Use of test tones to calibrate the scale factor for micro-electromechanical systems (MEMS) gyroscopes

Abstract

We provide a system that includes a MEMS gyroscope with reduced scale factor drift. [Solution] The system comprises a micro-electromechanical system (MEMS) gyroscope including a vibrating proof mass, and readout electronics coupled to the MEMS gyroscope, the readout electronics including a first electrical channel that monitors the amplitude of vibration of the proof mass at a first frequency and generates a drive output, and a second electrical channel that monitors the amplitude of the proof mass's response to an input rate representing the deflection of the proof mass and generates a rate output. The processing system includes a signal generator that generates a test tone at a second frequency different from the first frequency and outside the bandwidth of the MEMS gyroscope and injects it into the first and second electrical channels, and a scale factor adjustment function that adjusts the scale factor of the MEMS gyroscope by the ratio of the drive output at the second frequency to the rate output at the second frequency.

Description

[Technical Field]

[0001] A vibrating structure gyroscope (VSG) or Coriolis vibratory gyroscope (CVG) uses a vibrating structure (rather than a rotating structure) as its azimuth reference. The underlying physical principle is that a vibrating object tends to continue vibrating in the same plane even if its support rotates. The Coriolis effect exerts a force perpendicular to this object, and by measuring this force, the rotation rate can be determined.

[0002] Oscillating gyroscopes are simpler and less expensive than conventional rotary gyroscopes with similar accuracy. Manufactured using microelectromechanical system (MEMS) technology, these inexpensive oscillating gyroscopes are widely used in smartphones, gaming devices, cameras, and many other applications.

[0003] The nominal scale factor of a MEMS gyroscope describes the gyroscope's fundamental transfer function. It is a measure of the gradient of the best straight line that can be fitted to the gyroscope's expected output signal by least squares for an input inertial signal across the full dynamic range at room temperature. Scale factor stability refers to the temperature variation and reproducibility of the scale factor, typically given in parts per million (ppm). The scale factor temperature coefficient (ppm / °C) is the maximum deviation of the scale factor under variable external temperature conditions.

[0004] Scale factor drift caused by changes in the electrical gain of the readout electronics in MEMS gyroscopes limits the performance of MEMS gyroscopes and prevents them from replacing more expensive technologies (such as RLG and FOG) in high-end applications.

[0005] Therefore, in this field, there is a need for MEMS gyroscopes with reduced scale factor drift. [Overview of the project]

[0006] A system is provided. The system includes a microelectromechanical system (MEMS) gyroscope including a vibrating proof mass; a readout electronic device coupled to the MEMS gyroscope, the readout electronic device comprising: a first electrical channel configured to monitor the amplitude of vibration of the proof mass at a first frequency and generate a drive output; and a second electrical channel configured to monitor the amplitude of the response of the proof mass to an input rate representing the deflection of the proof mass and generate a rate output; and a processing system comprising: a signal generator configured to generate a test tone at a second frequency different from the first frequency and out of the bandwidth of the MEMS gyroscope, and to inject the test tone into the first and second electrical channels; and a scale factor adjustment function configured to adjust the scale factor of the MEMS gyroscope by the ratio of the drive output at the second frequency to the rate output at the second frequency. [Brief explanation of the drawing]

[0007] Embodiments of the present invention can be more easily understood by considering the description of the embodiments and the following drawings, and their further advantages and uses will become more readily apparent. [Figure 1] This is a schematic diagram of one embodiment of a microelectromechanical system (MEMS) gyroscope equipped with readout electronics having scale factor calibration using a test tone. [Figure 2A] These are schematic diagrams of two embodiments of interface circuits for injecting test tones into the first and second electrical paths of a MEMS gyroscope. [Figure 2B]These are schematic diagrams of two embodiments of interface circuits for injecting test tones into the first and second electrical paths of a MEMS gyroscope. [Figure 3] This is a flowchart of one embodiment of the process of using a test tone to calibrate the scale factor of a MEMS gyroscope.

[0008] Following convention, the various described features are not drawn to a fixed scale, but rather to emphasize features relevant to the invention. Reference letters indicate similar elements throughout the figures and text. [Modes for carrying out the invention]

[0009] The following detailed description will refer to the accompanying drawings, which form part of this specification, and which are shown as examples of specific illustrative embodiments in which the invention may be carried out. These embodiments are described in sufficient detail to enable those skilled in the art to carry out the invention, and it should be understood that other embodiments may be utilized and logical, mechanical, and electrical modifications may be made without departing from the scope of the invention. Therefore, the following detailed description should not be construed as restrictive.

