Patent Publication Number: US-2023161424-A1

Title: Predictive data-reconstruction system and method for a pointing electronic device

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 17/191,320, filed on Mar. 3, 2021, which claims the benefit of Italian Patent Application No. 102020000005428, filed on Mar. 13, 2020, which applications are hereby incorporated by reference herein in their entirety. 
    
    
     TECHNICAL FIELD 
     The present solution relates to a predictive data-reconstruction system and method, in particular for a pointing electronic device for so-called “air-pointer” applications. 
     BACKGROUND 
     As it is known, pointing electronic devices include traditional pointers (i.e. devices dedicated to pointing functions) and also smart pens or digital pens or styluses or smart pencils (or similar handheld devices having further and different functions in addition to a pointing function) that are to be coupled to an electronic host apparatus (e.g. a laptop, a tablet, a smart TV, a monitor or a smartphone). 
     Pointing electronic devices usually implement an HID (Human Interface Device) pointer (or mouse) interface, or protocol, to send displacement information (in particular, information associated with a displacement between a current and a previous position) to the host apparatus, in terms of coordinates in a screen-frame of the same host apparatus. A control unit of the host apparatus is thus able to move a displayed object (e.g. a cursor or the like) on the screen-frame based on the received displacement information. 
     SUMMARY 
     In accordance with an embodiment, a pointing electronic device includes an inertial measurement module, configured to generate motion input data, indicative of motion of the pointing electronic device, at an input data rate; a pointing determination unit, configured to implement a pointing algorithm at a processing data rate based on the motion input data, to generate screen-frame displacement data corresponding to 3D-space movements of the pointing electronic device, the input data rate being lower than the processing data rate; and a rate upscaling unit, interposed between the inertial measurement module and the pointing determination unit, configured to implement a data-rate upscaling of the motion input data, to generate upscaled motion input data to be processed by the pointing determination unit at a data rate matching the processing data rate, via a predictive data reconstruction of missing samples based on the actual motion input data. 
     In accordance with another embodiment, an electronic system includes a host apparatus having a display; and a pointing electronic device in communication with the host apparatus. The pointing electronic device includes: an inertial measurement module, configured to generate motion input data, indicative of motion of the pointing electronic device, at an input data rate; a pointing determination unit, configured to implement a pointing algorithm at a processing data rate based on the motion input data, to generate screen-frame displacement data corresponding to 3D-space movements of the pointing electronic device, the input data rate being lower than the processing data rate; a rate upscaling unit, interposed between the inertial measurement module and the pointing determination unit, configured to implement a data-rate upscaling of the motion input data, to generate upscaled motion input data to be processed by the pointing determination unit at a data rate matching the processing data rate, via a predictive data reconstruction of missing samples based on the actual motion input data; and a communication interface unit configured to transmit the screen-frame displacement data to the host apparatus, wherein the screen-frame displacement data are configured to control movement of a displayed element on a screen frame of the display. 
     In accordance with a further embodiment, a method of generating screen-frame displacement data based on 3D-space movements of a pointing electronic device includes: generating motion input data, indicative of motion of the pointing electronic device, at an input data rate; implementing a pointing determination algorithm at a processing data rate based on the motion input data, to generate the screen-frame displacement data, the input data rate being lower than the processing data rate; and upscaling a data-rate of the motion input data, to generate upscaled motion input data to be processed by the pointing algorithm at a data rate matching the processing data rate, wherein the upscaling comprises performing a predictive data reconstruction of missing samples based on the actual motion input data. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a better understanding of the present invention, preferred embodiments thereof are now described, purely by way of non-limiting example and with reference to the attached drawings, wherein: 
         FIG.  1    shows a schematic block diagram of a known pointing electronic device; 
         FIG.  2    is a schematic depiction of the pointing electronic device and corresponding gyroscope signal components; 
         FIG.  3    schematically shows a plot of cursor displacement in a screen-frame, compared to the actual movement of the pointing electronic device, with cursor positions computed according to a known prior art solution; 
         FIG.  4    shows a schematic and simplified block diagram of a pointing electronic device according to the present solution; 
         FIG.  5    shows a schematic and simplified block diagram of the pointing electronic device according to a possible embodiment; 
         FIG.  6    is a schematic block diagram of a data reconstruction unit in the pointing electronic device, according to an aspect of the present solution; 
         FIG.  7    is a schematic block diagram of the data reconstruction unit, according to an embodiment of the present solution; 
         FIG.  8    shows plots of reconstructed motion data, compared to sensed motion data; 
         FIG.  9    schematically shows a plot of cursor displacement in a screen frame, compared to the actual movement of the pointing electronic device, with cursor positions computed according to the present solution; and 
         FIG.  10    is a schematic block diagram of a system comprising the pointing electronic device and a host apparatus. 
     
