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Detection and Classification of Acoustic and Seismic Events using

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					           Detection and Classification of Acoustic and Seismic Events using a
                        Semi-Markov Energy Dynamical Model

                       Sze Kim Pang, Geok Lian Oh, Shanguo Lu, Adrian Yap Cheng Lock ∗



                           Abstract                                       also induce different characteristics of the measured energy
                                                                          level. We will show that the new dynamical model is able
   In acoustic and seismic remote sensing applications, the               to describe these characteristics reasonably.
intent is to detect and classify events based on the signal                  The paper is organised as follows. Section 2 presents
received. Very often, the detector is just a simple energy de-            the new energy dynamical model. Section 3 describes the
tector. In this paper, we will like to explore using the energy           Bayesian model for the event detection and classification.
profile to detect and classify different types of event. The               Section 4 develops the inference algorithm based on a parti-
event detection and classification will be treated jointly and             cle filter. The results for simulation and real data are shown
formulated as a Bayesian filtering problem. We will develop                in Section 5, followed by conclusions in Section 6.
a new semi-Markov dynamical model for the acoustic and
seismic energy level. A particle filter is then designed to ob-            2 Dynamical Model for Energy Profile
tain the posterior distribution of the quantities of interest,
including the probability of an event, as well as the types of
                                                                             Here, a pair of acoustic and seismic sensor is used to
event. We will demonstrate the results using both simulation
                                                                          measure the energy level of an event. Figure 1 and 2 shows
as well as real data.
                                                                          an example of the acoustic and seismic energy profile cap-
                                                                          tured.

1 Introduction                                                                                        20
                                                                                                                 Event 1

                                                                                                      10
   Detecting and classifying events is an important appli-
cation in many fields of work. There are applications in                                                0
                                                                                                                                                               Event 1
                                                                           Acoustic Energy ZA (dB)




Acoustic Event Detection (AED) [10], video analysis [13],                                                                                   Event 2            Event 2
                                                                                            t




EEG analysis [2], information protection [5], neuron spike                                           −10              Event 2
inference [15] etc. In some applications [11], the detection
                                                                                                     −20
and classification are treated as two separate processes. This
can potentially result in less optimal estimation.                                                   −30
   In this paper, we will look at a remote sensing applica-
tion, where a pair of acoustic and seismic sensor are used si-                                       −40
multaneously to collect energy data of events. We will like
to detect and classify different events based on the profile                                          −50
                                                                                                       1300   1400   1500   1600   1700     1800 1900   2000   2100   2200   2300
of the energy data. One common approach would be to ex-                                                                                   Time (s)

tract relevant event timing information, such as the rise time
of the event, and feed it into a classifier. Another approach
could be to define a model, and use a Bayesian filtering ap-                            Figure 1. This is an example of the acoustic
                                                                                                       A
proach [15, 14, 9] to do event detection and classification.                           energy profile Et captured.
   Here, we will formulate the problem in the Bayesian fil-
tering framework. We will develop a new semi-Markov en-
ergy dynamical model, based on a neuron spike model [15],                    The energy profiles show that besides the actual events,
which can describe the changes in acoustic and seismic en-                there are other noise events that can be potentially mistaken
ergy level. In this model, the event start time is unknown, as            as an actual event. Furthermore, the events may be closely
well as the length of the event. Different types of event will            spaced. It may not be easy to use heuristic rules to separate
   ∗ Sze Kim Pang, Geok Lian Oh, Shanguo Lu and Adrian Yap Cheng
                                                                          the two events.
Lock are with the Sensors Division of DSO National Laboratories, 20
                                                                             We will now develop a reasonable dynamical model for
                                                                                                         A
Science Park Drive, Singapore 118230. (emails: {pszekim, ogeoklia,        the acoustic energy profile Et . First, the events resemble
lshanguo, ychenglo}@dso.org.sg)                                           some impulses with finite rise time. The rise time may be

