Andrew Logothetis

An information theoretic approach to observer path design for bearings-only tracking

Open-loop control strategies, via information theoretic criteria, for the design of optimal observer trajectories in the bearings-only tracking problem are presented. The aim is to obtain tight bounds on the location and velocity of a single target through own ship maneuvers. In this paper, optimal paths are derived by maximizing the mutual information between the measurement sequence and the final target state or the entire target trajectory. Optimization techniques, such as dynamic programming and enumeration with optimal pruning are derived.

Comparison of suboptimal strategies for optimal own-ship maneuvers in bearings-only tracking

Suboptimal optimization techniques for computing observer trajectories in the bearings-only tracking problem, are considered. It is well known that the observer motion can aid in the quality of track performance, The aim is to obtain tight bounds on the location and velocity of this target through own ship maneuvers. The authors (1997), derived two mutual information measures and optimal trajectories were computed via dynamic programming. The memory requirements and the computational burden for computing optimal observer paths via dynamic programming is prohibitive. Thus, suboptimal strategies are explored here which considerably reduce the computational cost. The optimization methods are divided into two groups. In the first group a scalar function of the target state error covariance matrix is minimized, while in the second group approximate forward-reduced complexity-dynamic programming techniques are used. Simulation studies are carried out that compare the suboptimal optimization methods proposed in this paper.

On maneuvering target tracking via the PMHT

This paper presents an iterative off-line optimal state estimation algorithm, which yields the maximum a posteriori (MAP) state trajectory estimate of the state sequence of a target maneuvering in clutter. The problem is formulated as a jump Markov linear system and the expectation maximization algorithm is used to compute the state sequence estimate. The proposed algorithm optimally combines a hidden Markov model and a Kalman smoother to yield the MAP target state sequence estimate. The algorithm proposed uses probabilistic multi-hypothesis tracking (PMHT) techniques for tracking a single maneuvering target in clutter. Previous applications of the PMHT technique have addressed the problem of tracking multiple non-maneuvering targets. These techniques are extended to address the problem of optimal (in a MAP sense) tracking of a maneuvering target in clutter.

Iterative and recursive estimators for hidden Markov errors-in-variables models

In this paper we propose maximum-likelihood (ML) estimation of errors in variables models with finite-state Markovian disturbances. Such models have applications in econometrics, speech processing, communication systems, and neurobiological signal processing. We derive the maximum likelihood (ML) model estimates using the expectation maximization (EM) algorithm. Then two recursive or on-line estimation schemes are derived for estimating such models. The first on-line algorithm is based on the EM algorithm and uses stochastic approximations to maximize the Kullback-Leibler (KL) information measure. The second on-line algorithm we propose is a gradient-based scheme and uses stochastic approximations to maximize the log likelihood.

MAP state sequence estimation for jump Markov linear systems via the expectation-maximization algorithm

In a jump Markov linear system the state matrix, observation matrix and the noise covariance matrices evolve according to the realization of a finite state Markov chain. Given a realization of the observation process, the aim is to estimate the state of the Markov chain assuming known model parameters. In this paper, we present three expectation maximization (EM) algorithms for state estimation to obtain maximum a posteriori state sequence estimates (MAPSE). Our first EM algorithm yields the MAPSE for the entire sequence of the finite state Markov chain. The second EM algorithm yields the MAPSE of the (continuous) state of the jump linear system. Our third EM algorithm computes the joint MAPSE of the finite and continuous states. The three EM algorithms, optimally combine a hidden Markov model estimator and a Kalman smoother in three different ways to compute the desired MAPSEs.

Data fusion by optimal sensor switching

In this paper we consider the problem of selecting the optimal measurement sequence from two or more sensors given communication bandwidth limitations. In particular the constraints are such that only one sensor may be used at any one time. Our aim is to switch these sensors to obtain optimal (mean square error sense) estimates of the state of a linear continuous time Gauss-Markov system.

Bearings-only tracking using hidden Markov models

This paper addresses the problem of target tracking when only bearing information is available from the sensor. The authors describe a hidden Markov model formulation of this problem and present simulation results.<<ETX>>

Estimation of 1-bit quantized time-series with Markov regime

Abstract In this paper we consider de-interleaving a finite number of stochastic parametric sources. The sources are modeled as independent autoregressive (AR) processes. Based on a Markovian switching policy, we assume that the different sources transmit signals on the same single channel. The receiver records the 1-bit quantized version of the transmitted signal and aims to identify the sequence of active sources. Once the source sequence has been identified, the characteristics (parameters) of each source are estimated. We formulate the parametric pulse train de-interleaving problem as a 1-bit quantized Markov modulated AR series. The algorithm proposed in this paper combines Hidden Markov Model (HMM) and Binary Time Series (BTS) estimation techniques. Our estimation scheme generalizes Kedems (1980) binary time series algorithm for linear time series to Markov modulated time series.

De-interleaving of superimposed quantized autoregressive processes

We consider the de-interleaving of N independent autoregressive (AR) processes from 1-bit quantized measurements. De-interleaving has applications in radar and signal detection. Other possible applications are computer communications and neural systems. The received signal (pulse train) is the superposition of N 1-bit quantized Gaussian AR processes observed in white Gaussian noise. The aim is to identify which sources are responsible for the observed noisy pulses. Furthermore, it is desired to obtain parameter estimates for the N sources. The proposed algorithm, (subject to model assumptions) optimally combines hidden Markov model and binary time series estimation techniques.

Parametric Pulse Train De-Interleaving of Stochastic Sources

Abstract In this paper we consider de-interleaving a finite number of stochastic parametric sources. The sources are modeled as independent autoregressive (AR) processes. Based on a Markovian switching policy, we assume that the different sources transmit signals on the same single channel. The receiver records the 1-bit quantized version of the transmitted signal and aims to identify the sequence of active sources. Once the source sequence has been identified, the characteristics (parameters) of each source is estimated.