Adaptive Target Tracking by Noise-Estimated Particle filter
Masanori Ishibashi∗
Yumi Iwashita∗∗
Ryo Kurazume∗∗∗This paper proposes a new radar tracking ﬁlter named Noise-estimate Particle Filter (NPF). Kalman ﬁlter and particle ﬁlter are popular ﬁltering techniques for target tracking. The tracking performance of the
Kalman ﬁlter severely depends on the setting of several parameters such as system noise and observationnoise. However, it is an open problem how to choose proper parameters for various scenarios, and they areoften regulated in trial-and-error manner. The proposed ﬁlter estimates proper noise parameters of a Kalmanﬁlter on-line based on a scheme of particle ﬁlter. Simulation results show that the proposed ﬁlter has higher
tracking performance in various scenarios than conventional Kalman ﬁlter and particle ﬁlter.
Keywords: Radar tracking, Particle filter, Kalman filter, Marginalized Particle Filter, Rao-Blackwellizationceleration/deceleration. In addition, an observation error which represents the accuracy of sensor/radar andhas to be adjusted beforehand aﬀects the performanceof the Kalman ﬁlter, too. The observation model isalso diﬃcult to be set appropriately for various targets
with a variety of shapes, motion directions, heights, distances, etc. Currently, a target tracking system basedon Kalman ﬁlter has to be designed with proper system parameters in a try-and-error manner to meet thedesired performance (1) .
In few decades, particle ﬁlter has been attracting muchattention as a high-performance tracking ﬁlter. In particle ﬁlter, instead of estimating the probability distribution of the object state from the past observation andmotion model in a parametric way, the probability distribution is represented by a set of particles. Each particle
has a weight which represents the probability of the stateof the particle. The particle is updated and re-sampledaccording to the Bayesian recursion equation.
Particle ﬁlter has been applied to various applications
such as human tracking, state estimation, etc. (2)∼(8) .
Particle ﬁlter does not depend on the assumption of
linear or gaussian noise, and is able to be applied forvarious systems even with non-linear and non-gaussian
noise. However, the particle ﬁlter is less eﬀective thanthe optimized Kalman ﬁlter for a target moving by amotion model, and the improvement of the tracking performance for various conditions is an open problem inparticle ﬁlter.
This paper proposes a new tracking ﬁlter named thenoise-estimated particle ﬁlter (NPF), which combines
Kalman ﬁlter and particle ﬁlter. As mentioned above,
Kalman ﬁlter is an optimum ﬁlter in case that the motion model of targets and observation model of sensor/radar are correctly provided. In the proposed ﬁlter, instead of estimating the state of the target such as
position or velocity directly, the system error and theobservation error are estimated on-line by particle-ﬁlter
based approach. More correctly, the state of the tar-

1. Introduction
Target tracking is a fundamental technique in not only
computer vision but also various application ﬁelds. For
example, in air traﬃc control by a radar sensor, multiple high-speed ﬂight vehicles must be tracked simultaneously without lost-tracking while estimating theirvelocities and heights. However, in general, radar data
is severely corrupted by noise due to atmospheric conditions or radar reﬂection property of the target, and it
is still challenging to track targets stably under severe
noisy condition.
For target tracking, a time series ﬁlter is very eﬀective to suppress noise in sensory data and track targets
smoothly and stably. In a time series ﬁlter, the current
target position, which is estimated based on past observation and a motion model, are merged with current
observation and the optimum position is derived. Especially, the time series ﬁlter which removes the noise
component in the radar data and estimates the current
position and velocity of the target is called ”tracking
ﬁlter”.
Kalman ﬁlter is the most popular and widely-usedtracking ﬁlter and has been applied to various applications so far. Based on the assumptions on linear andgaussian noise in sensory data, this ﬁlter estimates thestatistically-optimized state of the target. Uniform linear motion is usually adopted as a motion model in simple Kalman ﬁlter. In case that target motion does notfollow the uniform linear model, a system noise parameter which should be adjusted beforehand to absorb thesystem error aﬀects the tracking performance severely.
However, it is an open problem how to choose a proper
value of the system noise parameter beforehand for various scenarios such as non-linear motion or rapid ac∗

Kyushu University, ishibashi@irvs.ait.kyushu-u.ac.jp
Kyushu University, yumi@ait.kyushu-u.ac.jp∗∗∗
Kyushu University, kurazume@ait.kyushu-u.ac.jp744, Motooka, Nishi-ku, Fokuoka, Japan 819-0395∗∗

