Estimation of states under Colored Measurement Noise (CMN) using

UFIR and Kalman Filters modified

Abstract: The estimate process of a moving target trajectory is a well-known problem, where the main objective

is to improve the estimation of object position. During the tracking are presented errors or variations between the

true position and the estimated. In this paper, we treat such variations as a Gauss-Markov colored measurement

noise (CMN). The estimation process is performed in predict and update, where the prediction indicates the next

position of the bounding box, and the update is a correction step, which includes the new measurement of the

tracking model and helps to improve the estimation. Looking for this improvement we use Kalman and Unbiased

Finite Impulse Response filters in the standard version and modified for CMN to demonstrate the filter with the

best performance. To test the most robust filter we use a high coloredness factor. The tests were carried out with

simulated data (ideal and no ideal conditions) and with benchmark data (no ideal conditions). The UFIR modified

for the CMN algorithm showed favorable results with high precision and low RMSE in the object tracking process

with benchmark data and under no ideal conditions. While KF CMN showed better results under ideal conditions.

Key-Words: Bounding box, colored measurement noise, estimation, Kalman filter, precision, tracking, Unbiased

FIR filter

Received: June 7, 2021. Revised: September 5, 2022. Accepted: September 28, 2022. Published: October 25, 2022.

1 Introduction

The object tracking process is a widely researched

topic and has a wide range of applications in the fields

of visual navigation, robotics, intelligent transporta-

tion, and security, among others [1, 2]. There are dif-

ferent research approaches, however, it continues to

present challenges in their treatment, there is no single

approach capable of overcoming all the impact factors

that affect the tracking algorithm’s performance.

Object tracking can be defined as the problem

of estimating the trajectory of an object as it moves

around a scene [3, 4]. This process is usually ac-

companied by variations in position, that is, the tar-

get is not tracked exactly. There are variations in the

estimate, that is, there is a discrepancy between the

real position and the estimated position. These varia-

tions can be considered as colored measurement noise

(CMN) that is not white [5].

The variations in object tracking can be more

clearly identified, during the tracking process, if we

use a bounding box to contain the information of the

object to be tracked. The bounding boxes generated

by the tracking algorithm do not always detect the tar-

get object, they may detect another object in the scene,

or they do not detect the exact shape of the target.

This may be due to various factors affecting the track-

ing process, such as camera movement, occlusion, or

blurred scene, among others. In this sense, a method

that has proven to be effective in avoiding large errors

in the tracking process is the use of a motion model

and state estimators. [5–9]. If the state-space model is

correct, it can very accurately represent the trajectory

of the tracked object. However, the performance of

the tracking algorithm will still depend on measure-

ment and process noise.

For these reasons, in this paper, we use Kalman

(KF) and Unbiased Finite Impulse Response (UFIR)

in their versions standard and modified to minimize

the error in the estimation, seeking to stabilize the tra-

jectory and size of the bounding box to obtain an algo-

rithm that produces greater precision in tracking tasks.

The process of state estimations were performed in

two phases of recursions and iterations: ”predict” and

”update”. Using root mean square errors and the pre-

cision to measure the performance of the algorithms.

2 Object processing

In order to carry out the object-tracking process, it is

necessary to identify the object to track. The image

processing operations look for the best recognition of

the objects tracked. Therefore, it is necessary to iden-

tify the appropriate characteristics to differentiate the

target from other objects and the background scene.

The content of an object can be described through its

properties. There are different ways to locate a tar-

get, for example, its contour or finding the pixels of

1ELI G. PALE-RAMON, 1YURIY S. SHMALIY, 2LUIS J. MORALES-MENDOZA,

2MARIO GONZÁLEZ-LEE, 2SILVERIO PÉREZ-CACERES,

2EFRÉN MORALES-MENDOZA

1Electrical Engineering Department, Universidad de Guanajuato, Salamanca,

Guanajuato, 36680, MEXICO

2Electronics Engineering Department, Universidad Veracruzana,

Poza Rica, Veracruz, 93380, MEXICO

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the object, one of the most used shape parameters in

object tracking is the bounding box, [10].

