Why Does Fusion Localization Accuracy Decrease with Vehicle Speed and How to Optimize?

Abstract

Multi-sensor fusion (typically GNSS (Global Navigation Satellite System) integrated with an IMU (Inertial Measurement Unit)) is the foundation of current vehicle positioning. Practitioners intuitively know that fusion-based localization works well at low speed (less than or equal to 30 km h⁻¹) and deteriorates substantially at higher speeds (greater than or equal to 80 km h⁻¹). This degradation can be a serious concern for autonomous driving applications, on highways in particular, as well as for fast manoeuvring. This technical paper provides a comprehensive investigation of the underlying causes for this speed-dependent error growth, quantifies the role of the contributing factors, and suggests a set of optimisation strategies for use in real-time autonomous vehicle pipelines.

We find the loss of accuracy is not due to a single factor but a complex combination of IMU integration drift, motion model mismatch, sensor-specific high speed limitations and system latencies. The discussion is based on error-propagation theory, analysis of specifications of sensors and best-practice fusion implementations (e.g., EKF/UKF, tightly-coupled architectures, factor-graph optimization)^{1 2}. Recommendations are to increase IMU sampling rates, use dynamic and adaptive motion models, use more robust fusion architectures such as tight coupling, and make use of complementary sensors such as wheel odometry and LiDAR to provide independent constraints³. A validation scheme for benchmarking is described for a wide range of speed regimes.

1. Introduction

Highly accurate, continuous and robust vehicle localization is a necessary prerequisite for the entire autonomous driving stack and directly affects path planning, motion control and system safety. While Global Navigation Satellite System (GNSS) is a global absolute position reference, its performance under harsh environments such as urban canyon and tunnel environments is very unreliable due to the occlusion of the signal and multipaths. Furthermore, it is not updated fast enough (typical update rates of 1-10 Hz) for capturing the fast dynamics of a moving vehicle.

In order to overcome these shortcomings, GNSS is almost universally combined with an Inertial Measurement Unit (IMU). The IMU, which consists of accelerometers and gyroscopes, provides high rate inertial measurements (e.g., 100-1000 Hz) which can be used to propagate the state of the vehicle between infrequent GNSS measurements. However, all IMUs have inherent biases and noise that when combined produce an error in position that scales cubically with time⁴.

The combination of GNSS and IMU is expected to address the shortcomings of both sensors; GNSS compensates for the long-term drift of the IMU, and IMU compensates for the disruptions between GNSS measurements⁵. While this synergy works well under benign conditions, propaganda from industry pilots and academic test-beds, reports empirical evidence of a speed-dependent increase in position error⁶. A localization system that is centimeter accurate in a parking lot might have errors on the order of meters in a highway. Understanding why and how to mitigate this is important for the creation of strong autonomous systems that can safely operate in a high-speed environment. This study breaks down this important problem by discussing the sources of this fundamental error and suggesting a holistic optimization strategy.

2. Basics of GNSS/IMU Fusion

A good localization system is based on a well chosen set of sensors and an advanced algorithm to combine their data. The key idea is that by taking advantage of the complementary nature of the different sensors, a result can be obtained that is more accurate and reliable than that possible with any single sensor.

2.1 Essential Components and Their Functions

Fundamentally, the performance of a fusion system is related to the quality and the characteristics of its input sensors. The table below lists the components that are generally used in a modern vehicle localisation system.