FCV20141

where ∆t is a sampling interval, I is an identity matrix, and H = (I 0) is an observation matrix. wki is avector of system noise with an average 0 and an error
covariance matrix Qik , respectively. vki is also a vector of observation noise with an average 0 and an error
covariance matrix Rik .

get is estimated based on Kalman ﬁlter, and its motion
noise and observation noise are optimized by particle ﬁlter. Since the critical parameters of the Kalman ﬁlter are
adjusted on-line according the observation, the proposedﬁlter can be applied for a variety of target motions including not only uniform linear motion, but also sudden
motion changes such as abrupt acceleration/deceleration
or steep turn.
Some authors proposed combination ﬁlters of particle
ﬁlter and Kalman ﬁlter (9)∼(12) . Rao-Blackwellized Particle Filters (11) is the most popular technique in SLAM
(Simultaneous Localization and Mapping). Localizationand mapping procedures are separated in this ﬁlter andimplemented using particle ﬁlter and Kalman ﬁlter, individually. Marginalized Particle Filter proposed Schonet al. (12) separates linear and nonlinear parts in the control system and assigns Kalman ﬁlter and particle ﬁlter
separately. However, to our best knowledge, the proposed ﬁlter which utilizes particle ﬁlter for estimating
the parameters of optimum Kalman ﬁlter has not been
proposed so far. Satoh et al. (10) proposed a color-based
tracking technique using Kalman Particle Filter (9) . As
the noise-estimated particle ﬁlter proposed in the paper,
the state of each particle si updated by Kalman ﬁlter.
In their method, however, the observation noise is determined according to the weight of the particle and thestate noise is determined previously.

2.1.2 Tracking process
A set of particles at{ i i i i }Ntime tk is deﬁned as Xk = xk , wk , qk , rk i=1 . Here, xik
is a hypnosis for a state vector of position and velocity,
wki is a weight of each particle, and qki and rki are systemand observation noises at each particle, respectively.
{( 1 ) Produce N initial particles X0 = xi0 , w0i , q0i ,}N
r0i i=1 . The position, velocity, and system andobservation noises are set with random numbers
in particular ranges.
( 2 ) Execute step (a) to step (f) at time tk (k =1, · · · , T )(a) Estimation
Execute prediction procedure in each particle
by Kalman ﬁlter and estimate the current statefrom the previous state and the motion model.
xik|k−1 = Φk xik−1|k−1 · · · · · · · · · · · · · · · · · (4)Pik|k−1 = Φk Pik−1|k−1 ΦTk + Qik · · · · · · · (5)where xik|k−1 is an estimated state in each particle and xik−1|k−1 is a previous state at time tk−1 .
Pik|k−1 is an error covariance matrix in each particle and Pik−1|k−1 is an previous error covariancematrix at time tk−1 .
An error covariance matrix of system noise Qik
at time tk is obtained
follows.
}{ 2 as22
Qik = diag qki , qki , qki · · · · · · · · · · · · · · (6)(b) Smoothing
To ﬁt the estimated state with the current
observation and estimate more accurate state,smoothing process in Kalman ﬁlter is applied ineach particle.
xik|k = xik|k−1 + Kik [zk − Hxik|k−1 ] · · · · (7)2. Noise-estimated Particle Filter (NPF)
In the noise-estimated particle ﬁlter (NPF), a numberof Kalman ﬁlters with a variety of sets of parameters
runs simultaneously in a parallel way. As conventional
particle ﬁlter, particles are re-sampled according to theerrors between the estimated and observed states. By
evaluating the performance of a number of Kalman ﬁlters with a variety of motion and observation parameters
estimated adaptively, optimum target tracking which
has similar high performance as optimized Kalman ﬁlter for a ﬁxed condition is achieved for various motion
pattens including uniform linear motion, abrupt acceleration/deceleration or steep turn.
2.1 Estimation of system and observationnoise parameters2.1.1 Model definition
In the proposed tracking ﬁlter, each particle executes a similar process as
Kalman ﬁlter individually. Firstly, a state space model
for a target system is deﬁned in each particle.

