Mohammad Bilal Malik

Tracking of linear time varying systems by state-space recursive least-squares

State-space recursive least-squares (SSRLS) allow the designer to choose an appropriate model. This attribute of SSRLS suits the model dependent nature of the tracking problem. On the other hand, the standard RLS and LMS assume a multiple linear regression model. Therefore, their tracking abilities are limited. In this paper, we begin with the derivation of time-varying SSRLS which is followed by some related details. Our major contribution is the development of versatile algorithms that can efficiently track time-varying SSRLS which is followed by some related details. Our major contribution is the development of versatile algorithms that can efficiently track time-varying systems. Superior tracking performance of SSRLS is demonstrated by a couple of examples in the end. The paper provides a guideline that would enable a designer to devise newer algorithms for a wide range of problems.

State-space recursive least-squares with adaptive memory

State-space recursive least-squares (SSRLS) is optimal a linear estimator for deterministic signals. The performance of SSRLS however, depends on model uncertainty, time-varying nature of the observed signal or nonstationary behavior of the observation noise. We incorporate stochastic gradient tuning of the forgetting factor to develop SSRLS with adaptive memory. This new algorithm addresses the limitations faced by standard SSRLS. An approximation of the actual filter, which alleviates the computational burden, is also derived. An example of tracking a noisy chirp signifies and demonstrates the overall capability and power of the new algorithm. It is expected that this new filter is able to track and estimate time-varying signals that are difficult to deal with the available tools.

Tracking of linear time-varying systems using state-space least mean square

In this paper, we present a generalized least mean square (LMS) algorithm. This new filter, which has been termed as state-space least mean square (SSLMS), incorporates linear time-varying state-space model of the underlying environment. The tracking ability of the LMS is limited due to linear regression model assumption. By overcoming this restriction, SSLMS exhibits a marked improvement in tracking performance over standard LMS and its known variants. The derivation of SSLMS is based on the minimum norm solution of an underdetermined linear least squares problem. An example of tracking a linear time-varying system demonstrates the ability and flexibility of SSLMS.

State-space RLS

Kalman filter is linear optimal estimator for random signals. We develop state-space RLS that is counterpart of Kalman filter for deterministic signals i.e. there is no process noise but only observation noise. State-space RLS inherits its optimality properties from the standard least squares. It gives excellent tracking performance as compared to existing forms of RLS. A large class of signals can be modeled as outputs of neutrally stable unforced linear systems. State-space RLS is particularly well suited to estimate such signals. The paper commences with batch processing the observations, which is later extended to recursive algorithms. Comparison and equivalence of Kalman filter and state-space RLS become evident during the development of the theory. State-space RLS is expected to become an important tool in estimation theory and adaptive filtering.

Optimal output quadratic regulation

To have an accurate information of system states is always being a challenging task for the control designers irrespective the system is linear or non linear. This information is used for state feedback in tracking of a reference signal. An observer based optimal linear quadratic scheme is presented in this paper. Linear time invariant (LTI) system is used for reference tracking in the presence of external disturbance once only plant input and output is available to us. The proposed closed loop structure is capable of rejecting the disturbance by utilizing the prior information of disturbance. A optimize quadratic cost function effectively utilizing the observed plant states is defined. Its performance in the presence of observer makes it more realistic for practical use. Suggested algorithm performance is discussed with the simulation results with third order linear system.

Bi-carrier Golay code based ranging with improved range resolution

In this paper, we present Golay code based bi-carrier detection and ranging algorithm that offers improved range resolution. We exploit the zero side lobe property of complementary Golay Code pair for detection and side lobe free ranging of targets. The complementary Golay code pair is transmitted on two orthogonal carriers of a bi-carrier signal We propose base band filtering of the complementary code pair for bandwidth reduction of the bi-carrier signal and to keep the two codes non-interacting. The detection and ranging algorithm for the Golay code based bi-carrier signal is based on a double quadrature demodulator and matched filtering. The performance of the filtered complementary code pair degrades in the presence of noise. Monte-carlo simulations were carried out to investigate the effect of noise on the correlation of filtered Golay code and some of conventional coding signals (PN and Gold sequence) in ranging applications. A comparison of the performance of these codes shows that Golay code is robust to noise among these codes. Improved range resolution and better noise rejection capability supports the unconventional use of Golay code in ranging applications.

Tracking of uncertain time-varying systems by state-space recursive least-squares with adaptive memory

State-space recursive least-squares (SSRLS) allows the designer to choose an appropriate model, resulting in superior tracking performance over the standard recursive least-squares (RLS) and least mean square (LMS). However, the tracking capability of this algorithm is dependent on the forgetting factor in presence of factors like model uncertainties and time-varying nature of observation noise etc. We address such problems In this work by developing time-varying SSRLS with adaptive memory. The tuning of the forgetting factor is done by stochastic gradient method. The ability to handle time-varying linear systems is a major enhancement of our previous work. The new filter is therefore, much more flexible and powerful. Based on this theory, we design a tracking algorithm that efficiently tracks time-varying systems.

Problem of tracking a reference with unknown derivatives

High-gain observers have been used as approximate differentiators in state estimation in nonlinear systems. The classical problem of tracking a reference signal requires knowledge of certain derivatives of the reference. This information may not be available on-line. We extend the use of high-gain observers to formulate special forms that estimate the requisite derivatives. The development is primarily based on tracking properties of thigh-gain observers, which have been termed as wide-band filters in this particular application. Related issues like estimation error have been discussed in the course of development. It has also been shown that step- and ramp-invariant discrete equivalents are the appropriate methods for implementation of wide-band filters.

Robust controller design for attitude control of control moment gyroscope

Robust controller design in presence of disturbance and system parameter uncertainties has been a challenging task. In this paper attitude control of ECP 750 Gyroscope in presence of uncertainties is solved using LMI based multi objective state feedback H2 /H∞ controller. The attitude control problem addressed here resembles the formulation of polytopic model of MIMO gyroscope model to cater the parameter uncertainty and subsequent robust controller design using LMI framework is novelty of this work. MATLAB simulation results show better robust attitude control and disturbance rejection.