2.2 Popular Fusion Architectures

The way in which the sensor data are fused has a strong effect on performance, robustness and computational complexity. The most popular architectures are:

• Loose Coupling: This is the easiest integration strategy. The GNSS receiver calculates its own position and velocity solution, and this is passed as a measurement update to a filter (usually an Extended Kalman Filter, EKF, or Unscented Kalman Filter, UKF) that also takes in imu data¹⁵. Its main disadvantage is that if the GNSS receiver is not able to compute a solution (less than four satellites visible), no correction can be provided for the IMU, even if some satellite signals are still available.
• Tight Coupling: In this more complex architecture, the raw GNSS observables (i.e., pseudoranges and Doppler shifts) are combined directly with the IMU measurements in a single, overall filter. Such methods are more resilient since they can retain information from as few as one or two visible satellites to constrain drift (i.e., speed assist), so that the filter can still be maintained with degraded accuracy during partial GNSS outage¹⁶.
• Factor-Graph / Batch Optimization: This algorithm solves the problem in a more different way. All measurement data (from IMU, GNSS, LiDAR etc.) over a time window are represented as constraints (factors) in a graph form¹⁷. An optimization algorithm then computes the trajectory that optimizes all the measurements at the same time. However, this type of global optimization is computationally more expensive, but may produce more accurate results, particularly in more complex problems. Incremental solvers such as iSAM2 make such an approach practical for real-time applications¹⁸.

Crucially, all three architectures are based on the use of a motion model to propagate the state (position, velocity, orientation) of the vehicle between measurement updates using IMU data . As we will discover, the choice of this model and its representation of real world vehicle physics have a significant effect on performance during high dynamic, high speed manoeuvres¹⁹.

3. Sources of Speed Dependent Error

The breakdown of localization accuracy with speed is not a single phenomenon, but the sum of several sources of error that grow strong as vehicle dynamics are increased.

3.1 Sampling Rate and Integration Drift of IMUs

The essential task of an IMU in a fusion filter is to forecast the vehicle state in the future. This is accomplished by combining the measured angular rates to obtain orientation and double integrating the linear accelerations to obtain position. This discrete integration procedure is one of the main sources of error.

A permanently remaining bias b of an accelerometer or gyro measurement, integrated over time interval DT, gives rise to velocity and position errors. The error in the constant bias is a power law in time:

• Velocity Error ∝ b ⋅ Δt
• Position Error ∝ b ⋅ Δt²

Higher accelerations and angular rates typically occur at higher vehicle speeds, when the vehicle is changing lane or braking. If the sampling rate of the IMU is low, the Δt between measurements is too large and cannot capture the curvature of the motion profile correctly. The filter also assumes a more basic motion between samples (e.g. constant acceleration), which causes large integration errors. For example, a transient acceleration event that happens for a very short duration may not be detected or could be averaged between two samples resulting in a change in the estimated state to a value different from the true state. The higher the sampling rate, the smaller the Δt becomes, and the more finely grained view of the vehicle dynamics is, and therefore the lower the integration error²⁰. In general, sampling rates that are too low (i.e., below 100 Hz) are a major factor in poor performance at high speeds.

3.2 Motion Model Mismatch

The prediction stage of the Kalman filter uses a motion model to characterize the motion of the vehicle. Some common models are Constant Velocity (CV) and Constant Acceleration (CA). These models are computationally easy, but are poor approximations of real vehicle dynamics at high speed.

• Low-Speed Regime (30 km/h or Less): Generally, in this range the vehicle movement is smooth. Kinematic models, which assume point mass, and do not take into account forces such as tire slip, are usually adequate. The CV/CA models perform fairly well for stop and go traffic, or parking maneuvers.
• High-Speed Regime (>=80 km/h): Here, on a highway, dynamics are much more complicated. Simple kinematic models can no longer describe the relationship between lane changes, steering and suspension effects. Dynamic models that involve vehicle parameters such as mass, tire parameters, steering geometry (e.g., the bicycle model) are needed for accurate prediction.

When the model used at high speed is a simple one (e.g., CV), then any deviation from the model (such as steering input in the case of a lane change) is considered as unmodeled error. The filter’s estimate will always be behind or ahead of the actual vehicle state, and when a GNSS update becomes available it results in a large correction step. This leads to noisy and inaccurate position estimate. the larger the discrepancy between the model and reality, the larger the prediction error, the worse the ultimate fused solution²¹.

