Note: Descriptions are shown in the official language in which they were submitted.
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Signal Recognition System for Wellbore Telemetry
The present invention relates an improved method and apparatus
for demodulating a telemetry signal, i.e., recognizing or
identifying digital information in an analog signal.
Specifically it pertains to drilling telemetric systems in
formation evaluation or borehole telemetry through noisy
transmission channels.
BACKGROUND OF THE INVENTION
In the development, completion, and operation of natural
hydrocarbon reservoirs, various telemetric systems and
techniques are known and employed to achieve what is known in
the art as measurement while drilling (MWD).
For the purpose of this application, MWD includes any type of
data transmission from sensor units in the drill bit, bottom
hole assembly, or any other part of the sub-surface drill
string. Another acronym often encountered in the art besides MWD
is LWD (Logging While Drilling). MWD includes in particular low
data bit rate transmission systems, as operating below 10 KHz,
preferably below 1 KHz, such as acoustic telemetry through the
drill string itself, mud pulse or electro-magnetic telemetry.
For the scope of the present invention however, the
technological field can be better characterized by the ratio of
the speed of data processing on the receiver side and the
transmission rate. The computing speed is measured in floating
point operations per second (flops). Thus, the invention is
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preferably operable for telemetry processing above 3*105
flop/bit, more preferably above 4*105 flop/bit.
In the currently prevailing techniques data are transmitted by
means of a mud pressure pulse generator located either inside or
being part of the drill string. The system generates pressure
pulses in the drilling fluid or mud, typically by way of a valve
or siren type of device. The pulses are detected at the surface
by suitable means, e.g., pressure sensors, strain gages,
accelerometers, and the like, which are in general directly
attached to the drill string or the stand pipe.
Borehole telemetry is a well established technology.
Improvements to this technology as have been made over the past
decades are published for example in a large number of patents,
including the US Patents US-A-3 790 930, US-A-3 820 063, US-A-4
739 325, US-A-4 932 005.
Of particular interest for the scope of the present invention
are the numerous attempts being made to improve the data
detection of the transmitted data at the surface. It should be
noted that the drilling process presents an exceedingly noisy
environment for telemetry owing to the mechanical generation of
broadband noise and to the drilling fluid circulation system.
To improve the signal-to-noise ratio, the data as gathered by
the sensor units can be encoded such that the distortion by
noise has less impact on the data recovery. Usually employed
encoding schemes include Frequency Shift Keying (FSK), Phase
Shift Keying (PSK) or m-ary pulse coding. Alternatively a binary
non return to zero coding may be used. Different encoding
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~~~~~4~
methods are described for example in US-A-3 789 355 or US-A-4
562 559.
In US-A-5 381 092 the signals from those sensors which evaluate
the earth formation are subdivided prior to transmission into a
plurality of groups, each group represented by one value.
In US-A-5 055 837 an attempt is described to improve the quality
of the transmission by determining a transfer function which
characterizes the transmission properties of the drilling fluid
column in the drill pipe.
In an acoustic telemetry system, as described in US-A-5 128 901,
the data signals are (pre-)conditioned to counteract distortions
caused by the drill string.
A filtering technique to cancel or minimize noise in the
transmitted data signals is disclosed in US-A-4 878 206. This
known approach uses independent measurements of the vibrations
of the drill string at the surface to remove pressure
disturbance caused by these vibrations and affecting the mud
column pressure. A similar technique is known from US-A-5 289
354.
The specific problem of bit synchronization is described for
example in US-A-4 001 775. Each bit is represented by a change
in phase of an acoustic signal. In addition to this, each bit,
i.e. each phase shift, is transmitted over a predetermined
number of cycles generated by a reference clock.
A combinatorial solution for en- and decoding of MWD signals is
known from US-A-4 908 804. Each datum is transformed prior to
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transmission into one of a combinatorial set of a number of
nominally identical pulses distributed over a larger number of
subintervals of a fixed time interval.