                                                                      1
                          40

                                                                                                                       A    A                       Tsamp A
                          30                                                                                          Et − Et−1         =       −      A
                                                                                                                                                                  A
                                                                                                                                                         (Et−1 − Eb ) + AA It
                                                                                                                                                                         k
                                                                                                                                                     τd
                                                                                                                                                  A
                          20
                                                                            Event 1                                                             +σP     Tsamp ǫA
                                                                                                                                                               t                 (3)
 Seismic Energy ZS(dB)




                                     Event 1
                 t




                          10                                                                                      Here, the impulse train It will last a randomn time length
                                                                             Event 2
                                          Event 2             Event 2                                             of τk . k ∈ {1, 2} here refers to the type of event. For sim-
                           0
                                                                                                                  plicity of the model, in this paper, the impulse train time
                         −10
                                                                                                                  length τk is chosen to be some integer multiples of the ob-
                                                                                                                  servation sampling time Tsamp . In more general case, the
                         −20                                                                                      impulse train time length is a continuous time variable [3].
                                                                                                                  The length of the impulse train is a randomn quantity. This
                         −30                                                                                      can be used to model different classes of event, as well mod-
                           1300   1400   1500   1600   1700   1800   1900   2000   2100   2200   2300
                                                                                                                  elling the variation of event length. This results in a semi-
                                                                                                                  Markov model [3, 9], as we will see in the subsequent sec-
                                                                                                                  tion. For the observation model, we use a additive standard
           Figure 2. This is an example of the seismic                                                                              A                            A
                                                                                                                  Gaussian noise νt with standard deviation σZ as follows
                           S
           energy profile Et captured.
                                                                                                                                     A             A    A A
                                                                                                                                    Zt          = Et + σZ νt .                   (4)

different for differnt types of event, and it can potentially be                                                     We assume that the events are mutually exclusive, i.e. at
random. Second, different types of event may give rise to                                                         any one time instance, there can only be one type of event
different sizes of impulse. Third, the reduction of energy af-                                                    happening. Furthermore, we also introduce independent
ter an event resembles an exponential decay with some time                                                        shot noise into each of the sensors to model more impul-
            A                            A
constant τd to a baseline level of Eb . Here we assume                                                            sive disturbances when no event occurs, i.e.
that the exponential decay is affected only by the surround-
ing environment where the sensor is located. Hence, if the
                                                                                                                     A    A                     Tsamp A       A      A A
surrounding is full of buildings, then we will expect the de-                                                       Et − Et−1       =       −        (Et−1 − Eb ) + Bt γt +
                                                                                                                                                 τdA
cay time to be longer due to more reverberation. Fourth,
                                                                                                                                             A
we model the dynamics to have some Gaussian noise un-                                                                                       σP       Tsamp ǫA
                                                                                                                                                            t                    (5)
certainty.
                                                                                                                            A                                   A
    A model that has been used in literature for modelling                                                        where γt is a Bernoulli randomn variables, Bt is the ran-
neuron spikes [15] has very similar properties. This is given                                                     domn amplitude of the shot noise and PShot is the probabil-
by                                                                                                                ity of a shot noise.


                          A    A                           Tsamp A                                                               A
                                                                                                                                γt            A
                                                                                                                                         ∼ B(γt |PShot Tsamp )                   (6)
                         Et − Et−1              =      −      A
                                                                         A
                                                                (Et−1 − Eb ) + AA nt
                                                            τd                                                                   A
                                                                                                                                Bt             A
                                                                                                                                         ∼ U(Bt |bA , bA )                       (7)
                                                                                                                                                  l    u
                                                         A
                                                       +σP      Tsamp ǫA ,
                                                                       t                                (1)
                                                                                                                  where U(·|a, b) is a continuous uniform distribution be-
where AA is the amplitude of the impulse, σP is the stan-
                                               A                                                                  tween a and b.
                                      A                                                                              Figure 3 and 4 show an example of the output of the
dard deviation of the process noise, ǫt is a standard Gaus-
sian variable and Tsamp is the observation sampling time.                                                         acoustic energy profile dynamical model for two different
Here, for each neuron spike, the event is modelled by nt ,                                                        types of event. It shows the relationship for the event nt ,
                                                                                                                                                              A
which is a Bernoulli random variable with probability of                                                          the impulse train It and the energy profile Et .
event PEvent , i.e.                                                                                                  A similar set dynamic and observation equations can be
                                                                                                                  developed for the seismic sensor,