2.1 Bounding box

The bounding box (BB) is a rectangular box that en-

closes all the objects in a scene and can be used to

represent an object during tracking. Using the BB as

a shape parameter in the tracking process, the infor-

mation about the position of the objects is contained

in an array of bounding boxes. The BB matrix con-

sists of 4 columns and n rows, the number of rows

corresponds to the total number of detections, while

the columns represent the dimensions of the bounding

boxes: coordinate ”x”, coordinate ”y”, width (xw),

height (yw) [11].

The information about the ”x”, ”y” coordinates,

the height and the width of the BB, is used to estimate

the position of the object during the tracking process.

However, there may be errors in the position estima-

tion. In this sense, the use of a filtering method is

an effective method, its aim is to mitigate the noise

present in tracking process. A filtering method is

used to predict the coordinates of BB. The estima-

tion method consists of 2 steps: prediction and cor-

rection. The prediction indicates the next position of

the bounding box based on its previous position. The

update is a correction step, which includes the new

measurement of the tracking model and helps to im-

prove the estimate of the filtering [12, 13].

3 State-space model of tracking

object

We consider a moving object with observation cor-

rupted by CMN can be represented in discrete-time

state-space with the following state and observation

equations:

xn=Anxn−1+Bnwn,(1)

vn= Ψnvn−1+ξn,(2)

yn=Cnxn+vn,(3)

where xn∈RKis the state vector, yn∈RMis the

observation vector, vn∈RMis the colored Gauss-

Markov noise, and An∈RK×Kis the state transi-

tion matrix, Bn∈RK×Pis the gain matrix model,

Cn∈RM×Kis the measurement matrix. Measure-

ment noise transfer matrix Ψnis chosen such that the

colored noise vnremains stationary. The zero mean

Gaussian noise vectors wn∼ N (0, Qn)∈RPand

ξn∼ N (0, Rn)∈RMhave the covariances Qnand

Rnand the property E{wnξT

k}= 0 for all nand k.

We will consider the following estimates: the prior

estimate ˆx−

n≜ˆxn|n−1, posterior estimate ˆxn≜ˆxn|n,

prior estimation error ϵ−

n=xn−ˆx−

n, the posterior

estimation error ϵn=xn−ˆxn, the prior error covari-

ance P−

n≜Pn|n−1=E{ϵ−

nϵ−T

n}, and the posterior

error covariance Pn≜Pn|n=E{ϵnϵnT}.

The matrices for the model were built considering

a constant velocity model [14]. For the moving object

state space model, the state transition A is a block di-

agonal matrix with:

1τ

0 1 ,(4)

where τis the sample time. This block is repeated for

the 4 coordinates of the bounding box.

The matrix B is given by equation (5), this set of

3by 1is repeated for each coordinate of bounding

box corners. Finally, it will obtain a matrix with di-

mensions 12 by 4, in which the equation (5) forms a

diagonal.

B=τ2

τ,(5)

The observation matrix (C) is defined as shown be-

low:

C=





10000000

00100000

00001000

00000010





.(6)

3.1 Avoid the CMN

To avoid the CMN vnin ynis necessary the model

modification using measurement differencing. For

which, it is considered a new observation znas a mea-

surement difference.

zn=yn−Ψnyn−1,

=Cnxn+vn−ΨnHn−1xn−1−Ψnvn−1,(7)

and transform (7) to

zn=Dnxn+ ¯vn,(8)

where Dn=Hn−Γn,Γn= ΨnHn−1F−1

n,¯vn=

ΓnBnwn+ξn, noise ¯vnis now white with the prop-

erties

Rn=E{¯vn¯vT

n}= ΓnΦn+Rn,(9)

E{¯vnwT

n}= ΓnBnQn,(10)

where Φn=BnQnBT

nΓT

n, and model (1) and (2) has

thus two white and time-correlated noise sources wn

and ¯vn.