[0010] Conventionally, MEMS gyroscopes use at least two electrical channels to read out or pick off signals from the gyroscope's vibrating proof mass. One electrical channel is used to measure the amplitude of the driving motion of the gyroscope's proof mass. This measurement is used in at least an amplitude-gain control loop to keep the proof mass vibrating with a controlled displacement. The other electrical channel is used to measure the amplitude of the gyroscope's proof mass response to an input rate (rotation). Multiplying this by a scale factor, this signal provides the output of the gyroscope. A change in the electrical gain of any component in these two channels changes the gyroscope's scale factor. Therefore, instability in the two readout channels is a contributing factor to scale factor drift in MEMS gyroscopes.

[0011] Embodiments of the present invention overcome the problem of scale factor drift caused by gain instability in these two channels. Embodiments of the present invention adjust the calibration of the scale factor using the gain ratio of the two channels. Embodiments of the present invention calibrate the drift of the gain ratio of the two channels by coupling an electrical test tone at a frequency outside the bandwidth of the MEMS gyroscope, unlike the frequency of the oscillating proof mass, to both electrical channels via a matching element such as a capacitor, inductor, or other suitable circuit element. This test tone is generated at a signal source and observed on both electrical channels. The information read out on the two electrical channels at the test tone frequency is used to adjust the calibration of the gyroscope's scale factor. Note that the test tone itself does not need to be stable, as long as the ratio of its coupling to the two channels, set by the matching element used for coupling, remains stable.

[0012] Figure 1 is a schematic diagram of one embodiment of a system 100, which includes a micro-electromechanical system (MEMS) gyroscope 101, readout electronics 103, and a processor 102 that performs scale factor calibration using a test tone. In this embodiment, the gyroscope 101 is a MEMS Coriolis vibration gyroscope (CVG) including a proof mass 104. The proof mass 104 is formed, for example, from silicon and vibrates along a line in one direction (the so-called drive direction 105). When the proof mass 104 is subjected to rotation, for example, due to the movement of a vehicle or rotation in space, the proof mass 104 flexes in a direction perpendicular to the drive direction 105, which is called the sensing direction 107. The gyroscope 101 picks up this flexure and generates a signal called a rate output that represents the rotation the gyroscope is subjected to.

[0013] The gyroscope 101 is coupled to two electrical channels in the readout electronics 103 used to operate the gyroscope 101. The first electrical channel 106 monitors the motion of the proof mass 104 in the drive direction 105. The proof mass 104 is driven in the drive direction 105 at its drive frequency (or resonant frequency). One objective of the design of the gyroscope 101 is to keep the drive motion (frequency and amplitude) of the proof mass 104 constant over the operating temperature range and the lifespan of the gyroscope 101. For example, the amplitude of the motion of the proof mass 104 may be set to 10, 20, 30 microns or any other suitable amplitude. The second electrical channel 108 is a sensing channel. The second electrical channel 108 measures the input rate by measuring the deflection of the proof mass 104 in the sensing direction 107. The output of the second electrical channel 108 is a signal representing the quantity to which the gyroscope 101 is designed to measure the rotation rate measured by the gyroscope. The stability of the first electrical channel 106 and the second electrical channel 108 determines the scale factor stability of the gyroscope 101.

[0014] During operation, the first electrical channel 106 and the second electrical channel 108 pick off signals from the proof mass 104 as small current signals. These small current signals are amplified by a charge amplifier 110 ("charge amp") and digitized by an analog-to-digital converter 112 in the readout electronics 103. The gains of the charge amplifier 110 and the analog-to-digital converter 112 can change over time. This instability can lead to fluctuations in the actual scale factor of the gyroscope 101 required to produce an accurate output. This source of error can be reduced by designing better charge amplifiers 110 and analog-to-digital converters 112. However, these improved circuit elements may be more expensive, heavier, larger, and consume more power. However, rather than sacrificing size, weight, power, and cost, embodiments of the present invention include a scheme to adjust the scale factor using the ratio of the signals passing through the first electrical channel 106 and the second electrical channel 108. In this method, the gain stability of individual channels is not a factor, as the ratio of signals within a channel provides a mechanism to calibrate the scale factor and thus reduce scale factor drift.

