Patent Document

RELATED APPLICATIONS 
   This application claims priority of U.S. Provisional Application Nos. 60/164,709 filed Nov. 11, 1999; 60/157,766 filed Oct. 5, 1999; 60/134,575 filed May 17, 1999; and 60/154,818 filed Sep. 20, 1999. 

   FIELD OF THE INVENTION 
   This invention relates to a theft detection system which can be attached to valuable objects such as laptop computers, other electronic devices, and even works of fine art. 
   BACKGROUND OF THE INVENTION 
   Computers have conveniently become smaller and smaller in size. There are now notebook computers, hand held personal computers, and personal data assistants in addition to laptop computers. 
   However, because of their smaller size, computers are now easier to steal, for example, when left unattended for even a brief moment at an airport. 
   In U.S. Pat. No. 5,574,786, incorporated herein by this reference, a motion detector is coupled to a computer and the computer is disabled whenever it is moved. 
   The primary problem with this device is that the computer is disabled whenever it is moved. Therefore, if the owner of the computer enables the motion detector and then accidentally moves the computer, her computer will be disabled. Another problem with the device of the &#39;786 patent is that it is an integral component of the computer and thus cannot be used in combination with other objects of value, for example, cellular telephones, other electronic devices, or works of fine art. 
   SUMMARY OF INVENTION 
   It is therefore an object of this invention to provide a more versatile theft detection system. 
   It is a further object of this invention to provide such a theft detection system for objects of value including computers, works of fine art, cellular telephones, and other electronic devices. 
   It is a further object of this invention to provide such a theft detection system that can be attached to the housing of any object of value. 
   It is a further object of this invention to provide such a theft detection system which is self-contained and can be easily attached to an object of value by the user, incorporated on a PC card, or added to the existing circuit board of a computer. 
   It is a further object of this invention to provide such a theft detection system which filters out any movement of the object which does not constitute a theft of the object thus eliminating false alarms. 
   It is a further object of this invention to provide a method of detecting the theft of objects of value. 
   This invention results from the realization that a theft of an object such as a laptop computer can be more accurately determined by attaching an accelerometer to the object and analyzing the frequency of the resulting acceleration signal to effectively filter out movement of the object which is not indicative of a theft (e.g., by filtering out any acceleration signals which cannot be the result of human movement) and then activating an alarm only when the analysis of the acceleration signal reveals a possible theft event. The resulting system thus intelligently differentiates between theft events and non-theft events. 
   This invention features a theft detection system comprising an accelerometer attachable to an object, the accelerometer providing an acceleration signal in response to movement of the object: an alarm mechanism responsive to the accelerometer for providing an alarm signal in response to movement of the object; and a filter for preventing false alarms, the filter including means for determining the frequency of the acceleration signal and providing an output to activate the alarm mechanism only when the frequency of the acceleration signal meets a predetermined criteria. 
   The security mechanism may be an audible alarm with three modes, a slow mode, a fast mode and a siren mode. The means for determining the frequency of the acceleration signal may include means for calculating the deviation of the amplitude of the acceleration signal in a predetermined time frame and the filter then includes means for activating the security mechanism only when the deviation of the amplitude of the acceleration signal in a predetermined time frame exceeds a predetermined threshold. The filter typically also further includes means for counting how often the deviation of the amplitude of the acceleration signal exceeds the predetermined threshold. 
   Alternatively, or in addition, the means for determining the frequency of the acceleration signal includes means for performing a spectral analysis of the acceleration signal and the filter includes means for activating the security mechanism only when the frequency of the acceleration signal is within a specified range and also means for counting how often the frequency of the acceleration signal is within the specified range. 
   In one embodiment of the theft detection system of this invention, an accelerometer provides an acceleration signal in response to movement of the object; an alarm mechanism provides an alarm signal in response to movement of the object; and a processor is programmed to determine the frequency of the acceleration signal by calculating the deviation of the amplitude of the acceleration signal in a predetermined time frame and to provide an output to activate the alarm mechanism only when the deviation of the amplitude of the acceleration signal exceeds a predetermined threshold. In the preferred embodiment, the processor is further programmed to count how often the deviation of the amplitude of the acceleration signal exceeds the predetermined threshold. 