4 Kalman Filter modified for CMN

In estimating the system state through the coordinates

of the BB, we can use the Kalman filter(KF). Within

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which the state is assumed to be distributed by white

Gaussian noise with mean zero. The estimate pro-

cess consists of two steps, prediction, and update. In

this case, the KF is recursive [15], which means that

the previously estimated state must be combined with

new observation to calculate the best estimate of the

current state. One of the important aspects to con-

sider when using the KF algorithm is that it requires

knowledge of the system parameters, initial values,

and measurement noise.

The KF can estimate the state dynamics of the sys-

tem iteratively [16]. Assuming that the process noise

wnis white Gaussian with zero mean, the prior state

estimate is computed by (11).

ˆx−

n=Aˆxn−1+Bnwn(11)

Next, in the update step, the current prior predictions

are combined with the current state observation to re-

define the state estimate and the error covariance ma-

trix. To obtain the optimal state estimate is combined

the prediction with the current observation, and now

it is called the posterior state estimate. The measure-

ment znis corrupted by a factor of colored measure-

ment noise Ψn(12).

zn=yn−Ψnyn−1(12)

The residual covariance matrix is obtained as follow:

Sn=CnP−

nCT

n+Rn(13)

The measurement residual is

sn=zn−Dnˆx−

=DnAnϵn−1+DnBnwn+ ¯vn,(14)

the innovation covariance Snis given by

Sn=E{snsT

=DnP−

nDT

n+Rn+CnΦn+ ΦT

nDT

n,(15)

and the estimation of KF for CMN is

ˆxn= ˆx−

n+Knsn

=Anˆxn−1+Kn(zn−DnAnˆxn−1),(16)

where Knis the bias correction gain that should be

optimized for correlated wnand ¯vn. the estimation

error ϵncan be written as

ϵn=xn−ˆxn

= (I−KnDn)Anϵn−1

+(I−KnDn)Bnwn−Kn¯vn(17)

and the error covariance Pn=E{ϵnϵT

n}transformed

Pn=P−

n−(P−

nDT

n+ Φn)KT

n−Kn(P−

nDT

n+ Φn)T

+KnSnKT

n,(18)

where P−

nis given by (18) and Snby (14). The opti-

mal gain Knis given by

Kn= (P−

nDT

n+ Φn)S−1

n(19)

and (18) becomes

Pn=P−

n−Kn(DnP−

n+ ΦT

n).(20)

A pseudo-code of the KF algorithm for CMN with

correlated wnand ¯vnis listed as Algorithm 1. It can be

observed, if the value Ψn= 0, the algorithm becomes

the standard Kalman filter algorithm.

Algorithm 1: KF for CMN and Correlated

wnand ¯vn

Data: yn,ˆx0,P0,Qn,Rn

Result: ˆ

xn,Pn

1begin

2for n= 1,2,· · · do

3Dn=Hn−ΨnCn−1A−1

4zn=yn−Ψnyn−1

5P−

n=AnPn−1AT

n+BnQnBT

6Sn=DnP−

nDT

n+Rn+CnΦn+ΦT

nDT

7Kn= (P−

nDT

n+ Φn)S−1

8ˆx−

n=Anˆxn−1

9ˆxn= ˆx−

n+Kn(zn−Dnˆx−

10 Pn= (I−KnDn)P−

n−KnΦT

11 end for

12 end

5 Unbiased Finite Impulse Response

Filter modified for CMN

In the same way as the KF, the UFIR filter can also

be generalized to colored measurement noise, consid-

ering that the unbiased average ignores zero average

noise. Next, we work with a modification to the UFIR

filter for CMN.

As already mentioned, the KF requires noise in-

formation. In the case of the UFIR filter, this require-

ment is not necessary, except for the assumption of a

zero mean [2, 4, 9, 17, 18]. For this reason, it is con-

sidered to be more suitable for use in object track-

ing as databases with incomplete information or in

time tracking, in which information about measure-

ment and process noises is not always known exactly.