3.3 Speed Problems Unique to Sensors

Different failure modes in each sensor of the suite, which are magnified at high speeds.

• IMU Vibration: High-frequency vibrations are injected into the car chassis through high speed on uneven road surfaces. These vibrations can lead to a degradation of the performance of consumer grade MEMS IMUs, introducing additional noise and bias instability, further corrupting the integration process.
• Wheel Odometry Slip (WOS): The WOS problem occurs in a case of fast acceleration or heavy braking, which are more likely to happen at high speed, and the wheels slip relative to the road surface. Wheel Odometry works under a no-slip assumption and will thus report an incorrect velocity, adding a large amount of error to the filter if it is not detected and canceled out.
• LiDAR/Camera Distortion: Perception sensors are also distorted at high speeds. LiDAR scanners are prone to motion distortion, where the point cloud is skewed or is deformed by significant motion of the vehicle while taking a single scan. This gets the scan-matching used for localization dirty²². Likewise, cameras can undergo large motion blur that can cause problems as features for visual odometry or map-based localization cannot be reliably extracted and tracked.

3.4 Latency and Time Synchronization of a system

Even very small delay times can have a significant position effect at 120 km/h (= 33.3 m/s). A system latency of 50 milliseconds between the time that the sensor makes the measurement and when the fused position is computed produces a baseline error of 1.67 meters. This latency error is in linear proportion to the speed. In addition, the high-rate IMU and low-rate GNSS time synchronization becomes more important. A timestamp error of 10 ms will cause the position corrected for to be wrong by 33 cm, which means the filter will “correct” the state based on incorrect information.

4. Optimization Strategies

The speed-dependent accuracy issue must be tackled from a variety of fronts, including hardware and fusion algorithms.

4.1 Enhancing the IMU Subsystem

Since the IMU is the main sensor for the state prediction, an improvement of its data quality is the first step.

• Increase Sampling Rate: The most direct method of decreasing integration error is to increase the sampling rate of the IMU. The point of the matter is: If you switch from 100 Hz IMU to 400 Hz or 1000 Hz, your time interval DT is dramatically decreased, and you can more accurately capture your high-frequency dynamics. This improves the error which is built up between the GNSS updates.
• Use Higher Grade IMUs: Automotive grade MEMS IMUs are low cost but lower in bias stability and higher in noise. Tactical-grade IMUs are an order of magnitude more stable (i.e., < 0.1 deg/hr vs. 1-10 deg/hr bias stability) and are significantly faster. This improves the overall system resiliency to drift, particularly in the case of prolonged GNSS outage.

4.2 Using Dynamic and Adaptive Motion Models

The simplistic CV/CA motion models need to be substituted by models that have a better reflection of vehicle physics and speed.

• Implementation of High Fidelity Models: Models of vehicles kinematics such as the dynamic or kinematic bicycle model must be employed. These models are capable of taking control inputs (such as steering angle from CAN bus) into account, which enables the filter to make proactive predictions rather than reactive ones of turns and lane changing. This hugely minimizes the error of prediction.
• Adaptive Filtering: Motion of the vehicle is not repetitive. The adaptive filter can change its parameters dynamically according to the current driving situation. As one example, the process noise covariance matrix (Q) of a Kalman filter (which represents the uncertainty of the motion model) can be increased during a turn (detected by high yaw rate), and decreased during straight-line driving. This has the effect of making the filter more responsive if required and more stable otherwise.

4.3 Improvements in Architecture and Algorithm

It is shown that the choice of fusion architecture is of vital importance for the robustness.

