Inertial Measurement Units and Inertial Navigation_V1

High Accuracy Edge Technology Used on Inertial Measurement Units

1.       Advanced Inertial Measurement Units for Low Cost Solution

The VAST Inertial Measurement Unit (V-IMU), an integrated multi-sensor package, combines multiple accelerometers, gyroscopes and magnetics to produce a three-dimensional measurement of both specific force, angular rate and magnetic fields. All sensor force, angular and magnetics signals are calculated and filtered using a powerful micro-processor to improve noise reduction and bandwidth improvement so that an inertial reference frame, as for example the Earth-Centered Inertial reference frame, can be successfully generated. Specific force is a measure of acceleration relative to free-fall. Subtracting the gravitational acceleration results in a measurement of actual coordinate acceleration. Angular rate is a measure of rate of rotation.

In recent years, the IMU has become an umbrella term used to describe a wide assortment of inertial systems including Attitude Heading Reference Systems and Inertial Navigation Systems.

Using the V-IMU functions in accordance with its classical applications, the combination of a 3-axis accelerometer, a 3-axis gyro and a 3-axis magnetic fields shown in Figure 1 with four layers of software design 

·                      to improve V-IMU security and accuracy and

·                      to help V-IMU quick calibration

·                      to optimally remove MEMS noises from V-IMU due to installation, environment, and MEMS itself

V-IMU can be produced to provide land, marine and aerial applications.  An onboard processor has memory, and temperature sensor to consolidate a digital interface, unit conversion and to apply a sensor with autonomous calibration model.

The VAST V-IMU by itself does not provide any kinds of navigation solution (position, velocity, attitude). It only actuates as MEMS sensors in the design, in opposition to the INS (Inertial Navigation System), which can be used to integrate the measurements of its internal IMU to provide a navigation solution. For instance, an Inertial Navigation System (INS) applies GPS data with an IMU to form a self-contained navigation system, which uses Kalman filter with IMU and GPS information to provide attitudes measurements to track the position, velocity, and orientation of an object relative to a starting point, orientation, and velocity.

Figure 1: V-IMU Design Diagram

IMU can also be embedded with GPS to form AHRS-GPS, which will bring aerospace navigation from pure sensor data to guidance and navigation system level, called Inertial Navigation System (INS). In fact, INS can be considered as blended IMU and GNSS Navigation System, which embeds a GPS/GNSS, fuses inertial, navigation, and aiding data (odometer, ADC, etc.).  Additionally, a good INS shall have the following algorithms being implemented in the software calculation and orientation for its accuracy:

·       Extended Kalman Filter is employed to provide roll, pitch, heading, position, and velocity.

·       Transformation conversion can be used to provide all GNSS earth and body coordination conversional data

Application of IMU can then be integrated from basic level to advanced guidance and navigation fields.

Similarly, to aerospace application, IMU can also be used for automobile industries. To achieve this goal, the satisfaction of the following electronic hardware design must be -pre-considered and implemented:

Certification On Electronics Hardware (EH):

Since VAST employees were originally worked in aerospace industries. Design of V-IMU EH had taken DO-160G related items into considerations.  This is so far the strictest metof to certify the electronics hardware in the world.  Therefore, VAST V-IMU satisfies most of DO-160G requirements shown in the below table, which will automatically satisfy the automotive and other industries:

·       To pass huminity * related items, the sensor board for all MEMS sensors are isolated and sealed by glue

·       To pass vibrations, low pass vibration filtering form such as (Mass-M, Damper-C, Spring-K) is used inside the sensor board to achieve the sensor board suspension design

·       To pass radiation and lightning # items, the metal case with sufficient surface ground between PCB and metal case is employed

·       For temperature /altitude related items, an additional suitable temperature sensor is called-out. Software related calculation for temperature compensation was implemented into the software.

·       To shorten manufaturing process due to MEM sensor velocity / anguler randam walk variance, innovated auto trim software algorithm is innovated and correctly trim the gyroscope and accelometers back to zeor while they are small drift off the center.

·       To correctly respond the MEMS healthy check, aerospace BIT tests are implemented to help verify MEMS self-test.

·       Dual MEMS were used to make sensor signals redudancy availbility.

By satifying the most criteria requirements from arospace inductries, it is belived that most UAV and automotive products in the market can automatically reach their best performance.