Pik|k = (I − Kik H)Pik|k−1 · · · · · · · · · · · · · (8)Kik = Pik|k−1 HT [HPik|k−1 HT + Rik ]−1 (9)where xik|k is the estimated state of the particle
at time tk , Pik|k is the estimated error covariancematrix in each particle, and Kik is a gain matrix.
The error covariance matrix of observation noise
Rik at time tk is obtained as follows.
222
Rik = diag{rki , rki , rki } · · · · · · · · · · · · · · (10)(c) Likelihood calculation
The likelihood p(zk |xik|k ) at each particle is calculated as follows.
( 2)
1
−di
p(zk |xik|k ) = √· · · · · (11)
exp
2
2σs2
2πσs
where σs is a parameter to evaluate the accuracyof the hypnosis, di is an Euclidean distance between the position compornent in xik|k and the observed position zk . In the following experiments,
we set σs = 300.

xik+1 = Φk xik + wki · · · · · · · · · · · · · · · · · · · · · · · · · (1)zik = Hxik + vki · · · · · · · · · · · · · · · · · · · · · · · · · · · (2)Eq.(1) is a motion model which represents a state transition and Eq.(2) is an observation model which shows
the relation of estimated and observed states. xik is astate vector which contains position and velocity terms.
Φk is a state transition matrix and, in this paper, theuniform linear motion is assumed in all particles as follows.
(
)
I ∆tI
Φk =
· · · · · · · · · · · · · · · · · · · · · · · · · · (3)0I
2FCV2014

Adaptive Target Tracking by Noise-Estimated Particle filter
up,i
up,i
up,i
qk−1
= qk−1+ ∆qk−1· · · · · · · · · · · · · · (16)Next, the weight of each particle is updated according to the obtained likelihood as follows.
iwki = wk−1
p(zk |xik|k ) · · · · · · · · · · · · · · · · · (12)In addition, the sum of the weight of all partii
cles is calculated by Wk = ΣN
i=1 wk and the weightof each particle is normalized as wki = wki /Wk .
(d) State estimation
Estimated state x̂k at time tk is calculated by
the weighted mean of N particles.
N
∑
x̂k ≈
wki xik|k · · · · · · · · · · · · · · · · · · · · · · (13)down,idown,iqk−1= αqk−1· · · · · · · · · · · · · · · · · · · · (17)up,iIn the above procedure, ∆qk−1
is given by anormal distribution of an average 0 and a variance σup , and α is a uniform distribution within[0, σdown ]. σup and σdown are control parameters.
In the following experiments, we set σup ≈ 100 ∼1000 and σdown ≈ 0.1. Consequently, Xkup is agroup of particles with a relatively large system
noise and Xkdown is a group with a system noise
smaller than the previous state.
up( 2 ) For these two groups of particles Xk−1
anddown
, update, smoothing and likelihood calcuXk−1
lation procedures are applied and new groups ofparticles at current period Xkup and Xkdown are
produced.
( 3 ) Choose N particle according to the following
rules.
• According to the observed data zk , P particles of Xkdown are selected among the particles
within the range of the sensor observation error. More correctly, particles which meet thefollowing condition are selected.
|zk − xdown,i| < C · σR · · · · · · · · · · · (18)kwhere σR is the accuracy of the radar. C isa gain parameter and controlled to be small
if the variance of particles is large, and to belarge if the variance is small, using a sigmoid
function and the variance of all the particles
σx as follows.
cC=+ d · · · · · · · · · · (19)
−a(−σ
x +b)
1+e
where a ∼ d are parameters of sigmoid function. In the following experiments, we set
a = 40, b = 0.14, c = 1.9, and d = 0.1, and C
is adjusted to vary from 0.1 to 3 according to
the variance of particles.
• N − P particles are selected among Xkup according to the likelihood.
( 4 ) Current particles Xk are replaced with N particles which are selected at Step (3).