                                     nt ∼ B(nt |PEvent Tsamp ) .                                        (2)
                                                                                                                       S    S                    Tsamp S
                                                                                                                      Et − Et−1      = −            S
                                                                                                                                                               S
                                                                                                                                                      (Et−1 − Eb ) + AS It
                                                                                                                                                                      k
   While the above model generally describe the energy                                                                                            τd
                                                                                                                                               S
profile, it is not able to describe the finite rise time of events                                                                             +σP        Tsamp ǫS
                                                                                                                                                               t                 (8)
shown in Figure 1 and 2. However, if we now instead of                                                                          S
                                                                                                                               Zt    =   +    S
                                                                                                                                             Et         S S
                                                                                                                                                       σZ νt    (9)
using a single impulse nt , but consider the event as a result
                                                                                                                       S    S           Tsamp S     S      S S
of a series of smaller impulses or a impulse train It , it can                                                        Et − Et−1      = − S (Et−1 − Eb ) + Bt γt
be better at modelling the energy profile. The new model                                                                                  τd
                                                                                                                                               S
with finite rise time can be written as                                                                                                       +σP        Tsamp ǫS
                                                                                                                                                               t                (10)

                                                                                                              2
   Figure 5 and 6 plot the generated observations from the
                                                                                               1
dynamical and observation models with empirically fitted




                                                                          Event nt
parameters (Table 1) against the actual acoustic and seismic                                 0.5

energy data. Visually, it shows that there is a reasonable fit
                                                                                               0
between the data and the model.                                                                350   400   450   500     550      600   650   700   750
                                                                                              1




                                                                         Impulse Train It
                                                                                             0.5
 Model Parameter                     Symbol         Value
 Time interval between measure-       Tsamp          0.5s                                     0
                                                                                              350    400   450   500     550      600   650   700   750
 ments
                                         S
 Seismic Decaying Time Con-             τd           8.0s




                                                                              A
                                                                                               0




                                                                      Energy Et
 stant                                                                                       −20
                                          S
 Seismic Energy Ambient Level           Eb       −15.0 dB                                    −40
                                                         1
                                          S
 Seismic Process Noise                  σP        0.70dB 2                                     350   400   450   500     550      600   650   700   750
                                                         1                                                             Time (s)
                                          S
 Seismic Observation Noise              σZ        1.25dB 2
                                       S S
 Seismic Shot Noise Amplitude         bl , bu   5dB to 10dB
 Range
                                         A                             Figure 3. These figures show the relation-
 Acoustic Decaying Time Con-            τd           9.6s
                                                                       ships between the event nt , impulse train It
 stant                                                                                   A
                                          A
                                                                       and energy level Et for two closely spaced
 Acoustic Energy Ambient Level          Eb         −36dB               Event 1.
                                                         1
                                          A
 Acoustic Process Noise                 σP        0.75dB 2
                                                       1
                                          A
 Acoustic Observation Noise             σZ         2dB 2
                                       A A
 Acoustic Shot Noise Amplitude        bl , bu   5dB to 15dB
 Range                                                                                         1
 Event 1 Parameters
                                                                          Event nt




 Mean Impulse Train Time               τ1             8s                                     0.5

