
## 4.2 Estimator'S Principle

In general the principle of our estimator is based on: 
- a sequential temporal combination of the current basic belief assignment (drawn from classifier decision, i.e. our *measurements*) with the prior bba estimated up to current time from all past classifier declarations; 
- Shafer's model for the frame of target types; 
- One and the same information (vacuous belief assignment) as prior belief and same sequence of measurements (classifier declarations). 

All the above assumptions are to get a fair comparative analysis according to: (i) performance evaluation of estimators, build on Dempster's rule of combination, Dezert-Smarandache Theory based PCR5 fusion rules and fuzzy-based fusion rule; (ii) different types of applied t-conorm and t-norm functions within TCN fusion rule. The algorithm's steps are: 
1. Initialization at k = 0 : 

$$\mathbf{\theta}$$- select the frame $\,\Theta=\left\{\theta_{1},...,\theta_{M}\,\right\}\,$. 
- set the a priori $m^{-}\left(\theta_{1}\cup...\cup\theta_{M}\right)=1$. (Full ignorance)

$$\mathrm{r\;declaration\;}T_{d}(k):$$

Then the sum of $\alpha$. 
 And from the $\text{CH}_3\text{SIT}$. 
$$m_{o b s}\left(T_{d}\left(k\right)\right)=c_{T_{d}\left(k\right)T_{d}\left(k\right)}$$
$$(15)$$
$${}_{a b s}\left(\theta_{1}\cup\ldots\cup\theta_{M}\right)=1-m_{a b s}\left(T_{d}\left(k\right)\right).$$

2. Generation of the current measurement from the classifier declaration kT )( d : 
 ( ) ( ) *dobs* () () dd kTkT = *ckTm* (15) 
The unassigned mass is committed to the total ignorance obs ( *...m* ∪∪ M ) ( = 1− ( ) dobs kTm ) θ1 θ . 

 3. Obtain the updated (estimated) bba ( ) [ ](.mm.m ) ⊕= obs
− on the base of particular fusion rules: 
DST, DSmT-PCR5, TCN with different t-conorm *(sum, max)* and t-norm functions, described in equations (6), (7), (8). 

4. Estimation of True Target Type by taking the hypothesis having the maximum of belief (or eventually the maximum Pignistic Probability [8]). 

5. Propagation to next time step k +1

## 5 Simulation Results

In order to evaluate the performances of all considered estimators, based on: Dempster's, DSmT based PCR5, TCN fusion rules with different types of t-conorm and t-norm functions applied, and in order to have a fair comparative analysis, Monte-Carlo simulations on a simple scenario for a 2D Target Type frame, i.e. Θ = { *oargC,Fighter* } is done for a classifier with the following confusion matrix: 