Abstract:
A micro-electro-mechanical systems (MEMS) inertial measurement system facilitates accurate location and/or attitude measurements via passive thermal management of MEMS inertial sensors. Accuracy of the system is also improved by subjecting the inertial sensors to programmed single-axis gimbal motion, and by performing coarse and fine adjustments to the attitude estimates obtained by the system based on the programmed motion and on the passive thermal management of the sensors.

Description:
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     This invention was made with government support under Contract Number N00024-03-D-6606, which was awarded by the United States Navy and funded, in part, by the United States Army. The U.S. Government has certain rights in the invention. 
    
    
     FIELD OF THE INVENTION 
     In various embodiments, the present invention relates to inertial-measurement systems and methods and, in particular, to micro-electro-mechanical systems (MEMS) based inertial-measurement systems and methods. 
     BACKGROUND 
     Inertial-measurement systems are commonly used in determining the location and/or attitude of an object and in navigation. Such systems are particularly important when communication-based location determination and navigation approaches, e.g., global positioning system (GPS)-based or cell-phone-based approaches, are unavailable or undesirable. Among various inertial-measurement systems, strap-down MEMS-based systems are of significant interest due to their small size, low weight, low cost, and/or low power consumption. 
     A typical MEMS inertial-measurement system includes a MEMS inertial sensor, such as, for example, an accelerometer for sensing motion in a fixed direction or a gyroscope for sensing angular motion. The motion sensed by the sensor is typically translated into an electrical signal by sensor circuitry associated with the sensor. The sensed signal then represents the detected motion, such as an acceleration or a rate of rotation. One or more sensors and sensor signals may be combined to determine the location and/or attitude of an object to which the measurement system is strapped. 
     Generally, a “bias” (i.e., an error component) is present in the motion reading provided by inertial sensors, including MEMS sensors. The bias corresponds to an erroneous detection of motion by a sensor when the sensor is not actually moving. The bias of a sensor does not, however, always remain constant. For example, each time the sensor is turned off and then on, the bias may change—a change that is known as turn-on-to-turn-on bias (and is sometimes referred to herein as, simply, the “turn-on” bias). Moreover, as the sensor continues to operate, the bias can “drift,” i.e. change over time. 
     The bias, bias drift, or both can also change due to a change in temperature of the sensor. In a MEMS system, this phenomenon is often of great concern. In particular, to avoid the introduction of electrical noise into the sensor signal it is often desirable to locate the sensor circuitry in proximity to the sensor, e.g., within a few millimeters from the sensor. But, typically, when the sensor circuitry is turned on it heats up rapidly, which may cause the temperature of the sensor to also increase quickly due to the sensor&#39;s small size and proximity to the sensor circuitry. In addition, in some situations, when the object to which the inertial-measurement system is attached moves from one location at a certain temperature to another location at a substantially different temperature, e.g., from the inside of a building to the outside, the temperature of the inertial sensor may also change quickly. Such a change in the temperature of the sensor, whether caused by the environment or the sensor circuitry, can change the sensor bias and/or increase bias drift, causing the location, attitude, or navigation information obtained from the sensor to be erroneous. 
     One approach to mitigate or avoid these problems is to use calibration. For example, the temperature of the inertial sensor may be measured and the sensor reading as indicated by the sensor circuitry adjusted according to a temperature-sensitivity curve known a priori from extensive pre-deployment testing. Unfortunately, such calibration is generally not very effective at detecting turn-on-to-turn-on bias. It also fails to effectively nullify the effect of sudden, large changes in temperature on the bias that can occur when, for example, the environment of the sensor changes. 
     Another approach is to employ active thermal control. Under this approach, heaters, coolers, or both are typically used to maintain the sensor&#39;s temperature nearly constant, regardless of the change in temperature of the sensor circuitry or the sensor&#39;s environment. The use of heaters and/or coolers can, however, increase the cost, size, weight, and/or power consumption of the measurement system. For certain applications in which the inertial-measurement system should be small and should operate on limited power, active thermal management may be impractical or infeasible. 
     Needs therefore exist for improved systems and methods of MEMS based inertial measurement. 
     SUMMARY 
     In various embodiments, the present invention enables accurate inertial measurement using MEMS inertial sensors without requiring active thermal management of the sensors. This is achieved, in part, by employing passive thermal management to decrease the rate of change of temperature of the inertial sensor. The passive thermal management described herein may be achieved in four exemplary ways. 