 Seismic Impulse Level                 AS
                                        1           3.5dB
                                                                                               0
 Acoustic Impulse Level                AA
                                        1          4.75dB                                      350   400   450   500     550      600   650   700   750
                                                                                               1
 Event 2 Parameters
                                                                          Impulse Train It




 Mean Impulse Train Time               τ2            17s                                     0.5
 Seismic Impulse Level                 AS
                                        2           0.5dB
 Acoustic Impulse Level                AA
                                        2          0.75dB                                      0
                                                                                               350   400   450   500     550      600   650   700   750
                                                                              A




                                                                                               0
                                                                      Energy Et




   Table 1. Parameters for the Energy Profile Dy-                                             −20

   namical Model                                                                             −40
                                                                                               350   400   450   500     550      600   650   700   750
                                                                                                                       Time (s)




                                                                       Figure 4. These figures show the relation-
3 Bayesian Framework                                                   ships between the event nt , impulse train It
                                                                                         A
                                                                       and energy level Et for a single Event 2.

   We now define a suitable Bayesian framework to do
the event detection and classification using the seismic and
acoustic energy observations introduced in the previous sec-        3.1                        Dynamical Model
tion.
   We first defined all the state variables. Let nt ∈ {0, 1}
                                                  S        A
represents whether there is an event at time t. Et and Et
                                                                      We are now ready to define the full dynamical model
represent the seismic and acoustic energy state respectively.
                                                                    p(St |St−1 ). We choose to expand the model according to
Let θt ∈ {0, 1, 2} represents the type of event. Event type
                                                                    Eq. (11).
0 here refers to the ambient condition where no event is
happening. Let τt be the randomn length of the current                 The dynamical model is moderately complex, as it has to
event, and Ct be the corresponding time sample at which             take into account the semi-Markov nature of each event, as
the current event happened. Also, let the joint state be            well as dealing with different types of possible events. Now
             A    S
St = {nt , Et , Et , θt , Ct , τt }.                                we give more details on each of the transition models.

                                                                3
                                                               p(St |St−1 )
                                                                          A   S                         A      S
                                                               = p(nt , Et , Et , θt , Ct , τt |nt−1 , Et−1 , Et−1 , θt−1 , Ct−1 , τt−1 )
                                                               = p(nt |nt−1 , Ct−1 , τt−1 )p(Ct |Ct−1 , τt−1 , nt )p(θt |θt−1 , Ct−1 , τt−1 , nt )
                                                                                                A   A            S    S
                                                               ×p(τt |τt−1 , Ct−1 , nt , θt )p(Et |Et−1 , θt )p(Et |Et−1 , θt )                                                                                       (11)



                           20                                                                                                              40
                                      Event 1
                                                               Actual Observations                                                                                             Actual Observations
                           10                                  Generated Observations                                                      30                                  Generated Observations


                                                                                    Event 1
                            0                                                                                                              20
Acoustic Energy ZA (dB)




                                                                                                                                                                                              Event 1




                                                                                                                  Seismic Energy ZS(dB)
                                                                                                                                                       Event 1
                                                                 Event 2                Event 2
                 t




                                                                                                                                  t
                          −10              Event 2                                                                                         10
                                                                                                                                                                                               Event 2
                                                                                                                                                           Event 2              Event 2
                          −20                                                                                                               0


                          −30                                                                                                             −10


                          −40                                                                                                             −20


                          −50                                                                                                             −30
                            1300   1400   1500   1600   1700     1800 1900   2000   2100     2200   2300                                    1300   1400   1500   1600   1700    1800   1900   2000   2100   2200   2300
                                                               Time (s)




           Figure 5. This figure plots the actual acoustic                                                                   Figure 6. This figure plots the actual seismic
           energy and the synthetic energy profile dy-                                                                       energy and the synthetic energy profile dy-
           namical model output together. This shows                                                                        namical model output together. This shows
           that the energy profile dynamical model is                                                                        that the energy profile dynamical model is
           flexible enough to model different types of                                                                       flexible enough to model different types of
           events.                                                                                                          events.