    
    
     DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS 
     As schematically shown in  FIGS.  1  and  2   , a known pointing electronic device  1  includes: 
     a first motion sensor, being an accelerometer sensor  2 , in particular a MEMS (Micro Electro Mechanical System) triaxial accelerometer, providing an acceleration signal Acc[x,y,z] indicative of accelerations acting on the pointing electronic device  1  along three axes X, Y, Z of a 3D-space inertial reference system associated with the pointing electronic device  1 ; 
     a second motion sensor, being a gyroscope sensor  4 , in particular a MEMS triaxial gyroscope, providing a gyroscope signal Gyro[x,y,z] indicative of the angular rate around the three axes X, Y, Z of the 3D-space inertial reference system associated with the pointing electronic device  1 ; and 
     a sensor-fusion processing unit  5 , coupled to the accelerometer sensor  2  and the gyroscope sensor  4 , to receive at its input the acceleration signal Acc and the gyroscope signal Gyro, and configured to jointly process the acceleration and gyroscope signals with a 6-DoF (six Degrees of Freedom) sensor fusion algorithm (the inputs of the algorithm being the same acceleration and gyroscope signals Acc, Gyro). 
     In a possible implementation, the sensor-fusion processing unit  5  is configured to generate at its output a roll estimation quantity β′, indicative of the orientation of the pointing electronic device  1 , particularly the roll or tilt angle about its longitudinal axis. 
     The accelerometer sensor  2 , the gyroscope sensor  4 , and the sensor-fusion stage  5  form an inertial measurement module  7 , providing at the output one or more of the above acceleration signal Acc[x,y,z], gyroscope signal Gyro and roll estimation quantity β′. 
     The pointing electronic device  1  further comprises a pointing determination unit  8 , coupled to the inertial measurement module  7 , configured to receive motion input data and to perform a pointing algorithm for translating the movements of the pointing electronic device  1  in the 3D-space into displacements in a bi-dimensional screen frame (i.e. in a display of a host apparatus coupled to the pointing electronic device  1 ). 
     In a possible implementation, the pointing determination unit  8  is configured to receive at its input, as the motion input data, the roll estimation quantity, and the gyroscope signal Gyro, to compensate the same gyroscope signal Gyro based on the roll estimation quantity β′ and to remap the compensated gyroscope measurements in displacements in the screen frame. 
     It is noted that the above roll estimation quantity may be an actual estimated roll angle or a different quantity that is indicative of the roll angle and/or from which the same roll angle may be determined. 
     For example, the sensor fusion unit  5  may be configured to combine the acceleration and gyroscope signals Acc, Gyro with a complementary filter (or any other suitable processing algorithm), and generate at the output a gravity vector estimation, as the above roll estimation quantity. As it is known, the gravity vector, denoted in general with g, is an array of three values [gx,gy,gz], which correspond to the respective projections of the gravity acceleration {right arrow over (g)} on the three axes X, Y, Z of the reference system associated with the pointing electronic device  1 . The gravity vector is normalized with respect to the value of the acceleration of gravity (about 9, 8 m/s 2 ), thus having a unitary module. 
       FIG.  2    schematically shows the pointing electronic device  1 , the three axes X, Y, and Z of an associated reference system and the gyroscope signal Gyro[x, y, z] along the same three axes X, Y, and Z. In particular, axis Y represents the axis of longitudinal extension of the pointing electronic device  1 ; axis X represents a transversal axis, with respect to the same longitudinal extension; and axis Z represents a vertical axis, orthogonal to the horizontal plane defined by the X and Y axes. 
     Angle β about axis Y represents here the true roll or tilt angle of the pointing electronic device  1 , which is ideally used to rotate (compensate) gyroscope signals to provide a roll-independent pointer output since the user cannot be forced to maintain a fixed device orientation during its use. It is indeed noted that rotation of the pointing electronic device  1  around the longitudinal axis does not participate in the pointing operation and thus in determining corresponding displacements in the screen-frame. 
     As it is known, new generation devices (in particular, the above-cited smart pens or similar devices) may require a very low-power consumption to improve battery life, since the size, and consequently battery size, is limited, and device battery duration is a key design parameter. 
     Moreover, in some systems, an accurate user experience may be guaranteed, e.g. in terms of accuracy, precision, latency, and smoothness of the overall use and operation of the devices, in possible use scenarios. 
     Since the operation of the motion sensors may require a considerable amount of current consumption (particularly in the case of an active sensor, such as the gyroscope sensor, having a moving mass that has to be actuated at a resonance frequency), a known solution to reduce power consumption envisages reducing the sensor output data rate and/or an advanced duty cycling between the different motion sensors, e.g. the accelerometer sensor  2  and the gyroscope sensor  4 , which are alternatively set in a power-on or power-off mode, for example in respective intervals of a processing duty cycle. 