     First, a thermal impedance path may be provided between the inertial sensor and corresponding sensor circuitry to which the sensor is proximately disposed but is not in direct physical contact with. With such a design, very little, if any, heat dissipated by the sensor circuitry reaches the sensor by conduction, and the temperature of the sensor is less likely to change rapidly when the sensor circuitry heats up after being turned on. 
     Second, the inertial sensor may be surrounded by a thermal mass. In this way, even if the temperature of the environment to which the thermal mass is exposed changes quickly (e.g., at a rate of a few ° C./min), the thermal mass can cause the temperature of the sensor contained therein to change at a slower rate. 
     Third, a circuit board that includes the sensor circuitry may also be attached to the same thermal mass as the sensor itself. By sharing the same thermal mass, both the circuitry and the sensor experience similar rates of change in temperature. 
     Fourth, the sensor circuitry may be connected to a heat sink. The inertial sensor may itself be disposed in proximity to the sensor circuitry but without being in direct physical contact with the heat sink. In this way, the heat generated by the sensor circuitry is dissipated by the heat sink away from the sensor, thereby decreasing the sensor&#39;s rate of change of temperature as the sensor circuitry heats up (e.g., once the circuitry is turned on). 
     In various embodiments, any one or a combination of two, three, or all of these approaches may be utilized to achieve the passive thermal management of a MEMS inertial-measurement system. 
     As described above, the signals generated by an inertial sensor and its corresponding circuitry typically include errors, such as, for example, turn-on-to-turn-on bias and in-run bias drift. In various embodiments of the invention, the bias error is mitigated or substantially eliminated by subjecting the inertial sensor to programmed single-axis gimbal motion. More specifically, in one embodiment, initial sensor readings obtained at different points of the programmed motion are used to generate coarse estimates of the bias. These estimates and subsequent sensor readings may then be filtered to fine tune various parameters of a model for the MEMS inertial-measurement system, such as bias-drift parameters, temperature sensitivity of the sensor, etc., so as to accurately measure the location and/or attitude of the object to which the measurement system is attached. 
     In general, in one aspect, embodiments of the invention feature an inertial-measurement system that includes a circuit board having circuitry, a MEMS inertial sensor disposed in proximity to the board, and a thermal impedance path. The sensor is not in direct physical contact with the circuit board. Rather, the sensor has a contact and the thermal impedance path couples the board to the sensor contact. The circuitry generates a sensor signal based on a motion sensed by the sensor. 
     In some embodiments, the thermal impedance path includes a material having a thermal conductivity lower than that of copper. For example, the material may be kovar. Alternatively, or in addition, the thermal impedance path may have a geometry that substantially reduces heat conduction between the board and the inertial sensor. The thermal impedance path may be sufficiently rigid to support the inertial sensor and maintain a location of the inertial sensor substantially fixed relative to the board. For example, the thermal impedance path may have a cross section of 0.015″ by 0.005″. 
     In some embodiments, the inertial-measurement system also includes a thermal mass that surrounds at least a part of the inertial sensor and that decreases a rate of change of temperature of the inertial sensor. The thermal mass may include a material having both a high thermal conductivity and a high specific heat. The thermal mass may, for example, include beryllium an/or aluminum. In some embodiments, the thermal mass includes a cavity and the inertial sensor is positioned within the cavity without contacting the thermal mass. The inertial-measurement system may also include a heat sink in contact with the board to dissipate heat generated by the circuitry away from the inertial sensor. 
     In some embodiments, the inertial sensor is disposed on a single-axis gimbal, and the motion of the gimbal is controlled according to a program. The inertial-measurement system may also include a coarse estimator for estimating one or more parameters of the inertial sensor based on the sensor signal and the programmed gimbal motion. In addition, the inertial-measurement system may also include a Kalman filter for estimating a plurality of tuning parameters based, at least in part, on the sensor signal and one or more parameters estimated by the coarse estimator. The Kalman filter may also estimate an attitude of the inertial sensor based, at least in part, on the plurality of estimated tuning parameters. 
     In general, in another aspect, embodiments of the invention feature a method of manufacturing an inertial-measurement system. The method includes disposing a MEMS inertial sensor in proximity to a circuit board without placing the sensor in direct physical contact with the board. The sensor has a contact, and the board includes circuitry for generating a sensor signal based on a motion sensed by the sensor. The method also includes coupling the board to the sensor contact via a thermal impedance path. 