In the UFIR filter, wk, and ˆvncan be ignored and

therefore the UFIR is unique for correlated and no-

correlated wk, and ˆvn. So its equation of state is given

by xn=Fnxn−1.

The state estimation is done in two steps. In the

prediction step, only the state (5) is calculated a pri-

ori, because the UFIR filter does not require know-

ing the statistical noise information. However, UFIR

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requires an optimal averaging horizon [m, n] to min-

imize the mean square error (MSE), that is, it oper-

ates simultaneously with N measurements on a hori-

zon [m, k]of m=k−N+ 1. The UFIR filter cannot

ignore the CMN vn, which violates the zero-mean as-

sumption at short horizons [19, 20].

Since we use an iterative algorithm using recur-

sion, in the update step, the state estimate is combined

with the actual observation state to refine the state.

The estimate is iteratively updated in a posteriori state

using: Matrix G, measurement residuals, and the bias

correction Gain.

A Matrix G or better known as generalized noise

power gain (GNPG) (21), the measurement residual,

and the bias correction gain.

Gl= [DT

lDl+ (FnGl−1FT

l)−1]−1(21)

The measurement residual zlis given by:

zl=yl−Ψlyl−1(22)

In the UFIR filter, the estimation errors are taken into

acount only on the horizon [m, k]and it is computed

in term of GNPG. The bias correction gain can be ex-

pressed as:

Kl=GlDT

l(23)

Then, it is computed the a posteriori state estimate as

follow:

¯xl= ¯x−

l+Kl(zl−Dl¯x−

l); (24)

Since the CMN is present in the tracking process

data, The recursive computation of the posterior es-

timate to avoid the CMN can be summarized in the

following pseudo-code, as shown in Algorithm 2. To

initialize the iterations, the algorithm requires a short

measurement vector y(m.k)=[ym…yk]Tand a ma-

trix (25).

Hm,s =





Dm(Fs...Fm+1)−1

Ds−1F−1







.(25)

Note that CT

m,sCm,s is singular if s−m < K−1, and

thus the generalized noise power gain Gscannot be

calculated on horizons shorter than K points. In the

same way as with the KF filter modified for CMN,

when the coloredness factor Ψn= 0, the Algorithm 2,

UFIR modified for CMN, becomes the standard UFIR

filter [19, 20].

Since UFIR filter operates on the horizon [m, k]of

the total horizon N. To minimize MSE, the horizon to

work with must be optimized as Nopt. According to

[5] we can determine Nopt, by the following equation:

Nopt =12σξ

τ2σw

(26)

Algorithm 2: UFIR Filter for CMN

Data: N,yn

Result: ˆxn

1begin

2for n=N−1, N, · · · do

3m=n−N+ 1 ,s=n−N+K

4Gs= (CT

m,sCm,s)−1

5¯xs=GsCT

m,sYm,s

6for l=s+ 1 : ndo

7Dl=Hl−ΨlHl−1F−1

8zl=yl−Ψlyl−1

9Gl= [DT

lDl+ (FlGl−1FT

l)−1]−1

10 Kl=GlDT

11 ¯x−

l=Fl¯xl−1

12 ¯xl= ¯x−

l+Kl(zl−Dl¯x−

13 end for

14 ˆxn= ¯xn

15 end for

16 end

Another method to calculate the optimal horizon Nopt

is using measurement residuals, given the property

that the derivative of its trace with respect to the

length of the horizon reaches a minimum when N

tends to Nopt. This allows determining Nopt, through

the minim value of MSE. This is a useful property

when ground truth is not available. [5, 20].

6 Performance metrics of tracking

algorithm

A widely used statistical metric to evaluate the track-

ing algorithm performance, from an overall perspec-

tive, is the root mean square error (RMSE). But, the

most common metric used to evaluate tracking per-

formance is precision.

