Abstract:
An inertial system is provided. The system includes at least one inertial sensor, a processing unit and a plurality of Kalman filters implemented in the processing unit. The Kalman filters receive information from the at least one inertial sensor, and at most one of the plurality of Kalman filters has processed zero velocity updates on the last cycle. The plurality of Kalman filters is used to optimize system response and performance during periods of intermittent motion.

Description:
TECHNICAL FIELD 
     The present invention relates generally to inertial systems and in particular to the use of Kalman filters to improve inertial systems. 
     BACKGROUND 
     Some inertial measurement systems are used to determine the attitude and propagate the position of an object on the ground. This is done by utilizing inertial sensors which measure rate information of the object relative to an inertial frame of reference. An inertial frame of reference is constant with respect to inertial space. Non-inertial frames of reference, such as an earth fixed frame, rotate and possibly translate with respect to an inertial frame. An example of an inertial sensor is an accelerometer which measures the change of velocity with respect to an inertial frame. Inertial sensors can be used by an inertial measurement system to realize 3-dimensional coordinates for the position of the object. To increase the accuracy of the coordinates, only the components of the body-sensed measurements which are relative to the actual motion of the vehicle are measured, and earth rotation, vibrations, and other random errors are eliminated. 
     Kalman filters are used by systems such as an inertial measurement system to estimate the state of a system from measurements, such as those from inertial sensors. Inertial sensor measurements are integrated up and contain random errors that the Kalman filter estimates in order to determine the attitude of the object. The accuracy of the position determined by an inertial system is dependent on processing zero velocity updates (ZUPTS). ZUPTS are measurements made by inertial sensors while the vehicle is stopped to ensure the accuracy of the position of the vehicle. ZUPTS are accurate only when the vehicle is stopped. When the vehicle moves, processing an observation to the Kalman filter that assumes the vehicle is stopped causes an error in the inertial measurement system. Detection of motion that would enable the system to avoid erroneous ZUPTS often occurs after the motion has started. 
     Techniques of detecting motion generally involve the use of a threshold. Unfortunately, in order to detect the motion as soon as possible the threshold level is reduced to a degree where vibrations, and not actual movement, have caused the threshold to be exceeded. Also, these techniques detect motion after it is started and allow erroneous ZUPTS to be processed. 
     For the reasons stated above and for other reasons stated below which will become apparent to those skilled in the art upon reading and understanding the present specification, there is a need in the art for a method of removing possible errors caused by incorrect zero velocity updates processed by Kalman filters. 
     SUMMARY 
     To be completed after inventor approval of the claims. 
     The above-mentioned problems and other problems are resolved by the present invention and will be understood by reading and studying the following specification. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention can be more easily understood and further advantages and uses thereof more readily apparent, when considered in view of the description of the preferred embodiments and the following figures in which: 
         FIG. 1  is an inertial system of one embodiment of the present invention. 
         FIG. 2  is a flow chart of one embodiment of a method of the present invention. 
         FIG. 3  is a view of one embodiment of a method of the present invention. 
         FIG. 4  is a block diagram of a vehicle of one embodiment of the present invention. 
         FIG. 5  is an inertial navigation system of one embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     In the following detailed description of the preferred embodiments, reference is made to the accompanying drawings, which form a part hereof, and in which is shown by way of illustration specific preferred embodiments in which the inventions may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention, and it is to be understood that other embodiments may be utilized and that logical, mechanical and electrical changes may be made without departing from the spirit and scope of the present invention. The following detailed description is, therefore, not to be taken in a limiting sense, and the scope of the present invention is defined only by the claims and equivalents thereof. 
     Embodiments of the present invention include an inertial system with improved accuracy by having a plurality of Kalman filters. The plurality of Kalman filters includes one that has processed zero velocity updates (ZUPTS) on the last cycle and at least one that has not processed ZUPTS on the last cycle but has processed ZUPTS on at least one previous cycle. When motion is detected, the inertial system can revert back to the solution maintained by a Kalman filter that has not processed ZUPTS on the last cycle (or has not processed ZUPTS on multiple cycles), thereby removing bad observations due to ZUPTS processed when the vehicle was in motion. 
     In another embodiment, the method of detecting motion using the multiple Kalman filters is enhanced. This is done by using a solution separation algorithm which is beneficial for detecting motion in slow moving objects. This technique overcomes problems with conventional threshold motion detection algorithms as applied to, for example, slow moving objects. 
     In another embodiment, a vehicle incorporating an inertial system with a plurality of Kalman filters is provided. The vehicle includes a guidance system and a position controller than moves the vehicle to the proper position. 