Many automobile and small UAV pain points have been identified through OVOC. These pain points are:

·                      Gyro movement heavily coupled with respect to acceleroment impact response

·                      Gyro and accelerometer outputs greatly affected by ambient temperature 

·                      Gyro nonlinearity

·                      Slow output data rate cannot be used for feedback control

·                      -3dB Bandwidthe not quick enough for application

·                      Data output shifts due to long endurance operation

The innovated advanced inertia measurement unit (V-IMU) has have taken the above requests and included the following innovated functions for the product improvement:

1)       Sensor board with (MCK) mechanical design to make the sensor suspended to work as high-pass filter to avoid mechnical frequencies and amplititudes into the sensor measurements

2)       Adjustable values of (MCK) values make sensor board to allow various automobile impact responses while the sensor is measuring

3)       Optimization of minimizing sensor noise energy function guarantees that the software calculation algorithm will be converged with better Allan Varince results.

4)       Dynamical lead transfer function will help remove the softtware calculation time delay to bring the sensor board back to desire measurement speed

5)       Software auto-trim artifitial-intelligent knowledge-based control algorithm to give the sensor board design without any temperature compensation.

6)       Dual sensor board output to allow the MEMS measurement to be redudancy measurement available to lower the sensor board failure rate from 10-3 to 10-5.

7)       Dual CAN outputs will allow one sensor board being used for two control units

8)       Dissimilarity MEMS sensors in one board to satisfy Aero common failure requirements

Beside the above advanced technologies, VAST also applies a trim command from aerospace to its V-IMU, which allows an operating system to inform a vehicle control server computer (VCSC) its trim position. Therefore, the vehicle internally in force and moment can be balanced during the entire operation by removing drift so that the aircraft or automobiles will have better steady state flight/drive.  All small noise variations from 6 DOF  forces and moment can be optimally reduced. Therefore, using VAST V-IMU can help improve the vehicles in disturbance performance.

3.       The Inertial MEMS IMU Sensor Market

The inertial sensor or MEMS IMU market spans an enormous range in terms product price and performance based on their accuracy and quickness. There are at least six orders of magnitude difference in price and performance between the highest end inertial systems and the lowest.

This can lead to great confusion for many buyers when dealing with component selection and pricing. The goal of VAST V-IMU innovation is to provide an edge technology to make low cost MEMS with high accuracy V-IMU being available and possible for IMU market and its adjacent markets.

IMU application can be classified based upon definitions of high, medium, and low-cost performance. What one expert considers high-end may be low-end to another and vice-versa. When searching for inertial MEMS IMU systems, one may come across the terms Tactical or Automotive applications. These terms define different performance classes which similar inertial sensors can be grouped. In general, inertial sensors can be grouped into one of the following four performance categories.

·       Marine & Navigation Applications

·       Tactical Applications

·       Industrial Applications

·       Automotive & Consumer Applications

3.1       Marine & Navigation Applications 

Aside from the custom IMU used on military applications, the marine inertial systems are the highest inertial sensors that are commercially available. They provide the best overall performance in terms of both determining position and orientation. These systems are typically used on ships, submarines, and some spacecraft. A high-end marine-application IMU can cost over 1 million dollars. These systems will typically provide un-aided navigation solution drifts that are less than 1.8 km per day. This means that if the device were left stationary for one day, due to slight errors in the sensors and imperfect sensor calibrations, after integrating the position solution, the calculated position after one day would be 1800 meters away from the sensors actual position. This represents the best that is possible with commercially available inertial sensing technology. Navigation grade systems have slightly lower performance than the marine systems and are typically used on commercial airliners and military aircraft worldwide. A navigation grade system will typically have less than 1.5km drift per hour. These systems cost around $100,000 and have a size of about 6in x 6in x 6in. A navigation grade system can be combined with GPS to create positioning systems that are accurate to within centimeters in real-time. An example of a navigation grade IMU is the HG9900 IMU made by Honeywell.

3.2       Automotive & Consumer Applications

The lowest grade of inertial sensors is often referred to as automotive applications. They are typically sold as individual accelerometers or gyros. However, many companies have begun to combine multiple accelerometers and gyros from different manufactures to create self-contained IMU units. The automotive applications of IMU's are not accurate enough to be used for inertial navigation even when it is integrated with other navigation systems such as GPS. These sensors typically have good repeatability, and if they are calibrated after installation then they can be used as part of an industrial grade sensor, an Attitude Heading Reference System (AHRS), or a Pedestrian Dead-Reckoning System. Typically, these sensors can be used in anti-lock braking systems, airbags, active suspension systems, gaming controllers, and entertainment systems. The main difference between automotive grade and industrial grade lies in the quality of sensor calibration.  If one can develop an auto calibration system for IMU, the cost on IMU manufacturing assemble will be extremely reduced. A low cost IMU solution can then be mass production in no time.