     In known solutions, the sensor output data rate may therefore be lower than the operating (or processing) frequency of the pointing determination unit  8 , which determines the final output data rate for the displacement information sent toward the host apparatus coupled to the pointing electronic device  1 , for the displacement of the displayed object (e.g. the cursor or the like) on the screen-frame. For example, the pointing determination unit  8  may operate at a processing data rate that is double the sensor output data rate (the processing data rate may be e.g. at 25 Hz and the sensor output data rate may be at 12.5 Hz). 
     As a consequence, in known solutions, either the processing data rate of the pointing determination unit  8  is lowered to match the sensor output data rate, or the sensor output data are duplicated for the processing by the pointing determination unit  8 , to achieve a sensor output data rate matching the processing data rate. This may entail a decrease in the user experience, particularly with respect to the display of the cursor movement in the screen-frame. 
     In this regard,  FIG.  3    shows with a solid line the movement of the pointing electronic device  1 , in the example with the user “air-drawing” a circular shape; the dashed line represents instead the shape “drawn” by the cursor displayed on the screen-frame of the host apparatus, based on the displacement information provided by the pointing determination unit  8 . 
     Moreover, the solid and dashed circles represent the positions of the cursor as updated by the pointing determination unit  8  (at each execution of the corresponding pointing algorithm), with the above dashed line being the line joining the various positions. In particular, the solid circles represent the positions determined by the pointing algorithm based on actual motion data sensed by the motion sensors, while the dashed circles represent the positions determined based on duplicated motion data (which are thus located at the middle of the line joining two consecutive solid circles). 
     It is clear that, in both solutions, the user experiences a cursor movement that is evidently different from the actual movement of the pointing electronic device  1  (in other words the user experiences a visible “jerkiness” of the cursor movement); in particular, also in case the motion sensor input data are duplicated, the cursor path remains the same as for the case where a reduced processing data rate is used by the pointing determination unit  8  (with only the solid-circle positions of the cursor being computed), with substantially the same resulting decrease of performance. 
     In some embodiments of the present invention, the abovementioned power consumption and user experience issues may be addressed. 
     As will be discussed in detail in the following, an aspect of the present solution envisages maintaining the desired value of the processing data rate of the pointing determination unit  8  (i.e. without reducing the same value to match the sensor output data rate) with a proper upscaling of the motion input data rate, in particular via a predictive data reconstruction of missing samples, based on the actual motion data sensed by the motion sensors (it is noted that in this context “missing samples” do not refer to samples lost but to samples that have to be reconstructed due to a lower sampling data rate). 
     As shown in  FIG.  4    (where same references are used to denote similar elements as those shown in  FIG.  1   , which are therefore not discussed again), the pointing electronic device  1  further comprises a rate upscaling unit  20 , interposed between the output of the inertial measurement module  7  and the input of the pointing determination unit  8 , configured to implement a data-rate upscaling of the motion input data, to generate upscaled motion input data to be processed by the same pointing determination unit  8  with a data rate matching the processing data rate of the pointing determination unit  8  (as a non-limiting example, the processing data rate being double than the data rate of the original motion input data, e.g. at 25 Hz against at 12.5 Hz). 
     The rate upscaling unit  20 , operating at the processing data rate, comprises a verification stage  22 , which acquires the motion input data from the inertial measurement module  7  (as in the embodiment discussed above, with reference to  FIG.  1   , the motion input data may include the roll estimation quantity β′, e.g. the gravity vector G processed by the sensor-fusion stage  5 , and the gyroscope signal Gyro) and a data reconstruction stage  24 , which is configured to perform a predictive data reconstruction in case of missing samples of the same motion input data. 
     It is noted that, in another possible embodiment, the rate upscaling unit  20  may receive as motion input data the acceleration and gyroscope signal data, again at a lower data rate; in this embodiment, the sensor fusion stage  5  may be interposed between the rate upscaling unit  20  and the pointing determination unit  8  (i.e. being not included in the inertial measurement module  7 ). 
     In particular, the verification stage  22  is configured to determine, at every cycle, or iteration, of the pointing algorithm implemented by the pointing determination unit  8  (at time intervals corresponding to the processing data rate) the need to reconstruct the motion input data. 