6.1 Precision

Performance evaluation of tracking algorithms can be

evaluated by precision metric. Precision can be de-

fined as the percentage of the number of correct pre-

dictions over the total number of predictions. [21,22].

Before establishing the precision calculation, it is

necessary to obtain another metric, intersection over

union (IoU). The IoU can be defined as the percentage

overlap of the predicted bounding box over the true

bounding box (TBB). The equation for the calculation

of IoU is shown below:

IoU =IA

(T BB −EBB)−IA (27)

Where the IA is the area of intersection between the

bounding box of the target object, the true bounding

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box (TBB), and the estimated bounding box (EBB).

The TP is a true positive, and FP is a false positive.

As already mentioned, the precision is calculated

from the IoU value for which it is necessary to estab-

lish an evaluation parameter, for this, an IoU thresh-

old is established [21, 23]. The equation for calculat-

ing precision is:

P recision =ΣT P

ΣT P + ΣF P (28)

Where TP is True Positive, that is a correct detection

of a bounding box, that is, the IoU between the EBB

and TBB is greater than or equal to the established

threshold value. FP is False positive, which is an

incorrect detection of an object or an off-site detec-

tion. The IoU is less than the given threshold value

but greater than zero. FN is a false negative.

7 Object tracking test results

7.1 Results of simulation test

The simulation was performed using the object track-

ing model can be described by (1) and (2) and the

known matrices. For the first simulation test, we

considered that a target is disturbed by white Gaus-

sian acceleration noise with a standard deviation of

σw= 2m/s2. The data noise originates from white

Gaussian with σξ= 30 m. The trajectory simulation

was 2000 points with sample time T= 0.05 seconds,

P0= 0,Q=σ2

w,R=σ2

V, on a short horizon

Nopt = 60.

The RMSE obtained by the standard and modified

filters for CMN, KF and UFIR, from the coloredness

factor Ψ 0 to 0.95 are shown in Fig. 1 a). The Nopt for

UFIR has used the same size for the entire range of Ψ.

Standard UFIR results are shown with a magenta line,

standard KF with a black line, and UFIR CMN with a

red line. For the KF CMN, the object tracking model

were established under ideal conditions, p=q= 1,

and with no ideal conditions, p= 1, represented with

blue line, and q= 1 with blue dotted line.

Assuming that noise information is incomplete, in

Fig. 1 a) are shown the relevant filtering errors pro-

duced by substituting Qwith p2Qand Rwith q2Rfor

{p, q}>0[5, 19]. As can be seen, even slight mod-

ifications in error factors (p= 2, q = 0.5) make the

KF CMN less accurate than the UFIR CMN. It even

has poorer performance than standard filters. The

UFIR and KF algorithms produced a high values of

RMSE with similar behavior on the all coloredness

factor Ψrange. Therefore, we consider that tmodi-

fied filters foe CMN showed better results with lower.

under ideal conditions the performance of KF CMN

is slightly lower than UFIR CMN, remembering that

this depends largely on the correct dynamic model.

To corroborate the effect of incomplete noise in-

formation. We performed another test considering

the relevant filtering errors produced by substituting

in the algorithms Qwith p2Qand Rwith q2Rfor

{p, q}>0, (p= 2, q = 0.5), and (p= 0.5, q = 2)

The results obtained are shown in Fig. 1 b).

As can be seen, a slight modification of the er-

ror factor generates a significant change in the per-

formance of the KF CMN, with which a worse per-

formance was obtained than that obtained under ideal

conditions. With this we can corroborate that the per-

formance of the KC CMN is highly related to the cor-

rect establishment of the state model. On the other

hand, UFIR is more robust when the noise informa-

tion is not available. Also, the UFIR filter does not re-

quire knowing the noise conditions Qand Rit shows

that the UFIR CMN is preferable for object tracking.

This gives another proof that the UFIR CMN is more

suitable for object tracking in real case or with bench-

mark data without complete noise information.