The Bayesian theory to discern different hypothesis when given
experimental evidence (data) has been attributed to Rev. Thomas
Bayes, who first discovered it back in 1763. A modern summary of
Bayesian theory is presented for example by E.T. Jaynes, in an
article titled "Confidence Intervals versus Bayesian Intervals",
which is published in: "Papers on Probability, Statistics and
Statistical Physics", R. D. Rosenkrantz (Ed.), Kluwer, 1983, pp.
149-209.
A possible application of this theory to telemetry is described
in a conference paper by C.S. Christensen, titled "An algorithm
for telemetry decommutation using Bayesian decisions", published
1970 in: Proceedings of the 3rd Hawaii international conference
on system science, B.S.M. Granborg (Ed.), pp. 822-4, by Western
Periodicals Co., Hollywood, Ca., USA. The author applies a
Bayesian decision algorithm to the 'received and demodulated
string of bits in order to eliminate bit errors and to associate
the corrected bits with one of several telemetry channels. This
and similar methods have apparently been used when receiving
signals transmitted from a spacecraft, such as launched by the
National Aeronautics and Space Administration (NASA) in their
Mariner and Voyager deep space exploration program.
To appreciate the scope of the present invention in the light of
this prior art, it is important to note that Christensen does
not attempt to solve the "demodulation" problem, i.e. the
problem to translate the analog signal into a string of bits
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In view of the above cited prior art it is an object of
embodiments of the invention to provide an improved method
and apparatus for demodulating an analog telemetry signal
into a digital data signal. It is a further object of
embodiments of the invention to provide a drilling telemetry
system with improved signal recognition. The system should
be compatible with or independent from the various
transmission media and encoding methods. It is a particular
object of embodiments of the invention to provide such a
system for mud pulse telemetry in the low frequency domain.
SUMMARY OF THE INVENTION
According to the present invention, there is
provided a receiver for wellbore telemetry or Control
signals, said receiver comprising: an input connector to
connect to a signal transmission channelrbetween a surface
location and a location within a drillstring in the vicinity
of a drill bit; a demodulator for converting signals
received while drilling into binary data for further
processing; said demodulator including a generator for
generating a plurality of possible analog signals, said
possible signals being representations of signals expected
to be received while drilling via said transmission channel,
and a comparator connected to said generator and connected
to said input connector for selecting from said plurality of
possible analog signals one signal with the highest
probability of representing a signal received via said
transmission channel while drilling and thereby demodulating
said received signal.
Also according to the present invention, there is
provided a receiving apparatus for gathering data related to
subsurface conditions, said apparatus including means for
reconverting analog signals received via a signal
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transmission channel between a surface location and a
location within a drillstring in the vicinity of a drill bit
into processable digital data, wherein said reconverting
means comprises means for selecting from a plurality of
possible analog signals one signal with the highest
probability of representing said received signal, means for
demodulating said most likely analog signal into said
processable digital data, and means for displaying
probability related information together with other log
information.
According to the present invention, there is
further provided a method for identifying a signal
comprising the steps of: transmitting a digital coded
wellbore telemetry signal through a signal transmission
channel between a surface location and a location within a
drillstring in the vicinity of a drill bit; receiving said
signal as distorted by transmission through said channel;
generating at a receiving location a plurality of possible
analog signals; and demodulating said received signal into
binary data for further processing by selecting from said
plurality of possible analog signals one signal with the
highest probability of representing said received signal.
It is seen as an important element of the
invention that the identification or demodulation of data
from a transmitted analog telemetry signal is achieved by
comparing a plurality of possible analog signals with the
transmitted signal and selecting the one of said possible
analog signals with the highest probability of representing
the transmitted signal.
Possible signals can be all or a subset of those
signals which are expected to be transmitted.
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To fully appreciate the invention, it should be
noted that the described process is entirely performed in
the analog domain, i.e., before individual parts (bits) of
data have been identified. As a matter of course, analog as
used throughout
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this description also includes any "digitized" analog signal, as
resulting for example from an analog-digital conversion (ADC).