     In more detail, at every cycle, a new or current value (i.e. sample) read for the motion input data is compared to an old or previous value (i.e. sample) acquired at a previous cycle (in particular, a bit-by-bit or bitwise data comparison is implemented for this comparison). It is noted that the old value is available to be read, e.g. at output registers of the motion sensors and/or of the sensor-fusion processing unit  5 , even when the same motion sensors are in a power-off mode; accordingly, at every cycle, all motion input data (e.g. both the gravity vector G and the gyroscope signal Gyro) are read (either being new sensed data or stored previous data). 
     If the new value for the motion input data equals the old value (in particular, according to the above bitwise comparison), this means that the corresponding output register (or analogous storage element) was not rewritten and that the current sample of the motion input data is missing (i.e. it has to be reconstructed due to the lower input data rate); therefore, execution of the data reconstruction stage  24  is enabled, to reconstruct the missing sample, via the predictive data-reconstruction. 
     If instead, the new value read for the motion input data differs from the old value (in particular, according to the same bitwise comparison), the new value of the motion input data is directly provided to the pointing determination unit  8 , as the current sample to be processed by the pointing algorithm (in other words, the current sample is an actual motion data sensed and provided by the inertial measurement module  7 ). 
     It is noted that the verification stage  22  is configured to perform the verification for each element of the motion input data, e.g. for both the gravity vector G and the gyroscope signal Gyro and in particular for each component thereof along the X, Y, and Z axes. 
     As shown in  FIG.  5   , in the embodiment where the motion input data include the gravity vector G and the gyroscope signal Gyro, the verification stage  22  includes: a first verification block  22   a , configured to receive, at each processing cycle, the gravity vector G, in particular, a new sample for each of the axis X, Y, and Z, and to perform the comparison with the old value stored for the same gravity vector (again, for each of the axis X, Y, and Z), being stored in a first storage element  25   a  (the first storage element  25   a  therefore storing the values received at the previous cycle or iteration of the processing algorithm); and a second verification block  22   b , separate and distinct with respect to the first verification block  22   a , configured to receive the gyroscope signal Gyro, in particular, the new sample for each of the axis X, Y, and Z, and to perform the comparison with the old value for the same gyroscope signal Gyro (again, for each of the axis X, Y, and Z), stored in a second storage element  25   b.    
     A respective data reconstruction stage  24  is provided at the output of each of the first and second verification blocks  22   a ,  22   b , being executed in case the new value for each of the axis X, Y, and Z equals the old value for each corresponding axis X, Y, and Z; otherwise, the same new value is sent as the current sample for processing by the pointing determination unit  8 . 
     In more detail, and with reference to  FIG.  6   , the above-discussed data reconstruction stage  24  is configured to receive at its input a current sample of the motion input data, here denoted in general with data t  (representing a generic sample, at a current time t, of motion input data, e.g. of any of the components of the gravity vector or gyroscope signal Gyro, along any of the axes X, Y, and Z) and to generate at the output a reconstructed (or predicted) data sample data t   pred  to be provided to the pointing determination unit  8  for processing by the pointing algorithm; it is noted that the data-reconstruction procedure is repeated for each and every axes of each and every motion input data element (in the example, of the gravity vector G and of the gyroscope signal Gyro). 
     It is also noted that data t =data t-1  (where datat−1 represents the old sample, i.e. the sample at the previous cycle), since the data reconstruction stage  24  is enabled when the verification stage  22  determines matching between the new (data t ) and the old (data t-1 ) samples. 
     In various embodiments, the pointing algorithm implemented by pointing determination unit  8  may be implemented using pointing algorithms known in the art. In one embodiment, the pointing algorithm disclosed in U.S. patent application Ser. No. 16/932,467 may be used. In this example, the pointing determination stage  8  receives as the inputs of the pointing algorithm, from the sensor-fusion processing stage  5 , the gravity vector g[g x , g y , g z ](generated by the same sensor-fusion processing stage  5  with a 6-DoF sensor-fusion algorithm based on the accelerometric and gyroscopic signals); and the same gyroscopic signal Gyro[x, y, z]. 
     The pointing determination stage  8  then performs an operation of axes selection. In particular, to avoid waste of resources, one gyroscope axis (the one representing the roll) can be removed from the subsequent computations: in the case of using an East North Up (ENU) reference system, the Y axis may be ignored in some embodiments. 
     The pointing determination stage  8  then performs a one-axis roll (or tilt) compensation of the gyroscopic signal Gyro[x, y, z] received at its input, to provide a natural user experience with any orientation of the electronic device  1  (i.e., independent from any rotation of the same electronic device  1  around its longitudinal axis, the Y axis in the above defined ENU orientation). 
     To perform the roll compensation operation, the input gyroscopic signal Gyro is back-rotated using a roll rotation matrix, according to the following expression: 
     