(a) KF and UFIR standard and modified filters

(b) KF and UFIR modified for CMN with the incomplete infor-

mation

Figure 1: RMSE results obtained by the KF and UFIR

standard and modified filters

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7.2 Results of benchmark data test

In this section, we used for test benchmark data [24].

The data is called ”SUV”. Taking into account the

tests carried out in the previous subsection, the test

was performed with the highest coloredness factor

Ψ = 0.95 in order to evaluate the robustness of the

algorithms.

The object tracking model considered that the car

target is disturbed by white Gaussian acceleration

noise with the standard deviation of σw= 3m/s2.

The data noise (CMN) originates from white Gaus-

sian σv= 2m. The trajectory is measured each sam-

ple time T= 0.05 seconds, P0= 0,Q=σ2

w,R=σ2

on a short horizon Nopt = 60. The model of a mov-

ing object is completed according to the section 3.

Then, to compare the performances of the UFIR

and Kalman filters consider the moving vehicle track-

ing problem, we examine the results of the benchmark

SUV test, where we used the bounding box coordi-

nates as a tool for metric evaluation. In Fig.2 to plot

the true estimated object trajectory, we use the bound-

ing box centroids, where the gray line is the ground

truth, the black line is KF standard (KF std), the blue

line is KF modified for CMN (KF CMN), the ma-

genta line is UFIR standard (UFIR Std) and the red

line is UFIR modified for CMN (UFIR CMN). The

graphed trajectories correspond to the coordinates on

the ”x” and ”y” axis of the centroid of each one of

the bounding boxes of the tracking of the moving

object. The trajectory followed by the object does

not correspond to a straight line; we can observe

curved paths. The standard algorithms UFIR and KF

present greater differences concerning the true trajec-

tory; while UFIR CMN and KF CMN presented a

closer estimate. Given the type of trajectory made

by the object, visual analysis is difficult, the differ-

ence between the estimates is especially neatly with

the root mean square error results. The RMSE val-

ues were 51.00 for UFIR CMN, 55.67 for KF CMN,

57.97 for UFIR std, and 79.97 for KF std. Over the

entire trajectory, the standard filters generates larger

errors than the filter modified for CMN. According to

these results, we consider that the algorithms modi-

fied for CMN presented a good performance with a

high value of ψ. While, the KF std showed a poor

performance.

To have a better perspective of the performance

of the algorithms, Fig.3 shows the bounding boxes of

a random point in the trajectory, in which it can be

seen that UFIR CMN presents a closer estimate, fol-

lowed by KF CMN, while KF std shows poor perfor-

mance on position and size compared to the ground

truth bounding box. One of the improvements ex-

pected by the algorithms used is the stabilization of

the bounding boxes both in their trajectory and in their

size. From these results, we can see that UFIR CMN

Figure 2: Centroids estimation in the x-y plane

(Nopt = 60),with Ψ = 0.95.

and KF CMN provide an improvement in object es-

timation. To determine the algorithm that presented

the best performance, the precision metric is used as

shown below.

Figure 3: Bounding box estimation.

The filter precision in the entire intersection over

the union (IoU) threshold range is shown in Fig.4.

The UFIR CMN and KF CMN filters presented the

best precision with a similar behavior up to the thresh-

old of 0.2, this means that the precision is close to 1

when the Predicted Bounding Box (PBB) overlaps at

least over 20% of true Bounding Box (TBB). At this

threshold level, it can be inferred that in each algo-

rithm both standard and modified for CMN present

good results, however the most used thresholds as a

parameter to measure the performance of the algo-

rithms are 0.5and 0.75 [21], being 0.5the most con-

ventional. Taking as reference the threshold of 0.5,

which can be inferred that the PBB overlaps at least

the 50% of the TBB. With these results, we can deter-

mine that the UFIR CMN filter has a higher precision

than KF CMN, with a significant difference. If we

take into account a threshold of 0.75, we again find

that UFIR CMN presents the best performance with

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Silverio Pérez-Caceres,

Efrén Morales-Mendoza

E-ISSN: 2224-3402

253

Volume 19, 2022

Figure 4: Precision of benchmark ”SUV”(Nopt =

60),with Ψ = 0.95.

