NLS using a bounded linear initial search space and a fixed grid with pre-calculated variables

A system comprising:

• at least one processor configured to:
• receive, via a sensor and at a first elevation angle relative to a boresight of the sensor, a first signal reflected by an object;
• receive, via the sensor and at a second elevation angle relative to the boresight of the sensor, a second signal reflected by the object and a ground plane;
• determine a range to the object based on at least one of the first signal or the second signal;
• establish a maximum height corresponding to an estimated maximum height of the object;
• establish a line of second elevation angles as a function of first elevation angles, a sensor height, and the range, wherein the first elevation angles are between a first value based on the sensor height and the range and a second value based on the sensor height, the range, and the maximum height;
• determine an initial elevation angle pair of one of the first elevation angles and one of the second elevation angles using a search algorithm along the line;
• refine, using a non-linear least squares method, the initial elevation angle pair to determine the first elevation angle and the second elevation angle;
• calculate a height of the object based on at least one of the first elevation angle or the second elevation angle and the sensor height;
• and
• perform a vehicle function based on the height of the object.

A non-transitory computer-readable storage media comprising instructions that, when executed, cause at least one processor to:

• receive, via a sensor and at a first elevation angle relative to a boresight of the sensor, a first signal reflected by an object;
• receive, via the sensor and at a second elevation angle relative to the boresight of the sensor, a second signal reflected by the object and a ground plane;
• determine a range to the object based on at least one of the first signal or the second signal;
• establish a maximum height corresponding to an estimated maximum height of the object;
• establish a line of second elevation angles as a function of first elevation angles, a sensor height, and the range, wherein the first elevation angles are between a first value based on the sensor height and the range and a second value based on the sensor height, the range, and the maximum height;
• determine an initial elevation angle pair of one of the first elevation angles and one of the second elevation angles using a search algorithm along the line;
• refine, using a non-linear least squares method, the initial elevation angle pair to determine the first elevation angle and the second elevation angle;
• calculate a height of the object based on at least one of the first elevation angle or the second elevation angle and the sensor height;
• and
• perform a vehicle function based on the height of the object.