[0015] The processor 102 receives a signal from the readout electronics 103 and performs four main functions: (1) applying a scale factor to the rate output (from the second electrical channel 108) to generate the output 113 of the gyroscope 101; (2) adjusting the scale factor to account for instability in either the first electrical channel 106 or the second electrical channel 108 using the ratio of the rate output at the test tone frequency (second electrical channel 108) to the drive output at the test tone frequency (first electrical channel 106); (3) providing test tone signals to be injected into the first electrical channel 106 and the second electrical channel 108 used to create the ratio for adjusting the scale factor; and (4) providing amplitude gain control for the movement of the proof mass 104 in the drive direction 105.

[0016] The processor 102 generates output 113 for the gyroscope 101. A second electrical channel 108 picks up the rate output from the proof mass 104 and passes the charge signal to the analog-to-digital converter 112-2, which is coupled in series via the charge amplifier 110-2. The output of the analog-to-digital converter 112-2 is demodulated at the drive frequency in the demodulator 116 and passed to the scale factor circuit 118. The scale factor circuit 118 applies the current scale factor to the output of the demodulator 116, which is provided as the output of the system 100 in output 113. Initially, the scale factor circuit 118 uses the scale factor created in the initial calibration. However, over time, its scale factor is adjusted by the scale factor adjustment function 124, as will be described in more detail below.

[0017] Processor 102 adjusts the scale factor applied by scale factor circuit 118. Processor 102 receives a rate output from the second electrical channel 108, and receives a drive output from the first electrical channel 106. In the first electrical channel 106, the drive output is extracted from proof mass 104, and passes a charge signal through charge amplifier 110-1 to the analog-to-digital converter 112-1 coupled in series. The output (drive output) of analog-to-digital converter 112-1 is demodulated at the test tone frequency in demodulator 120, and provided to scale factor adjustment function 124. In addition, in the second electrical channel 108, the rate output is extracted from proof mass 104, and passes a charge signal through charge amplifier 110-2 to analog-to-digital converter 112-2. The output (rate output) of analog-to-digital converter 112-2 is demodulated at the test tone frequency in demodulator 122, and provided to scale factor adjustment function 124. Demodulator 120 and demodulator 122 demodulate their respective inputs (drive output and rate output) at the test tone frequency set by signal generator 126 (described below). The test tone frequency is different from the drive frequency and is outside the bandwidth of gyroscope 101. The scale factor adjustment function 124 creates the ratio of the output of demodulator 120 to the output of demodulator 122. This ratio is the ratio of the drive output to the rate output at the test tone frequency. Then, the scale factor adjustment function 124 creates an updated (calibrated) scale factor according to Equation (1): (1)SF NEW =SF OLD * (DO tone / RO tone ) In the formula, SF represents the scale factor, RO represents the rate output at the frequency of the test tone, and DO represents the drive output at the frequency of the test tone.

[0018] The processor 102 includes a signal generator 126 that provides a test tone for use in calibrating the scale factor as described above. The signal generator 126 generates a test tone (at a frequency different from the drive frequency and outside the bandwidth of the gyroscope 101), and passes the test tone to the interface circuit 128. The interface circuit 128 injects the test tone into both the first electrical channel 106 and the second electrical channel 108 at the input to the charge amplifier 110. In one embodiment, the interface circuit 128 is a matched pair of capacitors or inductors. FIG. 2A illustrates an interface circuit 228 that can be used as the interface circuit 128 of FIG. 1. The interface circuit 200 includes a first capacitor 202-1 and a second capacitor 202-2. The first capacitor 202-1 and the second capacitor 202-2 are coupled to each other, and each receives a test tone signal from a signal generator, for example, the signal generator 126 of the processor 102 in FIG. 1. The output of the first capacitor 202-1 is coupled to the first electrical path of the gyroscope, for example, the first electrical channel 106 in FIG. 1. The output of the second capacitor 202-2 is coupled to the second electrical path of the gyroscope, for example, the second electrical channel 108 in FIG. 1. In an alternative embodiment, inductive circuit elements are used in the interface circuit 250 of FIG. 2B.

[0019] When the circuit elements in the interface circuit 128 are matched (for example, the matched capacitors in the interface circuit 200 of FIG. 2A, or the matched inductors in the interface circuit 250), the ratio of the drive output to the rate output at the test tone corresponds to a change in the scale factor. When the circuit elements are not matched but the ratio of the circuit elements remains constant, the same ratio of the drive output to the rate output at the test tone frequency also corresponds to a change in the scale factor.