     The method may include providing a heat sink in contact with the board to dissipate heat generated by the circuitry away from the inertial sensor. In various embodiments, the method includes surrounding at least a part of the inertial sensor with a thermal mass so as to decrease a rate of change of temperature of the inertial sensor. The thermal mass may include a cavity, and the disposing step may include positioning the inertial sensor within the cavity without contacting the thermal mass. In some embodiments, the disposing step includes positioning the inertial sensor on a single-axis gimbal. 
     In general, in yet another aspect, embodiments of the invention feature a method for determining an attitude of an inertial-measurement system. The method includes controlling a motion of a single-axis gimbal upon which the inertial-measurement system is disposed. The gimbal motion is controlled according to a program. The inertial-measurement system includes a circuit board having circuitry, a MEMS inertial sensor disposed in proximity to the board, and a thermal impedance path. The sensor is not in direct physical contact with the circuit board. Rather, the sensor has a contact and the thermal impedance path couples the board to the sensor contact. 
     In some embodiments, the controlling step includes maintaining the gimbal in a first dwell position for a first dwell period; moving the gimbal, over a slew period, to a second dwell position; and maintaining the gimbal in the second dwell position for a second dwell period. The first dwell position, the first dwell period, the movement of the gimbal, the slew period, the second dwell position, and the second dwell period may be specified by the program. Moving the gimbal may include rotating the gimbal in a clockwise direction, a counter-clockwise direction, or both. In some embodiments, one or more of the first dwell period, the second dwell period, and the slew period are adjusted according to a rate of change of temperature of the inertial sensor. 
     The program may include a sequence that repeats periodically, and the sequence may include several dwell positions and several movements. The period of the sequence may be determined according to a thermal sensitivity of the inertial sensor. 
     In some embodiments, the method also includes estimating, using a coarse filter, one or more parameters of the inertial sensor based on a sensor signal and the gimbal motion. The circuitry on the board generates the sensor signal based on a motion sensed by the inertial sensor. The estimated parameters may include a turn-on bias of the inertial sensor, a parameter of a thermal-bias model of the inertial sensor, and/or an attitude of the inertial sensor. 
     The method may also include estimating, using a Kalman filter, various tuning parameters based, at least in part, on the sensor signal and the parameters estimated by the coarse estimator. An attitude of the inertial sensor may then be estimated based, at least in part, on the various estimated tuning parameters. The tuning parameters may include an acceleration sensitivity of the inertial sensor, a parameter of a nonlinear thermal bias behavior model of the inertial sensor, and/or a bias instability of the inertial sensor. 
     The method may also include generating a sensor-error model, and the attitude may be estimated based, at least in part, on an error estimate obtained from the sensor-error model. In various embodiments, the gimbal motion includes a dwell position and a movement, and the sensor signal includes at least one value obtained from the dwell position and at least one value obtained from the movement. 
     These and other objects, along with advantages and features of the embodiments of the present invention herein disclosed, will become more apparent through reference to the following description, the accompanying drawings, and the claims. Furthermore, it is to be understood that the features of the various embodiments described herein are not mutually exclusive and can exist in various combinations and permutations. As used herein, the term “substantially” means±10%, and in some embodiments ±5%. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the drawings, like reference characters generally refer to the same parts throughout the different views. Also, the drawings are not necessarily to scale, emphasis instead generally being placed upon illustrating the principles of the invention. In the following description, various embodiments of the present invention are described with reference to the following drawings, in which: 
         FIG. 1  schematically illustrates a MEMS inertial-measurement system that includes a thermal-impedance path, according to one embodiment of the invention; 
         FIG. 2  schematically illustrates a MEMS inertial-measurement system that includes a thermal-impedance path and a thermal mass, according to one embodiment of the invention; 
         FIGS. 3A and 3B  illustrate a MEMS inertial-measurement system that includes a thermal mass, according to another embodiment of the invention; 
         FIG. 4  illustrates a MEMS inertial-measurement system that includes a gimbal and a heat sink, according to one embodiment of the invention; 
         FIG. 5  illustrates an exemplary programmed gimbal motion; and 
         FIG. 6  is a block diagram of a MEMS inertial-measurement system that includes a coarse estimator and a Kalman filter, according to one embodiment of the invention. 
