Benchmarks

kalman-py is compared with FilterPy in per-step mode (one predict + update call per measurement) and with pykalman in batch mode (the whole sequence in one call), on five frozen scenarios shared with the C, C++ and Rust implementations. Every library gets the same inputs, seeds and precision.

ID	Scenario	n / m	Filters	Length
S1	1-D constant velocity	2 / 1	KF	10,000 steps
S2	2-D constant velocity	4 / 2	KF	10,000 steps
S3	Range-bearing tracking	4 / 2	EKF, UKF	500 steps × 200 seeds
S4	Ill-conditioned problem, float32	4 / 2	KF	1,000,000 steps
S5	15-state INS error-state model	15 / 6	KF	10,000 steps

The scenario files and their format are described in tests/vectors/README.md in the repository.

Preliminary

These numbers come from a development laptop (Apple M3 Pro), not a dedicated machine with a fixed CPU frequency, so timings can vary by 10–20% between runs.

Speed

In batch mode the JAX backend is 93× (S1), 67× (S2) and 9.5× (S5) faster than pykalman. In per-step mode kalman-py is 0.78–0.84× FilterPy's speed: both make the same number of small NumPy calls, and kalman-py also symmetrizes every covariance. Estimates match in every linear case.

Float32 stability (S4)

Warning

On this problem the default NumPy configuration (Joseph form) is the first to fail. Use square_root=True when filtering in float32.

Full results

Measured on Apple M3 Pro (arm64), macOS 27.0.1, python-3.12.13, commit 9a2edc7, 2026-10-05.

Scenario	Filter	Precision	Metric	kalman-py	filterpy	kalman-py-jax	kalman-py-numpy	kalman-py-sqrt	naive	pykalman	Ours vs best other
S1	KF batch	float64	max_abs_diff (state)	n/a	n/a	n/a	n/a	n/a	n/a	5.99e-12	n/a
S1	KF batch	float64	peak_memory (bytes)	n/a	n/a	n/a	1,524,384	n/a	n/a	1,136,154	n/a
S1	KF batch	float64	rmse (state)	0.4233	n/a	n/a	0.4233	n/a	n/a	0.4233	1.00x
S1	KF batch	float64	time_per_step (ns)	406.8	n/a	n/a	2,606	n/a	n/a	38,047	93.53x
S1	KF per-step	float64	max_abs_diff (state)	n/a	1.78e-15	n/a	n/a	n/a	n/a	n/a	n/a
S1	KF per-step	float64	peak_memory (bytes)	164,260	163,912	n/a	n/a	n/a	n/a	n/a	1.00x
S1	KF per-step	float64	rmse (state)	0.4233	0.4233	n/a	n/a	n/a	n/a	n/a	1.00x
S1	KF per-step	float64	time_per_step (ns)	13,252	10,320	n/a	n/a	n/a	n/a	n/a	0.78x
S2	KF batch	float64	max_abs_diff (state)	n/a	n/a	n/a	n/a	n/a	n/a	3.32e-12	n/a
S2	KF batch	float64	peak_memory (bytes)	n/a	n/a	n/a	4,165,368	n/a	n/a	3,866,229	n/a
S2	KF batch	float64	rmse (state)	0.5073	n/a	n/a	0.5073	n/a	n/a	0.5073	1.00x
S2	KF batch	float64	time_per_step (ns)	577.5	n/a	n/a	2,786	n/a	n/a	38,978	67.49x
S2	KF per-step	float64	max_abs_diff (state)	n/a	3.55e-15	n/a	n/a	n/a	n/a	n/a	n/a
S2	KF per-step	float64	peak_memory (bytes)	325,324	324,632	n/a	n/a	n/a	n/a	n/a	1.00x
S2	KF per-step	float64	rmse (state)	0.5073	0.5073	n/a	n/a	n/a	n/a	n/a	1.00x
S2	KF per-step	float64	time_per_step (ns)	13,442	10,556	n/a	n/a	n/a	n/a	n/a	0.79x
S3	EKF	float64	nees (-)	4.002	4.002	n/a	n/a	n/a	n/a	n/a	–
S3	EKF	float64	rmse (state)	0.8896	0.8896	n/a	n/a	n/a	n/a	n/a	1.00x
S3	UKF	float64	nees (-)	4.001	3.979	n/a	n/a	n/a	n/a	n/a	–
S3	UKF	float64	rmse (state)	0.8896	0.8896	n/a	n/a	n/a	n/a	n/a	1.00x
S4	KF	float32	steps_to_failure (steps)	2,753	n/a	1,000,000	n/a	1,000,000	67,589	n/a	0.04x
S4	KF	float32	steps_to_indefinite (steps)	2,753	n/a	1,000,000	n/a	1,000,000	1,000,000	n/a	0.0028x
S5	KF batch	float64	peak_memory (bytes)	n/a	n/a	n/a	42,821,472	n/a	n/a	45,672,193	n/a
S5	KF batch	float64	rmse (state)	0.1865	n/a	n/a	0.1865	n/a	n/a	0.1865	1.00x
S5	KF batch	float64	time_per_step (ns)	5,535	n/a	n/a	23,730	n/a	n/a	52,290	9.45x
S5	KF per-step	float64	peak_memory (bytes)	1,222,492	1,220,296	n/a	n/a	n/a	n/a	n/a	1.00x
S5	KF per-step	float64	rmse (state)	0.1865	0.1865	n/a	n/a	n/a	n/a	n/a	1.00x
S5	KF per-step	float64	time_per_step (ns)	22,639	18,923	n/a	n/a	n/a	n/a	n/a	0.84x

• KF per-step rows: kalman-py is the step-by-step API (NumPy). KF batch rows: kalman-py is the JAX backend on CPU and kalman-py-numpy the NumPy backend; JAX has no peak_memory because tracemalloc can't see its buffers. max_abs_diff is the largest difference between kalman-py and that library's estimates.
• S3 UKF: kalman-py redraws sigma points from the predicted distribution before each update, while FilterPy reuses the propagated ones, so their estimates differ slightly; the EKFs agree to ~1e-13. A consistent filter has average NEES = 4.
• S4 (float32): FilterPy is n/a because it converts float32 inputs to float64 internally (its identity matrix is float64), so it can't run S4 as specified.
• S4: kalman-py is the default configuration (NumPy backend, Joseph form); kalman-py-sqrt uses square_root=True; kalman-py-jax is the JAX backend. 1,000,000 means the filter never failed.

Reproduce

ENV="$(git rev-parse --short HEAD),<cpu>,<os>,python-<version>,$(date +%F)"
uv run python benchmarks/run.py "$ENV"
uv run python benchmarks/accuracy.py "$ENV"
uv run python scripts/make_table.py results/results.csv kalman-py --readme README.md
uv run python scripts/plot_benchmarks.py