i=1(e) Resampling
Particles are re-sampled according the the probability proportional to the weight value wki . As
a result, particles with lower weight are removed
and ones with higher weight are increased.
(f) Update
In contrast to updating position and/or velocity
in a conventional particle ﬁlter, random oﬀset values obtained with a normal distribution are added
to the system noise qki and the observation noiserki , respectively.
qki = qki + ∆qki · · · · · · · · · · · · · · · · · · · · · · · (14)rki = rki + ∆rki · · · · · · · · · · · · · · · · · · · · · · · (15)where ∆qki and ∆rki are determined according to
the normal random number with an average of 0
and a variances of σq and σr , respectively. σq andσr are predetermined parameters, and in the following experiments, we set σq = 0.1 and σr = 5.
2.2 Estimation of system noise parameterIn the previous section, we showed a method to estimate
the system and observation noise parameters simultaneously. However, in some cases, observation noise parameter is given according to the pre-deﬁned accuracy of thesensor/radar, and on-line estimation is unnecessary.
Therefore, this section shows the another techniquewhich estimates the system noise parameter only by the
proposed noise-estimated particle ﬁlter.
2.2.1 Re-sampling procedure
As a result of
preliminary experiments, it was shown that dynamic
range of the optimum system noise is quite large for aradar tracking. For example, the optimum system noisefor a turning motion is about few hundreds in the following experiments. On the other hand, the optimum value
for straight motion should be almost zero to track accurately. To handle this large dynamic range, this section
introduces a new re-sampling technique for radar tracking system.
This re-sampling technique utilizes two kinds of particles. By distributing them in diﬀerent ranges, this ﬁlter
can handle a large dynamic range of the system noise.
The procedure of the re-sampling process is as follows.
( 1 ) Beside a group of particles Xk−1 at tk−1 , two{}Nupup,i up,ikinds of groups Xk−1
= xup,i
,
w
,
q
,
k−1
k−1 k−1i=1{}N
down,i down,i
down
Xk−1
= xdown,iare prok−1 , wk−1 , qk−1
i=1
duced. We adopt two update processes of thesystem noises in each group as follows.
FCV2014

3. Computer simulation
We conduct several computer simulations in order
to compare the performance of the proposed noiseestimated particle ﬁlter, Kalman ﬁlter, and conventional
particle ﬁlters optimized for straight and curved paths.
3.1 Simulation condition
We assume a radar
sensor is placed at the origin of the coordinate and set
the sampling interval as 0.5 [s], the accuracy of the radaras 30 [m] in distance and 0.2 [deg.] in azimuth and elevation angles. The target starts to move from 70 [km]apart from the radar toward the radar with a height of
10[km] and the velocity of 306 [m/s]. Two types of trajectories including straight and curved paths are tested.
For a scenario of the straight path, the target movesby the uniform linear motion between 0 to 150 [sec.].
For a scenario of the curved path, the target moves by
the uniform linear motion between 0 to 50 [sec.] and3

0.2

100 to 150 [sec.], and with the turning motion from 50
to 100 [sec.] during level ﬂight. In this scenario, thetarget turns 1 or 4 times on horizontal plane.
We runs Monte-Carlo simulation in 50 times and evaluates the RMS (Root Mean Square) error. Four typesof tracking ﬁlters are compared( 1 ) Kalman ﬁlters which are adjusted to provide thebest performance at straight path( 2 ) Kalman ﬁlters which are adjusted to provide thebest performance at curved path( 3 ) Conventional particle ﬁlter( 4 ) Proposed noise-estimated particle ﬁlter
The number of particles are 200 for conventional particle ﬁlter and 100 for noise-estimated particle ﬁlter, which
are determined experimentally.
3.2 Estimation of system and observationnoisesTracking results for the proposed noiseestimated particle ﬁlter which estimates system andobservation noises are shown in Fig.1.
In Fig.1,
KF Straight is the Kalman ﬁlter for straight trajectory,KF Curve is the Kalman ﬁlter for curved trajectory, PF
is the conventional particle ﬁlter, and NPF QR is the
proposed noise-estimated particle ﬁlter. In addition, theestimated system and observation noises for 4-turns trajectory are shown in Fig.2.

7
5
4

0.1

3
Turn

2
1

0
0

20

40

60
80
100
Time [sec.]

120

140

Observation noise

System noise

6

0
160

Fig. 2. Estimated system and observation noises(4 turns)(KF Curve). Though the Kalman ﬁlter optimized forstraight trajectory (KF Straight) shows the best performance in straight path, it cannot track the target whileturning at all. In addition, though the tracking delayis occurred for the Kalman ﬁlter for curved trajectory(KF Curve) at 4-turns scenario, the accuracy of the proposed ﬁlter is similar to the conventional particle ﬁlter(PF). Consequently, it is conﬁrmed that the proposed ﬁlter can be applied to various scenarios more adaptively
than other conventional ﬁlters.
3.3 Estimation of system noise
Tracking error for the proposed ﬁlter which estimates the system
noise are shown in Fig.3. NPF Q indicates the proposednoise-estimated particle ﬁlter.

500
RMS Error [m]RMS Error [m]

500
400
300
200
100
0
0

20

40

60
80 100Time [sec.]