       FIG. 1  is an inertial system of one embodiment of the present invention shown generally at  100 . Inertial system  100  is comprised of inertial sensor  102 . In one embodiment, inertial sensor  102  is an accelerometer. In another embodiment, inertial sensor  102  is a gyroscope. In another embodiment, inertial sensor  102  is a plurality of accelerometers or a plurality of gyroscopes or a combination of the two. Inertial sensor  102  is used in civil and military aviation, missiles and other projectiles, submarines and space technology as well as a number of other vehicles. Inertial sensor  102  measures rotational and linear movements without reference to external coordinates. For example, accelerometers measure a change of velocity with respect to an inertial frame. Gyroscopes measure change of rotation with respect to inertial space. Inertial sensor  102  is subject to errors such as vibration and other disturbances. 
     Inertial sensor  102  communicates with a processing unit  104  via a communication link  108 . In one embodiment, communication link  108  is wireless. In another embodiment, communication link  108  is a wired connection. Processing unit  104  includes but is not limited to digital electronic circuitry, a programmable processor (for example, a special-purpose processor or a general-purpose processor such as a computer) firmware, software, or in combinations of them. 
     Processing unit  104  implements a plurality of Kalman filters  106 - 1  . . .  106 -N. Kalman filters  106 - 1  . . .  106 -N, in general terms, estimate a series of parameters that describe and predict the behavior of a system. The Kalman filters  106 - 1  . . .  106 -N operate with a set of state variables that describe errors in the system and an associated covariance matrix that describes the current knowledge level of the state. The Kalman filters  106 - 1  . . .  106 -N maintain an estimate of the system errors and associated covariance over time and in the presence of external measurements through the use of propagation and updating processes. Kalman filters  106 - 1  . . .  106 -N take the information provided by the inertial sensor  102  and received by the processing unit  104 , including the errors created when they are integrated, and provides an estimate of the position, velocity, and attitude of the vehicle. 
     The accuracy of the position of the inertial system  100  is dependent on the Kalman filters  106 - 1  . . .  106 -N processing zero velocity observations (ZUPTS). ZUPTS are only accurate when the vehicle is stopped. When the vehicle moves, processing an observation to the Kalman filters  106 - 1  . . .  106 -N that assumes the vehicle is stopped causes an error. Detection of motion that allows the system  100  to avoid erroneous ZUPTS often occurs after the motion has started. This detection of motion is performed by the processing unit  104  using a motion detection algorithm. In one embodiment, the motion detection algorithm is a threshold algorithm. In another embodiment, the motion detection algorithm is a solution separation algorithm as described below in  FIG. 3 . To avoid erroneously processing ZUPTS system  100  maintains a plurality of Kalman filters  106 - 1  . . .  106 -N that have processed zero velocity updates on various cycles. 
     In one embodiment, Kalman filter  106 - 1  processes ZUPTS on all the cycles, and Kalman filter  106 -N does not process ZUPTS on the last cycle. This allows the processing unit  104  to revert back to Kalman filter  106 -N which did not process ZUPTS on the last cycle when motion is detected. This reduces the likelihood that the ZUPTS processed will have errors due to vehicle movement. 
     In one embodiment, N is equal to two and Kalman filter  106 - 2  does not process ZUPTS on the last cycle as described above. In another embodiment, N is greater than two and for each additional Kalman filter  106 - 1  . . .  106 -N there is an additional cycle where ZUPTS are not processed. For example, when N is equal to four, Kalman filter  106 - 1  processes ZUPTS on all cycles, Kalman filter  106 - 2  does not process ZUPTS on the last cycle, Kalman filter  106 - 3  does not process ZUPTS on the last two cycles, and Kalman filter  106 - 4  does not process ZUPTS on the last three cycles. In one embodiment, a cycle is approximately equal to one second. The length of a cycle and the number of Kalman filters  106 - 1  . . .  106 -N are application dependent. One embodiment of a process for preventing erroneous processing of ZUPTS is described with respect to  FIG. 2  below. 
       FIG. 2  is a flow chart of one embodiment of a method of improving the accuracy of an inertial system shown generally at  200 . A plurality of Kalman filters is initialized and the cycle starts ( 202 ). A plurality of Kalman filters are used because when a vehicle moves, processing an observation to the Kalman filters that assumes the vehicle is stopped causes an error. Detection of motion that allows the system  200  to avoid erroneous ZUPTS often occurs after the motion has started. Therefore, the method maintains a plurality of Kalman filters that have processed zero velocity updates on various cycles in order to revert back to a Kalman filter that processed zero velocity updates when no motion occurred. 
     In this embodiment, Kalman filter  1  represents the Kalman filter that processes ZUPTS on all cycles. Kalman filter N represents the Kalman filter that has not processed ZUPTS when motion was occurring. In one embodiment, Kalman filter N did not process ZUPTS on the last cycle. In another embodiment, Kalman filter N did not process ZUPTS on a number of sequential cycles. 
     The plurality of Kalman filters form non-zero velocity updates (ZUPTS) observations ( 204 ). These non-ZUPT observations are for the measurement vector (z) and the measurement sensitivity matrix (H) ( 204 ). Each of the plurality of Kalman filters are updated ( 206 ). The following list of equations describes this update process.
 
