Dead Reckoning (DR) is becoming increasingly important as more systems demand reliable, uninterrupted positioning in all environments. Traditional GNSS navigation, including RTK, multi-constellations and multi-frequencies, has developed and served many applications; however, in places where GNSS is weak such as in dense urban environments, indoors, and underground, dead reckoning using inertial navigation is needed to “fill in the blanks”. In applications such as fleet tracking and urban navigation, a continuous and reliable positioning solution is necessary. Which begs the question, “Can one inertial navigation system fit all applications?”

To put it simply, no. A properly designed Dead Reckoning solution needs to consider specific requirements of the problem at hand.

Dead Reckoning is based on quantifying any measurable change that would indicate a change in location or motion. Three potential sources of positioning information are shown in the graphic below:

Positioning Information Inputs and Outputs

There are three variable inputs that define the quality of positioning information a dead reckoning system can produce – (1) absolute sensors, (2) relative sensors, and (3) motion models & constraints.

Absolute Sensors

Absolute, or exteroceptive, sensors acquire information from the environment to give absolute position and orientation information, such as coordinates on a map. GNSS, radar, and lidar are all examples of absolute sensors that measure values related to the surroundings of the navigation platform. These sensors typically need infrastructure and previous knowledge of the environment (e.g. maps) to give absolute position.

Due to their external nature, absolute sensors can be disturbed, jammed, or spoofed causing potentially dangerous continuity issues. In applications such as autonomous driving or robotics, a high precision dead reckoning system must maintain positioning until information from these external sensors can be re-acquired. The sensors required for decimeter-level precision control in an automobile are not the same sensors required to obtain the 1-3m accuracy needed for tracking an escooter or ebike to ensure it is parked in a proper place and in a proper orientation.

Relative Sensors

Relative, or proprioceptive sensors, measure the internal state of the system. Using inertial sensors such as accelerometers, gyroscopes, and barometers, as well as speed sensors, a relative position can be determined based on the sensed dynamics of the platform. These self-contained sensors require no previous knowledge of their environment, as they quantify the platform’s current position based on direction and distance travelled from the last known point.

Inertial measurement units (IMU’s) are the backbone of inertial navigation systems and their performance varies widely from low-cost MEMS devices in consumer electronic devices to very high performance RLG/FOG technology in military equipment.  When choosing an IMU for positioning purposes, two of the most important factors are the gyro bias instability and the gyro angular random walk (ARW) parameters.  The below plot shows the results of an Allan Variance analysis performed on an InvenSense MEMS IMU.  The bias instability is obtained by taking the bottom curve where slope is zero and the ARW is taken at the beginning of the curve where the slope is -0.5.

Gyroscope Noise

Gyroscope AVAR

A theoretical assessment of the position errors resulting from different bias instabilities and ARW combinations is provided in the following table.  This shows the estimated error drift of a vehicle travelling with only IMU measurements for its positioning during a 30 second GNSS outage at 30 km/hr, after being calibrated with RTK GNSS.  An improvement of approximately 2x can be seen on positioning results between each example, which requires more than 10x improvement on both bias instability (BI) and ARW.



Figure 1: ICM-40607-i Allan Variance Assessment

Although bias instability and ARW are two important factors, there are many other error parameters that could be of interest for a specific application.  More in-depth details can be found from this excellent early reference on Allan Variance and error sources.

Motion Models & Constraints

The models and constraints vary based on the expected motion for each platform. To track a person walking with a mobile device, it is assumed that this person has 2 legs, and their arm movements balance their leg movements. These motion characteristics vary greatly from the motion model and constraints of a 4-wheel vehicle and how it turns or a 2-wheel micromobility vehicle, like an escooter or ebike.

Motion models and constraints can only be applied effectively to limit IMU errors if the IMU orientation is in the same 3D direction as the platform of motion.  This complicates matters significantly for mobile phones in pockets or IMU’s mounted inside vehicle infotainment systems that are not aligned with the vehicle.  Our team has spent decades solving these misalignment, use-case, and motion model problems for human and machine dynamics.  Several applicable applications can be found here:


Dead Reckoning is Not One-Size Fits-All.

Each platform requires a customized approach to optimize dead reckoning performance, and the Trusted Positioning team are experts inertial error modeling, designing motion models and integrating with sources of absolute positioning information. With over 100+ patents in inertial and integrated positioning, our team can utilize any combination of sensors to produce a dead reckoning solution tuned to your application.

For more information visit:

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