       
         
           
             
               [ 
               
                 
                   
                     
                       Gyro 
                       x 
                       ′ 
                     
                   
                 
                 
                   
                     
                       Gyro 
                       y 
                       ′ 
                     
                   
                 
                 
                   
                     
                       Gyro 
                       z 
                       ′ 
                     
                   
                 
               
               ] 
             
             = 
             
               
                 
                   [ 
                   
                     
                       
                         
                           cos 
                           ⁢ 
                           θ 
                         
                       
                       
                         0 
                       
                       
                         
                           
                             - 
                             sin 
                           
                           ⁢ 
                           θ 
                         
                       
                     
                     
                       
                         0 
                       
                       
                         1 
                       
                       
                         0 
                       
                     
                     
                       
                         
                           sin 
                           ⁢ 
                           θ 
                         
                       
                       
                         0 
                       
                       
                         
                           cos 
                           ⁢ 
                           θ 
                         
                       
                     
                   
                   ] 
                 
                 
                   - 
                   1 
                 
               
               [ 
               
                 
                   
                     
                       Gyro 
                       x 
                     
                   
                 
                 
                   
                     
                       Gyro 
                       y 
                     
                   
                 
                 
                   
                     
                       Gyro 
                       z 
                     
                   
                 
               
               ] 
             
           
         
       
     
     where θ is the roll angle, Gyro is the input gyroscopic signal defined by vector [Gyro x , Gyro y , Gyro z ] and Gyro′ is the roll-compensated gyroscopic signal defined by vector [Gyro′ x , Gyro′ y , Gyro′ z ]. 
     In some embodiments, instead of computing the roll angle θ and calculating cos θ and sin θ (with computationally expensive trigonometric function), the same quantities are determined based on a processed gravity vector g′. In particular, the processed gravity vector g′ corresponds to the 6-DoF gravity vector g, re-normalized using X and Z axes only: 
     
       
         
           
             
               
                 g 
                 ′ 
               
               = 
               
                 [ 
                 
                   
                     
                       
                         g 
                         x 
                         ′ 
                       
                     
                   
                   
                     
                       0 
                     
                   
                   
                     
                       
                         g 
                         z 
                         ′ 
                       
                     
                   
                 
                 ] 
               
             
             ⁢ 
             
 
             
               wherein 
               : 
             
             ⁢ 
             
 
             
               
                 g 
                 x 
                 ′ 
               
               = 
               
                 
                   g 
                   x 
                 
                 
                   
                     
                       g 
                       x 
                       2 
                     
                     + 
                     
                       g 
                       z 
                       2 
                     
                   
                 
               
             
             ⁢ 
             
 
             
               
                 g 
                 z 
                 ′ 
               
               = 
               
                 
                   g 
                   z 
                 
                 
                   
                     
                       g 
                       x 
                       2 
                     
                     + 
                     
                       g 
                       z 
                       2 
                     
                   
                 
               
             
           
         