1. p(nt |nt−1 , Ct−1 , τt−1 )                                                                                                             event occurs, i.e. nt = 1, Ct is set to the current time
                                                                                                                                          t.
                                   p(nt |nt−1 , Ct−1 , τt−1 )
                                                                                                                  3. p(θt |θt−1 , Ct−1 , τt−1 , nt )
                                         0                    if t < Ct−1 + τt−1 ;
                                   =
                                         B(nt |PEvent Tsamp ) Otherwise.                                                                           p(θt |θt−1 , Ct−1 , τt−1 , nt )
                                                                                                                                                     
                                                                               (12)                                                                   θt−1                   if t < Ct−1 + τt−1 ;
                                                                                                                                                   =      rand(0.5, 0.5) if t ≥ Ct−1 + τt−1 , nt = 1;
                          Here, the current event happened at τt−1 and it lasts                                                                      
                                                                                                                                                          0                   if t ≥ Ct−1 + τt−1 , nt = 0.
                          a length of Ct−1 time samples. If the current event is
                                                                                                                                                                                                        (14)
                          active, i.e. t < Ct−1 +τt−1 , then there is no possibility
                          of a new event happening. Otherwise, at each time                                                               If the current event is active, the current type of event
                          step, the probability for a new event is given by the                                                           θt remains unchanged from θt−1 . If there is currently
                          Bernoulli process Eq. (2).                                                                                      no event happening, θt is kept at 0. This represents
                                                                                                                                          the ambient condition. When a new event occurs, i.e.
2. p(Ct |Ct−1 , τt−1 , nt )                                                                                                               nt = 1, θt is set to the event 1 or 2 with equal proba-
                                     p(Ct |Ct−1 , τt−1 , nt )                                                                             bility (as indicated by the discrete random distribution
                                                                                                                                         rand(0.5, 0.5)).
                                        Ct−1 if t < Ct−1 + τt−1 ;
                                     =     t        if t ≥ Ct−1 + τt−1 , nt = 1;                                  4. p(τt |τt−1 , Ct−1 , nt , θt )
                                           0        if t ≥ Ct−1 + τt−1 , nt = 0.
                                       
                                                                                                                                                   p(τt |τt−1 , Ct−1 , nt , θt )
                                                                                                       (13)                                          
                                                                                                                                                      τt−1                           if t < Ct−1 + τt−1 ;
                          If the current event is active, the time of the current                                                                  =      Ud (·|τθt − τr , τθt + τr ) if t ≥ Ct−1 + τt−1 , nt = 1;
                                                                                                                                                          0                           if t ≥ Ct−1 + τt−1 , nt = 0.
                                                                                                                                                     
                          event Ct remains unchanged from Ct−1 . If there is no
                          new event happening, Ct is kept at 0. When a new                                                                                                                                      (15)

