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INTRO (part 3)

The starting point of my very f‌irst scientif‌ic contribution is the [MEM-EKF*] (Multiplicative Error Model - Extended Kalman Filter Star), the (2-dimensional) elliptic tracker proposed by Baum et al. The very simple underlying idea employed in my master thesis to f‌ind some signif‌icant contribution was to search for some improvement in the prediction or the correction steps of Baum's tracker. At the "end" of my graduation journey, I was able to f‌ind the searched improvements in both parts of the MEM-EKF*.

Prediction step → Λ:O idea

The MEM-EKF* predictor is a linear model that predicts the position and the orientation of the tracked object with two independent operations.
However, my observation is that in many cases an object, such as car that does not slip, moves in a direction that is alligned with the longitudinal axis. But the direction of the longitudinal axis is the by def‌inition the orientation (angle) of the object, meaning that the orientation angle provides useful information to predict the motion direction.
In order to take advantage from the implicit information in the orientation, in the definition of my tracker I've replaced the MEM-EKF* predictor with a brand new non-linear model, generalizing the well-known unicycle motion model, which I've called [Lambda:Omicron] - in short Λ:O.
I've presented Λ:O at [Fusion 2022] in the simplif‌ied context of point objects tracking (since the extension of an object does not play a relevant role during the prediction phase).

Correction step → SSMEM idea

The MEM-EKF* corrector generates the estimates of the tracked object position, orientation and extension with an iterative process that elaborates sequentially each detections observed by the sensor.
There are two drawbacks with the MEM-EKF* correction strategy:

  • 1) the values of the estimates depend on the order in which the detections are processed;
  • 2) the computational cost grows linearly with the number of detections.
These two problems can be solved by avoiding the sequential correction process. My idea to achieve this goal is to fuse the detections in just one single mean detection, then apply once the MEM-EKF* corrector to the mean detection.
I've called the new measurement model as SSMEM (Single Shot Multiplicative Error Model), in order to emphasize the single-correction of my approach.

I've called the ending tracker as LOMEM (Lambda Omicron Multiplicative Error Model), in order to recall the employment of my prediction model and the central role of Baum's work. I've also casted LOMEM in the PHD f‌ilter for extended objects but, despite the good performance, the f‌inal implementation was not exempt from problems.
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