Kalman filter

A Presentation On
A Fast Adaptive Kalman Filtering Algorithm
for Speech Enhancement
P.SHARFUDDIN (10731A0233)
P.MARUTHI BASKAR NAIDU (10731A0235)
M.RAGHAVA REDDY (10731A0223)
K.KHAMEER (10731A0219)
P.RAMA KRISHNA (10731A0237)
Presented BY
DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING
P.B.R VISVODAYA INSTITUTE OF TECHNOLOGYAND SCIENCE
(Affiliated to J.N.T.U, Anantapur)
KAVALI

Introduction
 Speech
Speech is the process associated with the production and perception of the noises used
in the spoken language. A huge number of disciplines study the speech and the speech
sounds, including acoustic ,psychology, speech pathology, linguistic, cognitive science
and computer science.
 Spoken language is used to communicate information from a speaker to a listener.
Speech production and perception are both important components of the speech chain.
 Speech perception
 Speech perception refers to processes by which humans are able to interpret and
understand the sounds used in the language. The study of the speech perception is
closely linked to the phonetic field and phonology. Speech perception researches seek
to understand how the humans recognize the speech sounds and use this information
to understand the spoken language

Cont…

Speech communications
 Speech is the most primary human communication. For that reason, it exists a big
trend to increase and improve telecommunications.
 Nowadays, all the people use the communication devices almost as a primary good:
telephones, mobiles internet…and the customers demand a high coverage and
quality.
 However, the background noise is an important handicap. If it is joined with other
distortions, it can seriously damage the service quality.

Speech Processing
 Speech processing is the study of speech signals and the processing methods of
these signals. The signals are usually processed in a digital representation
whereby speech processing can be seen as the intersection of digital signal
processing and natural language processing.
 Speech processing can be divided in the following categories:
 Speech recognition, which deals with analysis of the linguistic content of a
speech signal.
 Speaker recognition, where the aim is to recognize the identity of the
speaker.
 Enhancement of speech signals (this is the area of this project)
 Speech coding, a specialized form of data compression, which is important in
the telecommunication area.
 Speech synthesis: the artificial synthesis of speech, which usually means
computer generated speech.


 What is speech enhancement? Enhancement means the improvement in the
value or quality of something. When applied to speech, this simply means the
improvement in intelligibility and/or quality of a degraded speech signal by using
signal processing tools. By speech enhancement, it refers not only to noise
reduction but also to dereverberation and separation of independent signals.
 This is a very difficult problem for two reasons. First, the nature and
characteristics of the noise signals can change dramatically in time and between
applications. It is also difficult to find algorithms that really work in different
practical environments. Second, the performance measure can also be defined
differently for each application
Speech Enhancement

 There is an important algorithm for speech enhancement which belongs to the
group of parametric methods where the speech signal is modeled as an
autoregressive process embedded in Gaussian noise. Speech enhancement
algorithms belonging to this category consist of two steps:
 · Estimation of the AR coefficients and noise variances.
 · Application of the Kalman filtering using the estimated parameters to estimate
the clean speech from a sample of the noisy signal.

Speech Production
 Speech begins with a thought and an intention to communicate in the brain,
which activates the muscular movements to produce speech sounds. A listener
receives a sound in the auditory system, processing it for a conversion to
neurological signals the brain can understand. The speaker continuously
monitors and controls the vocal organs by receiving his or her own speech as
feedback.
 Speech signals are composed by analog units, which are the symbolic
representation of the spoken language: phonemes, syllables and words. But for
this project it is not necessary to go into this level of depth.

Linear Predictive Coding
(LPC)
 Linear predictive coding (LPC) is a tool used, mainly, in the audio signal and
speech processing to represent the spectral envelop of a speech digital signal in
a compressed way (using the information of linear prediction model). This
technique is one of the most powerful to analyze the speech, and one of the
most useful methods for encoding with good quality at low rate.
 LPC starts with the assumption that the speech signal is produced by a buzz at
the end of a tube, adding, sometimes, hissing and popping sounds. This model
is a good approximation to the reality.