                                                                                                              4
      If the current event is active, the current length of event       where Z1:t = [Z1 · · · Zm · · · Zt ] are the observations and
      τt remains unchanged from τt−1 . If there is no event             δ(·) denotes the Dirac delta function. The weight wt,p , of
      happening, τt is kept at 0. When a new event occurs,              the particle p, is updated according to
      i.e. nt = 1, τt is drawn from a discrete uniform dis-
      tribution Ud (·|·, ·) between τθt − τr and τθt + τr . τθt                                 p(Zt |St,p )p(St,p |St−1,p )
                                                                             wt,p = wt−1,p ×                                      (20)
      is the mean value of the length of the event θt . This                                       q(St,p |St−1,p , Zt )
      models the random nature of the length of the different
      type of events. For simplicity of the model, the ran-             The choice of the importance density q(St,p |St−1,p , Zt ) is
      domn length τt will be some discrete multiples of the             an important issue in particle filter design. It can be shown
      observation time Tsamp .                                          that the optimal importance density (in the sense of mini-
        A   A                 S   S
                                                                        mizing the variance of the importance weights), conditioned
  5. p(Et |Et−1 , θt ) and p(Et |Et−1 , θt )                            upon St−1,p and Zt is p(St,p |St−1,p , Zt ) [1]. However, the
                                             A        S
      The acoustic and seismic energy level Et and Et can               optimal importance density is generally not tractable. There
      be determined from Eq. (3), (5), (8) and (10), condi-             are other suboptimal choices. For example, a popular choice
      tional on the type of event θt .                                  is to use the prior model density p(St,p |St−1,p ). When sub-
                                                                        stituted into Eq. (20), we obtain
3.2     Observation Model
                                                                                     wt,p = wt−1,p × p(Zt |St,p )                 (21)
   The observation models will be based on Eq. (4) and
                  A    S
(9). Let Zt = {Zt , Zt }. We will assume that conditional               The simple and general algorithm above forms the basis of
on the state St the observation of the acoustic and seismic             most particle filters. However, it will result in the variance
sensors are independent, i.e.                                           of the importance weights increasing over time [1]. This
                                                                        will adversely affect the accuracy and lead to the degen-
                                                                        eracy problem where, after a certain number of recursive
                           A   A     S   S
           p(Zt |St ) = p(Zt |Et )p(Zt |Et )                (16)        steps, all but one particle will have negligible normalized
                                                                        weights. This will result in a large computational effort de-
                                                                        voted to updating particles whose contribution to the ap-
4 Inference Algorithm
                                                                        proximation of p(St |Z1:t ) is almost zero. A practical mea-
                                                                        sure of the degeneracy of the particle weights is the effective
  Assuming a Markovian state transition, the standard state             sample size Nef f introduced in [7]:
update and prediction equations are given by
                                                                                                              −1
                            p(Zt |St )p(St |Z1:t−1 )                                                Np
             p(St |Z1:t ) =                                 (17)                       Nef f =           wt,p 2                 (22)
                                p(Zt |Z1:t−1 )
                                                                                                    p=1

 p(St |Z1:t−1 ) =     p(St |St−1 )p(St−1 |Z1:t−1 ) dSt−1 (18)           It is easy to see that 1 ≤ Nef f ≤ Np . A small Nef f indi-
                                                                        cates a degeneracy problem. When this occurs (for example
with Z1:t = [Z1 · · · Zm · · · Zt ].
                                                                        when Nef f drops below some threshold Nthr ), a step called
                                                                        resampling [4] has to be performed. Resampling eliminates
4.1     Particle Filter                                                 sample with low weights and multiplies samples with high
                                                                        importance weights. This involves mapping a random mea-
    The filtering distribution of the dynamical and observa-                                Np                                  1 Np
                                                                        sure {St,p , wt,p }p=1 into a random measure {St,p , Np }p=1
tion probability model above is complex and non-linear.                 with uniform weights.
Sequential Monte Carlo methods such as particle filters
                                                                            There are several methods available when implementing
[12] can be used to do the inference. A particle fil-
                                                                        the remapping step. The first introduction of resampling
ter represents the required posterior density function by
                                                                        [4] uses random sampling of the particles based on their
a set of random samples (or particles) with associated
                      Np                                                weights. However, a complete random selection is not nec-
weights {St,p , wt,p }p=1 . These particles are then propa-             essary and it increases the Monte Carlo variation of the par-
gated through time to give predictions of the posterior dis-            ticles. Other methods such as stratified sampling [6] and
tribution function at future time steps. As the number of               residual sampling [8] may be applied. Systematic resam-
samples tends to infinity, this Monte Carlo characterization             pling [6] is another efficient method. It is simple to im-
becomes an equivalent representation to the functional de-              plement, it has order Np computational complexity and it
scription of the posterior density function. The posterior              minimizes the Monte Carlo variation.
filtered density at time t is approximated by
                                                                            In this paper, we make use of a particle filter to perform
                              Np                                        the inference. We use the prior p(St |St−1 ) as the impor-
             p(St |Z1:t ) ≈         wt,p δ(St − St,p )      (19)        tance function. For the resampling step, we use the system-
                              p=1                                       atic resampling method.