[0020] In an alternative embodiment, the first electrical channel 106 and the second electrical channel 108 use transimpedance amplifiers instead of the charge amplifier 110. In that embodiment, the interface circuit 128 uses a matched pair of resistors instead of, for example, the first capacitor 202-1 and the second capacitor 202-2.

[0021] The processor 102 provides amplitude gain control for the movement of the proof mass 104 in the drive direction 105. The first electrical channel 106 generates a drive output at the output of the analog-to-digital converter 112-1. This drive output is demodulated at the frequency of the motion of the proof mass 104 (drive frequency). This signal is fed back by the demodulator 114 to drive the movement of the proof mass 104.

[0022] Figure 3 is a flowchart of one embodiment of process 300 for calibrating the scale factor of a MEMS gyroscope using a test tone. For educational purposes, system 100 in Figure 1 is used in the following description of Figure 3 as an example of how process 300 may be implemented in a system having a MEMS gyroscope. References to system 100 and its various components in Figure 1 are provided as examples and are not intended to limit the scope of process 300. In block 301, process 300 drives the proof mass of the MEMS gyroscope at a first frequency. For example, process 300 may drive the proof mass 104 in the drive direction 105 at a first frequency using an amplitude gain control loop based on a signal demodulated from a first electrical channel 106 (demodulator 114) and fed back to the proof mass 104 in Figure 1.

[0023] In block 303, process 300 monitors the amplitude of the proof mass oscillation at a first frequency in the drive output from the first electrical channel of the MEMS gyroscope. As described above, the gyroscope 101 has a first electrical channel 106 that generates a drive output at the output of the analog-to-digital converter 112-1. This drive output is demodulated by the demodulator 114 at a first frequency (the frequency of the proof mass oscillation 104).

[0024] In block 305, process 300 monitors the amplitude of the response to an input rate, which represents the deflection of proof mass at a first frequency in the rate output from the second electrical channel of the MEMS gyroscope. As described above, the gyroscope 101 has a second electrical channel 108 that generates a rate output at the output of the analog-to-digital converter 112-2. This rate output is applied to a scale factor circuit 118 and demodulated at a first frequency by a demodulator 116 that generates the output of the gyroscope 101.

[0025] In block 307, process 300 injects a test tone of a second frequency, which is different from the first frequency and is outside the bandwidth of the gyroscope 101, into the first and second electrical channels, for example, the first electrical channel 106 and the second electrical channel 108 in Figure 1. The test tone is generated, for example, by the signal generator 126 of the processor 102 in Figure 1 and has a second frequency different from the first frequency.

[0026] In block 309, process 300 adjusts the scale factor of the MEMS gyroscope by the ratio of the drive output at a second frequency to the rate output at a second frequency. For example, process 300 demodulates the rate output at a second frequency (e.g., in demodulator 122 in Figure 1) and provides the demodulated signal to the scale factor adjustment function 124. Furthermore, in this example, process 300 demodulates the drive output at a second frequency (e.g., in demodulator 120 in Figure 1) and provides the demodulated signal to the scale factor adjustment function 124. The scale factor adjustment function 124 uses the signals from demodulators 120 and 122 to generate the ratio of the drive output at a second frequency to the rate output at a second frequency. The scale factor adjustment function 124 uses this ratio to calculate a new scale factor, for example, by using equation (1) described above with respect to Figure 1. This new scale factor is supplied to the scale factor circuit 118.

[0027] The methods and techniques described herein may be implemented in digital electronic circuits or using programmable processors (e.g., dedicated processors or general-purpose processors such as computers), firmware, software, or a combination thereof. Apparatus for implementing these techniques may include appropriate input and output devices, a programmable processor, and a storage medium that tangibly embodies program instructions ("program products") for execution by the programmable processor. The process for implementing these techniques may be carried out by a programmable processor that operates on input data and executes a program of instructions to perform a desired function by generating appropriate outputs. These techniques may be advantageously implemented in one or more programs executable on a programmable system including a data storage system, at least one input device, and at least one output device, each coupled with at least one programmable processor to receive and transmit data and instructions to them. Generally, the processor receives instructions and data from read-only memory and / or random-access memory or other non-temporary computer-readable media. Suitable storage devices for tangibly embodying computer program instructions and data include, for example, all forms of non-volatile memory, including semiconductor memory devices (such as EPROM, EEPROM, and flash memory devices), magnetic disks (such as internal hard disks or removable disks), magneto-optical disks, and DVD disks. Any of the above may be supplemented by or incorporated into application-specific integrated circuits (ASICs) or field-programmable gate arrays (FPGAs).