Kalman filtering
 The filter has its origin in a Kalman’s document (1960) where it is described as a
recursive solution for the linear filtering problem for discrete data. The research was
in a wide context of state – space models, where the point is the estimation through
the recursive least squares. Since that moment, due to the development of digital
calculation, Kalman filter has been researched and applied, particularly in self and
assisted navigation, missiles search and economy. The study of Kalman filter is based
on Wiener filter.
 The filter is a mathematical procedure which operates through a prediction and
correction mechanism. In essence, this algorithm predicts a new state from its
previous estimation by adding a correction term proportional to the predicted error.
In this way, this error is statistically minimized. This filter is the main algorithm to
estimate dynamic systems specified in state-space form.
 A Kalman filter is simply an optimal recursive data processing algorithm

 The Kalman filter is the main algorithm to estimate dynamics systems
represented as state-space. In this representation the system is described by a
set of variables denominated of state. The state contains all the information to
do with a certain point in time. This information must permit the deduction of
the past system behavior, with the goal of predicting its future behavior.

 The algorithm
 The Kalman filter estimates the previous process using a feedback control, that
is, it estimates the process to a moment over the time and then it gets the
feedback through the observed data.
 From the equation point of view that is used to derivate the Kalman filter, it is
possible to separate them into two groups:
 · Those which update the time or prediction equations
 · Those which update the observed data or update equations.

 The first group of equations has to throw the state to the n moment taking as
reference the state on n-1 moment and the intermediate update of the
covariance matrix of the state. The second group of equations has to take care
of the feedback; they add new information inside the previous estimation to
achieve an improved estimation of the state.
 The equations which update the time can be seen as prediction equations, while
the equations which add new information can be seen as correction equations.
Exactly, the final estimation algorithm can be defined as a prediction-correction
algorithm to solve many problems.

Advantages of Kalman Filter
 Below are some advantages of the Kalman filter, comparing with another famous
filter known as the Wiener Filter.
1. The Kalman filter algorithm is implementable on a digital computer, which this
was replaced by analog circuitry for estimation and control when Kalman filter was
first introduced.
2. Stationary properties of the Kalman filter are not required for the deterministic
dynamics or random processes. Many applications of importance include
nonstationary stochastic processes.

Cont…
3. The Kalman filter is compatible with state-space formulation
of optimal controllers for dynamic systems. It proves useful
towards the 2 properties of estimation and control for these
systems.
4. The Kalman filter requires less additional mathematical
preparation to learn for the modern control engineering
student.
5. Necessary information for mathematically sound, statistically-
based decision methods for detecting and rejecting
anomalous measurements are provided through the use of
Kalman filter.

Kalman Filter Working
 Firstly, it estimates a process by using a form of feedback control loop
whereby the filter estimates the process state at some time and then
obtains feedback in the form of (noisy) measurements.
 As such, these equations for the Kalman filter fall into two groups: “Time
Update equations” and “Measurement Update equations”
 The time update equations can also be thought of as “predictor” equations,
while the measurement update equations can be thought of as “corrector”
equations.

The ongoing discrete Kalman
filter cycle.

Implementation of Kalman
filter to Speech
 The idea of this project is to reconstruct a speech signal using the
Kalman filter technique.
 This speech signal will be modeled as an AR process and
represented in the state-space domain.
 In striving for this goal, certain parameters have to be taken into
consideration.

Implementation
 The all pole, or autoregressive (AR), signal model is
often used for speech. The AR signal model is
introduced as:
 Above equation can also be written in this form as
shown below:

Cont…
 In order to apply Kalman filtering to the speech expression shown
above, it must be expressed in state space form as

Cont…
 The Kalman filter functions in a looping method
here we denote the following steps within the
loop of the filter. Define matrix HT
k-1 as the row
vector
and zk = yk
where Xk will always be updated according to the
number of iterations, k.

Conclusion
 In this project, an implementation of employing Kalman
filtering to speech processing had been developed.
 The purpose of this approach is to reconstruct an output
speech signal by making use of the accurate estimating
ability of the Kalman filter.
 Furthermore, the results have also shown that Kalman
filter could be tuned to provide optimal performance.

Kalman filter

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