                                                                    5
4.2    State Regeneration                                                                        Parameter                                                               Symbol            Value
                                                                                                 Number of Particles                                                       NP               2000
    In the particle filter above, the simulation of the current                                   Probability of an Event                                                 PEvent            0.0025
event time length τt is not efficient. This is due to the fact                                    Probability of a Shot Noise                                              PShot             0.05
that the end of the current event Ct +τt is typically well into                                  Effective Sample Size Thresh-                                            Nthr              1800
the future. In the particle filter, once τCt is sampled at the                                    old
start of the event at time Ct , the state is never regenerated                                   Single sided range for event                                                  τr               4
and the particles can attain low weights at some point in                                        length
the future. The use of resampling also serve to deplete the
posterior representation of the particles. This can be address
by regenerating the values τCt :t .                                                              Table 2. Parameters for the Event Detection
    We will adopt the same approach as described in Godsill                                      and Classification Algorithm
and Vermaak [3]. We will regenerate the values τCt :t only
if does not affect any of the current or previous likelihood
computation. After resampling, for each particle, we will
                                                                                                                        1
regenerate the values τCt :t if t < Ct + τθt − τr . This is




                                                                                                   Event nt
given by                                                                                                              0.5

                                                                                                                        0
                                                                                                                            0         200         400              600              800         1000
                                                                                                                                                        Time (s)
                        A      S
      p(τCt :t |n0:t , E0:t , E0:t , θ0:t , C0:t , τ0:(Ct −1) , Z1:t )
                                                                                                   Impulse Train It
                                                                                                                        1

                             A     S
      = p(τCt :t |n0:t , E0:t , E0:t , θ0:t , C0:t , τ0:(Ct −1) )                                                     0.5

        (if t < Ct + τθt − τr )                                                                                         0
                                                                                                                            0         200         400              600              800         1000
            t                                                                                                                                           Time (s)

      =               p(τt′ |τt′ −1 , Ct′ −1 , nt′ , θt′ )                                                              2
                                                                                                   Event Type θt




          t′ =C   t                                                                                                     1
                                                             t
                                                                                                                        0
      = Ud (τCt |τθCt − τr , τθCt + τr )                                δ(τt′ − τCt )                                       0         200         400              600              800         1000
                                                                                                                                                        Time (s)
                                                      t′ =C      t +1

                                                                                 (23)

5 Results                                                                                        Figure 7. This is the ground truth for Simula-
                                                                                                 tion Scenario 1.
  In this section, we will demonstrate the joint detection
and classification results of the models described above.
                                                                                                                       40

5.1    Simulation Scenario 1                                                                                           20
                                                                                            Seismic ZS
                                                                                                     t




                                                                                                                        0
   In this scenario, we will use the dynamical model to gen-
erate a set of observations. Figure 7 shows the ground truth                                                          −20

of the events. There are 8 events, with 4 of them closely                                                                       100   200   300   400     500    600     700        800   900   1000
                                                                                                                                                        Time (s)
spaced between 750s and 820s. Figure 8 shows the syn-
                                                                                                                       20
thetic seismic and acoustic observations generated using dy-
namical model described in Section 2, and the parameters in                                                             0
                                                                                            Acoustic ZA
                                                                                                      t