       
     
     g′ x  and g′ z  being the components along the X axis and, respectively, along the Z axis of the processed gravity vector g′. 
     According to the above expressions, it follows that: 
       sin θ=− g′   x  
 
       cos θ= g′   z  
 
       sin 2 θ+cos 2 θ=1
 
     Substituting the above expressions for cos θ and sin θ in the above back-rotation expression and discarding the Y-axis component as specified above (referring to the axes selection operation at step  21 ), the components of the roll-compensated gyroscopic signal Gyro′ along the X and Z axes can be expressed as: 
       Gyro′ x =Gyro x   ·g′   z −Gyro z   ·g′   x  
 
       Gyro′ z =Gyro x   ·g′   x +Gyro z   ·g′   z  
 
     The pointing determination stage  8  then implements a remapping of the angular rate of the electronic device  1  into displacements into the screen-frame space coordinates, denoted in the following as [x′, y′]. For example, axes remapping can be implemented as follows: 
         x ′=−Gyro′ z ·σ
 
         y ′=−Gyro′ x ·σ
 
     The above expressions correspond to the election of the compensated yaw rate (i.e., the component of the roll-compensated gyroscopic signal Gyro′ along the Z axis) as the x′ displacement in the screen frame; and the compensated pitch rate (i.e., the component of the roll-compensated gyroscopic signal Gyro′ along the X axis) as the y′ displacement in the same screen frame; the two values are multiplied by −1 to be correctly remapped into screen space. 
     Moreover, multiplication by a scale factor σ, being indicative of the pointer sensitivity, may applied to get a desired pointer speed, i.e., a desired movement speed of the cursor or other element displayed on the screen and moving according to the displacement information provided by the electronic device  1  to the host apparatus. The pointing determination stage  8  then outputs the computed [x′, y′] values of displacement. 
     It should be understood that that the pointing algorithm described above is just one example of a number of possible pointing algorithms that may be implemented in embodiments of the present invention. 
     The data reconstruction stage  24  comprises a slope-computation block  30 , which is configured to compute the “slope” of the motion input data, for example as the difference (i.e. digital derivative) between the two previous samples (the information required for the computation being extracted from recent history, suitably stored in a storing element, here not shown) according to the following expression: 
       slope=data t −data t-2   (1)
 
     where data t-2  (with data t-2 =data t-3  for the same reason discussed above) represents the first previous different sample, i.e. the sample preceding the old sample data t-1 , in other words the sample at the still previous processing cycle. 
     It is noted that expression (1) envisages use of only real samples, i.e. actual motion data sensed by the motion sensors. 
     As an alternative (as shown by the dashed line in  FIG.  6   ), reconstructed samples may also be used in the determination of the slope, e.g. according to the following expression: 
       slope=data t −data t-2   pred   (2)
 
     where data t-2   pred  is the reconstructed (or predicted) data sample at the previous execution of the data-reconstruction stage  24  (it is again noted that data t-1  represents instead an actual motion data sensed by the motion sensors or determined based on the sensed data). 
     The use of only real data samples for the prediction is generally more conservative, with fewer possible errors but generally less prediction capability; while using predicted data samples may lead to more prediction capability (in particular, with respect to signal peak prediction) but with possible higher errors. 
     The data reconstruction stage  24  further comprises a reconstruction block  32 , configured to generate the reconstructed data sample data t   pred  to be provided to the pointing determination unit  8 , based on the current sample data t  and on the slope computed by the slope-computation block  30 , in particular according to the following expression: 
     
       
         
           
             
               
                 
                   
                     data 
                     t 
                     pred 
                   
                   = 
                   
                     
                       data 
                       t 
                     
                     + 
                     
                       slope 
                       k 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     where k is a weight factor (with k≥1), designed to properly weigh the slope contribution in the data prediction. 
     In particular, in the above expression (3) it is evident that if k=1, all the computed slope is used to determine the reconstructed data sample data t   pred  (in other words, the computed slope is predicted to remain unchanged); values of the weight factor k progressively higher than 1 instead determine a progressive reduction of the slope in the determination of the reconstructed data sample data t   pred . For example, a value of k=2 could be used in the data reconstruction stage  24 . 
     According to a particular aspect of the present solution, the data reconstruction stage  24  is configured to implement an additional algorithm to dynamically compute the value of the weight factor k, based on the characteristics of the motion input data, to minimize the error in the prediction of the reconstructed data sample data t   pred . 
     As shown in  FIG.  7   , the data reconstruction stage  24  in a possible embodiment further comprises a weight computation branch  40 , configured to dynamically compute the value of the weight factor k, and provide the computed value to the reconstruction block  32 , where it is used to determine the reconstructed data sample data t   pred  according to the above expression (3). 
     The weight computation branch  40  comprises a first computation block  41 , configured to compute a motion quantity parameter mix t , indicative of a current (i.e. at the current cycle and current time t) quantity of motion associated to the motion input data. 
     According to a possible embodiment, the first computation block  41  receives at its input the slope computed by the slope-computation block  30  and the current data sample data t , and computes the motion quantity parameter mix t  based on the following expression: 
     
