Reduced Integration Time Improves Accuracy in Dead Reckoning Navigation Systems

An automotive dead reckoning (DR) navigation system uses a gyroscope (gyro) to estimate the vehicle’s instantaneous heading. This information, combined with the distance traveled, allows the navigation system to correctly determine the vehicle’s position, even when the satellite signal is blocked in a crowded downtown area or a tunnel. A major challenge to using a gyro in DR navigation is that the satellite signal may be lost for a long time, causing the accumulated angle error to become too large to accurately position the vehicle. This article offers a simple way to solve this problem.

How DR Navigation Works

Figure 1 shows the basic operation of DR navigation. A gyro measures the vehicle’s rotation rate in degrees per second. The angle, which represents the vehicle’s instantaneous heading, is calculated by integrating the rotation rate over time. Combining the heading and distance traveled allows the vehicle’s position to be determined, as indicated by the red line.

Figure 1
Figure 1. How DR navigation works.

With a digital gyro, the integrated rate can be expressed as the sum of rate samples multiplied by the sampling interval:

Equation 1

where ri is rate sensed by the gyro, n is the number of samples, and τ is the sampling interval.

The angular error accumulated over time can be expressed as:

Equation 2

where ei is rate error for each sample, n is the number of samples, and τ is the sampling interval.

According to the formula, as the required integration time gets longer, the accumulated error gets bigger, as shown in Figure 2. These rate samples, measured using an evaluation board with the ADXRS810 high-performance angular rate sensor, simulate a DR navigation system with 3300 total rate samples recorded. The blue line shows the gyro rate samples; the red line shows the accumulated angular error. It is obvious that the accumulated angular error increases with time.

Figure 2
Figure 2. Rate measured using ADXRS810 evaluation board. (Note: angular error is not to scale.)

Using a Low-Pass Filter (LPF) to Reduce Integration Time

The traditional method to reduce angular error focuses on minimizing en, but today’s digital gyros already have very low rate error specifications. The ADXRS810, for example, features 80 LSB/°/sec sensitivity, ±2°/sec offset, and 0.03°/sec/g shock immunity, leaving limited room for improvement. In addition, the algorithm to compensate en is complicated. Compared to other applications, such as electronic stability control (ESC), for example, the gyro in a DR navigation system can run for long periods of time, as would be the case when the GPS signal is lost as the vehicle travels through a long tunnel. Longer running time causes the accumulated angular error to be more significant in DR navigation applications.

If the integration time could be reduced, it would significantly decrease the accumulated angular error. When the gyro is not rotating, the rate output is small, but nonzero, due to gyro noise. The ADXRS810 achieves very low gyro noise and very high sensitivity, making it easy to filter out noise in the digital domain simply by setting the appropriate threshold. This process is equivalent to low-pass filtering, as the gyro rate noise is at a high frequency compared to the rate output due to rotation.

Figure 3 shows the LPF version of Figure 2, where all rate samples less than 1°/s are zeroed and, therefore, ignored when doing rate integration. The remaining integration time, considered effective integration time, is only about 16% of the total integration time. This provides a significant reduction of integration time. As a result, the accumulated angular error is also significantly reduced, as indicated by the red line.

Figure 3
Figure 3. Rate measured using ADXRS810 evaluation board and digital LPF. (Note: angular error is not to scale.)

In a practical application, the vehicle steering wheel is normally positioned at zero degrees. Thus, the effective integration time for gyro rates can be reduced by ignoring it, just as was done in the experiment described in Figure 3. Figure 4 shows gyro rate samples from a real in-vehicle test. Traveling through a tunnel for about 180 sec, it requires 180 sec for rate integration. Without the LPF process, the accumulated error over 180 sec can be up to 4°, which is too big to correctly determine the vehicle’s location in the tunnel. By implementing the LPF process with a 0.5°/sec threshold, the effective integration time is reduced to only 84 sec, a reduction of about 53%. The accumulated error drops to about 0.5°, as shown in Figure 5. The LPF threshold can be set to achieve the accuracy required for the specific application.

Figure 4
Figure 4. Unfiltered in-vehicle gyro rate samples. (Note: angular error is not to scale.)
Figure 5
Figure 5. In-vehicle gyro rate samples after LPF. (Note: angular error is not to scale.)


Today’s digital gyroscopes have excellent specifications, so the room to improve performance is quite limited. In vehicle DR navigation systems and other applications that require long integration times, setting an LPF threshold to reduce integration time is a simple but also effective method to improve accuracy.

The ADXRS810 high-performance, low-cost digital gyro uses ADI’s innovative MEMS technology, making it a good choice for vehicle DR navigation applications. Housed in a very small package, it provides low offset, low noise, and high rate sensitivity. Temperature compensated on chip, it eliminates the need for an external temperature sensor and eases the algorithm for temperature compensation. Its high immunity to shock and vibration is very important in automotive applications.



Ben Wang

Ben Wang, a field applications engineer (FAE) in Shenzhen, China, graduated from Hunan University. Prior to joining Analog Devices in June 2009, Ben worked for six years at National Semiconductor.