 P   i   =P   i   T   +Q  
 
X i =X i  
 
 K   i   =P   i   H   T   [HP   i   H   T   +R]   −1  
 
 P   i =[1 −K   i   H]P   i  
 
 X   i   =X   i   +K[z−HX   i ]
 
P i  is the covariance of Kalman filter i.
 
X i  is the error state vector for Kalman filter i.
 
is the state transition matrix for Kalman filter i.
 
Q is the process noise for the error states in all Kalman filters.
 
K i  is the measurement gain matrix for the non-ZUPT observations for Kalman filter i.
 
H is the measurement sensitivity matrix for the non-ZUPT observations.
 
z is the measurement vector for the non-ZUPT observations for Kalman filter i.
 
K i   ZUPT  is the measurement gain matrix for the ZUPT observations for Kalman filter i.
 
H ZUPT  is the measurement sensitivity matrix for the ZUPT observations.
 
z ZUPT  is the measurement vector for the ZUPT observations.
 
     The method then determines whether motion has been detected by a motion detect algorithm ( 208 ). In one embodiment, the motion detection algorithm uses a threshold to determine if there has been motion. In another embodiment, the motion detection algorithm is a solution separation algorithm as described below in  FIG. 3 . If no motion is detected, then ZUPT observations are formed (z ZUPT  and H ZUPT ) ( 210 ). 
     If no motion is detected, each Kalman filter copies the covariance and error state vector of the Kalman filter that has processed one more cycle of ZUPTS ( 212 ). This process starts with the Kalman filter that has processed the least amount of ZUPTS and ends when the covariance and error state vector for the Kalman filter that processed ZUPTS on the last cycle is copied to the Kalman filter that did not process ZUPTS on the last cycle ( 212 ). In one embodiment, the Kalman filter that processed ZUPTS on the last cycle is Kalman filter  1 . After the Kalman filters are copied, the zero velocity updates are applied to Kalman filter  1  as demonstrated in the following equations ( 214 ).
 
 K   1   ZUPT   =P   1   [H   ZUPT ] T   [[H   ZUPT   ]P   1   [H   ZUPT ] T   +R   ZUPT ] −1  
 
 P   1   =[I−K   1   ZUPT   H   ZUPT   ]P   2  where I is an identity matrix.
 
 X   1   =X   1   +K   1   ZUPT   [z   ZUPT   −H   ZUPT   X   1 ]
 