a precision close to 0.7, while the precision for KF

CMN is around 0.3. UFIR CMN performs best un-

til the 0.8threshold, although its precision value at

this point is around 0.5. Therefore, we consider that

the UFIR CMN algorithm provided better results in a

wide threshold range, followed by KF CMN, which

we consider had an acceptable performance up to the

threshold of 0.5, which corresponds to the most used

threshold IoU range for evaluate the performance of

algorithms. On the other hand, the UFIR and KF

filters in their standard version showed poor perfor-

mance, since at the threshold of 0.5the precision of

the standard UFIR is less than 0.5and the precision

of the standard KF is close to 0.3. Since, the preci-

sion focuses on the percentage of the true bounding

box detected. From this test, it can be determined that

under a high coloredness factor Ψ=0.95 the UFIR

CMN filter obtained the best performance.

8 Conclusions

It was shown that the modified KF and UFIR algo-

rithms derived from the differentiation of measure-

ments for the colored measurement noise are better

than the standard KF and UFIR filters, both analyti-

cally and numerically, for the estimation of states in

the object tracking process.

The examples of simulations of the tracking prob-

lem confirm the theoretical inferences that under ideal

conditions, with complete noise information, the KF

CMN filter presents a better performance with lower

typical RMSE values.

According to the second experiment with data sim-

ulation under non-ideal conditions, it is verified that

the UFIR CMN works better in scenarios where the

information is not complete and is more robust to an

inadequate establishment of the dynamic model. be-

cause the UFIR filter does not require knowing the

statistical noise information.

In addition, with the experimental example of vi-

sual object tracking based on the benchmark ”SUV”

in presence of CMN with the highest coloredness fac-

tor. It is shown that the modified KF and UFIR al-

gorithms adjusted correctly have the ability to sup-

press CMN efficiently and provide state estimation

with higher precision than standard filters.

Based on the results of this work, we found that the

UFIR modified for CMN presented a better perfor-

mance, since it provides an estimation of the state with

greater precision and lower estimation error based on

RMSE. It is proving to be more robust under scenar-

ios of incomplete or unknown noise information and

with the highest coloredness factor. These character-

istics make it a highly applicable algorithm in cases

with tracking models where the information is not

well known or complete information is not available.

Therefore, we conclude that the use of modified

UFIR for CMN would contribute to the development

of applications and research and the improvement of

tracking tasks. We are currently working on mod-

ifications to the UFIR CMN algorithm, focused on

improving estimates when the values of Ψand IoU

threshold are the highest.

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Eli G. Pale-Ramon, Yuriy S. Shmaliy,

Luis J. Morales-Mendoza, Mario González-Lee,

Silverio Pérez-Caceres,

Efrén Morales-Mendoza

E-ISSN: 2224-3402

254

Volume 19, 2022

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Contribution of individual authors to

the creation of a scientific article

(ghostwriting policy)

Eli G. Pale-Ramon has written, reviewed, edited the

paper, and implemented the Algorithms in Matlab.

Yuriy S. Shmaliy has developed the methodology;

creation of models, and the project administration.

Luis J. Morales-Mendoza and Mario González-Lee

has supervised and reviewed the paper, was respon-

sible for the validation metrics, simulation and statis-

tics used.

Silverio Pérez-Caceres and Efrén Morales-Mendoza

were responsible for the validation and correction of

the computational methods applied, simulation and

statistics.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the Creative

Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en_US

WSEAS TRANSACTIONS on INFORMATION SCIENCE and APPLICATIONS

DOI: 10.37394/23209.2022.19.25

Eli G. Pale-Ramon, Yuriy S. Shmaliy,

Luis J. Morales-Mendoza, Mario González-Lee,

Silverio Pérez-Caceres,

Efrén Morales-Mendoza

E-ISSN: 2224-3402

255

Volume 19, 2022