Choosing a Filter

Use this guide to pick the right filter for your problem.

Decision Flowchart

Is the system linear?
  |
  +-- YES --> KalmanFilter
  |             (fastest, optimal for linear-Gaussian)
  |
  +-- NO
       |
       Is the noise Gaussian?
         |
         +-- NO --> ParticleFilter
         |            (handles any distribution, multimodal)
         |
         +-- YES
              |
              Can you compute Jacobians?
                |
                +-- YES --> ExtendedKalmanFilter
                |             (fast, needs analytical derivatives)
                |
                +-- NO
                     |
                     Is the state dimension large (>100)?
                       |
                       +-- YES --> EnsembleKalmanFilter
                       |             (scales to millions of states, Dask-parallel)
                       |
                       +-- NO --> UnscentedKalmanFilter
                                    (sigma-point accuracy, no Jacobians)

Filter Comparison

Property	KF	EKF	UKF	EnKF	PF
Linearity	Linear	Nonlinear	Nonlinear	Nonlinear	Any
Noise assumption	Gaussian	Gaussian	Gaussian	Gaussian	Any
Jacobians needed	No	Yes	No	No	No
Multimodal support	No	No	No	No	Yes
Smoothing	RTS	RTS	–	–	–
Forecasting	Yes	–	–	–	–
Dask parallel	–	–	–	Yes	Yes
Computation cost	O(n^3)	O(n^3)	O(n^3)	O(n^2 * M)	O(n * N)
Best accuracy	Linear systems	Mild nonlinearity	Strong nonlinearity	High-dim	Multimodal

Where n = state dimension, M = ensemble size, N = particle count.

When to Use Each Filter

KalmanFilter

• GPS/INS navigation with linear dynamics

• Signal denoising (e.g., sensor data, images, EEG)

• Financial time series smoothing

• Any system where x_{k+1} = F @ x_k + noise

ExtendedKalmanFilter

• Radar tracking (range + bearing observations)

• Satellite orbit determination

• SLAM (simultaneous localization and mapping)

• Systems where you can derive Jacobians analytically

UnscentedKalmanFilter

• Same problems as EKF but without needing Jacobians

• Strongly nonlinear dynamics where EKF linearization is poor

• Faster prototyping (just provide f(x) and h(x))

EnsembleKalmanFilter

• Weather prediction / data assimilation

• Ocean current modeling

• Any system with state dimension > 100 where full covariance is infeasible

• Set use_dask=True for parallel ensemble propagation

ParticleFilter

• Robot localization with landmark observations

• Target tracking with clutter

• Multimodal posterior distributions

• Non-Gaussian noise (e.g., heavy-tailed, uniform)

Memory Efficiency

For long time series, disable covariance storage:

kf = KalmanFilter(F, H, Q, R, x0, P0, store_covariances=False)
kf.fit(million_step_data)     # only stores state estimates
states = kf.predict()         # works
# kf.smooth()                 # raises error (needs stored covariances)

This saves approximately 80% of memory for the KalmanFilter on long sequences.