The plurality of possible signals which are compared with the
transmitted signal are preferably stored in a memory or
generated on-the-fly. Preference of either method depends on the
available equipment. The possible signals are generated using
prior knowledge of the data transmitted and the distorting
characteristics, or more generally, of the transfer function of
the transmission channel. Given the transfer function and the
data, the possible analog representations as are required for
the present invention are generated by a convolution process.
The data are known digital coded telemetry or control signals
with a limited range. However, it is a difficult task to
establish the transfer function of the wellbore through which
the data are transmitted in mud pulse or drill string telemetry.
Thus, either a simple model such as a low-pass filter can be
used or suitable test signals are transmitted and the transfer
function is derived from a deconvolution process known as such
in the art.
The comparison between received signal and the possible signals,
and the selection of the most probable of those possible signals
is based on a mathematical method named after Thomas Bayes. The
present invention seeks to include all mathematical equivalents
of this method as different notations, formulations, and
presentation, thereof, appear in the relevant literature.
It is a preferred feature of the present invention to use first
derivatives of signals to perform the comparisons. Even though
most of the received signal's energy is concentrated in its do
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component, it has been found that the use of first derivatives
in place of the signals often provides superior results.
Another preferred embodiment of the invention comprises making
use of prior knowledge of a data frame or format in which data
are transmitted and thus identifying subsections of said data
frame. In an alternative, data-independent embodiment, the
possible signals can be groups consisting of all possible
combinations of two bits. This data-independent variant might be
extended to larger groups of bits, i.e., groups of three or four
bits.
In a further embodiment, the synchronization or starting point
in the transmitted signal is retrieved by comparing the
probabilities of possible signals with different synchronization
points. Other embodiments make use of sudden change of the
variance of the signal between periods of silence and of data
transmission, respectively, and employ possible signals with
different variance.
In a further preferred embodiment, the synchronization point is
determined by jogging or shifting a possible signal in time,
determining the respective probabilities and determining the
most probable. This process is preferably extended to several or
all of the possible signals as the shift in the synchronization
point has a major influence on the calculated probabilities.
In a further preferred embodiment of the invention, the
calculated probability of a possible signal serves as a measure
for determining the optimum level of noise removal.
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These and other features of the invention, preferred embodiments
and variants thereof, and advantages will become appreciated and
understood be those skilled in the art from the detailed
description and drawings following hereinbelow.
BRIEF DESCRIPTION OF DRAWINGS
FIG. 1 shows a schematic view of a mud pressure pulse
generator and drill string suitable for use in the
present invention;
FIG. 2 illustrates major functional blocks of a decoding
system in accordance with the present invention;
FIG. 3 shows log information as generated by using an
embodiment of the present invention.
MODES) FOR CARRYING OUT THE INVENTION
Referring now to the drawings, there is shown in FIG. 1 a
tubular MWD tool 10 connected in a tubular drill string 11
having a rotary drill bit 12 coupled to the end thereof and
arranged for drilling a borehole 13 through earth formations 14.
As the drill string 11 is rotated by the drilling rig,
substantial volumes of drilling fluid ("drilling mud") are
continuously pumped by mud pumps 15 down through the drill
string 11 and discharged from the bit 14 to cool and lubricate
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the bit and carry away cuttings removed by the bit. The mud is
returned to the surface along the annular space 16 existing
between the walls of the borehole 13 and the exterior of the
drill string 11. This circulating stream of mud can be used for
the transmission of pressure pulse signal from the MWD tool 10
to the surface.
The MWD tool 10 of this example is an integral part of the
drill-string bottom hole assembly. It comprises measuring
devices 101 for environmental and drilling parameters and
appropriate encoders 102 to reduce and refine electrical signals
representative of the measured parameters for transmission via
mud pulse telemetry signals to the surface. In this example the
MWD tool measures direction and inclination of the hole, gamma
radiation, temperature, and weight and torque on bit. Sensors
and tools for other parameters such as downhole pressure,
downhole resistivity or conductivity of the drilling mud or
formation, neutron spectroscopy etc. might be added. It should
however be obvious that the present invention is not concerned
with any specific kind of parameter orTmeasuring device as used
in the wellbore.