4.       Which grade Inertial sensors are right for my application 

Determining which type of inertial sensor is right for your application can be a difficult process due to the lack of information available pertaining to the subject. Usually, the price is the first consideration while accuracy is within a certain value for example, the bias run-in value is within 10°/hour. Datasheets for inertial sensors can be very confusing and make it difficult for potential buyers to compare different products.

The first step is to determine which grade of sensors is required for your application. Trying to use an industrial grade IMU in an application that requires navigation grade performance will only lead to enormous levels of frustration and confusion. This is the step where you want to pick the right tool for the job. You don't want to use a bulldozer where you need a shovel, and you certainly don't want to use a shovel where you should be using a bulldozer.

In order to compare the performance of the different grade inertial sensors we will analyze them for two different use cases. Each case corresponds to a common use for inertial sensors.

5.       Case 1 - Unaided Position Estimate 

This case corresponds with using an IMU as a stand-alone inertial navigation solution without the assistance of GPS or any other external reference. Below is an overview of the typical errors for each grade of inertial sensors.

When determining how well an inertial system will perform as an inertial navigation system, a first order estimate is to assume that the errors in position will be caused only by the errors in the accelerometer bias. Errors in the position estimate will actually be caused by many factors including the gyro bias stability, accelerometer scale factor uncertainty, and many other parameters, however the largest contribution will be due to un-corrected errors in the accelerometer bias. Any bias in the accelerometer horizontal axes will cause an bias in the calculated orientation of the object in terms of pitch and roll. Since we have to subtract out gravity from the IMU accelerometer measurement prior to integration, any error in the calculated orientation will cause us to not correctly subtract out the gravity from the acceleration measurement. Since the amount of acceleration of an object is typically much smaller than the acceleration due to gravity (9.81 m/s^2), subtracting out gravity incorrectly can lead to very large errors in the estimated inertial acceleration which will directly integrate into position errors. The error in position due to a bias in the accelerometer will have quadratic growth with time.

The misalignment of the accelerometer axes will also performance of the inertial navigation system. It is important that each of the axes of the accelerometer are aligned perfectly with an orthogonal coordinate system. Errors in misalignment will propagate into position errors as shown in the table below.

The above table reinforces the importance of sensor calibration. Automotive sensors typically have package misalignments of around 1 and inter-axis misalignments of greater than 0.1. Industrial grade inertial sensors will typically have misalignments calibrated to within 0.05.

6.       Errors due to Gyro Bias Walk and Noise

The gyro noise and bias uncertainty will affect the position estimate error of an inertial navigation system. The affect of the white noise upon the integrated orientation angle is quantified by the gyro angle random walk parameter. The parameter multiplied by the square root of the integration time gives an estimate of the 1 sigma angle walk due to the gyro white noise. For navigation grade systems this can be a predominant source of error. For tactical, industrial, and automotive grades this does have an effect, however it can have an order of magnitude less effect than an accelerometer bias error that is left unaccounted for.

7.       How to estimate horizontal position error

You can estimate the amount of horizontal position error for a static case by simply using the accelerometer bias error given in the manufactures datasheet. For example let us look at a typical automotive grade MEMS accelerometer datasheet. The below excerpt is from the datasheet of the LIS344ALH 3-axis MEMS accelerometer made by ST Micro.

From the datasheet we find that the zero-g level is known to within 5%. Since Vdd for this part is 3V, this means we have a 75mV uncertainty. The datasheet also tells us that the sensitivity is 0.6 mV/mg. This means that the total uncertainty in the accelerometer bias is 125 mg. To calculate the maximum static case horizontal position error use the following formula:

In the above equation replace T with the time measured in seconds. For instance after 10 seconds with this accelerometer you could have as much as 60 meters error in calculated position.

The uncertainty in the accelerometer bias is the primary reason why automotive grade accelerometers cannot be used for inertial navigation. If this sensor is properly calibrated however, then the uncertainty in the accelerometer bias can be reduced by nearly two orders of magnitude, reducing the horizontal position error to within a few meters over the same 10 second period.

Errors due to axis misalignment can be calculated using the below formula.