     
    
    
     DESCRIPTION 
       FIG. 1  depicts an exemplary MEMS inertial-measurement system  100 . The system  100  includes a MEMS inertial sensor  102 , which can be, for example, an accelerometer or a gyroscope. The sensor  102  is disposed above a circuit board  104  at a distance of about 2 mm. Thus, the sensor  102  is not in direct physical contact with the circuit board  104 . For its part, the circuit board  104  includes sensor circuitry  106  that is in electrical communication with the sensor  102  and that produces a sensor signal representing the motion sensed by the sensor  102 . 
     In one embodiment, the sensor  102  has a contact  108  and is coupled to the circuit board  104  via a lead (or thermal impedance path)  110 . A lead  110  having sufficient strength and rigidity (e.g., a kovar lead having a cross section of about 0.015″×0.005″) is selected so as to support the sensor  102  and maintain the sensor  102  in a nearly fixed position relative to the circuit board  104  (e.g., at a distance of about 2 mm) over the operational range of acceleration and/or environmental shock that is experienced by the measurement system  100 . Thus, if an object to which the system  100  is attached moves, e.g., accelerates, rotates, vibrates, etc., the sensor  102  does not move substantially relative to the circuit board  104 . Thin wires  112 , such as copper, aluminum, or gold wires of 34 gauge, may be employed to provide electrical communication between the sensor  102  and the components of the circuit board  104  without adding rigidity to the interconnect between the board  104  and the sensor  102 . An excessively rigid interconnect can cause stress upon the inertial sensor  102  when the object to which the system  100  is attached moves. In various embodiments, more than one lead  110  (e.g., up to 20 leads  110 ) and fewer or more than the illustrated four thin wires  112  may be used in the system  100 . 
     In one embodiment, the lead  110  is made from a material having a thermal conductivity that is lower than that of copper, and provides a path of thermal impedance between the circuit board  104  and the sensor  102 . For example, the lead  110  may have a thermal conductivity lower than 400 W/m-K, lower than 350 W/m-K, lower than 300 W/m-K, lower than 250 W/m-K, lower than 200 W/m-K, lower than 150 W/m-K, lower than 100 W/m-K, or lower than 50 W/m-K; and in some embodiments may be approximately 17.3 W/m-K (which is, approximately, the thermal conductivity of kovar). In some embodiments, the geometry of the lead  110  is selected so as to substantially reduce heat conduction between the circuit board  104  and the inertial sensor  102 . For example, the lead  110  may have a cross section of 0.015″×0.005″, which is a geometry that provides high stiffness but minimizes the cross-sectional area for heat conduction. In addition, the material of the lead  110  may be selected such that the lead  110  can be soldered to the board  104 . Due to its relatively low thermal conductivity, the lead  110  generally does not conduct the heat dissipated by the components of the board  104  as effectively as a copper wire. In addition, even though the wires  112  may have high thermal conductivity, they are thin, so substantial heat flow by conduction does not occur between the board  104  and the sensor  102 . 
     Given this design, heat flow between the circuit board  104  and the sensor  102  generally occurs at a rate significantly slower than when the sensor  102  is soldered directly to the circuit board  104 . Therefore, even if the temperature of the circuitry  106  included on the circuit board  104  increases quickly when the circuitry  106  is turned on (e.g., within a few seconds), the temperature of the sensor  102  will change, if at all, at a significantly slower rate (e.g., over a few minutes). 
     In general, the thermal-expansion coefficients of the inertial sensor  102  and the circuit board  104  are different, causing them to expand/contract differently when exposed to a change in temperature. The different expansions of the sensor  102  and the circuit board  104  can cause stress on the sensor  102 , which can introduce an additional error in the sensor signal obtained from the board  104 . As such, in some embodiments, the number of the leads  110  and their locations on the circuit board  104  are selected to provide sufficient rigidity to the sensor  102  and also to absorb that stress. 
     It should be understood that the distance of 2 mm between the board  104  and the sensor  102  is illustrative, and that shorter or longer distances (e.g., 1 mm, 5 mm, etc.) are within the scope of the invention. The distance may be chosen such that the sensor  102  is located close enough to the board  104  that the noise introduced in the electrical paths between the sensor  102  and the board  104  (e.g., in the wires  112 ) is not substantial, yet such that the sensor  102  is located far enough away from the board  104  that the sensor temperature does not change rapidly due to the heat dissipated from the board  104 . 
