Robust Kalman filtering for vehicle localization under misspecification.

This project built a modular state-space simulation environment to compare standard Kalman filtering with robust variants under sensor dropout, delayed observations, outlier regimes, correlated process noise, measurement misspecification, and asynchronous updates.

See project summary Open GitHub repository

Key Outcomes

Robust filtering improved tail behavior under noisy regimes.

Median Error

-49%

relative to a standard Kalman filter

95th Percentile

-44%

tail error under mixed dropout/outlier regimes

Runtime

100 Hz

near-real-time C++ localization loop

Project Breakdown

Problem, method, system, validation, results, reliability, and research value.

Problem

Linear-Gaussian assumptions can fail sharply in vehicle localization.

Dropout, delayed observations, outliers, correlated process noise, and measurement misspecification can destabilize recursive estimates.
The project needed a controlled simulation environment to separate algorithmic robustness from scenario luck.

Method

Robust recursive estimators were compared against a standard Kalman filter.

Implemented innovation chi-square gating, covariance inflation, adaptive noise estimation, Huberized updates, Student-t observation models, residual clipping, and outlier rejection.
Derived the linear-Gaussian filter and motivated robust M-estimation variants in a technical note.

System / Stack

The simulation was modular enough to vary dynamics and sensor behavior.

Used Python, NumPy, SciPy, MATLAB, C++, stochastic simulation, state-space models, recursive Bayesian estimation, and robust statistics.
Included configurable dynamics, observation models, sensor dropout, delayed observations, outlier regimes, correlated process noise, measurement misspecification, and asynchronous update schedules.

Validation Methodology

Robustness was measured under controlled failure regimes.

Compared standard and robust filters under mixed dropout/outlier regimes, misspecified covariance, biased sensors, and delayed observations.
Measured median error, 95th-percentile error, update stability, and real-time feasibility.

Results

Robust variants improved both central and tail error.

Reduced median localization error by 49% and 95th-percentile error by 44% relative to a standard Kalman filter.
Preserved near-real-time execution at 100 Hz in a C++ loop.

Failure Modes / Reliability Checks

The analysis documented where the filters break.

Analyzed covariance misspecification, high-leverage measurements, biased sensors, delayed observations, loss of observability, and ill-conditioned covariance updates.

Why It Matters for Research

State-space estimation is a concrete bridge between theory and reliable systems.

The project connects derivation, numerical stability, stochastic simulation, and real-time constraints in a falsifiable experimental setup.