120

140

160

400
300
200
100
0
0

20

(a) Straight

300
200
100
20

40

60
80
100
Time [sec.]

120

140

160

0

20

40

RMS Error [m]RMS Error [m]

60
80
100
Time [sec.]

120

140 160(b) 1 turn
Turn

500

300
200
100
0
60
80
100
Time [sec.]

160

100

600

400

40

140

200

0

Turn

20

120

300

600

0

160

400

(b) 1 turn
500

140

Turn

500

400

0

120

600

500

0

60
80 100Time [sec.](a) StraightTurn
RMS Error [m]RMS Error [m]

600

40

120

140

160

400
300
200
100
0
0

(c) 4 turns
Fig. 1. Tracking error (system and observationnoises are estimated)

Fig. 3.

The smoothing performance of the proposed noiseestimated particle ﬁlter (NPF QR) outperforms theconventional particle ﬁlter (PF), and is similar to
the Kalman ﬁlter optimized for curved trajectory20

40

60 80 100
Time [sec.](c) 4 turns
Tracking error (system noise is estimated)

As shown in Fig.3, the tracking error for the straight
trajectory is considerably suppressed against the conventional particle ﬁlter. Moreover, for the curved trajectory in 4-turns scenario, the tracking performance of4

FCV2014

Adaptive Target Tracking by Noise-Estimated Particle filter

the proposed ﬁlter outperforms the conventional particle
ﬁlter.
However, the large delay occurred just after starting
turning motion temporarily and the transient response
is observed. This is because, after tracking in a straightline for a while, X down particles are increased and thesystem noise tends to be ignored, and thus the response
for the curved trajectory is delayed.

(9)

(10)

(11)

4. Conclusion
This paper proposed the new noise-estimated particle
ﬁlter for a target tracking system. The proposed ﬁlter estimates the system and the observation noises in
Kalman ﬁlter by using the particle ﬁlter and adapts theabrupt changes of the target motion characteristics.
We examined the tracking performance of the proposed noise-estimated particle ﬁlter by computer simulations for the radar tracking system, and conﬁrmedthat the proposed ﬁlter has high smoothing performancefor the tracking error and high stability performance forsudden changes of the target motions.
This paper focused on the radar-based target tracking, however, the applications of the proposed noiseestimated particle ﬁlter is not limited to radar tracking
and we can apply the proposed ﬁlter for a variety ofvision-based tracking systems. We are going to apply
the proposed ﬁlter for, for example, pedestrian tracking
using distributed cameras and laser range ﬁnders in near
future.
Acknowledgment
The present study was supported in part by a Grantin-Aid for Scientiﬁc Research (B) (23360115).

(12)

Masanori Ishibashi received the B.S. degree from Kyushu
University, Japan, in 2012. He is a master course student of the
Graduate School of Information Science and Electrical Engineering, Kyushu University.
Yumi Iwashita received her M.S. degree and Ph.D degree fromthe Graduate School of Information Science and electrical Engineering, Kyushu University in 2004 and 2007, respectively. She
was a research fellow of the Japan Society for the Promotion of
Science from 2006 to 2007. In 2007, she was a postdoc at Imperial
College London under Professor Maria Petrou. Currently she is
an assistant professor at the Graduate School of Information Science and electrical Engineering, Kyushu University. From 2011
to 2015, she is an aﬃliate researcher, Jet Propulsion Laboratory.
Her current research interests include robot vision, biometrics, andmedical image processing.
Ryo Kurazume received his M.S. and B.S. degrees from the
Department of Mechanical Engineering Science, Tokyo Instituteof Technology, in 1991 and 1989, respectively. His Ph.D degree was from the Department of Mechanical Engineering Science, Tokyo Institute of Technology, in 1998. Currently, he isa professor at the Graduate School of Information Science andElectrical Engineering, Kyushu University. He is a director of
the Robotics Society of Japan (RSJ, 2009-2011, 2013-2015) andthe Society of Instrument and Control Engineers (SICE, 20132015). He received JSME Hatakeyama Award(19891), RSJ Best
Paper Award(1993), RSJ Service Award(2008), JSME Robotics
and Mechatronics Award(2009), ICEST Best Paper Award(2010),
IEEE ROBIO T.J.Tarn Best Paper in Robotics(2010), JSME
Robotics and Mechatronics Academic Achievement Award(2012).
His current research interests include legged robot control, computer vision, multiple mobile robots, space robots, medical imaging, and biometrics.

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