constturn

State transition function for constant turn-rate and velocity-magnitude motion model

Syntax

predictedState = constturn(state)

predictedState = constturn(state,dt)

predictedState = constturn(state,w,dt)

Description

predictedState = constturn(state) returns the predicted state, predictedState, obtained from the current state, state, based on the constant turn-rate and velocity-magnitude motion model. The default time step is 1 second. Constant turn rate mean that motion in the xy-plane follows a constant angular velocity and motion in the vertical z directions follows a constant velocity model.

predictedState = constturn(state,dt) also specifies the time step, dt.

predictedState = constturn(state,w,dt) also specifies noise, w.

Examples

Update State for Constant Turn-Rate Motion

Define an initial state for 2-D constant turn-rate motion. The turn rate is 12 degrees per second. Update the state to one second later.

state = [500,0,0,100,12].';
state = constturn(state)

state = 5×1

  489.5662
  -20.7912
   99.2705
   97.8148
   12.0000

Update State for Constant Turn-Rate Motion with Specified Time Step

Define an initial state for 2-D constant turn-rate motion. The turn rate is 12 degrees per second. Update the state to 0.1 seconds later.

state = [500,0,0,100,12].';
state = constturn(state,0.1)

state = 5×1

  499.8953
   -2.0942
    9.9993
   99.9781
   12.0000

Input Arguments

state — Current state

real-valued five-element vector | real-valued seven-element vector | 5-by-N real-valued matrix | 7-by-N real-valued matrix

Current state for constant turn-rate motion, specified as a real-valued vector or matrix.

• When you specify the current state as a five-element vector, the state vector describes 2-D motion in the xy-plane. You can specify the state vector as a row or column vector. The components of the state vector are [x;vx;y;vy;omega], where

  • x and y represent the x-coordinate and y-coordinate in meters.

  • vx and vy represent the velocity in the x and y direction in meters/second.

  • omega represents the turn-rate in degrees/second.

  When specified as a 5-by-N matrix, each column represents a different state vector N represents the number of states.

• When you specify the current state as a seven-element vector, the state vector describes 3-D motion. You can specify the state vector as a row or column vector. The components of the state vector are [x;vx;y;vy;omega;z;vz], where:

  • x, y, and z represent the x-, y-, and z-coordinate in meters.

  • vx, vy, and vz represent the velocity in the x, y, and z direction in meters/second.

  • omega represents the turn-rate in degrees/second.

  When specified as a 7-by-N matrix, each column represents a different state vector. N represents the number of states.

Example: [5;0.1;4;-0.2;0.01]

Data Types: single | double

dt — Time step interval

1.0 (default) | positive scalar

Time step interval, specified as a positive scalar. Time units are in seconds.

Example: 0.5

Data Types: single | double

w — State noise

scalar | real-valued (D+1)-by-N matrix

State noise, specified as a scalar or real-valued (D+1)-length -by-N matrix. D is the number of motion dimensions and N is the number of state vectors. The components are each columns are [ax;ay;alpha] for 2-D motion or [ax;ay;alpha;az] for 3-D motion. ax, ay, and az are the linear acceleration noise values in the x-, y-, and z-axes, respectively, and alpha is the angular acceleration noise value. If specified as a scalar, the value expands to a (D+1)-by-N matrix.

Data Types: single | double

Output Arguments

predictedState — Predicted state at next time step

real-valued column or row vector | real-valued matrix

Predicted state, returned as a real-valued vector or real-valued matrix with same number of elements and dimensions as the input state vector.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2017a