   In another embodiment, the processor is programmed to determine the frequency of the acceleration signal by performing a spectral analysis of the acceleration signal and to provide an output to activate the alarm mechanism only when the frequency of the acceleration signal is within a specified range. In the preferred embodiment, the processor is further programmed to count how often the frequency of the acceleration signal is within the specified range. 
   A method of detecting the theft of an object in accordance with this invention features the steps of employing an accelerometer to provide an acceleration signal in response to movement of an object; determining the frequency of the acceleration signal and providing an output to activate an alarm mechanism only when the frequency of the acceleration signal meets a predetermined criteria. Determining the frequency of the acceleration signal may include calculating the deviation of the amplitude of the acceleration signal in a predetermined time frame and comparing the deviation to a predetermine threshold. The method may further include the step of counting how often the deviation of the amplitude of the acceleration signal exceeds the predetermined threshold. Determining the frequency of the acceleration signal may instead or also include performing a spectral analysis of the acceleration signal and calculating whether the frequency of the acceleration signal is within a specified range. This method may further include the step of counting how often the frequency of the acceleration signal is within the specified range. 
   In accordance with another aspect of this invention, the theft detection method includes attaching an accelerometer to an object, the accelerometer providing an acceleration signal in response to movement of the object and programming a processor to be responsive to the acceleration signal and to determine the frequency of the acceleration signal by calculating the deviation of the amplitude of the acceleration signal in a predetermined time frame and to provide an output to activate an alarm mechanism only when the deviation of the amplitude of the acceleration signal exceeds a predetermined threshold. Typically, the processor is further programmed to count how often the deviation of the amplitude of the acceleration signal exceeds the predetermined threshold and to activate the alarm mechanism in different modes depending on the count of how often the deviation exceeds the predetermined threshold. 
   In still another aspect of this invention, the theft detection method comprises attaching an accelerometer to an object, the accelerometer providing an acceleration signal in response to movement of the object; and programming a processor to be responsive to the acceleration signal and to determine the frequency of the acceleration signal by performing a spectral analysis of the acceleration signal and to provide an output to activate the alarm mechanism only when the frequency of the acceleration signal is within specified range. Typically, the processor is further programmed to count how often the frequency of the acceleration signal is within the specified range and to actuate the alarm mechanism in different modes depending on the count of how often the frequency is within the specified range. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Other objects, features and advantages will occur to those skilled in the art from the following description of a preferred embodiment and the accompanying drawings in which: 
       FIG. 1  is a schematic view of the theft detection system of subject invention attached to a laptop computer; 
       FIG. 2  is a block diagram showing the primary components of the theft detection system shown in  FIG. 1 ; 
       FIG. 3  is a more detailed block diagram showing the primary programming blocks associated with the microprocessor of the theft detection system of  FIG. 2 ; 
       FIG. 4  is a flow chart showing the primary steps associated with the programming resident on the microprocessor shown in  FIG. 2 ; 
       FIG. 5  is a graph illustrating a time based acceleration signal detected by the theft detection system of this invention when the object to which it is attached is not moving; 
       FIG. 6  is a graph illustrating a time based acceleration signal similar to  FIG. 5  when the object is being stolen by a human being; 
       FIG. 7  is a graph illustrating a frequency based acceleration signal when the same object is being stolen; 
       FIG. 8  is a graph illustrating a time based acceleration signal when the same object is on an airplane; 
       FIG. 9  is a graph illustrating a frequency based acceleration signal when the same object is on an airplane; 
       FIG. 10  is a graph of the scaling function of the subject invention; and 
       FIG. 11  is a graph showing the application of the preferred algorithm in accordance with the subject application. 
   

