Browse Prior Art Database

Robust Linear Phase Height/Depth Estimator

IP.com Disclosure Number: IPCOM000122779D
Original Publication Date: 1998-Jan-01
Included in the Prior Art Database: 2005-Apr-04
Document File: 4 page(s) / 127K

Publishing Venue

IBM

Related People

Ottesen, HH: AUTHOR [+2]

Abstract

This invention features a robust method for an improved estimate of the surface topological features, like on a disk surface, based on a sampled noisy signal from a proximity sensor. The signal sample values at the base and peak of a bump and/or at the top and bottom of a pit are usually noisy. This method uses an N-point Finite Impulse Response (FIR) filter that has the property of linear phase characteristics, which will retain the surface topological features independent of frequencies of additive noise and has Least Square Error (LSE) properties.

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Robust Linear Phase Height/Depth Estimator

      This invention features a robust method for an improved
estimate of the surface topological features, like on a disk surface,
based on a sampled noisy signal from a proximity sensor.  The signal
sample values at the base and peak of a bump and/or at the top and
bottom of a pit are usually noisy.  This method uses an N-point
Finite Impulse Response (FIR) filter that has the property of linear
phase characteristics, which will retain the surface topological
features independent of frequencies of additive noise and has Least
Square Error (LSE) properties.

      The basis for the height/depth estimation is the normal
equations of linear regression analysis.  See for example, [*].  The
coefficients is the straight line equation y_hat = b_o + b_1 x can be
determined, where b_o is the line intercept with the y-axis and b_1
is the slope of the straight line.  As to the least-squares-error
minimization method, it is possible to express b_o and b_1 from the N
measurements (x_k,y_k), k=1,2,...,N as

      If the sampling of the proximity sensor signal is taken at
regular intervals then x_k = k x_o, and if y_k = y(k), then in
Equation (1) the running zero intercept, now denoted as y_o(k) using
the N measurements {y(1),y(2),...,y(N)} can be expressed as

      The Finite Impulse Response (FIR), zero-intercept-estimate
filter has coefficients generating equation:

      Using Equation (3) as a starting point, it is possible to
derive the running projected 1-ahead-estimate y_N+1(k), using the
same N measurements {y(1),y(2),...,y(N)} as in Equation (3), as the
expression

      Correspondingly to Equation (4), the 1-ahead-estimate Finite
Impulse Filter (FIR) filter coefficients have a generating equation

      The coefficients of the FIR for the intercept filter i_N(n) are
equal to the folded (reverse) coefficients of the FIR for the 1-ahead
peak estimating filter p_N(n).  If we take the difference
delta_y_N+1(k) between the estimates in Equations (5) and (3) as
shown in Equation (7)

      Substitution of Equations (3) and (5) into Equation (7) we
obtain a special kind of height/depth estimator that uses only N
measurements {y(1),y(2),...,y(N)}, but span N+2 samples.  The two
extreme points are...