**2. Related works**

In order to deal with the MTT data association issues, we found in literature several methods are classified into Bayesian and other non-Bayesian filters, has been applied to address different scenarios, such as, Markov Chain Monte Carlo Data Association (MCMCDA) was proposed in [7] as a solution to replace the conventional method as known by The Multiple Hypothesis Tracking (MHT), to handle the low Signal-to-Noise Ratio (SNR) in the pre-processing phase. On the other hand, the Gaussian mixture (GM) combined with Probability Hypothesis Density (PHD), then the full GM-PHD algorithm [8] provides a promising framework to process the several measurements from multi sensors.

In [9], a joint optimization called distributed expectation-conditional maximization (DECM), has been suggested instead of the old method named Over-The Horizon Radar (OTHR) to solve the target state estimation and multipath association. Nash Equilibria method [10] is used to perform the track selection problem in MTT. The MTT by MIMO radar systems with widely distributed antennas and noncoherent processing is considered as a problem in [11], thus a hybrid algorithm is proposed based on Nearest-Neighbor Data Association (NN) and Extended KALMAN Filter (EKF).

The data association problem occurs for MTT applications and becomes more challenging in nonlinear and non-Gaussian estimation problems, hence, it is necessary to apply a Bayesian filter such as the Joint Probabilistic Data Association Filter (JPDAF) in different tracking scenarios. Thus, The JPDA algorithm calculates the association probabilities to the target being tracked for each validated measurement at the current time information, since the state and measurement equations are assumed to be linear. Therefore, in various related works we find it widely used in MTT issues, such as in [12] a new algorithm is used named Multiple Detection JPDAF (MD-PDAF) to avoid the arising multipath propagation effects for each target detection and tracking. Moreover, A Probabilistic Data Association-Feedback Particle Filter (PDA-FPF) for Multiple Target Tracking Applications is used in [13]. For multi Target tracking in passive multi-static radar system, the sequential of a

*Improved Multi Target Tracking in MIMO Radar System Using New Hybrid Monte… DOI: http://dx.doi.org/10.5772/intechopen.95948*

multi-sensor joint probabilistic data association (S-MSJPDA) [14] has great potentials compared to the parallel architecture of a multi-sensor joint probabilistic data association (P-MSJPDA).

To avoid the data association phenomenon in MIMO radar system, our main contribution is:

• The development of a new approach based on particle filter that we called Monte Carlo – Joint probabilistic data association filter (MC-JPDAF) algorithm, to make tracking more efficient.

This paper is organized as follows; Related works in section 2. Section 3, presents our algorithm which have been used in tracking scenarios, Experimental results are discussed in sections 4, finally, the conclusion and the future works are given in section 5.

## **3. The proposed algorithm**

#### **3.1 Joint probabilistic data association filter (JPDAF)**

JPDA algorithm aims to calculate the marginalized association probability based on all possible joint events for data association. In [12, 15], a joint event is an allocation of all measurements to all tracks. In JPDA, a feasible joint event is defined as one possible mapping of the measurements to the tracks such that: (1) each measurement (except for the dummy one) is assigned to at most one target and (2) each target is uniquely assigned to a measurement. Let {*θk*=*θ<sup>i</sup> <sup>k</sup>*} ∈ {1, 2, … ,*N*ð Þ *<sup>k</sup>=k*�<sup>1</sup> }, denote the joint association event. For each pre-existed target *i* ∈{1,2, … , *N*ð Þ *<sup>k</sup>=k*�<sup>1</sup> }, *θi <sup>k</sup>*∈{0,1, … ,*Mk*} denotes the association event, where *θ<sup>i</sup> k*=j means the jth measurement is originated from the ith target and *θ<sup>i</sup> <sup>k</sup>*=0 represents the dummy association in which the ith target is miss detected. JPDA assumes that each single association event is independent and the posterior of each target is:

$$P\left(X\_k^i/\varepsilon\_k^i = \mathbf{1}, Z\_k = \sum\_{\theta\_k^i} \left(X\_k^i/\theta\_k^i, \varepsilon\_k^i = \mathbf{1}, Z\_k\right).p\left(\theta\_k^i/\varepsilon\_k^i = \mathbf{1}, Z\_k\right)\right) \tag{1}$$

#### **3.2 The particle filter based on MONTE CARLO algorithm (MC)**

Sequential Monte Carlo techniques are a marginal particular filter are useful for state estimation in non-linear, non-Gaussian dynamic target. These methods allow us to approximate the joint posterior distribution using sequential importance sampling.

The MC algorithm uses the sequential resampling process to avoid the filter divergence scenario during the state estimation period, particularly when using high non-linear target models and non-Gaussian distributions. Further, the process needs sufficient probability under the observed region. Accordingly, it's necessary to provide a probabilistic interpretation through the following probabilistic interpolation:

$$\mathbf{I}(\mathbf{f}) = \mathbf{E} \, \mathbf{P}[\mathbf{f}(\mathbf{X})/\mathbf{Y}] = \int\_{1}^{\text{Np}} \mathbf{f}(\mathbf{X}) \, \mathbf{P}(\mathbf{X}/\mathbf{Y}) \tag{2}$$