   DESCRIPTION OF PREFERRED EMBODIMENT 
   Theft detection system  10 ,  FIG. 1 , in one embodiment, is enclosed in a small housing  5  which can be secured to an object of value such as laptop computer  12 . Other uses for system  10  includes personal data assistants, notebook computers, cellular telephones, other electronic devices, and even works of fine art. Alternatively, system  10  can reside on a PC card or even on an existing circuit board resident in an electronic device such as a computer. 
   The primary components of the preferred theft detection system  10 , in all embodiments, include a motion sensor such as accelerometer  20 ,  FIG. 2 , microprocessor  22 , and alarm subsystem  24  (for example, an audible alarm). Power supply  26 , for example, a lithium battery may be provided in some embodiments for providing power to accelerometer  20 , microprocessor  22  and alarm  24 . In an alternative embodiment, audible alarm  24  could be replaced or supplemented with an alarm mechanism which provides a signal to computer  12  to disable it until an appropriate password or the like is entered by the owner. In the embodiment where alarm mechanism  24  is an audible alarm, it is preferred that the alarm be capable of providing different audible sounds, for example, slow quiet beeps, fast louder beeps, and a very loud siren sound. 
   In the preferred embodiment, microprocessor  22  is programmed to determine the frequencies of the acceleration signal provided by accelerometer  20  and to filter out any frequencies indicative of movement of computer  12 ,  FIG. 1  which are not attributable to a theft event; it thus acts a filter between accelerometer  20  and alarm  24  to prevent false alarms. There are two ways to determine the frequency of the acceleration signal: first, by analyzing the rate of change of the amplitude of a time-based acceleration signal, and second, by converting the time based acceleration signal to a frequency based acceleration signal. 
   Microprocessor  22  is typically programmed to include five primary routines or “circuits”: arming circuit  30  which allows the user to arm the theft detection system, sampling circuit  32  which samples the signal from accelerometer  20  at a predetermined rate (e.g. 32 Hz), windowing circuit  34  which breaks the sampled data into predefined windows, and filtering circuit  36  and motion classifying circuit  38  defined infra. 
   In general, filtering circuit  36  determines the frequency of the acceleration signal output from accelerometer  20  either by performing a spectral analysis of the sampled varying amplitude acceleration signal to determine the frequency content of the acceleration signal or, more typically (or in addition), by calculating the amplitude deviation of the acceleration signal in a predetermined time frame, e.g. from one sample window to the next. 
   In this invention, it was determined that human movement typically falls into a frequency range between 0.5 to 2 Hz. Any frequency component less than 0.5 Hz is due to the effects of gravity and any frequency component greater than 2 Hz cannot normally be attributed to human movement. Thus, by filtering out any acceleration signal output from accelerometer  20  which does not fall within this range, theft detection system  10 ,  FIGS. 1–3 , once activated, properly sounds an alarm if a thief grabs unattended laptop computer  12  in an airport and begins running but will not sound a false alarm when the owner of laptop computer  12  uses the computer on board an airplane subject to many different acceleration frequencies. 
   System  10 ,  FIGS. 1–3  employs a motion analysis algorithm and uses the output of a 2-axis accelerometer  10  rigidly attached to computer  12  to determine whether or not the computer is being stolen rather than being used in the normal way by the owner. The system is armed when the laptop is intended to be kept at a given location (i.e. at the owner&#39;s desk). When armed, the algorithm described infra operates continuously and characterizes the motion of computer  12  as one of a plurality of hostility states. 
   System  10  supplies a stream of continuously sampled accelerometer outputs. The algorithm initially processes the 2-element time varying discreet data stream into a 1-element stream that is used in subsequent calculations. Next, the processed sensor data is windowed into overlapping finite sets (windows) of data. The algorithm may employ two separate calculation processes on the windowed data, each to detect suspect motion. Finally, a characterization stage uses the string of the most recent processed windows of data to determine whether or not potentially hostile motion is taking place. The process is then repeated, indefinitely, until either the system is unarmed or it is deemed that hostile motion is occurring. 
   In sample step  40 ,  FIG. 4 , sampling circuit or code  30 ,  FIG. 3 , samples the output from accelerometer  20  continuously at 32 Hz. This frequency is well above the Nyquist range for the types of motions a laptop would normally undergo (human motion frequencies range from in the 0.5 to 2 Hz). The thirty-two sample window of the 32 Hz sampled data is read into a 10 second buffer of processor  22  each second. The oldest one second window of the buffer is simultaneously discarded. 
   In step  42 ,  FIG. 4 , the sampled accelerometer data comprises the pair of X and Y samples and the acceleration amplitude A[n] is determined as:
 
