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From: jcarter on 22 Jan 2010 12:55
I must be missing something. I passed 128 records of 1300 samples each
(1300x128) through a Kalman Filter (This is basically a laser return signal
- often times quite small- buried in solar noise generated by an APD -
Avalanche Photo Diode) and the output appears as noisy as any one of the
record inputs. Simple Averaging of these 128 records yields a signal from
the noise, but I was under the impression that Kalman Filter is superior to
simple averaging for lifting signal from noise. I can only conclude that I
am doing something wrong. I had set my State Transition Matrix (A) and
Observation Matrix (H) to an Identity Matrix, and I played around with
process noise covariance(Q) and measurement noise covariance (R) values but
to no avail. This is a stationary process so I employed a Simple Discrete
Kalman Filter. Are there any limitations to the use of Kalman filters?
Sampling Rates? Any suggestions why a filter may fail you? Thanks.



From: Vladimir Vassilevsky on 22 Jan 2010 13:11


jcarter wrote:

> I must be missing something. I passed 128 records of 1300 samples each
> (1300x128) through a Kalman Filter (This is basically a laser return signal
> - often times quite small- buried in solar noise generated by an APD -
> Avalanche Photo Diode) and the output appears as noisy as any one of the
> record inputs. Simple Averaging of these 128 records yields a signal from
> the noise, but I was under the impression that Kalman Filter is superior to
> simple averaging for lifting signal from noise. I can only conclude that I
> am doing something wrong. I had set my State Transition Matrix (A) and
> Observation Matrix (H) to an Identity Matrix, and I played around with
> process noise covariance(Q) and measurement noise covariance (R) values but
> to no avail. This is a stationary process so I employed a Simple Discrete
> Kalman Filter. Are there any limitations to the use of Kalman filters?
> Sampling Rates? Any suggestions why a filter may fail you? Thanks.

What makes you think that Kalman filter should perform any better then
simple averaging in your case? FWIW, Kalman filter theory covers more
general situation; i.e. if your target moves with known dynamics, if the
noise is not white, etc.

Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com
From: HardySpicer on 22 Jan 2010 17:43
On Jan 23, 6:55 am, "jcarter" <jcar...(a)leupold.com> wrote:
> I must be missing something.  I passed 128 records of 1300 samples each
> (1300x128) through a Kalman Filter (This is basically a laser return signal
> - often times quite small- buried in solar noise generated by an APD -
> Avalanche Photo Diode) and the output appears as noisy as any one of the
> record inputs.  Simple Averaging of these 128 records yields a signal from
> the noise, but I was under the impression that Kalman Filter is superior to
> simple averaging for lifting signal from noise.  I can only conclude that I
> am doing something wrong.  I had set my State Transition Matrix (A) and
> Observation Matrix (H) to an Identity Matrix, and I played around with
> process noise covariance(Q) and measurement noise covariance (R) values but
> to no avail.  This is a stationary process so I employed a Simple Discrete
> Kalman Filter.  Are there any limitations to the use of Kalman filters?
> Sampling Rates?  Any suggestions why a filter may fail you?  Thanks.

You have probably implmented a steady-state Kalman filter or Wiener
state estimator.

Hardy
From: Tim Wescott on 22 Jan 2010 23:29
On Fri, 22 Jan 2010 12:11:46 -0600, Vladimir Vassilevsky wrote:

> jcarter wrote:
>
>> I must be missing something. I passed 128 records of 1300 samples each
>> (1300x128) through a Kalman Filter (This is basically a laser return
>> signal - often times quite small- buried in solar noise generated by an
>> APD - Avalanche Photo Diode) and the output appears as noisy as any one
>> of the record inputs. Simple Averaging of these 128 records yields a
>> signal from the noise, but I was under the impression that Kalman
>> Filter is superior to simple averaging for lifting signal from noise.
>> I can only conclude that I am doing something wrong. I had set my
>> State Transition Matrix (A) and Observation Matrix (H) to an Identity
>> Matrix, and I played around with process noise covariance(Q) and
>> measurement noise covariance (R) values but to no avail. This is a
>> stationary process so I employed a Simple Discrete Kalman Filter. Are
>> there any limitations to the use of Kalman filters? Sampling Rates?
>> Any suggestions why a filter may fail you? Thanks.
>
> What makes you think that Kalman filter should perform any better then
> simple averaging in your case? FWIW, Kalman filter theory covers more
> general situation; i.e. if your target moves with known dynamics, if the
> noise is not white, etc.

For that matter, what makes you think that a Kalman filter for your set
of assumptions isn't a simple averaging filter?

A pure Kalman (not extended, or unscented, or whatever) is just a garden-
variety time-varying (maybe) state-space filter that happens to have been
designed using a particular method. "Kalman filter" does not mean "Magic
filter".

--
www.wescottdesign.com
From: Tim Wescott on 23 Jan 2010 14:19
On Fri, 22 Jan 2010 11:55:31 -0600, jcarter wrote:

> I must be missing something. I passed 128 records of 1300 samples each
> (1300x128) through a Kalman Filter (This is basically a laser return
> signal - often times quite small- buried in solar noise generated by an
> APD - Avalanche Photo Diode) and the output appears as noisy as any one
> of the record inputs. Simple Averaging of these 128 records yields a
> signal from the noise, but I was under the impression that Kalman Filter
> is superior to simple averaging for lifting signal from noise.

Possibly, but that depends. For the right problem (a constant signal,
and uncorrelated white noise), the matching Kalman filter _is_ a simple
averaging filter.

> I can only conclude that I am doing something wrong. I had set my State
> Transition Matrix (A) and Observation Matrix (H) to an Identity Matrix,
> and I played around with process noise covariance(Q) and measurement
> noise covariance (R) values but to no avail.

You need to model the expected signal as a generating system, then use
that generating system to calculate your filter.

> This is a stationary
> process so I employed a Simple Discrete Kalman Filter. Are there any
> limitations to the use of Kalman filters?

Yes.

> Sampling Rates?

Yes.

> Any suggestions why a filter may fail you? Thanks.

Whomping up a Kalman filter from a model that is a poor match to the
reality is certainly a way. A Kalman filter is just a linear filter --
possibly time varying -- that has been designed with a specific technique
to make it optimal according to a set of criteria chosen to make
computation tractable.

If the performance you need is not well represented by the optimality
criteria that Kalman chose to make the math come out right, or if your
system model doesn't match reality, then your filter may waste time and
processor resources, but it won't necessarily make detection better.

If I read your post correctly you're trying to design an optimal signal
to extract a signal with known parameters from a return that is corrupted
by noise.

It sounds also like your procedure is to take 128 measurements, each
yielding a vector of 1300 points. Because of the passage of time, it's
pretty safe to assume that the nth point in any of these 128 vectors is
uncorrelated with any other such point. So starting out by averaging
those 128 vectors into one 1300 point vector is a very good step, and if
it's sufficient, you can stop there.

Doing time-domain filtering on each of the 1300 vectors may be to your
advantage, but only if the laser return spans more than one sample. If
this is the case, then rather than a Kalman filter you probably need a
simple matched filter, whose output gets fed to a comparator with a
varying threshold to account for any anticipated range vs. amplitude
variation.

--
www.wescottdesign.com
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