Speed and acceleration calculation and measurement method, device, and application based on regularization algorithms

A device for calculating speed and/or acceleration of a moving body based on a regularization algorithm, the device comprising:

• a controller including:
• (i) an acquisition module configured to acquire position data or displacement data for the moving body using a physical sensing device of an accelerometer or a global navigation satellite system (GNSS) device;
• and (ii) a regularization module configured to express the position data or displacement data as an integral equation of speed or acceleration and to use a regularization method to calculate speed and/or acceleration by using the position data or displacement data, the regularization module comprising:
• a discretization module configured to discretize the integral equation of speed or acceleration in order to obtain the matrix form of a linear discrete observation equation, wherein the matrix form is expressed as y=Aβ+ε, wherein y is a vector of the position data or displacement data, wherein A is a discrete coefficient matrix, wherein β is a speed or acceleration vector, and wherein ε is a random error vector of the position data or displacement data;
• and
• a recovery module configured to recover the speed or acceleration vector β from the position or displacement data y, wherein the recovery module is further configured to build an optimization objective function, wherein the objective function is expressed as min:
• F(β)=(y−Aβ)TW(y−Aβ)+κβTSβ, wherein W is a weight matrix of the position data or displacement data, wherein k is a regularization parameter for suppressing noise amplification, and wherein S is a positive definite or positive semi-definite matrix, and determine the regularization parameter k and recover the speed and/or acceleration vector β from the position data or displacement data y by using the following equation:
• β=(ATWA+κS)−1ATWy;
• wherein the controller is configured to generate a speed or acceleration signal based on the speed or acceleration vector β and cause the speed or acceleration signal to be output form the device.

A device for measuring speed and/or acceleration of a moving body based on a regularization algorithm, the device comprising:

• an output device configured to output position data or displacement data for the moving body, the output device being a physical sensing device of an accelerometer or a global navigation satellite system (GNSS) device;
• and
• a controller including:
• an acquisition module configured to acquire the position data or displacement data;
• and
• a regularization module configured to express the position data or displacement data as an integral equation of speed or acceleration and to use a regularization method to calculate speed and/or acceleration by using the position data or displacement data,
• wherein the regularization module comprises:
• a discretization module configured to discretize the integral equation of speed or acceleration in order to obtain the matrix form of a linear discrete observation equation, wherein the matrix form is expressed as y=Aβ+ε, wherein y is a vector of the position data or displacement data, wherein A is a discrete coefficient matrix, wherein β is a speed or acceleration vector, and wherein ε is a random error vector of the position data or displacement data;
• and
• a recovery module configured to recover the speed or acceleration vector β from the position or displacement data y by using the regularization method, wherein the recovery module is further configured to build an optimization objective function, wherein the objective function is expressed as min:
• F(β)=(y−Aβ)TW(y−Aβ)+κβTSβ, wherein W is a weight matrix of the position data or displacement data, wherein κ is a regularization parameter for suppressing noise amplification, and wherein S is a positive definite or positive semi-definite matrix, and determine the regularization parameter κ and recover the speed and/or acceleration vector β from the position data or displacement data y by using the following equation:
• β=(ATWA+κS)−1ATWy
• wherein the controller is configured to generate a speed or acceleration signal based on the speed or acceleration vector β and cause the speed or acceleration signal to be output form the device.