Electrical power for the operation of the tool is provided by a
battery producing electrical energy. The tool 10 also includes a
modulator, or mud siren, 103 which selectively interrupts or
obstructs the flow of the drilling mud through the drill string
in order to produce pressure pulses in the mud. Suitable
generators are for example described in US-A-4 785 300, US-A-4
847 815, US-A-4 825 421, US-A-4 839 870 or US-A-5 073 877.
The modulator 103 is controlled such that the pressure pulses
are produced in the form of encoded acoustic data signals which
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correspond to the encoded signals from the measuring devices
101. These signals, typically in the form of binary coded
sequences, are transmitted to the surface by way of the mud
flowing in the drill string.
In the present example NRZ (Non-Return-to-Zero) telemetry is
used to communicate information to the surface. In NRZ
modulation the symbols are binary ones and zeros. The system
states are the modulator closed (corresponding to a one) and the
modulator open (corresponding to a zero). Thus, if two
succeeding bits are the same the modulator does not move. If a
one follows a zero the modulator closes, if a zero follows a one
the modulator opens.
Other signal modulation techniques are usable, and selection of
the specific encoding and modulation schemes to be employed in
connection with the operation of the modulator are matters of
choice. A number of possible modulation schemes for acoustic
borehole telemetry are described by S.P.Monroe, "Applying
digital data-encoding techniques to mud pulse telemetry",
Proceedings of the 5th SPE Petroleum Computer Conference,
Denver, 25th-28th June 1990, SPE 20236, pp. 7-16.
When these signals reach the surface, they are detected, decoded
and converted into meaningful data by a suitable signal
detector, in the present example by an electro-mechanical
transducer which is generally known in the art as SPT (Stand-
pipe Pressure transducer) 17. Transducers suitable for a
acoustic signal/pressure conversion into electrical signals are
also found in the published UK Patent GB-A-2 140 599, in US-A-5
222 049, or in the published International Patent Application
WO-A-95/14 845.
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The analog signal of the SPT is appropriately filtered and
sampled at an appropriate frequency to derive a digitally coded
representation of the analog signal, which then can be further
processed as described in the following.
Conventional demodulation or bit detection is based on threshold
detection. If the current system state is that the actuator is
open then the pressure at the SPT must rise more than the
threshold amount to register a one, otherwise a zero is
registered. Similarly, to register a zero after a one the
pressure at the SPT must fall by more than the threshold value.
Even if the SPT received the transmitted signal with no
distortion due to the travel path, this method has problems to
cope with noise if the noise amplitude instantaneously exceeds
the pressure change on opening or shutting the actuator. The
effects of the travel path exacerbate this.
In the encoding scheme of this embodiment the data is formatted,
i.e., grouped into data frames. Each data frame begins with a
standard bit sequence for synchronization, and each data word is
preceded by a one and followed by a zero. A check sum is also
calculated, and this is transmitted along with the data. The
data words are all 8 bits long or-less. A full specification of
the data format is presented hereinbelow.
Using knowledge of the acoustic response of the system to the
NRZ signal, and the available knowledge of the format and
contents of the data, the present invention can be used as an
improved method of signal recognition.
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Before describing the new features of an example with reference
to the block diagram shown in FIG. 2, important formulas of the
Bayesian theory are shortly summarized.
Given some data D, and a model M, the basic theorem of Bayes
states
Pr (D I M) Pr (M)
~1~ Pr (M I D) -
Pr (D)
The quantity of interest is Pr (MID), known as the posterior
probability of the model M in light of the data D, Pr (DIM) is
the likelihood of the data given the model, Pr (M) is the prior
probability of the model. The latter represents the prior belief
in the chosen model. The denominator Pr (D) is a normalization
term that has the same value for different models applied to the
same data. This means that the relative probability of different
models on the same data could be found without finding an
absolute value for Pr (D). This is conditional, however, on
evaluating the likelihood Pr (DIM). The Bayesian approach treats
this problem as another application of Bayes' rule .
