Ben-Zion Bobrovsky

A lower bound on the estimation error for certain diffusion processes

A lower bound on the minimal mean-square error in estimating nonlinear diffusion processes is derived. The bound holds for causal and noncausal filtering.

Asymptotic a priori estimates for the error in the nonlinear filtering problem (Corresp.)

The minimal mean-square error for the scalar nonlinear filtering problem is considered. Asymptotic lower and upper bounds on the error are derived for the case where the intensity of the observation noise tends to zero.

Mean time to lose lock for the "Langevin"-type delay-locked loop

The classical result of Kramers (1940), originally related to chemical reaction rates, is applied in this letter to a second-order all-pole, coherent code tracking delay-locked loop (DLL). A very simple, explicit expression for the leading order term of the mean time to lose lock (MTLL) is presented. The dependence of the MTLL on the loop tension (offset) due to Doppler shift and code clock mismatch is given, and optimal loop parameters which minimize the MTLL are proposed. >

A Novel Approach for Modeling Land Vehicle Kinematics to Improve GPS Performance Under Urban Environment Conditions

The satellite blockage problem, which adversely affects Global Positioning System (GPS) accuracy in urban environments, is addressed in this work. To provide a position solution, there must be at least four satellites within line of sight (LOS) of the receiver (vehicle). However, when satellite blockage occurs, this requirement is not met because most of the sky is obscured by tall buildings, and only a narrow sky sector is exposed to the receiver. Given the short duration of satellite blockages, an efficient solution to this problem can be accomplished through reliable modeling of vehicle motion. In this manner, information regarding vehicle motion can be more precisely obtained in the absence of a sufficient number of measurements. In this paper, a model that uses intrinsic quantities as part of the description of the vehicle path, such as curvature, tangent angle, and tangential speed, is proposed to achieve a more accurate modeling of both the trajectory and kinematics of a land vehicle. The model, which was implemented via an extended Kalman filter, was examined against currently known models during satellite blockage scenarios and demonstrated superior performance.

Third-order delay-locked loop: mean time to lose lock and optimal parameters

A systematic approximation for the mean time to lose lock (MTLL) of a coherent third-order PN-code tracking loop has been derived. Such loops are essential in various spread spectrum systems (Global Positioning System, for example). The computation of the MTLL is based on the singular perturbation method. The application of this method to the coherent delay-locked loop (DLL) yields an approximate expression for the MTLL. Therefore, with the proposed loop model the authors are able to analyze this third-order system at a level that gives a well understanding of the nonlinear loop behavior and the exit phenomenon. The influence of a loop offset due to an acceleration rate (jerk) between transmitter and receiver on the optimal filter parameters is described by comparing MTLL and tracking error performance. As intuitively might be expected it turns out that acceleration rate and code rate are exchangeable in the sense that a lower code rate allows a higher acceleration rate (and vice versa) for the same signal-to-noise ratio in order to maintain the same performance. In a case study, GPS code tracking for objects with high jerk is briefly discussed. >

A new phase and frequency offset estimation algorithm for OFDM systems applying Kalman filter

In this paper the frequency offset problem in OFDM is addressed. An unknown frequency offset causes per subcarrier amplitude distortion, ICI and phase rotation. In coherent communication accurate frequency as well as phase estimates are required. The estimators are obtained by Kalman filtering, where a frequency domain approach is used. The Kalman filter derived has a structure of a combined phase and frequency tracking loop. The estimator outperforms conventional reported methods, has fast convergence and good tracking ability. Regarding the complexity of the algorithm, the current Kalman filter requires at most 2/spl times/2 matrix inversions.

Anti multipath cellular radio location for DS/CDMA systems using a novel EKF subchip RAKE tracking loop

This paper discusses an improved method for localization in a DS-CDMA based cellular-phone communication link. This method suggests an optimization for code synchronization, which allows for TDOA (time difference of arrival) estimations to be solved for the position of a mobile phone. It is known that the time delay of a received DS signal, derived from the classical DLL, may express severe timing errors due to multipath effects. A new anti multipath multi-tracking extended Kalman filter loop is shown to achieve far better results especially in the environment of specular multipath. Specifically, this new loop minimizes the errors due to multipath components by letting the EKF decide upon the best weights of its sub-chip processing branches, resulting in a RAKE-like tracking loop. This loop tracks not only the line of sight path, but also the other multipath components as well as their power and phase. It is shown that the implementation of this technique converges to the classical non-coherent code tracking DLL structure when no multipath is assumed, but results in a new and efficient tracking loop structure in the more realistic fading channel case. The application of this technique to the EIA IS-95 system is considered, where accurate location estimations as well as power management utilities are treated.

Error bounds for the nonlinear filtering of signals with small diffusion coefficients

New upper and lower bounds for the nonlinear filtering problem are presented. The lower bounds are especially useful in the region of small diffusion coefficients where previously known bounds are inefficient. The upper and lower bounds are shown to be tight. An example demonstrating the tightness of the bounds is presented. >

On the optimal filtering problem for the cubic sensor

We consider the problem of optimal filtering of a scalar diffusion process measured by a monotone nonlinear sensor in a low-noise channel. The specific sensors considered are of the formhn(x)=¦x¦n sgn(x). This case represents a wide class of sensors with a critical inflection point, since it is the leading term in Taylors expansion of the measurement function in the critical region.We give for the first time a formal asymptotic approximation of the conditional and of the mean square estimation errors of the optimal filter as interpolation formulas. We also construct an asymptotic approximation to the optimal filter and compare its performance with that of a constant gain filter.

The exit problem in a nonlinear system driven by 1/f noise : The delay locked loop

The frequency generated by high frequency oscillators contains a small but significant noise component known as phase noise, also known as oscillator noise or phase jitter. The phase noise belongs to the family of stochastic processes with spectra