A Constant Gain Kalman Filter for Wireless Sensor Network and Maneuvering Target Tracking

One of the well-known approaches to target tracking is the Kalman filter. The problem of applying the Kalman Filter in practice is that in the presence of unknown noise statistics, accurate results cannot be obtained. Hence the tuning of the noise covariances is of paramount importance in order to employ the filter. The difficulty involved with the tuning attracts the applicability of the concept of Constant Gain Kalman Filter (CGKF). It has been generally observed that after an initial transient the Kalman Filter gain and the State Error Covariance P settles down to steady state values. This encourages one to consider working directly with steady state or constant Kalman gain, rather than with error covariances in order to obtain efficient tracking. Since there are no covariances in CGKF, only the state equations need to be propagated and updated at a measurement, thus enormously reducing the computational load. The current work first applies the CGKF concept to heterogeneous sensor based wireless sensor network (WSN) target tracking problem. The paper considers the Standard EKF and CGKF for tracking various manoeuvring targets using nonlinear state and measurement models. Based on the numerical studies it is clearly seen that the CGKF out performs the Standard EKF. To the best of our knowledge, such a comprehensive study of the CGKF has not been carried out in its application to diverse target tracking scenarios and data fusion aspects

A wavelet based multiresolution extended Kalman filter approach to the reconstruction problem of curved-ray optical tomography

We present a wavelet based multiresolution extended Kalman filter (EKF) reconstruction approach to curved ray optical tomography. A state variable model describing the tomographic process is set up, and an EKF is applied to the wavelet transformed model to estimate the refractive index distribution of an optically transparent refracting object from noisy optical path-length difference (OPD) data. Preliminary results of reconstructions of a synthetic time invariant refractive index distribution from OPD data sets of various noise levels are comparable with those obtained from a typically used deterministic approach, the average correction per projection method

Extended- Kalman- filter based reconstruction approach to curved ray optical tomography

We present an extended Kalman filter (EKF) based approach to the reconstruction problem in curved ray optical tomography. A state variable model describing the tomographic process is set up, and an EKF is applied to the model to estimate the refractive index distribution of an optically transparent refracting object from noisy optical path-length difference data. Preliminary results of reconstructions of a synthetic time-invariant refractive index distribution from projection data of various noise levels are comparable with those obtained from a typically used deterministic approach, the average correction per projection method

Single-resolution and multiresolution extended-Kalman-filter-based reconstruction approaches to optical refraction tomography

The problem of reconstruction of a refractive-index distribution (RID) in optical refraction tomography (ORT) with optical path-length difference (OPD) data is solved using two adaptive-estimation-based extended-Kalman-filter (EKF) approaches. First, a basic single-resolution EKF (SR-EKF) is applied to a state variable model describing the tomographic process, to estimate the RID of an optically transparent refracting object from noisy OPD data. The initialization of the biases and covariances corresponding to the state and measurement noise is discussed. The state and measurement noise biases and covariances are adaptively estimated. An EKF is then applied to the wavelet-transformed state variable model to yield a wavelet-based multiresolution EKF (MR-EKF) solution approach. To numerically validate the adaptive EKF approaches, we evaluate them with benchmark studies of standard stationary cases, where comparative results with commonly used efficient deterministic approaches can be obtained. Detailed reconstruction studies for the SR-EKF and two versions of the MR-EKF (with Haar and Daubechies-4 wavelets) compare well with those obtained from a typically used variant of the (deterministic) algebraic reconstruction technique, the average correction per projection method, thus establishing the capability of the EKF for ORT. To the best of our knowledge, the present work contains unique reconstruction studies encompassing the use of EKF for ORT in single-resolution and multiresolution formulations, and also in the use of adaptive estimation of the EKF's noise covariances. (C) 2010 Optical Society of Americ

A heuristic reference recursive recipe for adaptively tuning the Kalman filter statistics part-1: formulation and simulation studies

Since the innovation of the ubiquitous Kalman filter more than five decades back it is well known that to obtain the best possible estimates the tuning of its statistics , , , R and Q namely initial state and covariance, unknown parameters, and the measurement and state noise covariances is very crucial. The manual and other approaches have not matured to a routine approach applicable for any general problem. The present reference recursive recipe (RRR) utilizes the prior, posterior, and smoothed state estimates as well as their covariances to balance the state and measurement equations and thus form generalized cost functions. The filter covariance at the end of each pass is heuristically scaled up by the number of data points and further trimmed to provide the for subsequent passes. The importance of as the probability matching prior between the frequentist approach via optimization and the Bayesian approach of the Kalman filter is stressed. A simultaneous and proper choice for Q and R based on the filter sample statistics and other covariances leads to a stable filter operation after a few iterations. A typical simulation study of a spring, mass and damper system with a weak nonlinear spring constant by RRR shows it to be better than earlier techniques. Part-2 of the paper further consolidates the present approach based on an analysis of real flight test data

Modelling, Design and Validation of Spatially Resolved Reflectance Based Fiber Optic Probe for Epithelial Precancer Diagnostics

Fiber-optic probes are imperative for in-vivo diagnosis of cancer. Depending on the access to a diseased organ and the mutations one aims to sense, the probe designs vary. We carry out a detailed numerical study of the efficacy of the common probe geometries for epithelial cancer characterization based on spatially resolved reflectance data. As per the outcomes of this comparative study, a probe has been manufactured and using Monte Carlo look up table based inversion scheme, the absorption and scattering coefficients of the epithelium mimicking top layer have been recovered from noisy synthetic as well as experimental data