       FIG. 2  depicts a MEMS inertial measurement system  200  that is similar to the system  100  shown in  FIG. 1 . In addition, in the system  200 , the sensor  102  is surrounded by a thermal mass  214 . The materials suitable for use as the thermal mass  214  include beryllium or aluminum because of their high heat capacity and metallic thermal conductivity, but other metals having these properties are suitable as well. In general, the heat dissipated from the circuit board  104  via convection and/or radiation, and/or the heat introduced to the system  200  by rapid environmental changes, is absorbed by the thermal mass  214  prior to reaching the sensor  102 , thereby further slowing the rate of change of temperature of the sensor  102 . 
     In some embodiments, however, the circuit board  104  may also be tightly thermally coupled to the thermal mass  214  so that the temperatures of the circuit board  104  and the sensor  102  track each other, i.e., their temperatures change at substantially the same rate. A compliant, relatively high thermally conductive material, e.g. k=1.5 W/m-K, where k is the thermal conductivity, may be sandwiched between the components on circuit board  104  and the thermal mass  214  to enhance the thermal coupling between the two. 
       FIG. 3A  depicts one embodiment of a thermal mass  302  that may be used in the exemplary inertial-measurement system  300  depicted in  FIG. 3B . The thermal mass  302  has six surfaces, of which three surfaces  304   a ,  304   b ,  304   c  are shown. The surfaces  304   a ,  304   b ,  304   c  define cavities  306   a ,  306   b ,  306   c , respectively. It should be understood that a thermal mass having fewer or more surfaces, and surfaces defining fewer or more cavities, are also within the scope of the invention. As illustrated in  FIG. 3B , circuits boards  308   a ,  308   b ,  308   c  are mounted on the surfaces  304   a ,  304   b ,  304   c , respectively. Each circuit board is in direct physical contact with the corresponding surface of the thermal mass  302 . A MEMS inertial sensor, coupled to each board (e.g., the board  308   a ) using a rigid but stress-absorbing interconnect, is positioned within the cavity defined by the corresponding surface (e.g., the cavity  306   a  defined by surface  304   a , as shown in  FIG. 3A ) without contacting the thermal mass  302 . This enables the sensor and the corresponding sensor electronics to reach thermal equilibrium rapidly, but without the stress that would be introduced into the sensor if it were attached directly to the thermal mass  302 . 
     A heat sink may also be attached to one or more of the circuit boards  304   a ,  304   b ,  304   c . In this way, some of the heat generated by the circuit boards  304   a ,  304   b ,  304   c  may be dissipated by the heat sink to the surrounding environment, away from the sensors located in the cavities  306   a ,  306   b ,  306   c . This aids in making the sensors less sensitive to the heating of the circuit boards typically caused when the system  300  and/or one or more of the circuit boards  304   a ,  304   b ,  304   c  are turned on. 
       FIG. 4  depicts one embodiment of a MEMS inertial-measurement system  400  that includes a heat sink  402 . The heat sink  402  is disposed in thermal contact with a circuit board of an inertial system, such as the system  100  shown in  FIG. 1 . As illustrated, the heat sink  402  is attached to a single-axis gimbal  404  that may be rotated by a gimbal motor  406 . Thus, the inertial sensors are disposed on the gimbal  404  and can be rotated via the gimbal motor  406 . The motion of the gimbal  404 , an example of which is illustrated in  FIG. 5 , is controlled by a program (i.e., a sequence of steps). The program may be executed by custom circuitry, or it may be implemented by software stored in memory and executed by a processor. The custom circuitry, memory, and/or processor may be located on one or more circuit boards mounted on the gimbal  404 , or may be located on a separate circuit board. 
     With reference to  FIG. 5 , an exemplary programmed gimbal motion includes a first position  502  at about 0° at which the gimbal  404  of  FIG. 4  dwells (i.e., rests) for a dwell period of about 5 seconds. Then, the gimbal  404  is rotated counter-clockwise by about 180° to a second position  504 . The rotation takes about 5 seconds to be completed, and the gimbal  404  dwells in the second position  504  for about 5 seconds. Thereafter, the gimbal  404  is moved back to the first position  502  by rotating it clockwise by about 180°. This rotation also takes about 5 seconds, and the gimbal  404  dwells in the first position  502  for about 5 seconds before it is rotated clockwise by about 180° to the second position  504 . The second clockwise rotation also takes about 5 seconds, and the gimbal  404  dwells in the position  504  for about 5 seconds. Then, the gimbal is rotated counter-clockwise by about 180° in about 5 seconds to the first position  502 . This sequence of dwelling positions and rotations may be periodically repeated approximately every 40 seconds. As will be understood by one of ordinary skill in the art, the gimbal motion is provided in order to increase the observability (i.e., the detection) of the turn-on bias. 
