Maneuvering Target Tracking by Using Particle Filter [N. Ikoma et al.]

Hope:A brighter light at the end of my reading. please ya Allah... the brighter the better

Simulation Based

1. Dynamics of the maneuvering target tracking model, for continuous model, is defined according to Singer 1970.
   
1. Gaussian white noise process is used as the input for system noise vector in the continuous time model.
2. After discretized, Cauchy distribution, as the typical heavy-tailed distribution, is proposed for the system noise to cater for manuvering target with an abrupt change of its acceleration.
3. Non-linear Observation model is used to represent the radar measurement process.
   
2. To estimate the non-Gaussian nonlinear state space model defined above, particle filtering (SMC) is considered as the most effective method compared to Gaussian-sum approximation and numerical representation.
1. Monte Carlo Filter (MCF) method is employed among other SMC methods, which are bootstrap and condensation (conditional density propagation).
2. State Space model: use the subset of the general class of state space reperesentation estimated byMCF.same as space model define aboved.
   
3. State Estimation: Calculate the conditional distribution from the given observation. 3 Steps: prediction, filtering, and smoothing with fixed lag.
4. MCF used an approximation of non-Gaussian distribution by particles to defined the state approximation.
   
5. Filtering procedure: Find the prediction value, then calculte the likelihood of each particle, then resample the particle.
6. Smoothing: By augmenting the particles where invoving the process of integrating past and current time (prediction and filtering) values.
7. Likelihood:The 'hyperparameter', that consist of covariance matrices of observation noise,R and system noice, Q, is determined by maximizing the log-likelihood. This 'hyperparameter' governs the performance of state estimation where if Q > R, the observation value is more reliable and state variables change quickly. While if R > Q, the state variables evolve smoothly and the observation value can be ignored.
   
3. Simulation:
1. Simulate with the assupmtion of small observation noise.
2. The simulation shows that Cauchy-MCF model can quickly follow the sudden change while Gaussian-EKF model has delayed response.
4. Future work:
1. Larger noise measurement
2. Application to real data
3. High SNR case is a real challange b'coz acceleration is much sensitive to the noise in position.