The radial distance is also called the radius or radial coordinate. In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane. The angles (`theta` and `phi`) are returned in decimal degrees. The length (`rho`) of the vector is in the units entered. This formula lets the user enter three Cartesian coordinates (X, Y and Z) This algorithm converts the spherical coordinates. However, these can be automatically converted to compatible units via the pull-down menu. Spherical Coordinates (ρ,θ,ϕ): The calculator returns the magnitude of the vector (ρ) as a real number, and the azimuth angle from the x-axis (ϕ) and the polar angle from the z-axis (θ) as degrees.

( V): Enter the x, y and z components of V separated by commas (e.g.

The benefits of this algorithm are illustrated in the contexts of autonomous vehicle navigation and missile tracking.The Cartesian to Spherical Coordinates calculator computes the spherical coordinates Vector in 3D for a vector given its Cartesian coordinates. It is not necessary to calculate any derivatives, and the algorithm can be extended to incorporate higher order information. It is shown that the performance of the algorithm is comparable to that of fourth order filters, thus ensuring consistency even when the uncertainty is large.

The transformation is then applied to each of the samples, and the mean and covariance are calculated from the result. A discrete set of samples are used to capture the first four moments of the untransformed measurement. This paper expands a method for nonlinear propagation which is described in a companion paper. A number of approaches have been proposed for using higher order transformation modes, but these approaches have found only limited use due to the often enormous implementation burdens incurred by the need to derive Jacobians and Hessians. However, this approximation can lead to biases and inconsistencies, especially when the uncertainties on the measurements are large. The most common approach is to approximate the transformation through linearization. In order to combine those measurements with those from other radars, however, a tracking system typically transforms all measurements to a common Cartesian coordinate system.

For example, a radar system generates measurements in its own local spherical coordinate system.

A significant problem in tracking and estimation is the consistent transformation of uncertain state estimates between Cartesian and spherical coordinate systems.

Spherical to cartesian coordinates