     It should be understood that the parameters of the programmed gimbal motion, e.g., the positions (as represented by the angles of rotation, such as 0° and 180°), the movements (such as the clockwise and counter-clockwise rotations), and the dwell and slew (i.e., rotation) periods (i.e., about 5 seconds), are illustrative only and that one or more of the parameters may take on different values. In some embodiments, the program (i.e., the sequence of gimbal positions and movements) may include more than two positions  502 ,  504 , and the period of the sequence may be determined according to a thermal sensitivity of the inertial sensor. 
     In general, the total period for the set of movements from the initial position through the intermediate stops (i.e., dwells) and back to the initial position must be short enough so that there is not a significant change in the sensor bias and/or other system-error parameters. Typically, when the temperature of a sensor changes, thereby causing the bias and/or other errors to change quickly, the total permissible period decreases. To achieve this, each dwell and/or slew period may be decreased. On the other hand, when the sensor temperature remains substantially constant, the total permissible period increases. In other words, the period may be lengthened if the sensor temperature is stable, thereby avoiding frequent, rapid movements of the gimbal, which in turn can save energy. To achieve this, each dwell and/or slew period may be increased. In effect, one or more of the dwell periods and/or the slew periods may be adjusted according to a rate at which the temperature of the inertial sensor is sensed to be changing. 
       FIG. 6  is a block diagram illustrating one embodiment of a MEMS inertial-measurement system  600  that includes a MEMS sensor  602  and a circuit board  604  in electrical communication therewith. The system  600  also includes a gimbal-motion controller  606 , a coarse estimator  608 , and a Kalman filter  610 . The gimbal-motion controller  606  moves the gimbal and the sensor  602  disposed thereupon according to a program, such as that described with reference to  FIG. 5 . As will be understood by one of ordinary skill in the art, the positions and movements of the gimbal are typically programmed such that analysis of the observed sensor data allows for detection of the bias errors and drift, as described below. Each of the gimbal motion controller  606 , coarse estimator  608 , and Kalman filter  610  may be implemented by custom circuitry or by software stored in a memory module and executed by a processor. The custom circuitry, memory, and/or processor may be located on the board  604 , or may be located on a separate circuit board that is in communication with the board  604 . 
     The program period (e.g., 40 seconds, as described above) is selected to be shorter than the typical sensor instability time period, i.e., the time period over which the sensor bias drifts substantially. The coarse estimator  608  uses the observability of system errors from the programmed gimbal motion to estimate various errors and model parameters as well as an attitude of the inertial-measurement system  600 . In particular, a coarse alignment sequence (i.e., the initial period of the program) is used by the coarse estimator  608  to estimate gross system errors, e.g., the turn-on bias, parameters of a thermal-bias model, etc. The coarse estimator  608  accepts as input the program information and the sensor data when the gimbal and the sensor  602  are in their dwell positions, e.g., the positions  502 ,  504  of  FIG. 5 . As is commonly known, the invariance of the turn-on bias in the sensor output to the orientation of the sensor&#39;s input axis with respect to an inertial rate (i.e., a rate of angular movement) provides a method for observing and estimating the turn-on bias. The inertial rate can be the earth&#39;s planetary polar axial rotation rate or a known platform rate. An example of a known platform rate is the orbital motion of a satellite on which the MEMS inertial-measurement system and the gimbal mechanism are mounted. 
     In general, the thermal sensitivity of the sensor  602  can be modeled based on various characteristics of the system  600  (e.g., the distance between the sensor  602  and the circuit board  604 , the size and material of the thermal impedance path coupling the senor  602  and the circuit board  604 , properties of the thermal mass, etc.). In some embodiments, the parameters of the thermal-bias model (also called a thermal-sensitivity model) are determined by the coarse estimator  608  by estimating the turn-on bias, as described above, during several periods of the programmed motion. The sensor temperature during each period is also measured. By correlating the changes in the turn-on bias between the different periods with the corresponding sensor temperatures, the coarse estimator  608  determines the parameters of the thermal-bias model of the sensor  602 . 