Pr (D I ~L, 6, M) Pr (~., 6 I M)
~2~ Pr (~L, 6, I D, M) - Pr (D I M)
Equation 2 gives the posterior probability of the model
parameters (in the example: the mean ~. and the variance a,
respectively, of a Gaussian model) as a function of the data
likelihood, a prior for the parameters, and a normalizing
constant. The likelihood can be explicitly evaluated given '
values for ~, and a. The prior is a joint probability distribution
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over the two parameters given the chosen model assumption. The
normalization term is the quantity of interest in equation 1.
The normalization term can be extracted from equation [2] by
integrating the left hand side over all possible values of the
model parameters. Integrating a distribution over all possible
events gives unity, and since the denominator is independent of
and 6, the value of Pr (DIM) can be determined by
[3] Pr (D I M) J~,6 Pr (D I ~., 6, M) Pr (~L, 6 I M)
Thus equation [3] gives the term required in equation 1. This
procedure is known as integrating out nuisance parameters, and
is one of the features of Bayesian statistics. The difficulty of
the integration depends on the form of the prior. If the models
are Gaussian, the integration is usually analytically tractable.
Monte-Carlo numerical solutions have been used for other cases.
In some situations, the integration can be approximated closely
enough by summing probabilities of discrete models. The latter
variant is used in this embodiment to determine the denominator
and, hence, the evidence, following an approach described as
such for example by D. MacKay in: Neural Computation, Vol.
4(1992), No. 3, pp.415-472, and no. 5, pp.698-714.
In the present embodiment of the invention, the data are the
samples from the SPT, and the Bayesian inference problem is to
detect the data as transmitted from the downhole MWD tool.
From prior knowledge or assumptions a set of possible data words
for the signal is derived. The probability of each data word of
the set is compared to that of other words of the same set.
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The signal path is schematically depicted by Fig. 2.
The analog signal, as measured by the SPT equipment 21, is
sampled and digitized in an Analog-to-Digital converter (ADC)
22. The such digitized analog signal is stored in a buffer 23
which collects data to form a signal vector, comprising 84
seconds of the signal. An optional subsequent differentiator 24
generates the first derivative of the original signal. The
signal vector or its first derivative enters as input to a
probabilistic comparator 25 which calculates the likelihood or
probability of a model vector to represent the actual data
vector. The comparator refers to a database 26 which stores
precalculated representations of possible data vectors. This
database could easily be replaced by a dedicated engine which
generates a sequence of possible data vectors on-the-fly, using
a convolution process with a transfer function.
The output of the probabilistic comparator 25 is a vector of
calculated probabilities associated with the tested possible
data vectors. A decoder 27 evaluates the probabilities of
measurement data and cyclic redundancy check (CRC) information
related to said measurements data and thereafter selects the
most likely representation of the transmitted signal. The
selected signal is presented as log information 28, which can be
either printed, displayed, or stored.
An example of the log information is displayed in Fig.3.
It is in important feature of the invention that the log output
is not necessarily restricted to the most probable of the stored
possible data vectors. Using data calculated during the process,
confidence information, such as the calculated absolute
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probability/evidence can be made available to the user. It is
also possible to display several possible data vectors as a
result of the process, combined with ranking information which
in turn again is related to the calculated probabilities.
In the following table an example of a formatted data string as
transmitted by the downhole equipment is listed:
Bit index in frame Bits Meaninct
1-3 110 synchronization
4 1 start
5-10 [6] tool face orientation
1
11 [1] M/H
12 0 stop
13 1 start
14-21 [ 8 ] gamma ray 1
22 0 stop
23 1 start
24-28 [5] crc 1
29 0 stop
1 start
31-36 [6] tool face orientation
2
37 [1] M/H
38 0 stop
25 39 1 start
40-47 [ 8 ] gamma ray 2
48 0 stop
49 1 start
50-54 [5] crc 2
30 55 0 stop
56 1 start
57-60 [4] shock
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61 [1] P
62 0 stop
where [n] indicates n bits, and 1 and 0 stand for themselves.