       
         
           
             
               
                 
                   
                     mix 
                     t 
                   
                   = 
                   
                     
                       abs 
                       ⁡ 
                       ( 
                       
                         
                           
                             data 
                             t 
                           
                           + 
                           slope 
                         
                         2 
                       
                       ) 
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     It is underlined, however, that other possible and more complex solutions may be implemented in the first computation block  41  to determine the quantity-of-motion parameter, e.g. envisaging evaluation of the variance of motion input data, the average, or maximum and minimum of the same motion input data in a given time interval. 
     The weight computation branch  40  moreover comprises an evaluation block  42 , coupled to the first computation block  41  to receive the motion quantity parameter mix t  and configured to compare the same motion quantity parameter mix t  with a given and fixed threshold thr. 
     In case the motion quantity parameter mix t  is lower than this threshold thr, in a second computation block  43  of the weight computation branch  40  the weight factor k is set to a minimum value k min  (for example equal or close to 1). In this case, since the quantity of motion is determined to be small (or in any case lower than the threshold thr), the slope is attributed a high weight in the determination of the reconstructed data sample data t   pred . 
     Instead, in case the motion quantity parameter mix t  is higher than (or equal to) the same threshold thr, in a third computation block  44  of the weight computation branch  40 , the weight factor k is computed as a function of the same motion quantity parameter mix t , in particular as a function of the ratio between the motion quantity parameter mix t  and the threshold thr, according to the following expression: 
     
       
         
           
             
               
                 
                   k 
                   = 
                   
                     ( 
                     
                       
                         
