More on Process Models

Later in the lesson I'm going to ask you to read a paper titled "A comparative study of multiple-model algorithms for maneuvering target tracking" but for now I'd like you to take a look at section 3.1 and 3.2 only . This section, titled MM Tracking Algorithms' Design, discusses the 9 process models used in the earlier part of the paper.

Before you read the section, I'll explain some of the uncommon notation you will see.

Notes on Notation

1. Matrix Notation

When you see something like the following:

F_{CV} = \text{diag}[F_2, F_2], F_2 = \begin{bmatrix} 1 & T \\ 0 & 1 \end{bmatrix}

it means that F is a 4x4 matrix, with F_{2_{}} as blocks along the diagonal. Written out fully, this means:

F_{CV} = \begin{bmatrix} 1 & T & 0 & 0\\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & T \\ 0 & 0 & 0 & 1 \end{bmatrix}

2. State Space

The process models all use cartesian coordinates. The state space is

\mathbf{x} = \begin{bmatrix} x\\ \dot{x} \\ y \\ \dot{y} \end{bmatrix}

3. Variables

The equation x_{k} = Fx_{k-1} + Gu_{k-1} + Gw_k, \ \ w_k \sim \mathcal{N}(0,Q) should be read as follows:

the predicted state at time k ( x_{k_{}} ) is given by evolving ( F ) the previous state ( x_{k-1_{}} ), incorporating ( G ) the controls ( u_{k-1_{}} ) given at the previous time step, and adding normally distributed noise ( w_k ).

The Paper

You can find the paper here: A comparative study of multiple-model algorithms for maneuvering target tracking

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