In the present example, for the purpose of forming a data model,
the start and stop bits are treated as (known) parts of the data
signal which they delimit.
Assuming that synchronization is achieved in accordance with the
steps described above or by any other known method, only the
sensor information, i.e. 7 and 8 bit data words, can vary at
least theoretically over all 2°possible values with 'n' denoting
the number of bits of the data word. Hence each set of possible
words contains 256 different words at the most. Each possible
word enters the Bayesian formula (eq. [1]) as a model M and its
probability against the received signals can be calculated
accordingly.
The use of check-sum information allows further probabilistic
evaluation. Most of the data words are transmitted with some
redundancy, containing 15 data bits, followed by a 5 bit check
sum derived from the data. The a-priori knowledge of the check
sum bits, given the data bits, improves the performance of the
demodulation. The probability of each data word is proportional
to the relative probability of each data word independently,
times the relative probability of the check sum word derived
from it. Although theoretically this increases the number of
calculations of probability from 28 to 215 , in practice,
selecting on only the more probable (for instance the most
probable 32) of each word allows the most probable demodulation
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to be found, and if it does not then the absolute probability of
the demodulation will be so low as to fall below any reasonable
threshold. However, it is also not unreasonable to compute all
215 - 32768 probabilities.
The probabilistic comparator 25 of Fig. 2 generates a vector
comprising the normalized posterior probabilities for all
possible data vectors or models by a process comprising the
steps of:
1. Calculating the residuals between a model data and the
signal data along the length of the vector, where the kth
element rkof the residual vector r is the difference between the
model and the signal for sample k.
2. Assuming the residuals form a Gaussian distribution with
zero mean, the variance of the this distribution is calculated
according to
T
2 r r 2
2o f4~ 6 - max , 61
n - 1
with n denoting the number of samples or elements in the model
and signal data vector and the corresponding residual vector,
multiplied by an oversampling factor (Fs/2*Fc), where Fs is the
sampling frequency and Fc is the cut-off frequency of the
filtered signal. A lower bound ale is introduced to avoid taking
a logarithm of zero. The larger the size of this lower boundary
is chosen, the larger is the likelihood of the best fit model
when the noise is insignificant. Suitable values for a12 are 1p-1~
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or 10-z° both of which are indistinguishable in computing devices
with 32 bit data register.
3. Given o~ the logarithm 1 of the likelihood for the data
given the model is calculated by
[5] 1 - - n log (262 ) _ n - 1
2 2
The calculation is simplified because the variance of the
distribution is set at the sample variance of the data. The
residue between the signal data and the possible data model
enters the likelihood through the variance.
This calculation process is extended to parts, sub-groups,
channels, and the like, of the signal, in which case the
likelihood of the complete data model is given by the product of
the likelihood for each part, sub-group, channel etc.
To generate from the likelihoods for each of the possible data
vector a vector which contains the normalized Bayesian posterior
probability (cf. eq. [1]) following steps are performed:
1. Generating a logarithmic likelihood vector 1, where the kth
element is the logarithmic likelihood of a model k as calculated
in accordance with eq.[4] and [5].
2. Scaling the logarithmic likelihood vector 1 to form a
scaled logarithmic likelihood vector 1, by
[ 6 ] IS - 1 - max ( 1 )
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where max(1) is the maximum of the elements of 1.
3. Evaluating the un-normalized posterior probability by
P a - exp ( 1S ) O Pr (M)
where Pr(M) is a vector of the normalized prior probabilities of
the model data such that the kth element of Pr(M) is the
normalized prior probability of the model k (in this example all
models have the same prior probability), ~ denotes an element-
wise multiplication operator and exp() is an element-wise
exponentiation operator.
4. To generate a vector Pr containing the normalized posterior
probabilities, the vector Pru is divided by the scalar sum of its
elements:
Pr
~a~ Pr - " .