 A[n ]=√{square root over ( X[n]   2   +Y[n]   2 )}.  (1)
 
   That magnitude is then detrended (its DC component is removed) and filtered by a first difference discrete time filter kernel:
 
 a[n]=A[n]−A[n− 1].  (2)
         a[n] is then used for all subsequent analysis.       

   In step  44 , the windowing circuit algorithm uses the last 10 seconds of data (320 data points, a[−319] . . . a[0] for analysis. These 320 points are broken into 9 smaller windows of data. Each window is two seconds long (64 samples) and overlaps the previous window by one second. Thus, if the ten second set of data covers from −10 to 0 seconds, the 9 windows will cover the following time ranges: −10 to −8, −9 to −7, −8 to −6, −7 to −5, −6 to −4, −5 to −3, −4 to −2, −3 to −1, and −2 to 0. 
   Filtering circuit  36 ,  FIG. 3  according to one of two methodologies or possibly both methodologies in parallel then analyzes the frequency of the acceleration signal. In accordance with the first methodology, a time-domain analysis is performed, step  46 ,  FIG. 4 . In this step, the average absolute deviation is calculated for each of the overlapping two second windows of the ten second data buffer. For a given 64 point window, this deviation D a  is: 
               D   a     =       1   64     ⁢       ∑     l   =   1     64     ⁢            a   ⁡     (     n   -   l     )       -       1   64     ⁢       ∑     k   =   1     64     ⁢     a   ⁡     (     n   -   k     )                              (   3   )             
 
