Particle Filter Flashcards
- What is the fundamental idea behind the Particle Filter (PF), and how does it address the limitations of traditional Kalman filters?
The Particle Filter (PF) is a non-parametric Bayesian filter that approximates the posterior distribution using weighted particles. It addresses limitations of traditional Kalman filters by handling non-linear and non-Gaussian systems.
- Explain the concept of sequential importance sampling in the context of particle filtering.
Sequential importance sampling involves recursively updating particle weights based on measurement likelihood. It ensures that likely states receive higher weights.
- What is resampling in the Particle Filter, and why is it necessary?
Resampling is the process of selecting particles with replacement based on their weights. It prevents particle degeneracy and maintains diversity.
- Describe the role of the proposal distribution in the PF.
The proposal distribution generates new particles from existing ones. It determines how particles propagate through the state space.
- Provide the weight update equation for particles in the Particle Filter.
The weight update equation for particles in the PF is: (w_t^{(i)} = \frac{p(z_t | x_t^{(i)})}{\sum_{j=1}^N p(z_t | x_t^{(j)})}) where (w_t^{(i)}) is the weight of particle (i) at time (t), (z_t) represents the measurement, and (x_t^{(i)}) is the state estimate.
- How do we measure the effectiveness of a set of particles in the Particle Filter?
The effective particle count is calculated as the reciprocal of the sum of squared weights. If it is close to the total number of particles, resampling is needed.
- Discuss the importance of the state transition model (motion model) in the PF.
The state transition model predicts how particles evolve over time. It guides the proposal distribution during resampling.
- What role does the observation model (measurement likelihood) play in the Particle Filter?
The observation model evaluates the likelihood of measurements given the predicted state. It updates particle weights based on measurement consistency.
- Explain the concept of the Bootstrap Particle Filter (BPF).
The Bootstrap Particle Filter (BPF) samples particles from the prior distribution and updates them using the observation likelihood.
- Provide examples of real-world applications where Particle Filters are commonly used. Also, discuss any challenges associated with their implementation.
Particle Filters find applications in tracking, robotics, and navigation. Challenges include computational complexity and handling multi-modal distributions.