P a
k
It will be appreciated by those skilled in the art that the
above described method of evaluating the posterior probability
by using scaled vectors and calculating with logarithms avoids
divisions by zero and significantly reduces the number and
complexity of computational operations. However, it is obviously
possible to calculate the posterior probabilities using for
example the actual values for the Gaussian model in place of
their logarithms. The Gaussian model for the distribution of the
residues further constitutes a particularly advantageous model,
other known or even specifically designed models for the -
distribution could be applied.
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In the following variants of the invention, use is made of
further information and assumptions characterizing the signal
transmission and being available prior to the data transmission
or derivable during the data transmission. These variants can
also be used to refine and accelerate the basic signal
recognition process as described hereinbefore.
Generally results generated by the new method can be improved by
taking the first derivative of the analog telemetry signal
rather than the signal itself as input data for the demodulation
process.
In a further step, a transfer function for the transmission
channel from the modulator 103 to the SPT is derived.
In practice the transfer function is unlikely to be known
exactly. Even if the shape of the transfer function were known,
difficulties of SPT calibration and actuator variation mean that
the overall scale factor is relativelyTunpredictable. These
difficulties can be overcome by deriving scale information from
the data itself, and using multiple transfer function models in
a Bayesian demodulation process. In other words, several models
of the transmission channel can be tested against the received
data.
The present embodiment uses as a model for the transmission
channel, i.e. as a transfer function, a low pass filter with 0.7
Hz as cut-off frequency.
In a further step, noise is removed from the data.
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To remove noise all frequency components higher than 0.7 Hz are
filtered from the signal by means of a cut-off filter. The cut-
off frequency is determined by the known bandwidth of the signal
as generated by the modulator. Other characteristics of the
signal or noise can be employed to design a filter which
effectively rejects at least a part of the noise.
In addition to the filtering step, noise is reduced by applying
Bayes' theorem to the data and a model of the data including a
noise model. Then the evidence, which is the normalization
constant in eq. [1], can be compared for this data model and a
second !noise-free) data model which does not make any
assumption about the noise.
Alternatively or in addition to the above, several noise models
may be tested by comparing their respective evidence. It is
further possible to optimize a noise model by adjusting one or a
plurality of parameters of the noise model by determining a
maximum of the evidence with respect to those parameters.
It is also possible to base the noise models on estimations or
measurements on known noise sources such as the mud pumps 15.
A further step includes the detection of synchronization signals
as being transmitted within each data frame generated by the
downhole modulator. Synchronization is an important part of
telemetry demodulation, since the demodulation can be completely
wrong if the models are fitted to the wrong part of the data.
A synchronization point can be found by evaluating the
probabilities of several data frame models, each modeling a
different synchronization time. By taking data over an inter-
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sync period, and applying models representing a frame starting
at all points in this period, the synchronization point can be
determined.
A quicker evaluation can be made by including fewer models,
covering for example a synchronization point every other sample
One model that has been used successfully is of a constant mean,
stepped variance model to fit the derivative of the data. Where
the data burst starts, the derivative changes sharply. In
between bursts (between the end of the data and the start of the
next sync pulse) the signal is quiet and ideally the derivative
is close to zero. A stepped variance model fits a wide variance
to the data and a narrow variance to the quiet period.
Alternatively, stepped-mean Gaussian models of the mean power in
the derivative can be used. The square of the derivative can be
fitted quickly to several such models by forming cumulative sums
along the data and making subtractions to find sums of
statistics of the data for this purpose.
lnlhen the data burst length is unknown, several models of the
data starting at the same synchronization time are needed. The
model probabilities are integrated and compared with sums of
other models of different synchronization times and data
lengths.
This model-based method of synchronization can be used as a
rough starting point for a more finely-tuned method using model
evidences.
By using the model evidences, synchronization can be found to
within a sample of the data.
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This can be done as follows. The probability of each member of a
set of models for a section of the data is evaluated. The same
models are used and their probabilities re-evaluated at points
displaced over a range of candidate synchronization points
either side of the original, that is, the section of interest is
moved around a sample or two.