     After the zero velocity updates are applied to Kalman filter  1  the cycle stops ( 216 ). If motion was detected, the error state vector and covariance of Kalman filter N is copied to all the Kalman filters because all of the other Kalman filters erroneously processed ZUPTS when the vehicle was in motion ( 218 ). After Kalman filter N is copied, the cycle stops ( 216 ). 
       FIG. 3  is a view of one embodiment of a method of the present invention shown generally at  300 . In this embodiment, a solution separation algorithm  302  is shown. In one embodiment, solution separation algorithm  302  is used to detect motion as shown in block  208  of  FIG. 2  rather than using a threshold method. Motion is assumed to have occurred if the position separation between a Kalman filter that assumed no motion and a Kalman filter that assumed motion is greater than the statistically expected separation. In order to understand the solution separation algorithm a listing of definitions is provided. 
     P i  (1,1) is the first position error covariance of Kalman filter i. 
     P i  (2,2) is the second position error covariance of Kalman filter i. 
     P i  (3,3) is the third position error covariance of Kalman filter i. 
     X i  (1) is the first position error state estimate of Kalman filter i. 
     X i  (2) is the second position error state estimate of Kalman filter i. 
     X i  (3) is the third position error state estimate of Kalman filter i. 
     The solution separation algorithm  302  takes the difference between the first position error state estimate of the n th  Kalman filter and the first Kalman filter and squares it. If this number is greater than the difference between the first position error covariance of the n th  Kalman filter and the first Kalman filter multipled by C then motion is implied. C is defined as the confidence level required for the test. A value of C greater than one implies a need for uncertainty associated with motion to be greater than one-sigma. This number is application dependent. 
     The solution separation algorithm  302  then takes the difference between the second position error state estimate of the n th  Kalman filter and the first Kalman filter and squares it. If this number is greater than the difference between the second position error covariance of the n th  Kalman filter and the first Kalman filter multipled by C then motion is implied. 
     The solution separation algorithm  302  then takes the difference between the third position error state estimate of the n th  Kalman filter and the first Kalman filter and squares it. If this number is greater than the difference between the third position error covariance of the n th  Kalman filter and the first Kalman filter multipled by C then motion is implied. 
     If any of these equations implies motion, zero velocity observations are formed as shown with respect to block  210  of  FIG. 2  above. If however, none of these equations implies motion, then Kalman filter N is copied to all Kalman filters as shown with respect to block  218  of  FIG. 2  above. 
       FIG. 4  is a block diagram of a vehicle of one embodiment of the present invention shown generally at  400 . Vehicle  400  comprises an inertial system  402 . Inertial system  402  provides vehicle  400  positioning information. Inertial system  402  uses multiple Kalman filters to enable maintaining a proper output even when ZUPTS are processed when the vehicle is in motion. One example of inertial system  402  is inertial system  100  described above in  FIG. 1 . Another example of inertial system  402  is inertial navigation system  500  described below in  FIG. 5 . Inertial system  402  communicates with a guidance system  404  via a communication link  408 . In one embodiment, communication link  408  is wireless. In another embodiment, communication link  408  is a wired connection. Guidance system  404  takes information received from inertial system  402  and determines what actions, if any, are necessary to maintain or achieve a proper heading. When guidance system  404  determines a course of action which requires a change in position of vehicle  400 , guidance system  404  communicates with a vehicle position controller  406  via a communication link  410 . In one embodiment, communication link  410  is wireless. In another embodiment, communication link  410  is a wired connection. Vehicle position controller  406  takes the information received from guidance system  404  and moves vehicle  400  to the appropriate position. 
       FIG. 5  is an inertial navigation system of one embodiment of the present invention shown generally at  500 . Inertial navigation system  500  is comprised of a processor  508 . Processor  508  includes navigation equations  510  which receive data from sensors and integrates the data before sending it to Kalman filters  512 . In one embodiment, the sensors are accelerometers  506 . In another embodiment, the sensors are gyroscopes  504 . In another embodiment, the sensors are aiding sources  502 , including but not limited to, global positioning systems (GPS) and odometers. 
     Accelerometers  506 , gyroscopes  504 , and aiding sources  502  communicate with processor  508  via a communication link  514 . In one embodiment, communication link  108  is wireless. In another embodiment, communication link  514  is a wired connection. Processor  508  includes but is not limited to digital electronic circuitry, a programmable processor (for example, a special-purpose processor or a general-purpose processor such as a computer) firmware, software, or in combinations of them. 
     Navigation equations  510  send data, including but not limited to, position, velocity, attitude, acceleration, and angular rates to the Kalman filters  512 . Kalman filters  512  receive the data, and after performing calculations, send back to the navigation equations  510  a navigation solution and sensor data corrections. 
     The accuracy of the data used in inertial navigation system  500  is dependant on processing zero velocity updates (ZUPTS). ZUPTS are only accurate when the vehicle in which the inertial navigation system  500  is located, is stopped. Inertial navigation system  500  uses multiple Kalman filters  512  to enable maintaining a proper output even when ZUPTS are processed when the vehicle is in motion. One example of a method of using multiple Kalman filters  512  to avoid errors due to processing ZUPTS while the vehicle is in motion is described above in  FIG. 2 . 
     Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that any arrangement, which is calculated to achieve the same purpose, may be substituted for the specific embodiment shown. This application is intended to cover any adaptations or variations of the present invention. Therefore, it is manifestly intended that this invention be limited only by the claims and the equivalents thereof.