   The deviation value D a  is proportioned to the overall amount of motion occurring in a given window. For each window, the deviation is compared with a threshold step  48 , to determine whether or not the window represents suspicious data. 
   Alternatively, or in parallel with steps  46  and  48 , microprocessor filter circuit  36 ,  FIG. 3  is programmed to calculate the power spectral density (PSD) of each two second window of data, step  50 ,  FIG. 4 . This step involves multiplying each 64 point window of data by a 64 point HANNING waveform and performing a 64 point FFT (fast Fourier transform) on the resulting waveform. The FFT yields 64 frequency outputs, spanning the frequency range of −16 Hz to 16 Hz. Because the input data is real, the FFT will be symmetric, and thus the negative frequencies are ignored. Because the FFT yields a complex output, each output point is multiplied by its complex conjugate. Thus, the output of the PSD is an array of 33 values, covering the frequency range from 0 Hz to 16 Hz. Each value represents the frequency content of the input waveform over a 0.5 Hz frequency span. Thus, the first element of the PSD contains the amount of DC present in the signal, while the 33 rd  element of the PSD represents the highest frequency components (16 Hz in this example). 
   At this stage in the processing, there is a 33 point PSD of each of the nine windows of data. For each of the nine PSD, the low frequency content (0.5 to 2 Hz) or the sum of the second through the fifth elements of the PSD&#39;s (L) is calculated. A high value of the low frequency content metric (L) is indicative of walking or carrying motion. 
   When the low frequency content (L) of nine windows of data (or the last ten seconds) and/or the deviation (D) are above a predetermined threshold, step  57 , a hostile motion (a theft) may possibly be taking place and the hostility state is incremented, step  58 . Alternatively, if (L) or (D) are not above their respective thresholds, the hostility state is decremented, step  60  and processing returns to step  40  as shown. 
   When the hostility state is incremented past a first threshold, a first alarm signal may be output to multi-mode alarm  62 ,  FIG. 4 , which in turn produces a series of slow soft beeps. When the hostility state is incremented past a second threshold, a second alarm signal is output to multi-mode alarm  62  which in turn produces a series of fast louder beeps. When the hostility state is incremented past a final threshold, a third alarm signal is output to multi-mode alarm  62 , which in turn produces a loud siren type audible alarm. Alternatively, or in addition, it is at this stage where the computer could be deactivated and reactivated only upon the entry of a secret password. 
   In the preferred embodiment, accelerometer  20 ,  FIG. 2  is a Analog Devices ADXL202,” and microprocessor  22  is a Microchip PIC16C63A. 
   Alarm  24 , as explained supra, may be replaced or supplemented with a device or programming which renders laptop computer  12 ,  FIG. 1  inoperable. Also, the threshold values provided by way of example, supra, can be changed depending on the implementation of system  10 . For example, for protecting a valuable work of fine art, the thresholds will be much lower than compared to those for a cellular telephone, which is typically moved quite often by the owner. 
   The operation of filtering circuit  36 ,  FIG. 3  is explained with reference to the highly illustrative acceleration signal waveforms of  FIGS. 5–9 . If there is no movement of laptop computer  12 ,  FIG. 1 , the only acceleration on computer  12  is due to gravity as shown at  70 ,  FIG. 5 . Filtering circuit  36  always filters out any acceleration signal output from accelerometer  20 ,  FIGS. 2–3  which is analyzed to be the result of gravitational forces. 
   If a thief takes computer  12  from a table in an airport, however, the acceleration signal output by accelerometer  20 ,  FIGS. 2–3 , is as shown at  72 ,  FIG. 6 . 
   Deviation analysis filtering step  46 ,  FIG. 4 , of the processing accomplished by filtering circuit  36 ,  FIG. 3 , of microprocessor  22  calculates the change from amplitude A 1  to amplitude A 2  in the time period t 1 . This is the first method of determining the frequency of acceleration signal  72 . The change in the deviation (D), as explained above, is then compared during threshold comparison step  48 ,  FIG. 4 , with a predetermined threshold to detect that a theft is occurring. 
   Alternatively, or in addition, signal  72 ,  FIG. 6 , is converted to the frequency domain as shown at  74 ,  FIG. 7 , during spectral analysis step  50 ,  FIG. 4 , of the processing accomplished by filtering circuit  36 ,  FIG. 3 , of microprocessor  22 . The low frequency content (L) calculated in step  52 ,  FIG. 4 , of the resulting analysis, between 0.5 and 2 Hz, is indicative of a theft of laptop computer  12 ,  FIG. 1 . 
   If, instead of a theft of laptop computer  12 ,  FIG. 1 , the owner is operating computer  12  on board an airborne airplane, the deviation (D),  FIG. 8  from amplitude A, to amplitude A 2  of acceleration signal  76  in the time period t 1  will not exceed the predetermined threshold as computed in steps  46  an  48 ,  FIG. 4 , since airplane vibrations fall outside of the 0.5 Hz to 2 Hz range also shown at  78  in  FIG. 9  when spectral analysis and calculation steps  50  and  52 ,  FIG. 4 , are undertaken by filtering circuit  36 ,  FIG. 3 . 
   In this way, by carefully choosing values for the acceptable amplitude deviation (D),  FIG. 4 , and/or frequency ranges (L), filtering circuit  36 ,  FIG. 3 , in combination with the carefully chosen values for the hostility state thresholds which must be reached before an alarm is emitted by alarm  24 , system  10 ,  FIG. 1 , is able to differentiate between authorized movement of laptop computer  12  (or any other object) such as airplane or vehicle transport, movement across a desk, or walking a short distance from one office to another in a short time period and unauthorized movements of laptop computer  12  such as when a thief steals it and begins running through an airport. Thresholds (D) and (L) may be set at the factory and/or established by the user via programming options resident in microprocessor  22 , FIG.  2 . 
   The current algorithm has several routines. The basic idea is that the accelerometer  20  output (X, Y) is sampled continuously at 32 Hz, step  32 ,  FIG. 3 . These X, Y values are combined into a single magnitude value. Multiple magnitude values are combined into a window of data, step  34 ,  FIG. 3 . For each window of data, a single window summary value is computed, step  36 . The last 10 window summary values are stored and are used to determine when state transitions in the alarm state machine occur, step  38 . A single magnitude metric for each X, Y acceleration pair is calculated. Currently this happens at a rate of 32 Hz. A window summary value is created that describes the level of motion across multiple recent magnitude values. This window summary value is thresholded to create a binary window summary value. Currently the window summary values are created at a rate of 2 Hz. A history of the most recent binary window summary values is then created. Currently this history is updated every time a new window summary value is created (2 Hz). A multi-state alarm state machine uses the history of window summary values to determine state changes. When the last state is reached, the alarm is triggered. Currently state transitions are checked for every time the history is updated (2 Hz). Currently the state machine has four states. Transitions from a state can move only one state up/down at a time. When the fourth state is reached, the system is considered stolen. 
   The accelerometer output is sampled at 32 Hz. Both the X axis output and the Y axis output are sampled each time. Each (X, Y) pair is combined into a single magnitude metric that will further be used by the algorithm. The procedure for computing the magnitude metric is to sample the X and Y accelerometer outputs at 32 Hz (X[n], Y[n]); and to calculate the difference between the current sample and the last sample for both the X and Y samples:
 