                           mix 
                           t 
                         
                         · 
                         
                           d 
                           thr 
                         
                       
                       + 
                       
                         k 
                         min 
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     where d is a proportionality factor, which determines the additional contribution of the above ratio between the motion quantity parameter mix t  and the threshold thr with respect to the minimum value k min , for the computation of the weight factor and the determination of the reconstructed data sample data t   pred . 
     It is underlined that the values of the above threshold thr, minimum value k min  and proportionality factor d may advantageously be determined via a regression analysis. 
     In a known manner, this regression analysis may envisage the use of a reference motion data signal sampled at the same rate of the pointing determination unit processing rate; the generation of subsampled data (e.g. by a factor of 2); the execution of several simulations with different combinations of the above parameters thr, k min , d; and, final, the selection of the parameter values which minimize the error between the reference motion data signal and the reconstructed one. 
       FIG.  8    shows an exemplary performance of the above discussed predictive data-reconstruction, for the reconstruction of missing samples of the components of the gyroscope signal Gyro along the axes X and Z. 
     It is noted that the reconstructed signals (shown in dashed line) closely follows the actual gyroscope signals (shown in solid lines); in particular, it is noted that the disclosed predictive data-reconstruction allows an accurate reconstruction of the signal peaks. 
     In a manner corresponding to what shown in the above-discussed  FIG.  3   ,  FIG.  9    shows with a solid line the movement of the pointing electronic device  1 , again, as an example, with the user “air-drawing” a circular shape; the dashed line represents the shape “drawn” by the cursor displayed on the screen-frame of the host apparatus, based on the displacement information provided by the pointing determination unit  8 . 
     Also in this case, the solid circles represent the positions determined by the pointing algorithm based on actual motion data sensed by the motion sensors, while the dashed circles represent the positions determined, in this case, based on the upscaled motion input data generated by the rate upscaling unit  20  (which are very close to the actual circular shape drawn by the user). 
     In this case, the user thus experiences a cursor movement that is updated at a high frequency (corresponding to the processing data rate) and is very close to actual movement of the pointing electronic device  1 , with an overall improved user experience in the use of the same pointing electronic device  1 . 
       FIG.  10    schematically shows the pointing electronic device  1 , for example of the hand-held or portable type, e.g. a smart pen or stylus, communicatively coupled to a host apparatus  50 , for example a smartphone, a phablet or a tablet. 
     The pointing electronic device  1  comprises, within a case or housing thereof, the inertial measurement module  7 , in a possible embodiment made as a 6 DoF (Degrees of Freedom) hardware module including (in a manner not shown in detail) the accelerometer sensor  2 , the gyroscope sensor  4  and the sensor-fusion stage  5  (both accelerometer and gyroscope sensors  2 ,  4  and the sensor-fusion stage  5 , e.g. made as an ASIC—Application Specific Integrated Circuit, may be integrated in a same packaged chip). 
     According to a possible embodiment, the pointing determination stage  8  may be implemented in a main control unit  52  of the pointing electronic device  1 , having a microcontroller (or similar processing or computing unit) and a suitable non-volatile memory storing computing instructions to execute the pointing algorithm and generate at the output displacement information to be received by the coupled host apparatus  50  to implement a user interface (for example for moving the cursor or similar displayed element on the screen frame of the same coupled host apparatus  50 ). The main control unit  52  implementing the pointing determination stage  8  may be a dedicated control unit, or may also have other functions, e.g. for controlling the general operation of the pointing electronic device  1 . 
     The pointing electronic device  1  may further comprise: a battery  53 , providing a power supply to the hardware module (including the accelerometer sensor  2 , the gyroscope sensor  4  and the sensor-fusion stage  5 ) and to the control unit  52  (implementing the pointing determination stage  8 ); and a communication interface unit  54 , designed for wireless communication towards the host apparatus  50 . The communication interface unit  54  may be implemented by a BLE (Bluetooth Low Energy) control unit implementing a Bluetooth low-power wireless communication between the pointing electronic device  1  and the coupled host apparatus  50 . 
     The same host apparatus  50  may comprise: a respective communication interface unit  55 , to communicate with the communication interface unit  54  of the pointing electronic device  1 ; a main controller  56 , e.g. a microprocessor unit; and a display  58 , defining the screen frame, on which movement of the cursor or other similar displayed element is controlled by the main controller  56  according to the displacement information provided by the pointing electronic device  1  (it is noted that, in addition to the displacement information, any kind of further information may be communicated between the electronic device  1  and the host apparatus  50 ). 
     In particular, the rate upscaling unit  20  of the pointing electronic device  1  according to the present solution may alternatively be implemented: in the inertial measurement module  7 ; in the main control unit  52 ; or in the BLE (Bluetooth Low Energy) control unit of the communication interface unit  54 . 
     In various embodiments, the algorithms and methods described herein may be implemented, at least in part, using a processor coupled to a non-transitory computer readable medium, such as a memory. The non-transitory computer readable medium may include instructions executable by the processor to implement embodiment algorithms. The processor may include a central processing unit (CPU), a microprocessor, a microcontroller or other processing circuitry known in the art that is capable of executing machine readable instructions. In alternative embodiments, the algorithms and methods described herein may be implemented using dedicated digital logic, programmable digital logic such as a field programmable gate array (FPGA), a digital signal processor (DSP), or other suitable digital hardware. 
     The advantages of the solution proposed are clear from the foregoing description. In any case, it is again underlined that the proposed solution provides the ability to achieve a very low power consumption, allowing to use low motion input data rates while keeping high pointer performance; in particular an improved precision and user experience are provided. 
     Finally, it is clear that modifications and variations may be made to what has been described and illustrated herein, without thereby departing from the scope of the present invention, as defined in the annexed claims. 
     In particular, it is again underlined that the sensor-fusion processing stage  5  may implement any suitable generic sensor-fusion filter algorithm, to combine the acceleration signal Acc and the gyroscope signal Gyro and to generate at the output the roll estimation quantity β′ (it is again underlined that the present disclosure is not to be limited to a particular implementation of the sensor-fusion processing stage  5 ). 
     Moreover, it is noted that the pointing determination stage  8  may also be implemented as a hardware module and be integrated in the same packaged chip with the MEMS inertial sensors (the accelerometer and gyroscope sensors  2 ,  4  and possibly further sensors, such as a magnetometer) and with the corresponding processing circuit. 
     Moreover, it is again underlined that the electronic device  1  may be a dedicated pointer device or may also have other or additional functions.