[0028] Exemplary Embodiments While specific embodiments are illustrated and described herein, those skilled in the art will understand that any configuration expected to achieve the same objective may be used instead of the specific embodiments shown. This application is intended to cover any modifications or variations of the present invention. Accordingly, it is clearly intended that the present invention is limited only by the claims and their equivalents.

[0029] Embodiment 1 is a system comprising: a micro-electromechanical system (MEMS) gyroscope including a vibrating proof mass; a readout electronic device coupled to the MEMS gyroscope, the readout electronic device comprising: a first electrical channel configured to monitor the amplitude of vibration of the proof mass at a first frequency and generate a drive output; and a second electrical channel configured to monitor the amplitude of the response of the proof mass to an input rate representing the deflection of the proof mass and generate a rate output; and a processing system comprising: a signal generator configured to generate a test tone at a second frequency different from the first frequency and out of the bandwidth of the MEMS gyroscope, and to inject the test tone into the first and second electrical channels; and a scale factor adjustment function configured to adjust the scale factor of the MEMS gyroscope by the ratio of the drive output at the second frequency to the rate output at the second frequency.

[0030] Embodiment 2 includes the system described in Embodiment 1, further comprising an interface circuit that receives a test tone from a signal generator and provides the test tone to a first electrical channel and a second electrical channel.

[0031] Example 3 includes the system described in Example 2, wherein the first electrical channel includes a first charge amplifier and a first analog-to-digital converter coupled in series, the second electrical channel includes a second charge amplifier and a second analog-to-digital converter, and the signal generator injects a test tone into the interface circuit.

[0032] Example 4 includes the system described in Example 3, the interface circuit includes a first capacitor and a second capacitor, a test tone is provided to the first capacitor and the second capacitor, the first capacitor provides the test tone to a first electrical channel, and the second capacitor provides the test tone to a second electrical channel.

[0033] Example 5 includes the system described in Example 4, and the first capacitor and the second capacitor comprise a matched pair.

[0034] Example 6 includes the system described in Example 3, and the interface circuit comprises a matched pair of inductors.

[0035] Example 7 includes the system according to any one of Examples 1 to 6, wherein the scale factor adjustment function is SF NEW =SF OLD * (DO tone / RO tone ), where SF represents the scale factor, RO represents the rate output, and DO represents the drive output at a second frequency.

[0036] Example 8 includes the system according to any one of Examples 1 to 7, wherein the drive output is used at a first frequency to provide amplitude gain control for driving a proof mass.

[0037] Example 9 includes the system according to any one of Examples 2, 6, 7, and 8, wherein the first electrical channel includes a first transimpedance amplifier and a first analog-to-digital converter coupled in series, the second electrical channel includes a second transimpedance amplifier and a second analog-to-digital converter, and the signal generator injects a test tone into the input of the first transimpedance amplifier through a first resistor in the interface circuit, and injects the test tone into the input of the second transimpedance amplifier through a second matched resistor in the interface circuit.

[0038] Example 10 includes a method for calibrating the scale factor of a micro-electromechanical system (MEMS) gyroscope, the method comprising: driving the proof mass of the MEMS gyroscope at a first frequency; monitoring the amplitude of the oscillation of the proof mass at the first frequency in the drive output from a first electrical channel of the MEMS gyroscope; monitoring the amplitude of the response to an input rate representing the deflection of the proof mass at the first frequency in the rate output from a second electrical channel of the MEMS gyroscope; injecting a test tone of a second frequency, different from the first frequency and outside the bandwidth of the MEMS gyroscope, into the first and second electrical channels; and adjusting the scale factor of the MEMS gyroscope by the ratio of the drive output at the second frequency to the rate output at the second frequency.

[0039] Example 11 includes the method described in Example 10, wherein driving the proof mass includes demodulating a drive output at a first frequency and feeding back the demodulated drive output to control the driving of the proof mass.

[0040] Example 12 includes the method described in either Example 10 or 11, wherein monitoring the amplitude of proof mass vibrations includes monitoring the drive output generated by a first electrical channel, which includes a charge amplifier and an analog-to-digital converter.

[0041] Example 13 includes the method of any of Examples 10 to 12, wherein monitoring the amplitude of the response to the input rate includes monitoring the rate output generated by a second electrical channel, which includes a charge amplifier and an analog-to-digital converter.