Jogging the section left and right means the data in the Bayes
calculation is not the same. This would appear to present a
problem in comparing the evidences since Bayes' rule (equation
[1]) requires the data to be the same. This problem can be side-
stepped by considering the data to be fixed but wide enough to
span all the sections of interest, and by considering the models
to be extended over the extra data points by including some
broad-variance elements. The models will all have the same
number of broad-variance elements, so they will be comparable,
and now the data is the same. This is a theoretical device and
can be ignored in practice.
Once the model probabilities for each jogged section have been
found, the evidences can be calculated. The section associated
with the greatest evidence gives the best synchronization point.
It is this set of models that can be used to decode the data.
This technique can be time consuming if there are many candidate
synchronization points. The number of candidate points can be
reduced by finding a rough synchronization point first, as
described above.
An efficient way to use these two techniques is to find the
synchronization point to within a few samples with the model-
based method, and then to evaluate the remaining samples using
the evidence method. How many 'a few' is will depend on the
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amount of data, the models, and the available computing
resources.
A log resulting from an application of the example to a mud
pressure signal is shown in Fig. 3. Displayed is from the left
side, the pressure signal of the SPT versus time in seconds, the
synchronization points as probability versus time, the
identified and decoded tool orientation in degrees, the
identified and decoded output of the gamma-ray counter in counts
per second (cps?, and a "confidence log", which shows the
probability of the related identified and decoded value. It can
be seen that the sudden rise of pressure at approximately 350
seconds distorted the signal such that the identified and
decoded values (denoted by open circles? show only a small
probability. This is in contrast to the rest of the values
(denotes by stars) which are identified with a probability of
close to 1. In the displayed data set, some data appears to be
missing, as evidenced by the change in the sync timing at around
450 seconds. The algorithm however automatically adjusts for
this glitch and continues to decode.
In another variant of the invention, the set of possible data
words is based on a transition model. The transition models
reflects the response of the transmission channel to a change
from its current state into the following. For digital coded
information the transmission channel, assumed to be originally
in a state "0", can change into "1" or remain "0" in the
following bit-time. Hence, this data model leads to set of four
possible transitions, 00, O1, 10, 11, each of which is described
by a probability distribution, which in turn can be
characterized by parameters such as mean and variance. Hence,
any two subsequently received signals are compared to the
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expected response of the transmission channel to each one of the
four possible transitions. In the absence of any other
information, the most probable transition is selected.
The method has the advantage of minimizing the necessary
knowledge or assumptions with respect to the transmission
channel and/or the signals. The probability distribution can
even be derived from a history of recognized signals.
In many cases the assumption can be used that each transition
distribution (in this model there are four) is Gaussian. The
only parameters of the Gaussian distribution,are the mean and
variance. Given a successfully demodulated signal then the
actual pressure changes produced by each bit transition may be
determined, and their sample mean and variance may be used as
estimators for the Gaussian parameters.
To allow for a slow change in the distribution parameters, a
moving buffer of the most recently demodulated data frames can
be used to evaluate the statistics.
Another possibility is to use values of the means from previous
experience in similar situations. Yet another is to use the data
from the synchronization bits, which will be described in
greater detail below, at the start of the first data frame, and
to make a few simplifying assumptions. If it is assumed that the
absolute value of the pressure change going from a one to a zero
is the same as from a zero to a one, and similarly for a one-one
transition and a zero-zero transition, and that the variances
for each distribution are the same, then the synchronization
bits allow a reasonable first estimate of the transition model
parameters - so long as the data is not too noisy.
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Once the entire first frame has been demodulated a better
probability model can be used. If this self-consistent method is
not successful, but the data frame can be demodulated by other
means (a human operator for instance?, then the statistics can
still be evaluated in order to produce a model for the next data
frame .
The above described variant, which is based on a transition
model, can be enhanced by taking into account transitions in two
or more bit-times, e.g., transition from 00 to 00, 01, 10, 11
and so forth.