 Xdiff[n]=X[n− 1]− X[n], Ydiff[n]=y[n− 1]− Y[n].   (4)
 
A “magnitude” value is calculated by summing the absolute values of the two difference signals:
 
 AbsMag[n]=|Xdiff[n]|+|Ydiff [n] |.   (5)
 
The magnitude value is compressed into an 8 bit number. Currently the magnitude value AbsMag is an 11 bit quantity. Because of hardware limitations the signal is compressed into 8 bits. This is something that is not fundamental to the algorithm and may not be implemented on some platforms: 
               AbsMag8   ⁢           [   n   ]     =     floor   ⁢     {       (       400         -   4     ⁢     AbsMag   ⁡     [   n   ]         B       -   1     )     +       (     55   1024     )     ⁢     AbsMag   ⁡     [   n   ]           }               (   6   )             
 
   Small magnitudes are pinned to zero thus:
 
if (AbsMag8[ n]&lt;= 2)AbsMag8[ n]= 0  (7)
 
   The algorithm next combines multiple samples of the AbsMag8 data stream. This is done by creating windows of data. Currently each window consists of 32 consecutive samples from the AbsMag8 data stream. The rate at which the data is windowed can be varied throughout an effective range of 1 Hz to 32 Hz. The amount of overlap between windows is determined by this rate. At a window rate of 1 Hz, the windows will not overlap. At a window rate of 32 Hz, 31 of the 32 values in each epoch will overlap. A window rate of 2 Hz is currently used. A single window summary value metric is computed for each window of data. 
   A create current window is created: 
               WindowMean   ⁢           [   n   ]     =       1   32     ⁢       ∑     k   =   1     32     ⁢     AbsMag8   ⁢           ⁢     (     n   -   K     )                   (   8   )             
 
   The mean of each window is then calculated:
 
WindowMean[ i ]=sum(WindowArray[ i ][ . . . ]−WindowMean)/32).  (9)
 
   A binary window summary value for each window summary value is calculated by comparing each WindowSummaryValue to a threshold value:
 
If (WindowMean[i]&gt;=WindowThreshold) then BinaryWindowSummary[i]=1; Else BinaryWindowSummary[i]=0.  (10)
 
   This BinaryWindowSummary stream is then further used to determine if the system has been stolen. Note that the frequency that the BinaryWindowSummary is created at is different than the rate at which the data is sampled. Currently the accelerometer is sampled at 32 Hz, while window summary values are computed at a rate of 2 Hz. 
   The algorithm next looks at a finite number of the most recent samples from the BinaryWindowSummary stream. This is the BinaryWindowHistoryArray. This history is updated each time a new window summary value is computed. The metrics WindowsAbove and WindowsBelow are computed based on the BinaryWindowHistoryArray and are used as inputs to a theft detection state machine. Transitions between states happen when WindowsAbove or WindowsBelow exceed state dependent thresholds. After a state transition, the BinaryWindowHistoryArray is set to be empty. The number of states can be varied. A system employing 4 states has been used. State 1 would be the resting state, States 2 and 3 are intermediate states and State 4 is the alarm state. Once State 4 has been reached, the system is considered stolen. It should also be noted that many of the parameters discussed previously can be state dependent. Examples include WindowThreshold, thresholds for WindowsAbove and WindowsBelow, and the frequency at which window summary values are computed. 
   Currently the algorithm keeps track of the last 10 BinaryWindowSummary values thus:
 