[0042] Example 14 includes the method described in any of Examples 10 to 13, wherein injecting a test tone includes generating a test tone using a signal generator and injecting the test tone into a first electrical channel and a second electrical channel through an interface circuit having a pair of capacitors, a pair of inductors, or a pair of resistors.

[0043] Example 15 includes the method described in any of Examples 10-14, and adjusting the scale factor is SF NEW =SF OLD * (DO tone / RO tone This involves adjusting the scale factor according to the formula, where SF represents the scale factor, RO represents the rate output, and DO represents the drive output at a second frequency.

[0044] Embodiment 16 includes a program product comprising a non-transient computer-readable medium on which program instructions configured to be executed by at least one processor are embodied, and when executed by at least one processor, the program instructions cause at least one processor to perform a method including: driving the proof mass of a MEMS gyroscope at a first frequency; monitoring the amplitude of the oscillation of the proof mass at a first frequency in the drive output from a first electrical channel of the MEMS gyroscope; monitoring the amplitude of the response to an input rate representing the deflection of the proof mass at a first frequency in the rate output from a second electrical channel of the MEMS gyroscope; injecting a test tone of a second frequency, which is different from the first frequency and is outside the bandwidth of the MEMS gyroscope, into the first and second electrical channels; and adjusting the scale factor of the MEMS gyroscope by the ratio of the drive output at the second frequency to the rate output at the second frequency.

[0045] Example 17 includes the program product described in Example 16, and monitoring the amplitude of proof mass vibrations includes monitoring the drive output generated by a first electrical channel, which includes a charge amplifier and an analog-to-digital converter.

[0046] Example 18 includes the program product described in either Example 16 or 17, and monitoring the amplitude of the response to the input rate includes monitoring the rate output generated by a second electrical channel, which includes a charge amplifier and an analog-to-digital converter.

[0047] Example 19 includes a program product described in any of Examples 16 to 18, wherein the injection of a test tone includes generating a test tone using a signal generator and injecting the test tone into a first electrical channel and a second electrical channel via an interface circuit having a pair of capacitors, a pair of inductors, or a pair of resistors.

[0048] Example 20 includes the program product described in any of Examples 16-19, and adjusting the scale factor is SF NEW =SF OLD * (DO tone / RO tone This involves adjusting the scale factor according to the formula, where SF represents the scale factor, RO represents the rate output, and DO represents the drive output at a second frequency.

Claims

1. It is a system, A microelectromechanical system (MEMS) gyroscope (101) including a vibrating proof mass (104), The readout electronic device (103) is coupled to the MEMS gyroscope, and the readout electronic device (103) is A first electrical channel (106) is configured to monitor the amplitude of the vibration of the proof mass at a first frequency and generate a drive output, A readout electronic device (103) includes a second electrical channel (108) configured to monitor the amplitude of the proof mass's response to an input rate representing the deflection of the proof mass and to generate a rate output. Processing system (102), A signal generator (126) is configured to generate a test tone at a second frequency that is different from the first frequency and is outside the bandwidth of the MEMS gyroscope, and to inject the test tone into the first and second electrical channels. A system comprising: a processing system (102) including a scale factor adjustment function (124) configured to adjust the scale factor (118) of the MEMS gyroscope by the ratio of the drive output at the second frequency to the rate output at the second frequency.

2. The aforementioned scale factor adjustment function is SF ＮＥＷ =SF ＯＬＤ ＊ (DO ｔｏｎｅ / RO ｔｏｎｅ ) The system according to claim 1, which operates in accordance with the formula, where SF represents the scale factor, RO represents the rate output, and DO represents the drive output at the second frequency.

3. A method for calibrating the scale factor of a micro-electromechanical system (MEMS) gyroscope, wherein the method is: The proof mass of the MEMS gyroscope is driven at a first frequency (301), (303) monitoring the amplitude of the vibration of the proof mass at the first frequency in the drive output from the first electrical channel of the MEMS gyroscope, (305) The rate output from the second electrical channel of the MEMS gyroscope is monitored for the amplitude of the response to the input rate representing the deflection of the proof mass at the first frequency, Injecting a test tone of a second frequency, which is different from the first frequency and outside the bandwidth of the MEMS gyroscope, into the first and second electrical channels (307), A method comprising adjusting the scale factor of the MEMS gyroscope by the ratio of the drive output at the second frequency to the rate output at the second frequency (309).

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