• Prefer Tight Coupling: Tight coupling is by its very nature more robust than loose coupling in poor GNSS environments as discussed²³. Through the use of raw observables, it can make use of partial satellite information that would be discarded in a loosely coupled system, offering valuable velocity constraints which compensate for IMU drift.
• Use Factor-Graph Smoothing: Factor graph smoothers are used when the highest degree of accuracy is desired²⁴. By optimizing over a sliding window of measurements, they can eliminate ambiguities and return a globally more consistent trajectory than recursive filters, which is especially useful after complex and high-dynamic manoeuvres.
• Multi-Rate Filtering: The fusion algorithm should be able to efficiently handle sensors with different update rates. A typical implementation would be to carry out the high-frequency IMU prediction with its native frequency (e.g. 400 Hz), and only apply the more computationally intensive correction step when a new measurement from a low-frequency sensor (GNSS, LiDAR) is received.

4.4 Fusing Complementary Sensors

To create a really robust system, it is important to implement sensors that are immune to failure modes of GNSS and IMU.

• Wheel Odometry: High resolution Wheel encoders give a direct measurement of the vehicle longitudinal velocity. This information is very useful for constraining the IMU’s accelerometer bias, a large source of along-track drift.
• LiDAR/Camera for SLAM and Map Matching: These perception sensors add geometric constraints through the matching of features in the environment with either a map that was previously built (SLAM) or a pre-existing HD map. This gives a source of absolute position information that is entirely independent of GNSS signals and vehicle dynamics. This is particularly efficient in correcting lateral position drift over long highway sections where the GNSS may not always be reliable.

5. Validation and Benchmarking System (VBS)

In order to systematically identify and validate improvements a strict validation framework should be established. Performance of localization systems must not be compared based on a single ‘average’ performance figure. Instead, performance has to be benchmarked over a full range of driving scenarios and speed regimes.

1. Design Test Scenarios: Design a test set of driving tests including:

• Low speed Urban stop and go driving (<= 30 km/h).
• Medium speed suburban driving (30 – 80 km/h) with turns and roundabouts.
• High speed driving on highways (>=80 km/h) including straight line, gentle bend and severe lane change.
• Driving scenarios that can challenge the system, such as driving through tunnels (GNSS outage) and hard braking maneuvers (high dynamics, possible wheel slip).

2. Establish Ground Truth: A high precision, post-processed inertial navigation system (INS) using multi-frequency, multi-constellation RTK-GNSS represents the ground truth reference.

3. Define KPIs: Performance should not be viewed solely as an aggregate measure, but broken down by scenario. Key metrics should include:

• Root Mean Square Error (RMSE) for 2D position, altitude and velocity (calculated independently in each speed regime).
• Maximum Absolute Error (Max Error) to determine worst case performance when making difficult maneuvers.
• Error Distribution (95th/99th percentile) to understand the tail end performance and reliability
• Availability/Continuity: The fraction of the time that the system produces a solution within a given accuracy bound.

By separating the performance metrics according to the speed and the dynamics, engineering personnel can identify certain weaknesses in detail and verify the effectiveness of the proposed optimization measures.

6. Conclusion

The generally observed decrease in fusion localization accuracy, as vehicle speed increases, is not a consequence of one particular defect, but a multifaceted systems engineering challenge. This is because of the compounding effects of IMU integration errors related to insufficient sampling rates, incomplete motion model where simple models break down when complex high-speed dynamics occurs, sensor-specific limitations such as vibration and motion distortion, and the amplified effect of system latencies.

There is no “silver bullet” solution. Robust, high accuracy localisation in all the speed regimes can only be achieved in a holistic way. This involves:

• Better Hardware: Higher frequency and less noisy IMUs.
• Smarter Algorithms: Using High Fidelity Adaptive Vehicle Dynamics Models.
• Robust Architectures: The use of tightly-coupled or factor-graph-based fusion engines, rather than simpler loosely-coupled designs.
• Sensor Redundancy: The use of complementary sensors such as wheel odometry, LiDAR, and cameras which provide independent constraints which are robust against the failure modes of a pure GNSS/IMU system.

By systematically treating each of these areas and proving performance against a robust, speed-binned benchmarking model, self-driving vehicle localization systems can be developed that are not only robust in the parking lot, but robust on the open highway as well.

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