BinaryWindowHistory[1.10]={BinaryWindowSummary[i] . . . BinaryWindowSummary[i]};  (11)
         and counts the number of elements of BinaryWindowHistory that are 1. This is WindowsAbove. It then determines, starting from the most recent value of BinaryWindowHistory, how many consecutive values are 0. This is WindowsBelow. A transition to the next highest state is required if WindowsAbove&gt;WindowsAboveThresh. If a transition to the next lower state is required, (if WindowsBelow&lt;WindowsBelowThresh), then the transition state increments downward. If a state change happened, a check is made to see if the alarm state has been reached. If so, the system is considered “stolen.” If a state change happened, the BinaryWindowHistoryArray is reset and any state dependant constants are initialized (currently WindowsAboveThresh, WindowsBelowThresh, window summary value frequency).       

   In the current system, the magnitude value is 11 bits nominally. Because of the processors limitations, it is desirable to compress and scale this magnitude into 8 bits. The absolute magnitude is compressed into an 8 bit value using the following monotonically increasing, sigmoidal scaling function: 
               AbsMag8   ⁢           [   n   ]     =     floor   ⁢     {       (       400         -   4     ⁢     AbsMag   ⁡     [   n   ]         B       -   1     )     +       (     55   1024     )     ⁢     AbsMag   ⁡     [   n   ]           }               (   12   )             
 
   The first term on the right hand side of this equation is a sigmoidal function. The parameter B can be predetermined or used as a ‘sensitivity’ variable. The second term on the right hand side is a linear function added to the sigmoid to allow the scaling function to continue to rise even thought the sigmoid has approached its maximum. Examples of the effect of this scaling function are plotted in  FIG. 10  for several values of the parameter B (B=40, 100, 400, 1000, 4,000, 10000). The X-axis represents the 11 bit number that is to be scaled and the Y-axis is the 8 bit (scaled) equivalent. Smaller values of B result in steeper sigmoidal regions (left-most curves on the plot). This steepness translates to a higher sensitivity to small accelerations. This increased sensitivity comes at the expense of sensitivity in the higher acceleration range. In this region the linear term is seen to dominate. As B becomes very large (right-most curves on the plot) the scaling function is approximately linear throughout its domain but does not take advantage of the entire 8 bit dynamic range. A value of B=40 has been used successfully. In order to stabilize the output of the algorithm for very small (stationary accelerometer with noise), scaled (8 bit) magnitudes are set to zero if they are below a given value:
 
if ( AbsMag 8[ n]&lt;= 2)  AbsMag 8[ n]= 0.  (13)
 
     FIG. 11  shows the results of applying the algorithm to actual motion data. The X-axis is time in seconds. The data was acquired while walking in a “sneaky” manner. Waveforms  100  and  102  are the 2 axis outputs of the accelerometer. Trace  104  is a plot of window values calculated at 32 Hz (one for every data point). Plot  106  shows the window values for a window rate of 1 Hz and the stars indicate what the window values are when the bin rate if 2 Hz. Line  108  is a possible window threshold value (1). 
   In summary, the frequency of the resulting acceleration signal emitted by accelerometer  20 ,  FIG. 2 , is analyzed by filtering circuit  36 ,  FIG. 3 , to filter out any movement of the object which is not indicative of a theft such as, for example, by filtering out any acceleration signals which cannot be the result of human movement. Alarm  24  is then activated only when the analysis of the acceleration signal reveals a possible theft event. 
   As a result, theft detection system  10 ,  FIG. 1  can be rendered self-contained and may be attached to or incorporated as a part of any object of value to automatically filter out movement of the object which does not constitute a theft of the object thus eliminating false alarms. Also, although a processor based system is disclosed in the preferred embodiments, other circuits configured to discriminate between motion signals indicative of a theft event and a non-theft event may be used including a properly configured circuit board, an application specific integrated circuit, a computer routine operating on the computer to which the system is attached, and any after developed or existing equivalent devices or subsystems. 
   Therefore, although specific features of the invention are shown in some drawings and not in others, this is for convenience only as each feature may be combined with any or all of the other features in accordance with the invention. Moreover, other embodiments will occur to those skilled in the art and are within the following claims:

Technology Category: 3