Improvement of GM-PHD algorithm for multi-target and multi-sensor tracking with the help of bias estimation

Field of study: Electricity

Treatment: Telecommunications

Dissertation

Abstract

In this thesis, multi-objective and multi-sensor tracking problems are investigated using the random particle set rule. The regression probability density hypothesis (PHD) is implemented dynamically. This dynamic mode is performed by combining the transfer bias value with the intensity function. We have assumed the dynamic bias as linear Gaussian in the intensity function. Gaussian filter implementation is closed form Gaussian components. The target position and the transfer bias value are coupled by the accuracy function in each step. Using the two-stage Kalman filter leads to a significant reduction in the complexity of calculations. Here are two examples to check the proposed filter.

Keywords:

multi-target tracking, probability density hypothesis filter, bias estimation

Since there is constant error and noise in tracking targets using data received from a single sensor. Several sensors can be used to reduce these errors. But using multiple sensors has the problem of bias error not being the same. that this error is combined with the actual value of the target position and as a result it is not possible to estimate the correct position of the targets by means of several sensors in common coordinates. Therefore, to reduce the sensor error, we need to estimate the bias value of each sensor, and finally, by subtracting the bias error from the data value measured by the sensor, we estimate the correct position of the target in the joint coordinates. Here we examine the upcoming problems in target tracking using multiple sensors and bias estimation. 1-1 Problem statement In this thesis, the problems of multi-target and multi-sensor tracking are investigated using the rule of random particle collection. The recursive probability density theorem (PHD[1]) is implemented dynamically, and this dynamic state is performed by combining the transfer bias value with the intensity function.

GM-PHD filter [2] has the ability to estimate the number and status of targets, based on noisy observations and in the presence of false targets. However, in collision situations where the targets cross over each other, the GM-PHD filter faces problems and loses its efficiency. On the other hand, compensating the error recorded in the integrity of the data received from several sensors is an important issue, regardless of whether their measurement is centralized or distributed.

There are different methods for sensor bias, for example:

transitional bias

rotational bias

transitional and rotational bias (Sudano, 1993).

Here we seek to choose the appropriate bias in terms of response speed and accuracy in tracking multiple targets, by receiving data from several sensors in 2D coordinates with the help of PHD filter.

The problem of estimating the size of the unknown bias has received much attention. If it is possible to estimate the bias value correctly, multi-sensor measurements can be used in the form of joint coordinates. In Figure 1-1, you can see the measurement of multiple sensors without recording errors. Figure 1-1: Measurement of multiple sensors in a common coordinate without recording errors. unknown, various methods have been proposed.

Probability method[3]

2-

Of these methods, the Kalman filter method has received a lot of attention.

By combining the target position and the bias value in a single vector and using the developed Kalman filter[4], the bias value can be estimated.

Although it is computationally practical and Numerically, implementation by ASKF [5] is possible, but it causes problems such as ill-posedness [6]. To reduce this complexity Friedland [7], two-stage estimation by separating the bias from the target position can be proposed (Friedland, 1969). When there is a special relationship between the initial parameters of the 2 filters, this two-stage estimation is equal to the one-stage ASKF estimation (Ignagni, 1981).

It should be noted here that the problem of many existing methods is the uncertainty in the source measurement, which often occurs in multi-target tracking.Although techniques such as joint data probability [8] and multi-probability tracking [9] that have been obtained so far can be used. But they may not have a favorable result due to not considering the bias effect. Recently, the set of statistical particle set theory [10] has been used to deal with multi-objective tracking problems in data communication (Mahler, MA, 2007). The structure of the set of statistical particles is such that it models the position of the target and the bias value as 2 random finite sets [11], and as a result, the problem of tracking unknown targets at different times in environments that have interference is naturally solved. In addition, the multi-objective tracking can be expressed in the Bayesian framework by creating the transfer density and the multi-objective accuracy function [12]. However, the use of Bayesian filter for multi-objective tracking is difficult due to the existence of multiple integral sets and the hybrid nature of the multi-objective density. To reduce the complexity of this filter, the hypothesis of probability density (PHD [13]) is expressed. It should be noted here that this return filter still needs to solve multi-dimensional integrals. There are mainly 2 methods to implement the PHD recursive filter:

1-Sequential Monte Carlo method (SMC[14]) (Vo, Singh, & Doucet, 2005)

2-Gaussian mixture (GM[15]) (Vo & Ma, 2006)

In the SMC-PHD[16] filter, a large number of particles are used for multi-dimensional approximation, so the main form of the filter This is that the calculation load is high, in addition, in some clustering techniques, it is necessary to extract the estimation of the target position, which are often unreliable.

In order to overcome these disadvantages, a linear Gaussian GM-PHD[17] filter is proposed for dynamic targets and Gaussian models. Kalman nonlinearity has also been used to investigate nonlinear dynamic targets and measured models directly.

The covariance properties of 2 implementation methods have been investigated (Clark & ??Vo, 2007). DA Clark in 2007 showed that the GM-PHD filter can be a good approximation of the PHD filter with any degree of accuracy for linear Gaussian dynamic models (Clark & ??Bell, Jul.2006). In 2004, Wu applied the GM-PHD filter to a multi-sensor tracking system and estimated the position of each target according to the data obtained from each sensor. hit, however they omitted to record the errors from each sensor (Ma, Singh, & Vo, 2004).

E.L. In 2011, Fallah used GM-PHD[18] filter for multi-sensor tracking system and he considered a simple version of error registration (El-Fallah & Mahler, May 2011).

F. Lian, C. Chan, H. In 2011, Chen investigated the registration of the transfer bias value in the recursive PHD [19], he tracked the targets by registering the bias value and using the SMC-PHD filter (((Lian, Han, Liu, & Chen, 2011)). But due to the use of SMC filter [20], this method has disadvantages such as high computational cost and unreliability of clustering.

1-2 Research Objectives

Providing accurate and up-to-date information about the location and speed of a certain object only with the help of a sequence of observations about the position of those objects

Reducing the error in tracking multiple targets

Using multiple sensors for optimal tracking

1-3   Hypotheses

If it is possible to correctly estimate the bias value, multi-sensor measurements can be used in the form of joint coordinates. We also assume here that all sensors observe all targets. 1-4 Research Background In 2004, Vo used the GM-PHD filter for a multi-sensor tracking system and estimated the position of each target according to the data obtained from each sensor, however, he omitted to record the errors from each sensor (Ma, Singh, & Vo, 2004). El. In 2011, Fallah used the GM-PHD[21] filter for a multi-sensor tracking system, and he considered a simple version of error registration (El-Fallah & Mahler, May 2011).

F. Lian, C. Chan, H. In 2011, Chen investigated the registration of transfer bias value in recursive PHD [22], he performed the tracking of targets by registering the bias value and using the SMC-PHD filter [23] (Lian, Han, Liu, & Chen, 2011).