Table 1.
                                                                                                                      −20
   Figure 9 shows the results of the detection and classifi-
cation using the particle filter described in Section 4, with                                                          −40

parameters in Table 2. The event probability shows that all                                                                     100   200   300   400     500    600     700        800   900   1000
                                                                                                                                                        Time (s)
the 8 events are detected, even with the 4 targets closely
spaced between 750s and 820s. The classification also ac-
curately recognised all the 8 events.
                                                                                                 Figure 8. This is the set of synthetic seis-
5.2    Real Data Set 1                                                                           mic and acoustic observations for Simulation
                                                                                                 Scenario 1.
   Here we will use the same method to analyse a set of real
data. In this set of data, there are a total of 16 events. This
can be seen in the manually-tagged ground truth in Figure

                                                                                        6
                                   1                                                                                                                           40
   Event Probability




                                  0.8
                                                                                                                                                               20




                                                                                                                        Seismic ZS
                                                                                                                                 t
                                  0.6

                                  0.4                                                                                                                           0

                                  0.2
                                                                                                                                                              −20
                                   0
                                            100    200   300     400     500    600     700   800     900   1000                                                    500   1000     1500     2000   2500   3000
                                                                       Time (s)                                                                                                  Time (s)
   Classification Probabilities




                                   1                                                                                                                           20

                                  0.8
                                                                                                                                                                0




                                                                                                                        Acoustic ZA
                                                                                                                                  t
                                  0.6

                                  0.4                                                                                                                         −20

                                  0.2
                                                                                                                                                              −40
                                   0
                                            100    200   300     400     500    600     700   800     900   1000                                                    500   1000     1500     2000   2500   3000
                                                                       Time (s)                                                                                                  Time (s)




   Figure 9. These figures show the Event Prob-                                                                               Figure 11. This is the set of seismic and
   ability and Classification Probabilities (Blue                                                                             acoustic observations for Real Data Set 1.
   for Ambient, Red for Event 1 and Green for
   Event 2).
                                                                                                                                                                1
                                                                                                                               Event Probability

                                                                                                                                                              0.8

                                                                                                                                                              0.6
10. Figure 11 shows the actual observations by the seismic
                                                                                                                                                              0.4
and acoustic sensors.
                                                                                                                                                              0.2
   Figure 12 shows the result of the detection and classifi-
                                                                                                                                                                0
cation. Almost all the events are detected at probability of                                                                                                        500   1000     1500     2000   2500   3000
                                                                                                                                                                                 Time (s)
0.8 and above. The classification of events are all correct,
                                                                                                                               Classification Probabilities




                                                                                                                                                                1
except for an unusual deviation of Event type 1 at around
                                                                                                                                                              0.8
2750s.
                                                                                                                                                              0.6

                                                                                                                                                              0.4
                                   1
                                                                                                                                                              0.2
    Event nt




                                  0.5                                                                                                                           0
                                                                                                                                                                    500   1000     1500     2000   2500   3000
                                                                                                                                                                                 Time (s)
                                   0
                                        0         500     1000           1500         2000     2500         3000
                                                                       Time (s)
   Impulse Train It




                                   1

                                  0.5                                                                                        Figure 12. These figures show the Event
                                                                                                                             Probability and Classification Probabilities
                                   0
                                        0         500     1000           1500
                                                                       Time (s)
                                                                                      2000     2500         3000             (Blue for Ambient, Red for Event 1 and Green
                                   2                                                                                         for Event 2).
         Event Type θt




                                   1

                                   0
                                        0         500     1000           1500         2000     2500         3000       also developed a complete Bayesian model for the joint
                                                                       Time (s)
                                                                                                                       event detection and classification. This is based on a flexi-
                                                                                                                       ble semi-Markov model formulation, which generalises the
                                                                                                                       sojourn time of typical Markov models. We have also de-
   Figure 10. This is the ground truth for Real                                                                        signed a particle filter to do the inference. Both the synthetic
   Data Set 1.                                                                                                         and real data results show good detection and classification
                                                                                                                       performances. Further work includes looking at other type
                                                                                                                       of events that can be modelled by the same type of dynami-
                                                                                                                       cal model.
6 Concluding Remarks
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