The uncertainty due to the gyro angle random walk can be calculated as

8.       Case 2 - Relative Orientation Determination

Inertial sensor can also be used to determine the orientation as a function of time. Without an absolute reference an IMU can only be used to track changes in orientation from some initial point in time. For absolute orientation tracking you will need to combine an IMU with an absolute reference sensor such as magnetometer, camera, or GPS. Combining an IMU with a magnetic sensor creates what is known as an Absolute Heading Reference System (AHRS). For this case we will look at the error caused by the accelerometer that influence the orientation estimate. An AHRS determines orientation by making the assumption that the measured acceleration vector minus the known inertial acceleration is equal to the gravity vector. For cases where the actual inertial acceleration is unknown the AHRS assumes that the measured acceleration on the accelerometer is the actual gravity vector. Due to this assumption any errors in the accelerometer will translate into errors in the estimated direction of the downward direction. The gyros will dampen out much of the time based disturbances in the acceleration, however any constant errors in the accelerometer calibration parameters will directly propagate into orientation errors.

9.       Static Errors Due to Accelerometer Bias

A bias in accelerometer will affect the pitch/roll by perturbing the measured acceleration vector. This will affect the direction of the measured gravity vector, directly contributing to errors in the estimated pitch and roll. The below table shows typical errors in pitch and roll that are contributed due to the errors in accelerometer bias.

Errors in accelerometer bias for automotive grade sensors are mainly due to imprecise calibration. The errors in the industrial and tactical grade are typically due to changes in temperature which cause the accelerometer bias to deviate in ways that cannot be accounted for by the sensor calibration model. The accelerometer bias may also be subject to long-term drift that isn't accounted for in the sensor model.

10.       Static Errors Due to Accelerometer Misalignment

Errors due to accelerometer misalignment will on a first order translate directly into errors in pitch/roll. Shown below are typical misalignment calibration accuracy for each grade inertial sensors.

Misalignments are removed by performing a tumble test during the calibration procedure.

11.       Static Errors Due to Accelerometer Scale Factor 

The errors due to scale factor of the accelerometer can also contribute to the errors in the measured orientation. The magnitude of error is dependent upon the residuals after calibration. Shown below is the typical accelerometer scale factor errors for each of the different grad IMU's.

The maximum error in pitch/roll can be analyzed by assuming that the sensor is in an orientation where the pitch and roll both equal 45. In this case a scale factor error in either axis will stretch one dimension of the vector, thus affecting the measured angle.

12.       Dynamic Errors Due to Gyro Scale Factor

The gyro scale factor has a substantial error on the accuracy of the integration of the angular rates during dynamic motion. If the scale factor is off, then the motion tracked by the gyros will not be correctly scaled and significant errors may result after the motion is complete. As an example consider the case of picking up an IMU, rotating it around the one of its axes by 360 degrees and setting it back down. Ideally the unit should read the same orientation as it did prior to the maneuver. The table below shows some the errors for this simple maneuver for each grade sensor.

The above table shows an order of magnitude difference from the navigation grade to the tactical grade, an order of magnitude from the tactical to the industrial, and two orders of magnitude from the industrial to the automotive. As you can see from the table, automotive grade sensors do not provide sufficient accuracy for neither inertial navigation nor accurate orientation tracking. Only when the automotive sensors are subjected to a thorough calibration do they provide sufficient performance to perform basic navigation techniques.

13.       Dynamic Errors Due to Gyro Misalignment

The gyro misalignment will affect how the angular rates are measured in each of the coordinate directions. Misalignment causes distortions in the measured angular rate vector, which result in errors in resulting orientation after the angular rates are integrated. As a simple example consider the same case described above for the gyro scale factor where we rotate the IMU around a only the Z-axis by 360 degrees and return to the same orientation. If there exists misalignments in the other X and Y axes then they will inadvertently pick up angular rate from the Z-axis rotation even though no physical rotation was conducted around the X and Y axes. The table below outlines the maximum amount of error that would be recorded in pitch and roll assuming that the given amount of axis misalignment was present.

As with many of the other parameters you can see that there is clearly an order of magnitude difference in performance between each of the different grades with respect to errors due to gyro axis alignment.

14.       Summary

Due to installation misalignment during assembly, the total IMU error from accelerometers and gyroscopes can be as high as several thousand of mg and ppm. In addition, the IMU natural bias will also contribute to the most portions of total error.  Therefore, in order to make a great autonomous vehicle, the aspects from IMU installation, IMU selection, vehicle ground level measurement and method of IMU alignment to the vehicle must be carefully arranged and inspected. VAST had these technologies and knowledge to provide our customers their integration solution.