     In addition, the coarse estimator  608  may also provide an initial estimate of the inertial-measurement system&#39;s attitude, i.e., the orientation of the inertial-measurement system with respect to the platform providing the inertial rate, e.g., the surface of the earth or the orbiting satellite. The attitude on an earth mounted system is derived by using accelerometers to estimate the orientation of the inertial-measurement system with respect to a reference level and by using gyroscopes to sense the proportion of the earth&#39;s polar rate on the level gyroscope axes to estimate the angular motion of the system. 
     Even though the coarse estimator  608  can estimate and reduce, or substantially eliminate, turn-on bias, other errors such as bias drift and errors in sensor readings due to a change in the temperature of the sensor  602  and/or the circuit board  604  may affect the performance of the inertial-measurement system  600 . The estimates generated by the coarse estimator  608  (i.e., the turn-on bias, the thermal bias model parameters, and the attitude of the sensor  602 ) may thus be utilized by the Kalman filter  610  to fine tune the system  600 . The Kalman filter  610  converges faster and more reliably to an accurate estimate of a measured value when the errors the Kalman filter  610  must estimate are small. As described above, the coarse estimator  608  can remove large turn-on bias, and may provide initial attitude estimates so that the errors the Kalman filter  610  needs to estimate during convergence are small. 
     The Kalman filter  610  may also estimate other system errors having a smaller impact on attitude estimation. These errors may be modeled using various sensor-error models, such as a sensor bias instability model, a sensor misalignment model, a model for acceleration sensitivity, a nonlinear thermal-bias behavior model, and a nonlinear scaling model. In particular, using the sensor bias instability model and the acceleration-sensitivity model, the Kalman Filter  610  can provide an estimate of the bias drift as the sensor  602  is operated continuously over a certain time period. For this, the Kalman Filter  610  may correlate additional sensor measurements, as described below, and estimate coefficients for various parameters of each of these models. 
     The nonlinear thermal-bias behavior model, which may be related to the thermal bias model that is based on the characteristics of the system  600 , as described above, can provide accurate estimates of the bias drift due to a change in temperature of the sensor  602 . In general, the Kalman filter  610  is operated in a similar fashion as the coarse estimator  608  to determine the parameters of the temperature-bias model. By correlating various sensor data and sensor-temperature values, the Kalman filter  610  can determine and refine the parameters of the nonlinear thermal-bias model. 
     The Kalman filter  610  also receives additional sensor data from the circuit board  604  while the gimbal is in a dwell position or while it is moving (e.g., rotating clockwise or counter-clockwise). The angle readout from the gimbal motion controller  606  is measured prior to and after a programmed motion step. The measured angular change is compared with the estimated angular change derived from the inertial sensors and is used along with temperature sensor measurements to estimate inertial sensor errors. Using the estimates from the coarse estimator  608 , the additional sensor data, and the program information from the gimbal motion controller  606 , the Kalman filter  610  generates parameters of the various sensor models described above to fine tune the system  600 . 
     In this it is assumed that the inertial inputs to the sensors derive from the platform (earth or satellite orbital trajectory) motion and the programmed motion only. A small level of user or base motion in each of the six degrees of freedom of inertial sensing can be tolerated. Examples of small user or base motions include small amplitude vibrations at the mounting base of the inertial-measurement unit exciting linear or rotational vibratory motions at the sensors that do not significantly degrade the system performance. Large disturbances or user motions are detected by the coarse estimator  608  that may then pause the estimation process until the disturbance subsides. In some embodiments, the gimbal-motion controller  606  includes additional control circuitry and/or software to detect a large disturbance based on a signal received from the coarse estimator  608 , and to signal the coarse estimator  608  to pause the estimation process. 
     Combining the constrained motion assumptions described above with a precise knowledge of the gimbal position based on the angle readout and measurements of the temperature of the sensor  602 , the Kalman filter  610  can further reduce or substantially eliminate the bias and/or drift errors. Accordingly, the MEMS inertial-measurement system  600  can quickly converge to a substantially error-free state and may operate in that state to provide accurate estimates of the location and/or attitude of the object to which the system  600  is attached. 
     While the invention has been particularly shown and described with reference to specific embodiments, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. The scope of the invention is thus indicated by the appended claims and all changes that come within the meaning and range of equivalency of the claims are therefore intended to be embraced.