MIMO radar context, it is sometimes more accurate to model the radar clutter as a non-Gaussian process, more specifically, by using the spherically invariant random process (SIRP) model. In this paper, we focus on the estimation and performance analysis of the angular spacing between two targets for the MIMO radar under the SIRP clutter. First, we propose an iterative maximum likelihood as well as an iterative maximum a posteriori estimator, for the target's spacing parameter estimation in the SIRP clutter context. Then we derive and compare various Cram\'er-Rao-like bounds (CRLBs) for performance assessment. Finally, we address the problem of target resolvability by using the concept of angular resolution limit (ARL), and derive an analytical, closed-form expression of the ARL based on Smith's criterion, between two closely spaced targets in a MIMO radar context under SIRP clutter. For this aim we also obtain the non-matrix, closed-form expressions for each of the CRLBs. Finally, we provide numerical simulations to assess the performance of the proposed algorithms, the validity of the derived ARL expression, and to reveal the ARL's insightful properties.Comment: 34 pages, 12 figure

The use of fake algebraic Riccati equations for co-channel demodulation

Copyright © 2003 IEEEThis paper describes a method for nonlinear filtering based on an adaptive observer, which guarantees the local stability of the linearized error system. A fake algebraic Riccati equation is employed in the calculation of the filter gain. The design procedure attempts to produce a stable filter at the expense of optimality. This contrasts with the extended Kalman filter (EKF), which attempts to preserve optimality via its linearization procedure, at the expense of stability. A passivity approach is applied to deduce stability conditions for the filter error system. The performance is compared with an EKF for a co-channel frequency demodulation application.Einicke, G.A.; White, L.B.; Bitmead, R.R

Impairments in ground moving target indicator (GMTI) radar

Radars on multiple distributed airborne or ground based moving platforms are of increasing interest, since they can be deployed in close proximity to the event under investigation and thus offer remarkable sensing opportunities. Ground moving target indicator (GMTI) detects and localizes moving targets in the presence of ground clutter and other interference sources. Space-time adaptive processing (STAP) implemented with antenna arrays has been a classical approach to clutter cancellation in airborne radar. One of the challenges with STAP is that the minimum detectable velocity (MDV) of targets is a function of the baseline of the antenna array: the larger the baseline (i.e., the narrower the beam), the lower the MDV. Unfortunately, increasing the baseline of a uniform linear array (ULA) entails a commensurate increase in the number of elements. An alternative approach to increasing the resolution of a radar, is to use a large, but sparse, random array. The proliferation of relatively inexpensive autonomous sensing vehicles, such as unmanned airborne systems, raises the question whether is it possible to carry out GMTI by distributed airborne platforms. A major obstacle to implementing distributed GMTI is the synchronization of autonomous moving sensors. For range processing, GMTI processing relies on synchronized sampling of the signals received at the array, while STAP processing requires time, frequency and phase synchronization for beamforming and interference cancellation. Distributed sensors have independent oscillators, which are naturally not synchronized and are each subject to different stochastic phase drift. Each sensor has its own local oscillator, unlike a traditional array in which all sensors are connected to the same local oscillator. Even when tuned to the same frequency, phase errors between the sensors will develop over time, due to phase instabilities. These phase errors affect a distributed STAP system. In this dissertation, a distributed STAP application in which sensors are moving autonomously is envisioned. The problems of tracking, detection for our proposed architecture are of important. The first part focuses on developing a direct tracking approach to multiple targets by distributed radar sensors. A challenging scenario of a distributed multi-input multi-output (MIMO) radar system (as shown above), in which relatively simple moving sensors send observations to a fusion center where most of the baseband processing is performed, is presented. The sensors are assumed to maintain time synchronization, but are not phase synchronized. The conventional approach to localization by distributed sensors is to estimate intermediate parameters from the received signals, for example time delay or the angle of arrival. Subsequently, these parameters are used to deduce the location and velocity of the target(s). These classical localization techniques are referred to as indirect localization. Recently, new techniques have been developed capable of estimating target location directly from signal measurements, without an intermediate estimation step. The objective is to develop a direct tracking algorithm for multiple moving targets. It is aimed to develop a direct tracking algorithm of targets state parameters using widely distributed moving sensors for multiple moving targets. Potential candidate for the tracker include Extended Kalman Filter. In the second part of the dissertation,the effect of phase noise on space-time adaptive processing in general, and spatial processing in particular is studied. A power law model is assumed for the phase noise. It is shown that a composite model with several terms is required to properly model the phase noise. It is further shown that the phase noise has almost linear trajectories. The effect of phase noise on spatial processing is analyzed. Simulation results illustrate the effect of phase noise on degrading the performance in terms of beam pattern and receiver operating characteristics. A STAP application, in which spatial processing is performed (together with Doppler processing) over a coherent processing interval, is envisioned

Radio Frequency Emitter Geolocation Using Cubesats

The ability to locate an RF transmitter is a topic of growing interest for civilian and military users alike. Geolocation can provide critical information for the intelligence community, search and rescue operators, and the warfighter. The technology required for geolocation has steadily improved over the past several decades, allowing better performance at longer baseline distances between transmitter and receiver. The expansion of geolocation missions from aircraft to spacecraft has necessitated research into how emerging geolocation methods perform as baseline distances are increased beyond what was previously considered. The CubeSat architecture is a relatively new satellite form which could enable small-scale, low-cost solutions to USAF geolocation needs. This research proposes to use CubeSats as a vehicle to perform geolocation missions in the space domain. The CubeSat form factor considered is a 6-unit architecture that allows for 6000 cm3 of space for hardware. There are a number of methods which have been developed for geolocation applications. This research compares four methods with various sensor configurations and signal properties. The four methods\u27 performance are assessed by simulating and modeling the environment, signals, and geolocation algorithms using MATLAB. The simulations created and run in this research show that the angle of arrival method outperforms the instantaneous received frequency method, especially at higher SNR values. These two methods are possible for single and dual satellite architectures. When three or more satellites are available, the direct position determination method outperforms the three other considered methods

A methodology for airplane parameter estimation and confidence interval determination in nonlinear estimation problems

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. With the fitted surface, sensitivity information can be updated at each iteration with less computational effort than that required by either a finite-difference method or integration of the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, and thus provides flexibility to use model equations in any convenient format. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. The degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels and to predict the degree of agreement between CR bounds and search estimates